diff options
Diffstat (limited to '2048')
205 files changed, 5211 insertions, 0 deletions
diff --git a/2048/CH10/EX10.1/delay.sce b/2048/CH10/EX10.1/delay.sce new file mode 100755 index 000000000..990d695aa --- /dev/null +++ b/2048/CH10/EX10.1/delay.sce @@ -0,0 +1,50 @@ +// Effect of delay in control performance
+// 10.1
+
+exec('zpowk.sci',-1);
+exec('pp_im.sci',-1);
+exec('cosfil_ip.sci',-1);
+exec('polsplit3.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('polyno.sci',-1);
+
+Ts = 1; B = 0.63; A = [1 -0.37];
+k = input('Enter the delay as an integer: ');
+if k<=0, k = 1; end
+[zk,dzk] = zpowk(k);
+
+// Desired transfer function
+phi = [1 -0.5];
+delta = 1; // internal model of step introduced
+
+// Controller design
+[Rc,Sc,Tc,gamm] = pp_im(B,A,k,phi,delta);
+
+// simulation parameters for stb_disc.xcos
+// y1: 0 to 1; u1: 0 to 1.2
+st = 1.0; // desired change in setpoint
+t_init = 0; // simulation start time
+t_final = 20; // simulation end time
+
+// simulation parameters for stb_disc.xcos
+N_var = 0; C = 0; D = 1; N = 1;
+
+[Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+[Rcp1,Rcp2] = cosfil_ip(1,Rc); // 1/Rc
+[Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+[Bp,Ap] = cosfil_ip(B,A); // B/A
+[zkp1,zkp2] = cosfil_ip(zk,1); // zk/1
+[Cp,Dp] = cosfil_ip(C,D); // C/D
+
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\ No newline at end of file diff --git a/2048/CH10/EX10.10/vande_imc.sce b/2048/CH10/EX10.10/vande_imc.sce new file mode 100755 index 000000000..90990c8c0 --- /dev/null +++ b/2048/CH10/EX10.10/vande_imc.sce @@ -0,0 +1,25 @@ +// Design of conventional controller for van de Vusse reactor problem
+// 10.10
+
+exec('tf.sci');
+exec('myc2d.sci');
+exec('imcsplit.sci',-1);
+exec('imc_stable.sci');
+exec('zpowk.sci',-1);
+exec('flip.sci',-1);
+exec('poladd.sci',-1);
+exec('polsize.sci',-1);
+
+num = [-1.117 3.1472]; den = [1 4.6429 5.3821];
+G = tf(num,den);
+Ts = 0.1;
+[B,A,k] = myc2d(G,Ts);
+alpha = 0.5;
+[k,HiN,HiD,R,S] = imc_stable(B,A,k,alpha);
+[zk,dzk] = zpowk(k);
+Bp = B; Ap = A;
+
+
+
+
+
diff --git a/2048/CH10/EX10.2/smith.sce b/2048/CH10/EX10.2/smith.sce new file mode 100755 index 000000000..2ae3fbc0a --- /dev/null +++ b/2048/CH10/EX10.2/smith.sce @@ -0,0 +1,51 @@ +// Smith predictor for paper machine control in Example 10.2 on page 385.
+// 10.2
+
+exec('zpowk.sci',-1);
+exec('poladd.sci',-1);
+exec('polsize.sci',-1);
+exec('pp_im.sci',-1);
+exec('polsplit3.sci',-1);
+exec('polmul.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('seshft.sci',-1);
+exec('cosfil_ip.sci',-1);
+exec('polyno.sci',-1);
+
+Ts = 1; B = 0.63; A = [1 -0.37]; k = 3;
+Bd = convol(B,[0 1]);
+kd = k - 1;
+[zkd,dzkd] = zpowk(kd);
+[mzkd,dmzkd] = poladd(1,0,-zkd,dzkd);
+
+// Desired transfer function
+phi = [1 -0.5]; delta = 1;
+
+// Controller design
+[Rc,Sc,Tc,gamm] = pp_im(B,A,1,phi,delta);
+
+// simulation parameters for smith_disc.xcos
+st = 1.0; // desired change in setpoint
+t_init = 0; // simulation start time
+t_final = 20; // simulation end time
+
+// simulation parameters for smith_disc.xcos
+N_var = 0; C = 0; D = 1; N = 1;
+
+[Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+[Rcp1,Rcp2] = cosfil_ip(1,Rc); // 1/Rc
+[Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+[Bdp,Ap] = cosfil_ip(Bd,A); // Bd/Ad
+[zkdp1,zkdp2] = cosfil_ip(zkd,1); // zkd/1
+[mzkdp1,mzkdp2] = cosfil_ip(mzkd,1); // mzkd/1
+[Cp,Dp] = cosfil_ip(C,D); // C/D
+
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\ No newline at end of file diff --git a/2048/CH10/EX10.2/u1_smith_disc.png b/2048/CH10/EX10.2/u1_smith_disc.png Binary files differnew file mode 100755 index 000000000..98526b1dc --- /dev/null +++ b/2048/CH10/EX10.2/u1_smith_disc.png diff --git a/2048/CH10/EX10.2/y1_smith_disc.png b/2048/CH10/EX10.2/y1_smith_disc.png Binary files differnew file mode 100755 index 000000000..b00c987d4 --- /dev/null +++ b/2048/CH10/EX10.2/y1_smith_disc.png diff --git a/2048/CH10/EX10.3/imcsplit.sci b/2048/CH10/EX10.3/imcsplit.sci new file mode 100755 index 000000000..59e6ef95f --- /dev/null +++ b/2048/CH10/EX10.3/imcsplit.sci @@ -0,0 +1,37 @@ +// Splitting a polynomial B(z)
+// 10.3
+// Splits a polynomial B into good, nonminimum with
+// positive real & with negative real parts.
+// All are returned in polynomial form.
+// Gain is returned in Kp and delay in k.
+
+function [Kp,k,Bg,Bnmp,Bm] = imcsplit(B,polynomial)
+k = 0;
+Kp = 1;
+if(polynomial)
+ rts = roots(B);
+ Kp = sum(B)/sum(coeff(poly(rts,'z')));
+else
+ rts = B;
+end
+Bg = 1; Bnmp = 1; Bm = 1;
+for i = 1:length(rts),
+ rt = rts(i);
+ if rt == 0,
+ k = k+1;
+ elseif (abs(rt)<1 & real(rt)>=0)
+ Bg = convol(Bg,[1 -rt]);
+ elseif (abs(rt)>=1 & real(rt)>=0)
+ Bnmp = convol(Bnmp,[1 -rt]);
+ else
+ Bm = convol(Bm,[1 -rt]);
+ end
+end
+
+
+
+
+
+
+
+
diff --git a/2048/CH10/EX10.4/imc_stable1.sci b/2048/CH10/EX10.4/imc_stable1.sci new file mode 100755 index 000000000..6b8dec788 --- /dev/null +++ b/2048/CH10/EX10.4/imc_stable1.sci @@ -0,0 +1,19 @@ +// Design of internal model controller
+// 10.4
+// Designs Discrete Internal Model Controller
+// for transfer function z^{-k}B(z^{-1})/A(z^{-1})
+// Numerator and Denominator of IMC HQ are outputs
+// Controller is also given in R,S form
+
+function [k,HiN,HiD] = imc_stable1(B,A,k,alpha)
+
+[Kp,d,Bg,Bnmp,Bm] = imcsplit(B,mtlb_logical(1));
+Bg = Kp * Bg;
+Bnmpr = flip(Bnmp);
+Bms = sum(Bm);
+HiN = A;
+HiD = Bms * convol(Bg,Bnmpr);
+k = k+d;
+endfunction;
+
+
diff --git a/2048/CH10/EX10.5/flip.sci b/2048/CH10/EX10.5/flip.sci new file mode 100755 index 000000000..c19564c9a --- /dev/null +++ b/2048/CH10/EX10.5/flip.sci @@ -0,0 +1,4 @@ +// 10.5
+function b = flip(a)
+b = a(length(a):-1:1);
+endfunction;
diff --git a/2048/CH10/EX10.6/visc_imc1.sce b/2048/CH10/EX10.6/visc_imc1.sce new file mode 100755 index 000000000..1f896dc1e --- /dev/null +++ b/2048/CH10/EX10.6/visc_imc1.sce @@ -0,0 +1,20 @@ +// IMC design for viscosity control problem
+// 10.6
+
+exec('imc_stable1.sci',-1);
+exec('zpowk.sci',-1);
+exec('imcsplit.sci',-1);
+exec('flip.sci',-1);
+
+B = [0.51 1.21];
+A = [1 -0.44];
+k = 1;
+alpha = 0.5;
+
+[k,GiN,GiD] = imc_stable1(B,A,k,alpha);
+
+[zk,dzk] = zpowk(k);
+Bp = B; Ap = A;
+Ts = 0.1; t0 = 0; tf = 20; Nvar = 0.01;
+
+
diff --git a/2048/CH10/EX10.7/vande_imc1.sce b/2048/CH10/EX10.7/vande_imc1.sce new file mode 100755 index 000000000..ab6710f9a --- /dev/null +++ b/2048/CH10/EX10.7/vande_imc1.sce @@ -0,0 +1,21 @@ +// IMC design for the control of van de Vusse reactor
+// 10.7
+
+exec('tf.sci');
+exec('myc2d.sci');
+exec('imc_stable1.sci');
+exec('imcsplit.sci',-1);
+exec('flip.sci',-1);
+exec('zpowk.sci',-1);
+
+num = [-1.117 3.1472]; den = [1 4.6429 5.3821];
+G = tf(num,den);
+Ts = 0.1;
+[B,A,k] = myc2d(G,Ts);
+alpha = 0.9;
+[k,GiN,GiD] = imc_stable1(B,A,k,alpha);
+[zk,dzk] = zpowk(k);
+Bp = B; Ap = A;
+t0 = 0; tfi = 10; st = 1; Nvar = 0;
+
+
diff --git a/2048/CH10/EX10.8/lewin_imc1.sce b/2048/CH10/EX10.8/lewin_imc1.sce new file mode 100755 index 000000000..df0f7f97d --- /dev/null +++ b/2048/CH10/EX10.8/lewin_imc1.sce @@ -0,0 +1,24 @@ +// IMC design for Lewin's example
+// 10.8
+
+exec('tf.sci');
+exec('myc2d.sci');
+exec('imc_stable1.sci');
+exec('zpowk.sci',-1);
+exec('imcsplit.sci',-1);
+exec('flip.sci',-1);
+
+num = 1; den = [250 35 1]; Ts = 3;
+G = tf(num,den);
+
+[B,A,k] = myc2d(G,Ts);
+
+alpha = 0.9;
+[k,GiN,GiD] = imc_stable1(B,A,k,alpha);
+
+[zk,dzk] = zpowk(k);
+Bp = B; Ap = A;
+t0 = 0; tfi = 100; st = 1; Nvar = 0;
+
+
+
diff --git a/2048/CH10/EX10.9/imc_stable.sci b/2048/CH10/EX10.9/imc_stable.sci new file mode 100755 index 000000000..d53da9c82 --- /dev/null +++ b/2048/CH10/EX10.9/imc_stable.sci @@ -0,0 +1,31 @@ +// Design of conventional controller which is an equivalent of internal model controller
+// 10.9
+
+// Designs Discrete Internal Model Controller
+// for transfer function z^{-k}B(z^{-1})/A(z^{-1})
+// Numerator and Denominator of IMC HQ are outputs
+// Controller is also given in R,S form
+
+
+function [k,HiN,HiD,R,S,mu] = imc_stable(B,A,k,alpha)
+
+[Kp,d,Bg,Bnmp,Bm] = imcsplit(B,mtlb_logical(1));
+Bg = Kp * Bg;
+
+Bnmpr = flip(Bnmp);
+Bms = sum(Bm);
+HiN = A;
+HiD = Bms * convol(Bg,Bnmpr);
+k = k+d;
+
+[zk,dzk] = zpowk(k);
+Bf = (1-alpha);
+Af = [1 -alpha];
+S = convol(Bf,A);
+R1 = convol(Af,convol(Bnmpr,Bms));
+R2 = convol(zk,convol(Bf,convol(Bnmp,Bm)));
+
+[R,dR] = poladd(R1,length(R1)-1,-R2,length(R2)-1);
+R = convol(Bg,R);
+endfunction;
+
diff --git a/2048/CH11/EX11.1/recursion.sci b/2048/CH11/EX11.1/recursion.sci new file mode 100755 index 000000000..ead807bfb --- /dev/null +++ b/2048/CH11/EX11.1/recursion.sci @@ -0,0 +1,35 @@ +// Recursive computation of Ej and Fj
+// 11.1
+
+function [Fj,dFj,Ej,dEj] = recursion(A,dA,C,dC,j)
+Fo = C; dFo = dC;
+Eo = 1; dEo = 0;
+A_z = A(2:dA+1); dA_z = dA-1;
+zi = 1; dzi = 0;
+for i = 1:j-1
+ if (dFo == 0)
+ Fn1 = 0;
+ else
+ Fn1 = Fo(2:(dFo+1));
+ end
+ dFn1 = max(dFo-1,0);
+ Fn2 = -Fo(1)*A_z; dFn2 = dA-1;
+ [Fn,dFn] = poladd(Fn1,dFn1,Fn2,dFn2);
+ zi = convol(zi,[0,1]); dzi = dzi + 1;
+ En2 = Fn(1)*zi; dEn2 = dzi;
+ [En,dEn] = poladd(Eo,dEo,En2,dEn2);
+ Eo = En; Fo = Fn;
+ dEo = dEn; dFo = dFn;
+end
+if (dFo == 0)
+ Fn1 = 0;
+else
+Fn1 = Fo(2:(dFo+1));
+end;
+dFn1 = max(dFo-1,0);
+Fn2 = -Fo(1)*A_z; dFn2 = dA-1;
+[Fn,dFn] = poladd(Fn1,dFn1,Fn2,dFn2);
+Fj = Fn; dFj = dFn;
+Ej = Eo; dEj = dEo;
+endfunction;
+
diff --git a/2048/CH11/EX11.10/ast_12p9.sce b/2048/CH11/EX11.10/ast_12p9.sce new file mode 100755 index 000000000..28d8c1f4a --- /dev/null +++ b/2048/CH11/EX11.10/ast_12p9.sce @@ -0,0 +1,35 @@ +// Minimum variance control for nonminimum phase example of Example 11.6 on page 416.
+// 11.10
+
+exec('mv_nm.sci',-1);
+exec('cl.sci',-1);
+exec('zpowk.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+exec('polsplit3.sci',-1);
+exec('flip.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('poladd.sci',-1);
+exec('tfvar.sci',-1);
+exec('l2r.sci',-1);
+exec('transp.sci',-1);
+exec('tf.sci',-1);
+exec('covar_m.sci',-1);
+
+A = convol([1 -1],[1 -0.7]); dA = 2;
+B = [0.9 1]; dB = 1; k = 1;
+C = [1 -0.7]; dC = 1; int1 = 0;
+[Sc,dSc,Rc,dRc] = mv_nm(A,dA,B,dB,C,dC,k,int1);
+[Nu,dNu,Du,dDu,Ny,dNy,Dy,dDy,yvar,uvar] = ...
+cl(A,dA,B,dB,C,dC,k,Sc,dSc,Rc,dRc,int1);
+
diff --git a/2048/CH11/EX11.11/mv_visc.sce b/2048/CH11/EX11.11/mv_visc.sce new file mode 100755 index 000000000..c2db2d28f --- /dev/null +++ b/2048/CH11/EX11.11/mv_visc.sce @@ -0,0 +1,35 @@ +// Minimum variance control of viscosity control problem
+// 11.11
+
+// Viscosity control problem of MacGregor
+
+exec('mv_nm.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+exec('zpowk.sci',-1);
+exec('polsplit3.sci',-1);
+exec('flip.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('cl.sci',-1);
+exec('poladd.sci',-1);
+exec('tfvar.sci',-1);
+exec('l2r.sci',-1);
+exec('transp.sci',-1);
+exec('tf.sci',-1);
+exec('covar_m.sci',-1);
+
+A = [1 -0.44]; dA = 1; B = [0.51 1.21]; dB = 1;
+C = [1 -0.44]; dC = 1; k = 1; int1 = 1;
+[Sc,dSc,Rc,dRc] = mv_nm(A,dA,B,dB,C,dC,k,int1);
+[Nu,dNu,Du,dDu,Ny,dNy,Dy,dDy,yvar,uvar] = ...
+cl(A,dA,B,dB,C,dC,k,Sc,dSc,Rc,dRc,int1);
diff --git a/2048/CH11/EX11.12/gmv.sci b/2048/CH11/EX11.12/gmv.sci new file mode 100755 index 000000000..1e3ee068c --- /dev/null +++ b/2048/CH11/EX11.12/gmv.sci @@ -0,0 +1,17 @@ +// General minimum variance controller design, as given by Eq. 11.66 on page 421 and Eq. 11.70 on page 422.
+// 11.12
+
+// function [Sc,dSc,Rc,dRc] = gmv(A,dA,B,dB,C,dC,k,rho,int)
+// implements the generalized minimum variance controller
+// if int>=1, integrated noise is assumed; otherwise,
+// it is not integrated noise
+
+function [Sc,dSc,R,dR] = gmv(A,dA,B,dB,C,dC,k,rho,int1)
+zk = zeros(1,k+1); zk(k+1) = 1;
+if int1>=1, [A,dA] = polmul([1 -1],1,A,dA); end
+[Fk,dFk,Ek,dEk] = xdync(zk,k,A,dA,C,dC);
+[Gk,dGk] = polmul(Ek,dEk,B,dB);
+alpha0 = Gk(1)/C(1);
+Sc = alpha0 * Fk; dSc = dFk;
+[R,dR] = poladd(alpha0*Gk,dGk,rho*C,dC);
+endfunction;
diff --git a/2048/CH11/EX11.13/gmv_mac1.sce b/2048/CH11/EX11.13/gmv_mac1.sce new file mode 100755 index 000000000..28b4bb14d --- /dev/null +++ b/2048/CH11/EX11.13/gmv_mac1.sce @@ -0,0 +1,34 @@ +// GMVC design of MacGregor's first example, as discussed in Example 11.9 on page 421.
+// 11.13
+
+// MacGregor's first control problem by gmv
+
+exec('gmv.sci',-1);
+exec('cl.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('polsize.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('polmul.sci',-1);
+exec('zpowk.sci',-1);
+exec('poladd.sci',-1);
+exec('tfvar.sci',-1);
+exec('l2r.sci',-1);
+exec('transp.sci',-1);
+exec('tf.sci',-1);
+exec('covar_m.sci',-1);
+
+A = [1 -1.4 0.45]; dA = 2; C = [1 -0.5]; dC = 1;
+B = 0.5*[1 -0.9]; dB = 1; k = 1; int1 = 0;
+rho = 1;
+[Sc,dSc,Rc,dRc] = gmv(A,dA,B,dB,C,dC,k,rho,int1);
+[Nu,dNu,Du,dDu,Ny,dNy,Dy,dDy,yvar,uvar] = ...
+ cl(A,dA,B,dB,C,dC,k,Sc,dSc,Rc,dRc,int1);
diff --git a/2048/CH11/EX11.14/gmv_visc.sce b/2048/CH11/EX11.14/gmv_visc.sce new file mode 100755 index 000000000..e8adeb79f --- /dev/null +++ b/2048/CH11/EX11.14/gmv_visc.sce @@ -0,0 +1,35 @@ +// GMVC design of viscosity problem, as described in Example 11.10 on page 423.
+// 11.14
+
+// MacGregor's Viscosity control problem by gmv
+
+exec('gmv.sci',-1);
+exec('cl.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('poladd.sci',-1);
+exec('zpowk.sci',-1);
+exec('tfvar.sci',-1);
+exec('l2r.sci',-1);
+exec('transp.sci',-1);
+exec('tf.sci',-1);
+exec('covar_m.sci',-1);
+
+A = [1 -0.44]; dA = 1; B = [0.51 1.21]; dB = 1;
+C = [1 -0.44]; dC = 1; k = 1; int1 = 1;
+rho = 1;
+[Sc,dSc,R1,dR1] = gmv(A,dA,B,dB,C,dC,k,rho,int1);
+[Nu,dNu,Du,dDu,Ny,dNy,Dy,dDy,yvar,uvar] = ...
+ cl(A,dA,B,dB,C,dC,k,Sc,dSc,R1,dR1,int1);
+
diff --git a/2048/CH11/EX11.15/miller.sce b/2048/CH11/EX11.15/miller.sce new file mode 100755 index 000000000..bac47c35e --- /dev/null +++ b/2048/CH11/EX11.15/miller.sce @@ -0,0 +1,36 @@ +// PID tuning through GMVC law, as discussed in Example 11.11.
+// 11.15
+
+exec('gmvc_pid.sci',-1);
+exec('zpowk.sci',-1);
+exec('ch_pol.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('filtval.sci',-1);
+exec('polyno.sci',-1);
+
+// GMVC PID tuning of example given by Miller et al.
+// Model
+A = [1 -1.95 0.935]; B = -0.015; k = 1; Ts = 1;
+
+// Transient specifications
+N = 15; epsilon = 0.1;
+T = ch_pol(N,epsilon);
+
+// Controller Design
+[Kc,tau_i,tau_d,L] = gmvc_pid(A,B,k,T,Ts);
+L1 = filtval(L,1);
+zk = zpowk(k);
+
+
diff --git a/2048/CH11/EX11.16/filtval.sci b/2048/CH11/EX11.16/filtval.sci new file mode 100755 index 000000000..1d4dcb6b5 --- /dev/null +++ b/2048/CH11/EX11.16/filtval.sci @@ -0,0 +1,11 @@ +// Value of polynomial p(x), evaluated at x
+// 11.16
+
+// finds the value of a polynomial in powers of z^{-1}
+// function Y = filtval(P,z)
+
+function Y = filtval(P,z)
+N = length(P)-1;
+Q = polyno(P,'x');
+Y = horner(Q,z)/z^N;
+endfunction;
diff --git a/2048/CH11/EX11.17/gmvc_pid.sci b/2048/CH11/EX11.17/gmvc_pid.sci new file mode 100755 index 000000000..c00f2b000 --- /dev/null +++ b/2048/CH11/EX11.17/gmvc_pid.sci @@ -0,0 +1,42 @@ +// PID tuning through GMVC law
+// 11.17
+
+// function [Kc,tau_i,tau_d,L] = gmvc_pid(A,B,k,T,Ts)
+// Determines p,i,d tuning parameters using GMVC
+// Plant model: Integrated white noise
+// A, B in discrete time form
+
+function [Kc,tau_i,tau_d,L] = gmvc_pid(A,B,k,T,Ts)
+
+dA = length(A)-1; dB = length(B)-1;
+dT = length(T)-1;
+if dA > 2,
+ disp('degree of A cannot be more than 2')
+ exit
+elseif dB > 1,
+ disp('degree of B cannot be more than 1')
+ exit
+elseif dT > 2,
+ disp('degree of T cannot be more than 2')
+ exit
+end
+delta = [1 -1]; ddelta = 1;
+
+[Adelta,dAdelta] = polmul(A,dA,delta,ddelta);
+
+[Q,dQ,P,dP] = ...
+xdync(Adelta,dAdelta,B,dB,T,dT);
+PAdelta = P(1)*Adelta;
+
+[zk,dzk] = zpowk(k);
+[E,degE,F,degF] = ...
+xdync(PAdelta,dAdelta,zk,dzk,P,dP);
+nu = P(1)*E(1)*B(1);
+Kc = -1/nu*(F(2)+2*F(3));
+tau_i = -(F(2)+2*F(3))/(F(1)+F(2)+F(3))*Ts;
+tau_d = -F(3)/(F(2)+2*F(3))*Ts;
+L(1) = 1+Ts/tau_i+tau_d/Ts;
+L(2) = -(1+2*tau_d/Ts);
+L(3) = tau_d/Ts;
+L = Kc * L';
+endfunction;
diff --git a/2048/CH11/EX11.2/recursion_ex1.sce b/2048/CH11/EX11.2/recursion_ex1.sce new file mode 100755 index 000000000..aca798303 --- /dev/null +++ b/2048/CH11/EX11.2/recursion_ex1.sce @@ -0,0 +1,12 @@ +// Recursive computation of Ej and Fj for the system presented in Example 11.2 on page 408.
+// 11.2
+
+exec('poladd.sci',-1);
+exec('polsize.sci',-1);
+exec('recursion.sci',-1);
+
+C = [1 0.5]; dC = 1;
+A = [1 -0.6 -0.16]; dA = 2;
+j = 2;
+[Fj,dFj,Ej,dEj] = recursion(A,dA,C,dC,j)
+
diff --git a/2048/CH11/EX11.3/pm_10.sce b/2048/CH11/EX11.3/pm_10.sce new file mode 100755 index 000000000..b37096c57 --- /dev/null +++ b/2048/CH11/EX11.3/pm_10.sce @@ -0,0 +1,20 @@ +// Solution of Aryabhatta's identity Eq. 11.8, as discussed in Example 11.3 on page 409.
+// 11.3
+
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('polsize.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+
+C = [1 0.5]; dC = 1; j=2;
+A = [1 -0.6 -0.16]; dA = 2;
+zj = zeros(1,j+1); zj(j+1) = 1;
+[Fj,dFj,Ej,dEj] = xdync(zj,j,A,dA,C,dC)
diff --git a/2048/CH11/EX11.4/mv_mac1.sce b/2048/CH11/EX11.4/mv_mac1.sce new file mode 100755 index 000000000..ea499c83c --- /dev/null +++ b/2048/CH11/EX11.4/mv_mac1.sce @@ -0,0 +1,48 @@ +// MacGregor's first control problem, discussed in Example 11.4 on page 213.
+// 11.4
+
+exec('mv.sci',-1);
+exec('cl.sci',-1);
+exec('cosfil_ip.sci',-1);
+exec('zpowk.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('polsize.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('polmul.sci',-1);
+exec('poladd.sci',-1);
+exec('tfvar.sci',-1);
+exec('l2r.sci',-1);
+exec('transp.sci',-1);
+exec('tf.sci',-1);
+exec('covar_m.sci',-1);
+exec('polyno.sci',-1);
+
+// MacGregor's first control problem
+A = [1 -1.4 0.45]; dA = 2; C = [1 -0.5]; dC = 1;
+B = 0.5*[1 -0.9]; dB = 1; k = 1; int1 = 0;
+[Sc,dSc,Rc,dRc] = mv(A,dA,B,dB,C,dC,k,int1);
+[Nu,dNu,Du,dDu,Ny,dNy,Dy,dDy,yvar,uvar] = ...
+cl(A,dA,B,dB,C,dC,k,Sc,dSc,Rc,dRc,int1);
+
+// Simulation parameters for stb_disc.xcos
+Tc = Sc; gamm = 1; [zk,dzk] = zpowk(k);
+D = 1; N_var = 1; Ts = 1; st = 0;
+t_init = 0; t_final = 1000;
+
+[Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+[Rcp1,Rcp2] = cosfil_ip(1,Rc); // 1/Rc
+[Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+[Bp,Ap] = cosfil_ip(B,A); // B/A
+[zkp1,zkp2] = cosfil_ip(zk,1); // zk/1
+[Cp,Dp] = cosfil_ip(C,D); // C/D
+
+
diff --git a/2048/CH11/EX11.4/stb_disc.xcos b/2048/CH11/EX11.4/stb_disc.xcos new file mode 100755 index 000000000..a487292f3 --- /dev/null +++ b/2048/CH11/EX11.4/stb_disc.xcos @@ -0,0 +1 @@ +<?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1" finalIntegrationTime="1000.0" title="stb_disc"><!--Xcos - 1.0 - scilab-5.5.0 - 20140411 1208--><mxGraphModel as="model"><root><mxCell id="-7476484f:145f8cd2a3c:-7be8"/><mxCell id="-7476484f:145f8cd2a3c:-7be9" parent="-7476484f:145f8cd2a3c:-7be8"/><BasicBlock blockType="h" id="-7476484f:145f8cd2a3c:-7be4" interfaceFunctionName="STEP_FUNCTION" ordering="1" parent="-7476484f:145f8cd2a3c:-7be9" simulationFunctionName="csuper" simulationFunctionType="DEFAULT" style="STEP_FUNCTION;flip=false;mirror=false"><ScilabDouble as="exprs" height="0" width="0"/><Array as="realParameters" scilabClass="ScilabMList" varName=""><ScilabString height="1" width="5"><data column="0" line="0" value="diagram"/><data column="1" line="0" value="props"/><data 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\ No newline at end of file diff --git a/2048/CH11/EX11.4/u1_mv_mac1.png b/2048/CH11/EX11.4/u1_mv_mac1.png Binary files differnew file mode 100755 index 000000000..65a43c27e --- /dev/null +++ b/2048/CH11/EX11.4/u1_mv_mac1.png diff --git a/2048/CH11/EX11.4/y1_mv_mac1.png b/2048/CH11/EX11.4/y1_mv_mac1.png Binary files differnew file mode 100755 index 000000000..813b990b4 --- /dev/null +++ b/2048/CH11/EX11.4/y1_mv_mac1.png diff --git a/2048/CH11/EX11.5/mv.sci b/2048/CH11/EX11.5/mv.sci new file mode 100755 index 000000000..532fc6b4d --- /dev/null +++ b/2048/CH11/EX11.5/mv.sci @@ -0,0 +1,16 @@ +// Minimum variance control law design, given by Eq. 11.40 on page 413.
+// 11.5
+
+// function [S,dS,R,dR] = mv(A,dA,B,dB,C,dC,k,int)
+// implements the minimum variance controller
+// if int>=1, integrated noise is assumed; otherwise,
+// it is not integrated noise
+
+function [S,dS,R,dR] = mv(A,dA,B,dB,C,dC,k,int1)
+zk = zeros(1,k+1); zk(k+1) = 1;
+if int1>=1, [A,dA] = polmul([1 -1],1,A,dA); end
+[Fk,dFk,Ek,dEk] = xdync(zk,k,A,dA,C,dC);
+
+[Gk,dGk] = polmul(Ek,dEk,B,dB);
+S = Fk; dS = dFk; R = Gk; dR = dGk;
+endfunction;
diff --git a/2048/CH11/EX11.6/cl.sci b/2048/CH11/EX11.6/cl.sci new file mode 100755 index 000000000..561874cb8 --- /dev/null +++ b/2048/CH11/EX11.6/cl.sci @@ -0,0 +1,28 @@ +// Calculation of closed loop transfer functions
+// 11.6
+
+// function [Nu,dNu,Du,dDu,Ny,dNy,Dy,dDy,yvar,uvar] = ...
+// cl(A,dA,B,dB,C,dC,k,S,dS,R,dR,int)
+// int>=1 means integrated noise and control law:
+// delta u = - (S/R)y
+// Evaluates the closed loop transfer function and
+// variances of input and output
+
+function [Nu,dNu,Du,dDu,Ny,dNy,Dy,dDy,yvar,uvar] = ...
+ cl(A,dA,B,dB,C,dC,k,S,dS,R,dR,int1)
+[zk,dzk] = zpowk(k);
+
+[BS,dBS] = polmul(B,dB,S,dS);
+[zBS,dzBS] = polmul(zk,dzk,BS,dBS);
+[RA,dRA] = polmul(R,dR,A,dA);
+if int1>=1, [RA,dRA] = polmul(RA,dRA,[1 -1],1); end
+
+[D,dD] = poladd(RA,dRA,zBS,dzBS);
+
+[Ny,dNy] = polmul(C,dC,R,dR);
+[Nu,dNu] = polmul(C,dC,S,dS);
+
+[Nu,dNu,Du,dDu,uvar] = tfvar(Nu,dNu,D,dD);
+[Ny,dNy,Dy,dDy,yvar] = tfvar(Ny,dNy,D,dD);
+
+endfunction;
diff --git a/2048/CH11/EX11.7/tfvar.sci b/2048/CH11/EX11.7/tfvar.sci new file mode 100755 index 000000000..424624d9f --- /dev/null +++ b/2048/CH11/EX11.7/tfvar.sci @@ -0,0 +1,16 @@ +// Cancellation of common factors and determination of covariance
+// 11.7
+
+// function [N,dN,D,dD,yvar] = tfvar(N,dN,D,dD)
+// N and D polynomials in z^{-1} form; discrete case
+
+function [N,dN,D,dD,yvar] = tfvar(N,dN,D,dD)
+
+[N,dN,D,dD] = l2r(N,dN,D,dD);
+N = N/D(1); D = D/D(1);
+LN = length(N); LD = length(D);
+D1 = D;
+if LD<LN, D1 = [D zeros(1,LN-LD)]; dD1 = dD+LN-LD; end
+H = tf(N,D1,1);//TS=1 (sampling time) has been taken constant in tfvar
+yvar = covar_m(H,1);
+endfunction;
diff --git a/2048/CH11/EX11.8/sumsq.sce b/2048/CH11/EX11.8/sumsq.sce new file mode 100755 index 000000000..7d830d5c9 --- /dev/null +++ b/2048/CH11/EX11.8/sumsq.sce @@ -0,0 +1,9 @@ +// Computing sum of squares, as presented in Example 11.5 on page 415.
+// 11.8
+
+exec('tf.sci',-1);
+exec('covar_m.sci',-1);
+
+Y = tf([1 0],[1 -0.9],-1);
+covar_m(Y,1)
+
diff --git a/2048/CH11/EX11.9/mv_nm.sci b/2048/CH11/EX11.9/mv_nm.sci new file mode 100755 index 000000000..23b902f45 --- /dev/null +++ b/2048/CH11/EX11.9/mv_nm.sci @@ -0,0 +1,16 @@ +// Minimum variance control for nonminimum phase systems
+// 11.9
+
+// function [Sc,dSc,Rc,dRc] = mv_mv(A,dA,B,dB,C,dC,k,int)
+// implements the minimum variance controller
+// if int>=1, integrated noise is assumed; otherwise,
+// it is not integrated noise
+
+function [Sc,dSc,Rc,dRc] = mv_nm(A,dA,B,dB,C,dC,k,int1)
+if int1>=1, [A,dA] = polmul([1 -1],1,A,dA); end
+[zk,dzk] = zpowk(k);
+[Bzk,dBzk] = polmul(B,dB,zk,dzk);
+[Bg,Bb] = polsplit3(B); Bbr = flip(Bb);
+RHS = convol(C,convol(Bg,Bbr)); dRHS = length(RHS)-1;
+[Sc,dSc,Rc,dRc] = xdync(Bzk,dBzk,A,dA,RHS,dRHS);
+endfunction;
diff --git a/2048/CH12/EX12.1/gpc_ex11.sce b/2048/CH12/EX12.1/gpc_ex11.sce new file mode 100755 index 000000000..bbd5e557d --- /dev/null +++ b/2048/CH12/EX12.1/gpc_ex11.sce @@ -0,0 +1,35 @@ +// Model derivation for GPC design in Example 12.1 on page 439.
+// 12.1
+
+exec('xdync.sci',-1);
+exec('polmul.sci',-1);
+exec('flip.sci',-1);
+exec('rowjoin.sci',-1);
+exec('polsize.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+
+// Camacho and Bordon's GPC example; model formation
+
+A=[1 -0.8]; dA=1; B=[0.4 0.6]; dB=1; N=3; k=1;
+D=[1 -1]; dD=1; AD=convol(A,D); dAD=dA+1; Nu=N+k;
+zj = 1; dzj = 0; G = zeros(Nu);
+H1 = zeros(Nu,k-1+dB); H2 = zeros(Nu,dA+1);
+
+for j = 1:Nu,
+ zj = convol(zj,[0,1]); dzj = dzj + 1;
+ [Fj,dFj,Ej,dEj] = xdync(zj,dzj,AD,dAD,1,0);
+ [Gj,dGj] = polmul(B,dB,Ej,dEj);
+ G(j,1:dGj) = flip(Gj(1:dGj));
+ H1(j,1:k-1+dB) = Gj(dGj+1:dGj+k-1+dB);
+ H2(j,1:dA+1) = Fj;
+end
+
+G,H1,H2
diff --git a/2048/CH12/EX12.10/gpc_pid_test.sce b/2048/CH12/EX12.10/gpc_pid_test.sce new file mode 100755 index 000000000..5f9436051 --- /dev/null +++ b/2048/CH12/EX12.10/gpc_pid_test.sce @@ -0,0 +1,34 @@ +// PID controller, tuned with GPC, as discussed in Example 12.5 on page 452.
+// 12.10
+
+exec('gpc_pid.sci',-1);
+exec('zpowk.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('polsize.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+
+A = [1 -1.95 0.935];
+B=-0.015;
+C=1;
+degA=2;
+degB=0;
+degC=0;
+N1=1;
+N2=5;
+Nu=2;
+gamm=0.05;
+gamma_y=1;
+lambda=0.02;
+
+[Kp,Ki,Kd] = ...
+gpc_pid(A,degA,B,degB,C,degC,N1,N2,Nu,lambda,gamm,gamma_y)
+
diff --git a/2048/CH12/EX12.11/gpc_pid.sci b/2048/CH12/EX12.11/gpc_pid.sci new file mode 100755 index 000000000..2359a5dfe --- /dev/null +++ b/2048/CH12/EX12.11/gpc_pid.sci @@ -0,0 +1,52 @@ +// Predictive PID, tuned with GPC, as explained in Sec. 12.2.3.
+// 12.11
+
+function [Kp,Ki,Kd] = ...
+gpc_pid(A,dA,B,dB,C,dC,N1,N2,Nu,lambda,gamm,gamma_y)
+Adelta=convol(A,[1 -1]); G=[];
+for i=N1:N2
+ zi=zpowk(i);
+ [E,dE,F,dF]=xdync(Adelta,dA+1,zi,i,C,dC);
+ [Gtilda,dGtilda,Gbar,dGbar] = ...
+ xdync(C,dC,zi,i,E*B,dE+dB);
+ for j = 1:i, Gtilda1(j)=Gtilda(i+1-j); end
+ Gtilda2 = Gtilda1.'; // Added because Scilab forms a column vecor
+ // while Matlab forms a row vector, by default
+ if i<=Nu-1
+ G=[G;[Gtilda2,zeros(1,Nu-i)]];
+ else
+ G=[G;Gtilda2(1:Nu)];
+ end
+end
+es=sum(C)/sum(A); gs=sum(B)/sum(A); F_s=es*A; G_s=[];
+for i=1:Nu
+ if ((Nu - i) == 0)
+ row=gs*ones(1,i);
+ else
+ row=gs*ones(1,i); row=[row,zeros(Nu-i,Nu-i)];
+ end;
+ G_s=[G_s;row];
+end
+lambda_mat=lambda*(diag(ones(1,Nu)));
+gamma_mat=gamm*(diag(ones(1,Nu)));
+gamma_y_mat=gamma_y*(diag(ones(1,N2-N1+1)));
+mat1=inv(G'*gamma_y_mat*G+lambda_mat+G_s'*gamma_mat*G_s);
+mat2=mat1*(G'*gamma_y_mat);
+mat2_s=mat1*(G_s'*gamma_mat);
+h_s=sum(mat2_s(1,:)); h=mat2(1,:);
+T=C; R=C*(sum(h(:))+h_s); S=0;
+for i=N1:N2
+ zi=zpowk(i);
+ [E,dE,F,dF]=xdync(Adelta,dA+1,zi,i,C,dC);
+ [Gtilda,dGtilda,Gbar,dGbar]=...
+ xdync(C,dC,zi,i,E*B,dE+dB);
+ S=S+F*h(i);
+end
+S=S+F_s*h_s;
+if length(A)==3
+ Kp=S(1)-R-S(3); Ki=R; Kd=S(3);
+else
+ Kp=S(1)-R; Ki=R; Kd=0;
+end
+
+endfunction;
diff --git a/2048/CH12/EX12.2/gpc_bas.sci b/2048/CH12/EX12.2/gpc_bas.sci new file mode 100755 index 000000000..dd742e0c5 --- /dev/null +++ b/2048/CH12/EX12.2/gpc_bas.sci @@ -0,0 +1,23 @@ +// Calculates the GPC law given by Eq. 12.19 on page 441.
+// 12.2
+
+function [K,KH1,KH2,Tc,dTc,Sc,dSc,R1,dR1] = ...
+gpc_bas(A,dA,B,dB,N,k,rho)
+D=[1 -1]; dD=1; AD=convol(A,D); dAD=dA+1; Nu=N+1;
+zj = 1; dzj = 0; G = zeros(Nu,Nu);
+H1 = zeros(Nu,k-1+dB); H2 = zeros(Nu,dA+1);
+for j = 1:Nu,
+ zj = convol(zj,[0,1]); dzj = dzj + 1;
+ [Fj,dFj,Ej,dEj] = xdync(zj,dzj,AD,dAD,1,0);
+ [Gj,dGj] = polmul(B,dB,Ej,dEj);
+ G(j,1:dGj) = flip(Gj(1:dGj));
+ H1(j,1:k-1+dB) = Gj(dGj+1:dGj+k-1+dB);
+ H2(j,1:dA+1) = Fj;
+end
+K = inv(G'*G+rho*eye(Nu,Nu))*G';
+// Note: inverse need not be calculated
+KH1 = K * H1; KH2 = K * H2;
+R1 = [1 KH1(1,:)]; dR1 = length(R1)-1;
+Sc = KH2(1,:); dSc = length(Sc)-1;
+Tc = K(1,:); dTc = length(Tc)-1;
+endfunction;
diff --git a/2048/CH12/EX12.3/gpc_ex12.sce b/2048/CH12/EX12.3/gpc_ex12.sce new file mode 100755 index 000000000..e8523daba --- /dev/null +++ b/2048/CH12/EX12.3/gpc_ex12.sce @@ -0,0 +1,36 @@ +// GPC design for the problem discussed in Example 12.2 on page 441.
+// 12.3
+
+exec('gpc_bas.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('polsize.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('polmul.sci',-1);
+exec('flip.sci',-1);
+exec('filtval.sci',-1);
+
+// Camacho and Bordon's GPC example; Control law
+A=[1 -0.8]; dA=1; B=[0.4 0.6]; dB=1; N=3; k=1; rho=0.8;
+[K,KH1,KH2,Tc,dTc,Sc,dSc,R1,dR1] = ...
+gpc_bas(A,dA,B,dB,N,k,rho)
+// C=1; dC=0; [K,KH1,KH2,Tc,dTc,Sc,dSc,R1,dR1] = ...
+// gpc_col(A,dA,B,dB,C,dC,N,k,rho)
+
+
+
+
+
+
+
+
+
+
diff --git a/2048/CH12/EX12.4/gpc_wt.sce b/2048/CH12/EX12.4/gpc_wt.sce new file mode 100755 index 000000000..09a0f3fe1 --- /dev/null +++ b/2048/CH12/EX12.4/gpc_wt.sce @@ -0,0 +1,26 @@ +// GPC design for the problem discussed in Example 12.3.
+// 12.4
+
+exec('gpc_N.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('polsize.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('polmul.sci',-1);
+exec('flip.sci',-1);
+
+A=[1 -0.8]; dA=1; B=[0.4 0.6]; dB=1;
+rho = 0.8; k = 1;
+N1 = 0; N2 = 3; Nu = 2;
+
+[K,KH1,KH2,Tc,dTc,Sc,dSc,R1,dR1] = ...
+gpc_N(A,dA,B,dB,k,N1,N2,Nu,rho)
+
diff --git a/2048/CH12/EX12.5/gpc_N.sci b/2048/CH12/EX12.5/gpc_N.sci new file mode 100755 index 000000000..2abbe0f74 --- /dev/null +++ b/2048/CH12/EX12.5/gpc_N.sci @@ -0,0 +1,31 @@ +// Calculates the GPC law given by Eq. 12.36 on page 446.
+// 12.5
+
+function [K,KH1,KH2,Tc,dTc,Sc,dSc,R1,dR1] = ...
+gpc_N(A,dA,B,dB,k,N1,N2,Nu,rho)
+D=[1 -1]; dD=1; AD=convol(A,D); dAD=dA+1;
+zj = 1; dzj = 0;
+for i = 1:N1+k-1
+ zj = convol(zj,[0,1]); dzj = dzj + 1;
+end
+G = zeros(N2-N1+1,Nu+1);
+H1 = zeros(N2-N1+1,k-1+dB); H2 = zeros(N2-N1+1,dA+1);
+for j = k+N1:k+N2
+ zj = convol(zj,[0,1]); dzj = dzj + 1;
+ [Fj,dFj,Ej,dEj] = xdync(zj,dzj,AD,dAD,1,0);
+ [Gj,dGj] = polmul(B,dB,Ej,dEj);
+ if (j-k >= Nu)
+ G(j-(k+N1-1),1:Nu+1) = flip(Gj(j-k-Nu+1:j-k+1));
+else
+ G(j-(k+N1-1),1:j-k+1) = flip(Gj(1:j-k+1));
+end
+ H1(j-(k+N1-1),1:k-1+dB) = Gj(j-k+2:j+dB);
+ H2(j-(k+N1-1),1:dA+1) = Fj;
+end
+K = inv(G'*G+rho*eye(Nu+1,Nu+1))*G';
+// Note: inverse need not be calculated
+KH1 = K * H1; KH2 = K * H2;
+R1 = [1 KH1(1,:)]; dR1 = length(R1)-1;
+Sc = KH2(1,:); dSc = length(Sc)-1;
+Tc = K(1,:); dTc = length(Tc)-1;
+endfunction;
diff --git a/2048/CH12/EX12.6/gpc_col.sci b/2048/CH12/EX12.6/gpc_col.sci new file mode 100755 index 000000000..569718f08 --- /dev/null +++ b/2048/CH12/EX12.6/gpc_col.sci @@ -0,0 +1,30 @@ +// Calculates the GPC law given by Eq. 12.36 on page 446.
+// 12.6
+
+function [K,KH1,KH2,Tc,dTc,Sc,dSc,R1,dR1] = ...
+gpc_col(A,dA,B,dB,C,dC,N,k,rho)
+D=[1 -1]; dD = 0; AD=convol(A,D); dAD=dA+1; zj=1; dzj=0;
+Nu = N+1; G=zeros(Nu,Nu); H1=zeros(Nu,2*k+N-2+dB);
+H2 = zeros(Nu,k+N+dA);
+for j = 1:Nu,
+ zj = convol(zj,[0,1]); dzj = dzj + 1;
+ [Fj,dFj,Ej,dEj] = ...
+ xdync(zj,dzj,AD,dAD,C,dC);
+ [Nj,dNj,Mj,dMj] = ...
+ xdync(zj,dzj,C,dC,1,0);
+ [Gj,dGj] = polmul(Mj,dMj,Ej,dEj);
+ [Gj,dGj] = polmul(Gj,dGj,B,dB);
+ [Pj,dPj] = polmul(Mj,dMj,Fj,dFj);
+ [Pj,dPj] = poladd(Nj,dNj,Pj,dPj);
+ j,Fj,Ej,Mj,Nj,Gj,Pj
+ G(j,1:j) = flip(Gj(1:j));
+ H1(j,1:dGj-j+1) = Gj(j+1:dGj+1);
+ H2(j,1:dPj+1) = Pj;
+end
+K = inv(G'*G+rho*eye(Nu,Nu))*G'
+// Note: inverse need not be calculated
+KH1 = K * H1; KH2 = K * H2;
+R1 = [1 KH1(1,:)]; dR1 = length(R1)-1;
+Sc = KH2(1,:); dSc = length(Sc)-1;
+Tc = K(1,:); dTc = length(Tc)-1;
+endfunction;
diff --git a/2048/CH12/EX12.7/gpc_ex2.sce b/2048/CH12/EX12.7/gpc_ex2.sce new file mode 100755 index 000000000..16ea52aa5 --- /dev/null +++ b/2048/CH12/EX12.7/gpc_ex2.sce @@ -0,0 +1,26 @@ +// GPC design for viscosity control in Example 12.4 on page 446.
+// 12.7
+
+exec('gpc_col.sci',-1);
+exec('poladd.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('polsize.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('polmul.sci',-1);
+exec('flip.sci',-1);
+
+// GPC control of viscosity problem
+A=[1 -0.44]; dA=1; B=[0.51 1.21]; dB=1; N=2; k=1;
+C = [1 -0.44]; dC = 1; rho = 1;
+
+[K,KH1,KH2,Tc,dTc,Sc,dSc,R1,dR1] = ...
+gpc_col(A,dA,B,dB,C,dC,N,k,rho)
diff --git a/2048/CH12/EX12.8/gpc_wtc.sce b/2048/CH12/EX12.8/gpc_wtc.sce new file mode 100755 index 000000000..e776699f0 --- /dev/null +++ b/2048/CH12/EX12.8/gpc_wtc.sce @@ -0,0 +1,27 @@ +// GPC design for the problem discussed in Example 12.3.
+// 12.8
+
+exec('gpc_Nc.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('polsize.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('polmul.sci',-1);
+exec('poladd.sci',-1);
+exec('flip.sci',-1);
+
+A=[1 -0.44]; dA=1; B=[0.51 1.21]; dB=1;
+C = [1 -0.44]; dC = 1;
+k=1; N1 = 0; N2 = 2; Nu = 0; rho = 1;
+
+[K,KH1,KH2,Tc,dTc,Sc,dSc,R1,dR1] = ...
+gpc_Nc(A,dA,B,dB,C,dC,k,N1,N2,Nu,rho)
+
diff --git a/2048/CH12/EX12.9/gpc_Nc.sci b/2048/CH12/EX12.9/gpc_Nc.sci new file mode 100755 index 000000000..9401ffde1 --- /dev/null +++ b/2048/CH12/EX12.9/gpc_Nc.sci @@ -0,0 +1,37 @@ +// Calculates the GPC law for different prediction and control horizons
+// 12.9
+
+function [K,KH1,KH2,Tc,dTc,Sc,dSc,R1,dR1] = ...
+gpc_Nc(A,dA,B,dB,C,dC,k,N1,N2,Nu,rho)
+D=[1 -1]; dD=1; AD=convol(A,D); dAD=dA+1;
+zj = 1; dzj = 0;
+for i = 1:N1+k-1
+ zj = convol(zj,[0,1]); dzj = dzj + 1;
+end
+M = 2*k+N2-2+dB; P = max(k+N2+dA-1,dC-1)
+G = zeros(N2-N1+1,Nu+1); H1 = zeros(N2-N1+1,M);
+H2 = zeros(N2-N1+1,P+1);
+for j = k+N1:k+N2
+ zj = convol(zj,[0,1]); dzj = dzj + 1;
+ [Fj,dFj,Ej,dEj] = xdync(zj,dzj,AD,dAD,C,dC);
+ [Nj,dNj,Mj,dMj] = xdync(zj,dzj,C,dC,1,0);
+ [Gj,dGj] = polmul(Mj,dMj,Ej,dEj);
+ [Gj,dGj] = polmul(Gj,dGj,B,dB);
+ [Pj,dPj] = polmul(Mj,dMj,Fj,dFj);
+ [Pj,dPj] = poladd(Nj,dNj,Pj,dPj);
+ if (j-k >= Nu)
+ G(j-(k+N1-1),1:Nu+1) = flip(Gj(j-k-Nu+1:j-k+1));
+else
+ G(j-(k+N1-1),1:j-k+1) = flip(Gj(1:j-k+1));
+end
+ H1(j-(k+N1-1),1:j+k-2+dB) = Gj(j-k+2:2*j+dB-1);
+ dPj = max(j-1+dA,dC-1);
+ H2(j-(k+N1-1),1:dPj+1) = Pj;
+end
+K = inv(G'*G+rho*eye(Nu+1,Nu+1))*G';
+// Note: inverse need not be calculated
+KH1 = K * H1; KH2 = K * H2;
+R1 = [1 KH1(1,:)]; dR1 = length(R1)-1;
+Sc = KH2(1,:); dSc = length(Sc)-1;
+Tc = K(1,:); dTc = length(Tc)-1;
+endfunction;
diff --git a/2048/CH13/EX13.1/spec_ex.sce b/2048/CH13/EX13.1/spec_ex.sce new file mode 100755 index 000000000..a120413fa --- /dev/null +++ b/2048/CH13/EX13.1/spec_ex.sce @@ -0,0 +1,12 @@ +// Spectral factorization, as discussed in Example 13.3 on page 467.
+// 13.1
+
+exec('spec1.sci',-1);
+exec('flip.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+exec('poladd.sci',-1);
+
+A = convol([-0.5 1],[-0.9 1]); dA = 2;
+B = 0.5*[-0.9 1]; dB = 1; rho = 1;
+[r,beta1,sigma] = spec1(A,dA,B,dB,rho)
diff --git a/2048/CH13/EX13.10/gmv_mac1_loop.sce b/2048/CH13/EX13.10/gmv_mac1_loop.sce new file mode 100755 index 000000000..2e360dd5a --- /dev/null +++ b/2048/CH13/EX13.10/gmv_mac1_loop.sce @@ -0,0 +1,40 @@ +// Performance curve for GMVC design of MacGregor's first control problem
+// 13.10
+
+exec('gmv.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('polsize.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('polmul.sci',-1);
+exec('poladd.sci',-1);
+exec('cl.sci',-1);
+exec('zpowk.sci',-1);
+exec('tfvar.sci',-1);
+exec('l2r.sci',-1);
+exec('transp.sci',-1);
+exec('tf.sci',-1);
+exec('covar_m.sci',-1);
+
+// MacGregor's first control problem
+A = [1 -1.4 0.45]; dA = 2; C = [1 -0.5]; dC = 1;
+B = 0.5*[1 -0.9]; dB = 1; k = 1; int1 = 0;
+u_gmv = []; y_gmv = []; uy_gmv = [];
+
+for rho = 0:0.1:10,
+ [S,dS,R,dR] = gmv(A,dA,B,dB,C,dC,k,rho,int1);
+ [Nu,dNu,Du,dDu,Ny,dNy,Dy,dDy,yvar,uvar] = ...
+ cl(A,dA,B,dB,C,dC,k,S,dS,R,dR,int1);
+ u_gmv = [u_gmv uvar]; y_gmv = [y_gmv yvar];
+ uy_gmv = [uy_gmv; [rho uvar yvar]];
+end
+plot(u_gmv,y_gmv,'b')
+save('gmv_mac1.dat','uy_gmv');
diff --git a/2048/CH13/EX13.2/spec1.sci b/2048/CH13/EX13.2/spec1.sci new file mode 100755 index 000000000..c749f9695 --- /dev/null +++ b/2048/CH13/EX13.2/spec1.sci @@ -0,0 +1,23 @@ +// Function to implement spectral factorization, as discussed in sec. 13.1.
+// 13.2
+
+function [r,b,rbbr] = spec1(A,dA,B,dB,rho)
+AA = rho * convol(A,flip(A));
+BB = convol(B,flip(B));
+diff1 = dA - dB;
+dBB = 2*dB;
+for i = 1:diff1
+ [BB,dBB] = polmul(BB,dBB,[0 1],1);
+end
+[rbbr,drbbr] = poladd(AA,2*dA,BB,dBB);
+rts = roots(rbbr); // roots in descending order of magnitude
+rts = flip(rts);
+rtsin = rts(dA+1:2*dA);
+b = 1;
+for i = 1:dA,
+ b = convol(b,[1 -rtsin(i)]);
+end
+br = flip(b);
+bbr = convol(b,br);
+r = rbbr(1) / bbr(1);
+endfunction;
diff --git a/2048/CH13/EX13.3/specfac.sci b/2048/CH13/EX13.3/specfac.sci new file mode 100755 index 000000000..1a8ff1332 --- /dev/null +++ b/2048/CH13/EX13.3/specfac.sci @@ -0,0 +1,34 @@ +// Spectral factorization, to solve Eq. 13.47 on page 471.
+// 13.3
+
+// function [r,b,dAFW] = ...
+// specfac(A,degA,B,degB,rho,V,degV,W,degW,F,degF)
+// Implements the spectral factorization for use with LQG control
+// design method of Ahlen and Sternard
+
+function [r,b,dAFW] = ...
+ specfac(A,degA,B,degB,rho,V,degV,W,degW,F,degF)
+AFW = convol(A,convol(W,F));
+dAFW = degA + degF + degW;
+AFWWFA = rho * convol(AFW,flip(AFW));
+BV = convol(B,V);
+dBV = degB + degV;
+BVVB = convol(BV,flip(BV));
+diff1 = dAFW - dBV;
+dBVVB = 2*dBV;
+for i = 1:diff1
+ [BVVB,dBVVB] = polmul(BVVB,dBVVB,[0 1],1);
+end
+[rbb,drbb] = poladd(AFWWFA,2*dAFW,BVVB,dBVVB);
+Rbb = polyno(rbb,'z');
+rts = roots(Rbb);
+rtsin = rts(dAFW+1:2*dAFW);
+b = 1;
+for i = 1:dAFW,
+ b = convol(b,[1 -rtsin(i)]);
+end
+b = real(b);
+br = flip(b);
+bbr = convol(b,br);
+r = rbb(1) / bbr(1);
+endfunction;
diff --git a/2048/CH13/EX13.4/lqg1.sci b/2048/CH13/EX13.4/lqg1.sci new file mode 100755 index 000000000..2ce4a74ec --- /dev/null +++ b/2048/CH13/EX13.4/lqg1.sci @@ -0,0 +1,48 @@ +// LQG control design by polynomial method, to solve Eq. 13.51 on page 472.
+// 13.4
+
+// LQG controller design by method of Ahlen and Sternad
+// function [R,degR,S,degS] = ...
+// lqg(A,degA,B,degB,C,degC,k,rho,V,degV,W,degW,F,degF)
+
+function [R,degR,S,degS] = ...
+lqg1(A,degA,B,degB,C,degC,k,rho,V,degV,W,degW,F,degF)
+
+[r,b,degb] = ...
+specfac(A,degA,B,degB,rho,V,degV,W,degW,F,degF);
+
+WFA = flip(convol(A,convol(F,W)));
+dWFA = degW + degF + degA;
+
+[rhs1,drhs1] = polmul(W,degW,WFA,dWFA);
+[rhs1,drhs1] = polmul(rhs1,drhs1,C,degC);
+rhs1 = rho * rhs1;
+rhs2 = convol(C,convol(V,flip(convol(B,V))));
+drhs2 = degC + 2*degV + degB;
+for i = 1:degb-degB-degV,
+ rhs2 = convol(rhs2,[0,1]);
+end
+drhs2 = drhs2 + degb-degB-degV;
+C1 = zeros(1,2);
+
+[C1,degC1] = putin(C1,0,rhs1,drhs1,1,1);
+[C1,degC1] = putin(C1,degC1,rhs2,drhs2,1,2);
+rbf = r * flip(b);
+D1 = zeros(2,2);
+[D1,degD1] = putin(D1,0,rbf,degb,1,1);
+for i = 1:k,
+ rbf = convol(rbf,[0 1]);
+end
+[D1,degD1] = putin(D1,degD1,rbf,degb+k,2,2);
+N = zeros(1,2);
+[N,degN] = putin(N,0,-B,degB,1,1);
+[AF,dAF] = polmul(A,degA,F,degF);
+[N,degN] = putin(N,degN,AF,dAF,1,2);
+
+[Y,degY,X,degX] = xdync(N,degN,D1,degD1,C1,degC1);
+
+[R,degR] = ext(X,degX,1,1);
+[S,degS] = ext(X,degX,1,2);
+X = flip(Y);
+
+endfunction;
diff --git a/2048/CH13/EX13.5/lqg_mac1.sce b/2048/CH13/EX13.5/lqg_mac1.sce new file mode 100755 index 000000000..ea231a5d2 --- /dev/null +++ b/2048/CH13/EX13.5/lqg_mac1.sce @@ -0,0 +1,40 @@ +// LQG design for the problem discussed in Example 13.4 on page 472.
+// 13.5
+
+// MacGregor's first control problem
+
+exec('lqg1.sci',-1);
+exec('cl.sci',-1);
+exec('specfac.sci',-1);
+exec('flip.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+exec('poladd.sci',-1);
+exec('polyno.sci',-1);
+exec('putin.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('ext.sci',-1);
+exec('zpowk.sci',-1);
+exec('tfvar.sci',-1);
+exec('l2r.sci',-1);
+exec('transp.sci',-1);
+exec('tf.sci',-1);
+exec('covar_m.sci',-1);
+
+A = [1 -1.4 0.45]; dA = 2; C = [1 -0.5]; dC = 1;
+B = 0.5*[1 -0.9]; dB = 1; k = 1; int1 = 0; F = 1; dF = 0;
+V = 1; W = 1; dV = 0; dW = 0;
+rho = 1;
+[R1,dR1,Sc,dSc] = lqg1(A,dA,B,dB,C,dC,k,rho,V,dV,W,dW,F,dF)
+[Nu,dNu,Du,dDu,Ny,dNy,Dy,dDy,yvar,uvar] = ...
+ cl(A,dA,B,dB,C,dC,k,Sc,dSc,R1,dR1,int1);
diff --git a/2048/CH13/EX13.6/lqg_visc.sce b/2048/CH13/EX13.6/lqg_visc.sce new file mode 100755 index 000000000..fa7f2d608 --- /dev/null +++ b/2048/CH13/EX13.6/lqg_visc.sce @@ -0,0 +1,40 @@ +// LQG control design for viscosity control problem discussed in Example 13.5.
+// 13.6
+
+
+exec('lqg1.sci',-1);
+exec('cl.sci',-1);
+exec('specfac.sci',-1);
+exec('flip.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+exec('poladd.sci',-1);
+exec('polyno.sci',-1);
+exec('putin.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('ext.sci',-1);
+exec('zpowk.sci',-1);
+exec('tfvar.sci',-1);
+exec('l2r.sci',-1);
+exec('transp.sci',-1);
+exec('tf.sci',-1);
+exec('covar_m.sci',-1);
+
+// Viscosity control problem of MacGregor
+A = [1 -0.44]; dA = 1; B = [0.51 1.21]; dB = 1;
+C = [1 -0.44]; dC = 1; k = 1; int1 = 1; F = [1 -1]; dF = 1;
+V = 1; W = 1; dV = 0; dW = 0;
+rho = 1;
+[R1,dR1,Sc,dSc] = lqg1(A,dA,B,dB,C,dC,k,rho,V,dV,W,dW,F,dF);
+[Nu,dNu,Du,dDu,Ny,dNy,Dy,dDy,yvar,uvar] = ...
+ cl(A,dA,B,dB,C,dC,k,Sc,dSc,R1,dR1,int1);
diff --git a/2048/CH13/EX13.7/lqg_simple.sci b/2048/CH13/EX13.7/lqg_simple.sci new file mode 100755 index 000000000..fe72ef752 --- /dev/null +++ b/2048/CH13/EX13.7/lqg_simple.sci @@ -0,0 +1,16 @@ +// Simplified LQG control design, obtained by the solution of Eq. 13.53 on page 476.
+// 13.7
+
+// LQG controller simple design by method of Ahlen and Sternad
+// function [R1,dR1,S,dS] = ...
+// lqg_simple(A,dA,B,dB,C,dC,k,rho,V,dV,W,dW,F,dF)
+
+function [R1,dR1,S,dS] = ...
+lqg_simple(A,dA,B,dB,C,dC,k,rho,V,dV,W,dW,F,dF)
+[r,b,db] = specfac(A,dA,B,dB,rho,V,dV,W,dW,F,dF);
+[D,dD] = polmul(A,dA,F,dF);
+[zk,dzk] = zpowk(k);
+[N,dN] = polmul(zk,dzk,B,dB);
+[RHS,dRHS] = polmul(C,dC,b,db);
+[S,dS,R1,dR1] = xdync(N,dN,D,dD,RHS,dRHS);
+endfunction;
diff --git a/2048/CH13/EX13.8/lqg_as1.sce b/2048/CH13/EX13.8/lqg_as1.sce new file mode 100755 index 000000000..438669db9 --- /dev/null +++ b/2048/CH13/EX13.8/lqg_as1.sce @@ -0,0 +1,30 @@ +// LQG control design for the problem discussed in Example 13.6 on page 474.
+// 13.8
+
+// Solves Example 3.1 of Ahlen and Sternad in Hunt's book
+exec('lqg1.sci',-1);
+exec('specfac.sci',-1);
+exec('flip.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+exec('poladd.sci',-1);
+exec('polyno.sci',-1);
+exec('putin.sci',-1);
+exec('clcoef.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('cindep.sci',-1);
+exec('ext.sci',-1);
+
+A = [1 -0.9]; dA = 1; B = [0.1 0.08]; dB = 1;
+k = 2; rho = 0.1; C = 1; dC = 0;
+V = 1; dV = 0; F = 1; dF = 0; W = [1 -1]; dW = 1;
+[R1,dR1,Sc,dSc] = ...
+lqg1(A,dA,B,dB,C,dC,k,rho,V,dV,W,dW,F,dF)
diff --git a/2048/CH13/EX13.9/lqg_visc_loop.sce b/2048/CH13/EX13.9/lqg_visc_loop.sce new file mode 100755 index 000000000..04f4daf29 --- /dev/null +++ b/2048/CH13/EX13.9/lqg_visc_loop.sce @@ -0,0 +1,46 @@ +// Performance curve for LQG control design of viscosity problem
+// 13.9
+
+exec('lqg1.sci',-1);
+exec('specfac.sci',-1);
+exec('flip.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+exec('poladd.sci',-1);
+exec('polyno.sci',-1);
+exec('putin.sci',-1);
+exec('clcoef.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('cindep.sci',-1);
+exec('ext.sci',-1);
+exec('cl.sci',-1);
+exec('zpowk.sci',-1);
+exec('tfvar.sci',-1);
+exec('l2r.sci',-1);
+exec('transp.sci',-1);
+exec('tf.sci',-1);
+exec('covar_m.sci',-1);
+
+// MacGregor's Viscosity control problem
+A = [1 -0.44]; dA = 1; B = [0.51 1.21]; dB = 1;
+C = [1 -0.44]; dC = 1; k = 1; int1 = 1; F = [1 -1]; dF = 1;
+V = 1; W = 1; dV = 0; dW = 0;
+u_lqg = []; y_lqg =[]; uy_lqg = [];
+
+for rho = 0.001:0.1:3,
+ [R1,dR1,Sc,dSc] = lqg1(A,dA,B,dB,C,dC,k,rho,V,dV,W,dW,F,dF);
+ [Nu,dNu,Du,dDu,Ny,dNy,Dy,dDy,yvar,uvar] = ...
+ cl(A,dA,B,dB,C,dC,k,Sc,dSc,R1,dR1,int1);
+ u_lqg = [u_lqg uvar]; y_lqg = [y_lqg yvar];
+ uy_lqg = [uy_lqg; [rho uvar yvar]];
+end
+plot(u_lqg,y_lqg,'g')
+save('lqg_visc.dat','uy_lqg');
diff --git a/2048/CH14/EX14.1/pend.sce b/2048/CH14/EX14.1/pend.sce new file mode 100755 index 000000000..d7a3531e1 --- /dev/null +++ b/2048/CH14/EX14.1/pend.sce @@ -0,0 +1,24 @@ +// Pole placement controller for inverted pendulum, discussed in Example 14.1 on page 490. 2.1 should be executed before starting this code
+// 14.1
+
+exec('pol2cart.sci',-1);
+
+C = eye(4,4);
+D = zeros(4,1);
+Ts = 0.01;
+G = syslin('c',A,B,C,D);
+H = dscr(G,Ts);
+[a,b,c,d] = H(2:5);
+rise = 5; epsilon = 0.1;
+N = rise/Ts;
+omega = %pi/2/N;
+r = epsilon^(omega/%pi);
+r1 = r; r2 = 0.9*r;
+[x1,y1] = pol2cart(omega,r1);
+[x2,y2] = pol2cart(omega,r2);
+p1 = x1+%i*y1;
+p2 = x1-%i*y1;
+p3 = x2+%i*y2;
+p4 = x2-%i*y2;
+P = [p1;p2;p3;p4];
+K = ppol(a,b,P)
diff --git a/2048/CH14/EX14.2/ex_comp.sce b/2048/CH14/EX14.2/ex_comp.sce new file mode 100755 index 000000000..1198950c2 --- /dev/null +++ b/2048/CH14/EX14.2/ex_comp.sce @@ -0,0 +1,26 @@ +// Compensator calculation for Example 14.6 on page 507.
+// 14.2
+
+exec('polyno.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+
+A = [1 2; 0 3]; c = [1 0];
+p = roots(polyno([1 -0.5 0.5],'z'));
+b = [0; 1];
+K = ppol(A,b,p);
+
+p1=0.1+0.1*%i; p2=0.1-0.1*%i;
+phi = real(convol([1 -p1],[1 -p2]));
+Obs = [c; c*A];
+alphae = A^2-0.2*A+0.02*eye(2,2);
+Lp = alphae*inv(Obs)*[0; 1];
+Lp = ppol([1 0;2 3], ...
+[1; 0],[0.1+0.1*%i 0.1-0.1*%i]);
+Lp = Lp';
+
+C = [1 0 0.5 2;0 1 -4.71 2.8];
+dC = 1;
+
+[HD,dHD] = polmul(K,0,C,dC);
+[HD,dHD] = polmul(HD,dHD,Lp,0);
diff --git a/2048/CH14/EX14.3/kalrun.sce b/2048/CH14/EX14.3/kalrun.sce new file mode 100755 index 000000000..606e03ba5 --- /dev/null +++ b/2048/CH14/EX14.3/kalrun.sce @@ -0,0 +1,21 @@ +// Kalman filter example of estimating a constant, discussed in Example 14.7.
+// 14.3
+
+exec('kal_ex.sci',-1);
+
+x = 5; xhat = 2; P = 1; xvec = x;
+xhat_vec = xhat; Pvec = P; yvec = x;
+for i = 1:200,
+ xline = xhat; M = P;
+ [xhat,P,y] = kal_ex(x,xline,M);
+ xvec = [xvec;x];
+ xhat_vec = [xhat_vec;xhat];
+ Pvec = [Pvec;P]; yvec = [yvec;y];
+end
+n = 1:201;
+plot(Pvec);
+xtitle('','n');
+halt();
+clf();
+plot(n,xhat_vec',n,yvec',n,xvec');
+xtitle('','n');
diff --git a/2048/CH14/EX14.4/kal_ex.sci b/2048/CH14/EX14.4/kal_ex.sci new file mode 100755 index 000000000..739e96537 --- /dev/null +++ b/2048/CH14/EX14.4/kal_ex.sci @@ -0,0 +1,12 @@ +// Kalman filter example of estimating a constant
+// 14.4
+
+function [xhat,P,y] = kal_ex(x,xline,M)
+y = x + rand();
+Q = 0; R = 1;
+xhat_ = xline;
+P_ = M + Q;
+K = P_/(P_+R);
+P = (1-K)*P_;
+xhat = xhat_ + K*(y-xhat_);
+endfunction;
diff --git a/2048/CH2/EX2.1/pend_model.sce b/2048/CH2/EX2.1/pend_model.sce new file mode 100755 index 000000000..1181fc69f --- /dev/null +++ b/2048/CH2/EX2.1/pend_model.sce @@ -0,0 +1,33 @@ +// Model of inverted pendulum
+// 2.1
+
+Km = 0.00767;
+Kg = 3.7;
+Rm = 2.6;
+r = 0.00635;
+M = 0.522;
+m = 0.231;
+g = 9.81;
+L = 0.305;
+J = 0;
+
+D1 = (J+m*L^2)*(M+m)-m^2*L^2;
+alpha = m*g*L*(M+m)/D1;
+beta1 = m*L/D1;
+gamma1 = m^2*g*L^2/D1;
+delta = (J+m*L^2)/D1;
+
+alpha1 = Km*Kg/Rm/r;
+alpha2 = Km^2*Kg^2/Rm/r^2;
+
+A = zeros(4,4);
+A(1,3) = 1;
+A(2,4) = 1;
+A(3,2) = -gamma1;
+A(3,3) = -alpha2*delta;
+A(4,2) = alpha;
+A(4,3) = alpha2*beta1;
+
+B = zeros(4,1);
+B(3) = alpha1*delta;
+B(4) = -alpha1*beta1;
diff --git a/2048/CH2/EX2.2/mat_exp.sce b/2048/CH2/EX2.2/mat_exp.sce new file mode 100755 index 000000000..9127e89db --- /dev/null +++ b/2048/CH2/EX2.2/mat_exp.sce @@ -0,0 +1,5 @@ +// Exponential of the matrix
+// 2.2
+
+F = [-1 0;1 0];
+expm(F)
diff --git a/2048/CH2/EX2.3/ZOH1.sce b/2048/CH2/EX2.3/ZOH1.sce new file mode 100755 index 000000000..f48504f34 --- /dev/null +++ b/2048/CH2/EX2.3/ZOH1.sce @@ -0,0 +1,13 @@ +// ZOH equivalent state space system
+// 2.3
+
+F = [-1 0;1 0]; G = [1; 0];
+C = [0 1]; D = 0; Ts=1;
+sys = syslin('c',F,G,C,D);
+sysd = dscr(sys,Ts)
+
+
+
+
+
+
diff --git a/2048/CH3/EX3.1/energy.sce b/2048/CH3/EX3.1/energy.sce new file mode 100755 index 000000000..ca16729bd --- /dev/null +++ b/2048/CH3/EX3.1/energy.sce @@ -0,0 +1,8 @@ +// Energy of a signal
+// 3.1
+
+u = [4 5 6];
+Eu = norm(u)^2;
+ruu = xcorr(u);
+Lu = length(ruu);
+Eu = ruu(ceil(Lu/2));
diff --git a/2048/CH3/EX3.2/conv2.sce b/2048/CH3/EX3.2/conv2.sce new file mode 100755 index 000000000..f3945a6d3 --- /dev/null +++ b/2048/CH3/EX3.2/conv2.sce @@ -0,0 +1,7 @@ +// Convolution of two sequences
+// 3.2
+
+h = [1 2 3];
+u = [4 5 6];
+y = convol(u,h)
+
diff --git a/2048/CH4/EX4.1/aconv1.sce b/2048/CH4/EX4.1/aconv1.sce new file mode 100755 index 000000000..48b7bbb29 --- /dev/null +++ b/2048/CH4/EX4.1/aconv1.sce @@ -0,0 +1,16 @@ +// To produce a^n 1(n)
+// 4.1
+
+exec('stem.sci',-1);
+exec('label.sci',-1);
+
+a = 0.9;
+n = -10:20;
+y = zeros(1,size(n,'*'));
+for i = 1:length(n)
+ if n(i)>=0,
+ y(i) = a^n(i);
+ end
+end
+stem(n,y)
+label('u1',4,'Time(n)','0.9^n1(n)',4)
diff --git a/2048/CH4/EX4.10/respol6.sce b/2048/CH4/EX4.10/respol6.sce new file mode 100755 index 000000000..aad80d70b --- /dev/null +++ b/2048/CH4/EX4.10/respol6.sce @@ -0,0 +1,15 @@ +// Partial fraction expansion for Example 4.30
+// 4.10
+
+// 3 - (5/6)z^-1 3z^2 - (5/6)z
+// G(z) = --------------------------- = --------------------------
+// (1-(1/4)z^-1)(1-(1/3)z^-1) (z - (1/4))(z - (1/3))
+
+// No equivalent of residuez
+
+exec('respol.sci',-1);
+exec('flip.sci',-1);
+
+num = [3 -5/6 0];
+den = convol([1 -1/4],[1 -1/3]);
+[res,pol,q] = respol(num,den)
diff --git a/2048/CH4/EX4.11/division.sce b/2048/CH4/EX4.11/division.sce new file mode 100755 index 000000000..08a54e3b3 --- /dev/null +++ b/2048/CH4/EX4.11/division.sce @@ -0,0 +1,15 @@ +// Long division of problems discussed in Example 4.32 on page 102
+// 4.11
+
+exec('tf.sci',-1);
+exec('label.sci',-1);
+
+num = [11 -15 6];
+den = convol([1 -2], convol([1 -1],[1 -1]));
+u = [1 zeros(1,4)];
+y = filter(num,den,u);
+G = tf(num,den,-1);
+u1=zeros(1,90); u1(1)=1;
+x1=dsimul(tf2ss(G),u1);
+plot2d(x1)
+label('Impulse Response',4,'Time(seconds)','Amplitude',4)
diff --git a/2048/CH4/EX4.2/aconv2.sce b/2048/CH4/EX4.2/aconv2.sce new file mode 100755 index 000000000..026cad325 --- /dev/null +++ b/2048/CH4/EX4.2/aconv2.sce @@ -0,0 +1,20 @@ +// Plot of -0.9^n1(-n-1)
+// 4.2
+
+exec('stem.sci',-1);
+exec('label.sci',-1);
+
+a = 0.9;
+n = -10:20;
+y = zeros(1,size(n,'*'));
+for i = 1: length(n)
+ if n(i)<= -1,
+ y(i) = -(a^n(i));
+ else y(i) = 0;
+ end
+end
+stem(n,y)
+label('u2',4,'Time(n)','-0.9^n1(-n-1)',4)
+
+
+
diff --git a/2048/CH4/EX4.3/pz.sce b/2048/CH4/EX4.3/pz.sce new file mode 100755 index 000000000..31894dd9d --- /dev/null +++ b/2048/CH4/EX4.3/pz.sce @@ -0,0 +1,13 @@ +// To produce pole-zero plots
+// 4.3
+
+exec('label.sci',-1);
+
+zero = [0 5/12];
+num = poly(zero,'z',"roots");
+pole = [1/2 1/3];
+den = poly(pole,'z',"roots");
+h = syslin('d',num./den);
+plzr(h);
+
+label('Pole-Zero Plot',4,'Real(z)','Imaginary(z)',4);
diff --git a/2048/CH4/EX4.4/disc1.sce b/2048/CH4/EX4.4/disc1.sce new file mode 100755 index 000000000..456181fe1 --- /dev/null +++ b/2048/CH4/EX4.4/disc1.sce @@ -0,0 +1,8 @@ +// Discrete transfer function of the continuous state space system
+// 4.4
+
+F = [0 0; 1 -0.1]; G = [0.1; 0];
+C = [0 1]; dt = 0.2;
+sys = syslin('c',F,G,C);
+sysd = dscr(sys,dt);
+H = ss2tf(sysd);
diff --git a/2048/CH4/EX4.5/respol.sci b/2048/CH4/EX4.5/respol.sci new file mode 100755 index 000000000..ea6818967 --- /dev/null +++ b/2048/CH4/EX4.5/respol.sci @@ -0,0 +1,110 @@ +// Computation of residues
+// 4.5
+// Numerator and denominator coefficients
+// are passed in decreasing powers of z(say)
+
+function [res,pol,q] = respol(num,den)
+len = length(num);
+if num(len) == 0
+ num = num(1:len-1);
+end
+
+[resi,q] = pfe(num,den);
+res = resi(:,2);
+res = int(res) + (clean(res - int(res),1.d-04));
+pol = resi(:,1);
+pol = int(pol) + (clean(pol - int(pol),1.d-04));
+endfunction;
+
+///////////////////////////////////////////////////
+// Partial fraction expansion
+
+function [resid1,q] = pfe(num,den)
+x = poly(0,'x');
+s = %s;
+
+num2 = flip(num);
+den2 = flip(den);
+num = poly(num2,'s','coeff');
+den = poly(den2,'s','coeff');
+[fac,g] = factors(den);
+polf = polfact(den);
+n = 1;
+
+r = clean(real(roots(den)),1.d-5);
+//disp(r);
+l = length(r);
+r = gsort(r,'g','i');
+r = [r; 0];
+j = 1;
+t1 = 1; q = [];
+rr = 0;
+rr1 = [0 0];
+m = 1;
+
+ for i = j:l
+ if abs(r(i)- r(i+1)) < 0.01 then
+ r(i);
+ r(i+1);
+ n = n+1;
+ m = n;
+ //pause
+ t1 = i;
+ //disp('Repeated roots')
+ else
+ m = n;
+ //pause
+ n = 1;
+ end
+ i;
+ if n == 1 then
+ rr1 = [rr1; r(i) m];
+ //pause
+ end;
+ j = t1 + 1;
+ end;
+rr2 = rr1(2:$,:);
+[r1,c1] = size(rr2);
+den1 = 1;
+
+for i = 1:r1
+ den1 = den1 * ((s-rr2(i,1))^(rr2(i,2)));
+end;
+[rem,quo] = pdiv(num,den);
+q = quo;
+if quo ~= 0
+ num = rem;
+end
+
+tf = num/den1;
+res1 = 0;
+res3 = [s 0];
+res5 = [0 0];
+for i = 1:r1
+ j = rr2(i,2) + 1;
+ tf1 = tf; //strictly proper
+ k = rr2(i,2);
+ tf2 = ((s-rr2(i,1))^k)*tf1;
+ rr2(i,1);
+ res1 = horner(tf2,rr2(i,1));
+ res2 = [(s - rr2(i,1))^(rr2(i,2)) res1];
+ res4 = [rr2(i,1) res1];
+ res3 = [res3; res2];
+ res5 = [res5; res4];
+ res = res1;
+ for m = 2:j-1
+ k;
+ rr2(i,1);
+ tf1 = derivat(tf2)/factorial(m-1); //ith derivative
+ res = horner(tf1,rr2(i,1));
+ res2 = [(s - rr2(i,1))^(j-m) res];
+ res4 = [rr2(i,1) res];
+ res5 = [res5; res4];
+ res3 = [res3; res2];
+ tf2 = tf1;
+ end;
+end;
+resid = res3(2:$,:); //with s terms
+resid1 = res5(2:$,:); //only poles(in decreasing no. of repetitions)
+endfunction;
+////////////////////////////////////////////////////////////
diff --git a/2048/CH4/EX4.6/respol1.sce b/2048/CH4/EX4.6/respol1.sce new file mode 100755 index 000000000..1b5dba73b --- /dev/null +++ b/2048/CH4/EX4.6/respol1.sce @@ -0,0 +1,13 @@ +// Partial fraction expansion for Example 4.24
+// 4.6
+
+// 2z^2 + 2z
+// G(z) = ---------------
+// z^2 + 2z - 3
+
+exec('respol.sci',-1);
+exec('flip.sci',-1);
+
+num = [2 2 0];
+den = [1 2 -3];
+[res,pol] = respol(num,den) //respol is a user defined function
diff --git a/2048/CH4/EX4.7/respol2.sce b/2048/CH4/EX4.7/respol2.sce new file mode 100755 index 000000000..48e7875a8 --- /dev/null +++ b/2048/CH4/EX4.7/respol2.sce @@ -0,0 +1,24 @@ +// Partial fraction expansion for Example 4.26
+// 4.7
+
+// z^2 + z A B C
+// G(z) = ----------- = ------- + --------- + ---------
+// (z - 1)^3 (z - 1) (z - 1)^2 (z - 1)^3
+
+exec('respol.sci',-1);
+exec('flip.sci',-1);
+
+num = [1 1 0];
+den = convol([1 -1],convol([1 -1],[1 -1])); // poly multiplication
+[res,pol] = respol(num,den)
+
+// Output interpretation
+// res =
+//C = 2
+//B = 1
+//A = 0
+
+// pol =
+// 1 (z - 1)^3
+// 1 (z - 1)^2
+// 1 (z - 1)
diff --git a/2048/CH4/EX4.8/respol3.sce b/2048/CH4/EX4.8/respol3.sce new file mode 100755 index 000000000..fa5574077 --- /dev/null +++ b/2048/CH4/EX4.8/respol3.sce @@ -0,0 +1,13 @@ +// Partial fraction expansion for Example 4.27
+// 4.8
+
+// 11z^2 - 15z + 6 A1 A2 B
+// G(z) = ----------------- = ------- + --------- + -------
+// (z - 2) (z - 1)^2 (z - 1) (z - 1)^2 (z - 2)
+
+exec('respol.sci',-1);
+exec('flip.sci',-1);
+
+num = [11 -15 6];
+den = convol([1 -2],convol([1 -1],[1 -1]));
+[res,pol] = respol(num,den) //User defined function
diff --git a/2048/CH4/EX4.9/respol5.sce b/2048/CH4/EX4.9/respol5.sce new file mode 100755 index 000000000..146db429c --- /dev/null +++ b/2048/CH4/EX4.9/respol5.sce @@ -0,0 +1,13 @@ +// Partial fraction expansion for Example 4.29
+// 4.9
+
+// z^2 + 2z
+// G(z) = --------------------
+// (z + 1)^2 (z - 2)
+
+exec('respol.sci',-1);
+exec('flip.sci',-1);
+
+num = [1 2 0];
+den = convol(convol([1 1],[1 1]),[1 -2]);
+[res,pol] = respol(num,den)
diff --git a/2048/CH5/EX5.1/incr_freq.sce b/2048/CH5/EX5.1/incr_freq.sce new file mode 100755 index 000000000..349ad92c1 --- /dev/null +++ b/2048/CH5/EX5.1/incr_freq.sce @@ -0,0 +1,15 @@ +// Sinusoidal plots for increasing frequency
+// 5.1
+
+exec('stem.sci',-1);
+
+n=0:16;
+subplot(2,2,1), stem(n,cos(n*%pi/8))
+xgrid,xtitle('','n','cos(n*pi/8)')
+subplot(2,2,2), stem(n,cos(n*%pi/4))
+xgrid,xtitle('','n','cos(n*pi/4)')
+subplot(2,2,3), stem(n,cos(n*%pi/2))
+xgrid,xtitle('','n','cos(n*pi/2)')
+subplot(2,2,4), stem(n,cos(n*%pi))
+xgrid,xtitle('','n','cos(n*pi)')
+
diff --git a/2048/CH5/EX5.2/filter1.sce b/2048/CH5/EX5.2/filter1.sce new file mode 100755 index 000000000..fb7eb044e --- /dev/null +++ b/2048/CH5/EX5.2/filter1.sce @@ -0,0 +1,20 @@ +// Bode plots for Example 5.7 on page 141
+// 5.2
+
+exec('label.sci',-1);
+
+omega = linspace(0,%pi);
+g1 = 0.5 ./ (cos(omega)-0.5+%i*sin(omega));
+mag1 = abs(g1);
+angle1 = phasemag(g1);
+g2 = (0.5+0.5*cos(omega)-1.5*%i*sin(omega)) ...
+ * 0.25 ./ (1.25-cos(omega));
+mag2 = abs(g2);
+angle2 = phasemag(g2);
+subplot(2,1,1)
+plot(omega,mag1,omega,mag2,'--');
+label('',4,' ','Magnitude',4);
+subplot(2,1,2);
+plot(omega,angle1,omega,angle2,'--');
+label('',4,'w (rad/s)','Phase',4);
+
diff --git a/2048/CH5/EX5.3/ma_bode.sce b/2048/CH5/EX5.3/ma_bode.sce new file mode 100755 index 000000000..60929da6f --- /dev/null +++ b/2048/CH5/EX5.3/ma_bode.sce @@ -0,0 +1,14 @@ +// Bode plot of the moving average filter, discussed in Example 5.5 on page 129
+// 5.3
+
+exec('label.sci',-1);
+
+w = 0.01:0.01:%pi;
+subplot(2,1,1);
+mag = abs(1+2*cos(w))/3;
+plot2d("ll",w,mag,2);
+label('',4,' ','Magnitude',4);
+subplot(2,1,2);
+plot2d("ln",w,phasemag(1+2*cos(w)),style = 2,rect =[0.01 -0.5 10 200]);
+label('',4,'w','Phase',4)
+
diff --git a/2048/CH5/EX5.4/derv_bode.sce b/2048/CH5/EX5.4/derv_bode.sce new file mode 100755 index 000000000..e45509fff --- /dev/null +++ b/2048/CH5/EX5.4/derv_bode.sce @@ -0,0 +1,15 @@ +// Bode plot of the differencing filter, discussed in Example 5.6 on page 130
+// 5.4
+
+exec('label.sci',-1);
+
+w = 0.01:0.01:%pi;
+G = 1-exp(-%i*w);
+subplot(2,1,1)
+plot2d1("gll",w,abs(G),style = 2);
+label('',4,' ','Magnitude',4);
+subplot(2,1,2)
+plot2d1("gln",w,phasemag(G),style = 2);
+label('',4,'w','Phase',4)
+
+
diff --git a/2048/CH5/EX5.5/nmp.sce b/2048/CH5/EX5.5/nmp.sce new file mode 100755 index 000000000..99faf6b7f --- /dev/null +++ b/2048/CH5/EX5.5/nmp.sce @@ -0,0 +1,18 @@ +// Bode plot of minimum and nonminimum phase filters, discussed in Example 5.9 on page 145
+// 5.5
+
+exec('label.sci',-1);
+
+omega = linspace(0,%pi);
+ejw = exp(-%i*omega);
+G1 = 1.5*(1-0.4*ejw);
+mag1 = abs(G1); angle1 = phasemag(G1);
+G2 = -0.6*(1-2.5*ejw);
+mag2 = abs(G2); angle2 = phasemag(G2);
+subplot(2,1,1);
+plot(omega,mag1,omega,mag2,'--');
+label('',4,' ','Magnitude',4);
+subplot(2,1,2);
+plot(omega,angle1,omega,angle2,'--');
+label('',4,'w (rad/s)','Phase',4);
+
diff --git a/2048/CH6/EX6.1/LS_ex.sce b/2048/CH6/EX6.1/LS_ex.sce new file mode 100755 index 000000000..25b3076d7 --- /dev/null +++ b/2048/CH6/EX6.1/LS_ex.sce @@ -0,0 +1,11 @@ +// Least squares solution of the simple problem discussed in Example 6.4 on page 164
+// 6.1
+
+Mag = 10; V = 10; No_pts = 100; theta = 2;
+Phi = Mag * (1-2*rand(No_pts,1));
+E = V * (1-2*rand(No_pts,1));
+Z = Phi*theta + E;
+LS = Phi \ Z
+Max = max(Z ./ Phi), Min = min(Z ./ Phi)
+
+
diff --git a/2048/CH6/EX6.10/pacf.sci b/2048/CH6/EX6.10/pacf.sci new file mode 100755 index 000000000..df383297c --- /dev/null +++ b/2048/CH6/EX6.10/pacf.sci @@ -0,0 +1,24 @@ +// Determination of the PACF of AR(p) process, as explained in Sec. 6.4.5.
+// 6.10
+
+function [ajj] = pacf(v,M)
+exec('label.sci',-1);
+rvvn = xcorr(v,'coeff');
+len = length(rvvn);
+zero = (len+1)/2;
+rvvn0 = rvvn(zero);
+rvvn_one_side = rvvn(zero+1:len);
+ajj = [];
+exec('pacf_mat.sci',-1);
+for j = 1:M,
+ ajj = [ajj pacf_mat(rvvn0,rvvn_one_side,j,1)];
+end
+p = 1:length(ajj);
+N = length(p);
+lim = 2/sqrt(length(v));
+
+// Plot the figure
+plot(p,ajj,p,ajj,'o',p,lim*ones(N,1),'--',...
+ p,-lim*ones(N,1),'--');
+label('',4,'Lag','PACF',4);
+endfunction;
diff --git a/2048/CH6/EX6.11/pacf_mat.sci b/2048/CH6/EX6.11/pacf_mat.sci new file mode 100755 index 000000000..ba250b63f --- /dev/null +++ b/2048/CH6/EX6.11/pacf_mat.sci @@ -0,0 +1,44 @@ +// Construction of square matrix required to compute PACF ajj, useful for the calculations in Sec. 6.4.5.
+// 6.11
+
+function ajj = pacf_mat(rvv0,rvv_rest,p,k)
+if argn(2) == 3,
+ k = 1;
+end
+for i = 1:p
+ for j = 1:p
+ index = (k+i-1)-j;
+ if index == 0,
+ A(i,j) = rvv0;
+ elseif index < 0,
+ A(i,j) = rvv_rest(-index);
+ else
+ A(i,j) = rvv_rest(index);
+ end
+ end
+ b(i) = -rvv_rest(k+i-1);
+end
+a = A\b;
+ajj = a(p);
+endfunction;
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/2048/CH6/EX6.12/ma_pacf.sce b/2048/CH6/EX6.12/ma_pacf.sce new file mode 100755 index 000000000..dbf7ee700 --- /dev/null +++ b/2048/CH6/EX6.12/ma_pacf.sce @@ -0,0 +1,13 @@ +// PACF plot of an MA process decays slowly, as discussed in Example 6.19 on page 190.
+// 6.12
+
+exec('plotacf.sci',-1);
+exec('pacf.sci',-1);
+exec('label.sci',-1);
+
+m = armac(1,0,[1,-0.9,0.2],1,1,1);
+xi = 0.1*rand(1,10000);
+v = arsimul(m,xi);
+plotacf(v,1,11,1);
+xset('window',1);
+pacf(v,11);
diff --git a/2048/CH6/EX6.13/arma_ex.sce b/2048/CH6/EX6.13/arma_ex.sce new file mode 100755 index 000000000..9a90baaae --- /dev/null +++ b/2048/CH6/EX6.13/arma_ex.sce @@ -0,0 +1,39 @@ +// Implementation of trial and error procedure to determine ARMA(1,1) process, presented in Example 6.20 on page 191.
+// 6.13
+
+exec('plotacf.sci',-1);
+exec('pacf.sci',-1);
+exec('label.sci',-1);
+
+// Set up the model for simulation
+arma_mod = armac([1 -0.8],0,[1 -0.3],1,1,1);
+
+// Generate the inputs for simulation
+// Deterministic Input can be anything
+u = zeros(1,2048);
+e = rand(1,2048,'normal');
+
+// Simulate the model
+v = arsimul(arma_mod,[u e]);
+
+// Plot ACF and PACF for 10 lags
+plotacf(v,1e-03,11,1);
+xset('window',1), pacf(v,10);
+
+// Estimate AR(1) model and present it
+// compute the residuals
+[mod_est1,err_mod1] = armax1(1,0,0,v,zeros(1,length(v)));
+disp(mod_est1);
+
+// Plot ACF and PACF for 10 lags
+xset('window',2), plotacf(err_mod1,1e-03,11,1);
+xset('window',3), pacf(err_mod1,10);
+
+// Check ACF and PACF of residuals
+[mod_est2,err_mod2] = armax1(1,0,1,v,zeros(1,length(v)));
+disp(mod_est2);
+
+// Plot ACF and PACF for 10 lags
+xset('window',4), plotacf(err_mod2,1e-03,11,1);
+xset('window',5), pacf(err_mod2,10);
+
diff --git a/2048/CH6/EX6.14/fir_cra_ex1.sce b/2048/CH6/EX6.14/fir_cra_ex1.sce new file mode 100755 index 000000000..3905e0a76 --- /dev/null +++ b/2048/CH6/EX6.14/fir_cra_ex1.sce @@ -0,0 +1,34 @@ +// Determination of FIR parameters as described in Example 6.22 on page 200.
+// 6.14
+
+exec('cra.sci',-1);
+exec('filt.sci',-1);
+exec('covf.sci',-1);
+
+sig = 0.05;
+process_mod = armac([1 -0.5],[0 0.6 -0.2],1,1,1,sig);
+
+u = prbs_a(2225,40);
+xi = rand(1,2225,'normal');
+y = arsimul(process_mod,[u xi]);
+u = [u zeros(1,length(y)-length(u))];
+z = [y' u'];
+
+// Plot y as a function of u and xi
+exec('label.sci',-1)
+subplot(3,1,1), plot(y(1:500)),
+label('',4,'','y',4)
+subplot(3,1,2), plot(u(1:500))
+label('',4,'','u',4)
+subplot(3,1,3), plot(sig*xi(1:500))
+label('',4,'n','xi',4)
+
+xset('window',1);
+[ir,r,cl_s] = cra(detrend(z,'constant'));
+ir_act = filt([0 0.6 -0.2],[1 -0.5],...
+ [1 zeros(1,9)]);
+replot([0,min(min(ir),min(ir_act)) - 0.1,9,max(max(ir),max(ir_act)) + 0.1]);
+t = 0:9;
+plot(t,ir_act,'ko');
+plot2d3(t,ir_act);
+legends(['Estimated'; 'Actual'], [2;-9],'ur');
diff --git a/2048/CH6/EX6.15/arx_est.sce b/2048/CH6/EX6.15/arx_est.sce new file mode 100755 index 000000000..e6e1dda0d --- /dev/null +++ b/2048/CH6/EX6.15/arx_est.sce @@ -0,0 +1,35 @@ +// Determination of ARX parameters as described in Example 6.25 on page 203.
+// 6.15
+
+exec('armac1.sci',-1);
+exec('cra.sci',-1);
+exec('arx.sci',-1);
+exec('filt.sci',-1);
+exec('covf.sci',-1);
+exec('stem.sci',-1);
+
+process_arx = armac1([1 -0.5],[0 0 0.6 -0.2],1,1,1,0.05);
+u = prbs_a(5000,250);
+xi = rand(1,5000,'normal');
+y = arsimul(process_arx,[u xi]);
+z = [y(1:length(u))' u'];
+zd = detrend(z,'constant');
+
+// Compute IR for time-delay estimation
+[ir,r,cl_s] = cra(detrend(z,'constant'));
+
+// Time-delay = 2 samples
+// Estimate ARX model (assume known orders)
+na = 1; nb = 2; nk = 2;
+[theta_arx,cov_arx,nvar,resid] = arx(zd,na,nb,nk);
+
+// Residual plot
+[cov1,m1] = xcov(resid,24,"coeff");
+xset('window',1);
+subplot(2,1,1)
+stem(0:24,cov1(25:49)');xgrid();
+xtitle('Correlation function of residuals from output y1','lag');
+[cov2,m2] = xcov(resid, zd(:,2),24,"coeff");
+subplot(2,1,2)
+stem(-24:24,cov2');xgrid();
+xtitle('Cross corr. function between input u1 and residuals from output y1','lag');
diff --git a/2048/CH6/EX6.16/armax_est.sce b/2048/CH6/EX6.16/armax_est.sce new file mode 100755 index 000000000..f093e8e89 --- /dev/null +++ b/2048/CH6/EX6.16/armax_est.sce @@ -0,0 +1,39 @@ +// Determination of ARMAX parameters as described in Example 6.27 on page 206.
+// 6.16
+
+exec('cra.sci',-1);
+exec('stem.sci',-1);
+exec('filt.sci',-1);
+exec('covf.sci',-1);
+
+process_armax = armac([1 -0.5],[0 0 0.6 -0.2],[1 -0.3],1,1,0.05);
+u = prbs_a(5000,250);
+xi = rand(1,5000);
+y = arsimul(process_armax,[u xi]);
+z = [y(1:length(u))' u'];
+zd = detrend(z,'constant');
+
+//Compute IR for time-delay estimation
+[ir,r,cl_s] = cra(detrend(z,'constant'));
+
+//Estimate ARMAX model (assume known orders)
+na = 1; nb = 3; nc = 1; nk = 2;
+[theta_armax,resid] = armax1(na,nb,nc,zd(:,1)',zd(:,2)',1);
+disp(theta_armax)
+
+// Residual plot
+[cov1,m1] = xcov(resid,24,"coeff");
+xset('window',1);
+subplot(2,1,1)
+stem(0:24,cov1(25:49));xgrid();
+xtitle('Correlation function of residuals from output y1','lag');
+[cov2,m2] = xcov(resid, zd(:,2),24,"coeff");
+subplot(2,1,2)
+stem(-24:24,cov2);xgrid();
+xtitle('Cross corr. function between input u1 and residuals from output y1','lag');
+
+
+
+
+
+
diff --git a/2048/CH6/EX6.17/oe_est.sce b/2048/CH6/EX6.17/oe_est.sce new file mode 100755 index 000000000..017cdcd38 --- /dev/null +++ b/2048/CH6/EX6.17/oe_est.sce @@ -0,0 +1,40 @@ +// Determination of OE parameters as described in Example 6.28 on page 209.
+// 6.17
+
+exec('armac1.sci',-1);
+exec('oe.sci',-1);
+exec('cra.sci',-1);
+exec('stem.sci',-1);
+exec('filt.sci',-1);
+exec('covf.sci',-1);
+exec('deconvol.sci',-1);
+
+b = [0 0 0.6 -0.2];
+f = [1 -0.5];
+c = 1; d = 1;
+process_oe = armac1(1,b,c,d,f,0.05);
+u = prbs_a(2555,250);
+xi = rand(1,2555,'normal');
+y = arsimul(process_oe,[u xi]);
+z = [y(1:length(u))' u'];
+zd = detrend(z,'constant');
+
+// Compute IR for time-delay estimation
+[ir,r,cl_s] = cra(zd);
+
+// Time-delay = 2 samples
+// Estimate ARX model (assume known orders)
+nb = 2; nf = 1; nk = 2;
+[thetaN,covfN,nvar,resid] = oe(zd,nb,nf,nk);
+
+// Residual plot
+[cov1,m1] = xcov(resid,24,"coeff");
+xset('window',1);
+subplot(2,1,1)
+stem(0:24,cov1(25:49)');xgrid();
+xtitle('Correlation function of residuals from output y1','lag');
+[cov2,m2] = xcov(resid, zd(:,2),24,"coeff");
+subplot(2,1,2)
+stem(-24:24,cov2');xgrid();
+xtitle('Cross corr. function between input u1 and residuals from output y1','lag');
+
diff --git a/2048/CH6/EX6.2/ACF_def.sce b/2048/CH6/EX6.2/ACF_def.sce new file mode 100755 index 000000000..195fa2a80 --- /dev/null +++ b/2048/CH6/EX6.2/ACF_def.sce @@ -0,0 +1,6 @@ +// ACF calculation for the problem discussed in Example 6.5 on page 167
+// 6.2
+
+u = [1 2];
+r = xcov(u);
+rho = xcov(u,"coeff");
diff --git a/2048/CH6/EX6.3/acf_ex.sce b/2048/CH6/EX6.3/acf_ex.sce new file mode 100755 index 000000000..c3249f7ba --- /dev/null +++ b/2048/CH6/EX6.3/acf_ex.sce @@ -0,0 +1,22 @@ +// To demonstrate the periodicity property of ACF as discussed in Example 6.7 on page 173
+// 6.3
+
+exec('plotacf.sci',-1);
+exec('label.sci',-1);
+
+L = 500;
+n = 1:L;
+w = 0.1;
+S = sin(w*n);
+m = 1;
+xi = m*rand(L,1,'normal');
+Spxi = S+xi';
+xset('window',0);
+plot(Spxi);
+label('',4,'n','y',4)
+xset('window',1);
+plotacf(Spxi,1,L,1);
+
+
+
+
diff --git a/2048/CH6/EX6.4/max_ex.sce b/2048/CH6/EX6.4/max_ex.sce new file mode 100755 index 000000000..876554a37 --- /dev/null +++ b/2048/CH6/EX6.4/max_ex.sce @@ -0,0 +1,26 @@ +// To demonstrate the maximum property of ACF at zero lag, as discussed in Example 6.8 on page 175.
+// 6.4
+
+exec('label.sci',-1);
+
+S1 = [1 2 3 4];
+S2 = [1,-2,3,-4];
+S3 = [-1,-2,3,4];
+len = length(S1)-1;
+xv = -len:len;
+m = 1;
+xi = rand(4,1,'normal');
+Spxi1 = S1 + m*xi';
+Spxi2 = S2 + m*xi';
+Spxi3 = S3 + m*xi';
+n = 1:length(S1);
+plot(n,Spxi1,'o-',n,Spxi2,'x--',n,Spxi3,'*:');
+label('',4,'n','y',4);
+ACF1 = xcov(Spxi1,"coeff");
+ACF2 = xcov(Spxi2,"coeff");
+ACF3 = xcov(Spxi3,"coeff");
+xset('window',1);
+a = gca();
+a.data_bounds = [-len -1; len 1];
+plot(xv,ACF1,'o-',xv,ACF2,'x--',xv,ACF3,'*:');
+label('',4,'Lag','ACF',4);
diff --git a/2048/CH6/EX6.5/ma.sce b/2048/CH6/EX6.5/ma.sce new file mode 100755 index 000000000..d6f78d452 --- /dev/null +++ b/2048/CH6/EX6.5/ma.sce @@ -0,0 +1,28 @@ +// Demonstrate the order of MA(q) as discussed in Example 6.11 on page 182.
+// 6.5
+
+exec('plotacf.sci',-1);
+exec('label.sci',-1);
+
+xi = 0.1*rand(1,10000,'normal');
+a = 1; b = [];
+d = [1 1 -0.5];
+ar = armac(a,b,d,1,1,1);
+v = arsimul(ar,xi);
+z = [v xi];
+
+// Plot noise, plant output and ACF
+subplot(2,1,1), plot(v(1:500))
+label('',4,'','v',4)
+subplot(2,1,2), plot(xi(1:500))
+label('',4,'n','xi',4)
+xset('window',1)
+plotacf(v,1,11,1);
+
+
+
+
+
+
+
+
diff --git a/2048/CH6/EX6.6/plotacf.sci b/2048/CH6/EX6.6/plotacf.sci new file mode 100755 index 000000000..2264eea28 --- /dev/null +++ b/2048/CH6/EX6.6/plotacf.sci @@ -0,0 +1,36 @@ +// Procedure to plot the ACF, as discussed in Sec. 6.4.3. An example usage is given in 6.5.
+// 6.6
+
+// PLOTACF: Plots normalized autocorrelation function
+//
+// USAGE:: [acf]=plotacf(x,errlim,len,print_code)
+//
+// WHERE:: acf = autocorrelation values
+// x = time series data
+// errlim > 0; error limit = 2/sqrt(data_len)
+// len = length of acf that need to to be plotted
+// NOTE: if len=0 then len=data_length/2;
+// print_code = 0 ==> does not plot OR ELSE plots
+//
+// Pranob Banerjee
+
+function [x]=plotacf(y,errlim,len,code)
+exec('label.sci',-1)
+x = xcov(y); l = length(y); x = x/x(l);
+r=l:2*(l-1); lim=2/sqrt(l); rl=1:length(r) ;
+N=length(rl); x=x(r);
+if len>0 & len<N, rl=1:len; x=x(rl); N=len; end;
+if(code > 0 )
+ if(errlim > 0 )
+ rl=rl-1;
+ plot(rl,x,rl,x,'o' , rl,lim*ones(N,1),'--', ...
+ rl,-lim*ones(N,1),'--')
+ xgrid
+ else
+ plot(rl,x)
+ end
+end;
+a = gca();
+a.data_bounds = [0 min(min(x),-lim-0.1); len-1 1.1];
+label(' ',4,'Lag','ACF',4)
+endfunction;
diff --git a/2048/CH6/EX6.7/unique_ma.sce b/2048/CH6/EX6.7/unique_ma.sce new file mode 100755 index 000000000..8c468a393 --- /dev/null +++ b/2048/CH6/EX6.7/unique_ma.sce @@ -0,0 +1,27 @@ +// Illustration of nonuniqueness in estimation of MA model parameters using ACF, discussed in Example 6.14 on page 184
+// 6.7
+
+exec('plotacf.sci',-1);
+exec('pacf.sci',-1);
+exec('label.sci',-1);
+
+xi = 0.1*rand(1,10000);
+
+// Simulation and estimation of first model
+m1 = armac(1,0,[1,-3,1.25],1,1,1);
+v1 = arsimul(m1,xi);
+M1 = armax1(0,0,2,v1,zeros(1,10000))
+disp(M1)
+
+// Simulation and estimation of second model
+m2 = armac(1,0,[1,-0.9,0.2],1,1,1);
+v2 = arsimul(m2,xi);
+M2 = armax1(0,0,2,v2,zeros(1,10000))
+disp(M2)
+
+// ACF and PACF of both models
+plotacf(v1,1,11,1);
+xset('window',1), plotacf(v2,1,11,1);
+xset('window',2), pacf(v1,11);
+xset('window',3), pacf(v2,11);
+
diff --git a/2048/CH6/EX6.8/ma_larger.sce b/2048/CH6/EX6.8/ma_larger.sce new file mode 100755 index 000000000..6a478f066 --- /dev/null +++ b/2048/CH6/EX6.8/ma_larger.sce @@ -0,0 +1,10 @@ +// Estimation with a larger order model results in large uncertainty, as discussed in Example 6.15 on page 185.
+// 6.8
+
+m = armac(1,0,[1 -0.9 0.2],1,1,1);
+xi = 0.1*rand(1,10000);
+v = arsimul(m,xi);
+M1 = armax1(0,0,2,v,zeros(1,10000))
+disp(M1)
+M2 = armax1(0,0,3,v,zeros(1,10000))
+disp(M2)
diff --git a/2048/CH6/EX6.9/pacf_ex.sce b/2048/CH6/EX6.9/pacf_ex.sce new file mode 100755 index 000000000..6234614c2 --- /dev/null +++ b/2048/CH6/EX6.9/pacf_ex.sce @@ -0,0 +1,20 @@ +// Determination of order of AR(p) process, as discussed in Example 6.18 on page 189.
+// 6.9
+
+exec('pacf.sci',-1);
+exec('label.sci',-1);
+
+// Define model and generate data
+m = armac([1,-1,0.5],0,1,1,1,1);
+xi = 0.1*rand(1,10000,'normal');
+v = arsimul(m,xi);
+
+// Plot noise, plant output and PACF
+subplot(2,1,1), plot(v(1:500));
+label('',6,'','v',6);
+subplot(2,1,2), plot(xi(1:500));
+label('',6,'n','xi',6);
+xset('window',1)
+pacf(v,10);
+
+
diff --git a/2048/CH7/EX7.1/rlocus_ex1.sce b/2048/CH7/EX7.1/rlocus_ex1.sce new file mode 100755 index 000000000..02cdde20f --- /dev/null +++ b/2048/CH7/EX7.1/rlocus_ex1.sce @@ -0,0 +1,9 @@ +// Procedure to draw root locus for the problem discussed in Example 7.1 on page 247.
+// 7.1
+
+exec('tf.sci',-1);
+
+H = tf(1,[1 -1 0],-1);
+evans(H)
+
+
diff --git a/2048/CH7/EX7.10/data05.sce b/2048/CH7/EX7.10/data05.sce new file mode 100755 index 000000000..4cc7dbe16 --- /dev/null +++ b/2048/CH7/EX7.10/data05.sce @@ -0,0 +1,32 @@ +// Solution to polynomial equation, as discussed in Example 7.14 on page 295.
+// 7.10
+
+exec('move_sci.sci',-1);
+exec('makezero.sci',-1);
+exec('seshft.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('indep.sci',-1);
+exec('t1calc.sci',-1);
+exec('left_prm.sci',-1);
+exec('polsize.sci',-1);
+exec('rowjoin.sci',-1);
+exec('xdync.sci',-1);
+
+N = [0 4 0 1
+ -1 8 0 3];
+dN = 1;
+D = [0 0 1 4 0 1
+ 0 0 -1 0 0 0];
+dD = 2;
+C = [1 0 1 1
+ 0 2 0 1];
+dC = 1;
+[Y,dY,X,dX,B,dB,A,dA] = xdync(N,dN,D,dD,C,dC)
+
+
+
+
+
+
diff --git a/2048/CH7/EX7.2/nyquist_ex1.sce b/2048/CH7/EX7.2/nyquist_ex1.sce new file mode 100755 index 000000000..0028b9f6e --- /dev/null +++ b/2048/CH7/EX7.2/nyquist_ex1.sce @@ -0,0 +1,7 @@ +// Procedure to draw the Nyquist plot, as discussed in Example 7.2 on page 250.
+// 7.2
+
+exec('tf.sci',-1);
+
+H = tf(1,[1 -1 0],-1);
+nyquist(H,0.1,0.5)
diff --git a/2048/CH7/EX7.3/lead_exp.sce b/2048/CH7/EX7.3/lead_exp.sce new file mode 100755 index 000000000..5fd795b1d --- /dev/null +++ b/2048/CH7/EX7.3/lead_exp.sce @@ -0,0 +1,17 @@ +// Procedure to draw Bode plots in Fig. 7.11 on page 255.
+// 7.3
+
+exec('tf.sci',-1);
+
+pol1 = [1 -0.9]; pol2 = [1 -0.8];
+G1 = tf(pol1,[1 0],-1);
+G2 = tf(pol2,[1 0],-1);
+w = linspace(0.001,0.5,1000);
+xset('window',1);
+bode([G1;G2],w);
+G = tf(pol1,pol2,-1);
+xset('window',2);
+bode(G,w);
+
+
+
diff --git a/2048/CH7/EX7.4/lead_lag.sce b/2048/CH7/EX7.4/lead_lag.sce new file mode 100755 index 000000000..0a7fbb640 --- /dev/null +++ b/2048/CH7/EX7.4/lead_lag.sce @@ -0,0 +1,30 @@ +// A procedure to design lead controllers, as explained in Fig. 7.12 on page 257.
+// 7.4
+
+exec('tf.sci',-1)
+
+w = linspace(0.001,%pi,1000);
+a = linspace(0.001,0.999,100);
+lena = length(a);
+omega = []; lead = [];
+for i = 1:lena,
+ zero = a(i);
+ pole = 0.9*zero;
+ sys = tf([1 -zero],[1 -pole],-1);
+ frq = w/(2*%pi);
+ [frq,repf]=repfreq(sys, frq);
+ [db,phase] =dbphi(repf);
+ [y,j] = max(phase);
+ omega = [omega w(j)];
+ lead = [lead y];
+ comega = (pole+zero)/(pole*zero+1);
+ clead = zero-pole;
+ clead1 = sqrt((1-zero^2)*(1-pole^2));
+ clead = clead/clead1;
+// [w(j) acos(comega) y atan(clead)*180/pi]
+end
+subplot(2,1,1), plot(lead,omega)
+xtitle('','','Frequency, in radians'), xgrid;
+halt;
+subplot(2,1,2), plot(lead,a)
+xtitle('','Lead generated, in degrees','Zero location'), xgrid;
diff --git a/2048/CH7/EX7.5/lead_vfy.sce b/2048/CH7/EX7.5/lead_vfy.sce new file mode 100755 index 000000000..8dc1a53d5 --- /dev/null +++ b/2048/CH7/EX7.5/lead_vfy.sce @@ -0,0 +1,9 @@ +// Bode plot of a lead controller, as shown in Fig. 7.13 on page 257.
+// 7.5
+
+exec('tf.sci',-1);
+
+w = linspace(0.001,0.5,1000);
+G = tf([1 -0.8],[1 -0.24],-1);
+bode(G,w)
+
diff --git a/2048/CH7/EX7.6/ant_lead.sce b/2048/CH7/EX7.6/ant_lead.sce new file mode 100755 index 000000000..26c62d759 --- /dev/null +++ b/2048/CH7/EX7.6/ant_lead.sce @@ -0,0 +1,27 @@ +// Verification of performance of lead controller on antenna system, as discussed in Example 7.3.
+// 7.6
+
+// Continuous time antenna model
+a = 0.1;
+F = [0 1;0 -a]; g = [0; a]; c = [1 0]; d = 0;
+Ga = syslin('c',F,g,c,d); [ds,num,den] = ss2tf(Ga);
+Num = clean(num); Den = clean(den);
+Ts = 0.2;
+G = dscr(Ga,Ts);
+
+// lead controller
+beta1 = 0.8;
+N = [1 -0.9802]*(1-beta1)/(1-0.9802); Rc = [1 -beta1];
+
+// simulation parameters using g_s_cl2.cos
+gamm = 1; Sc = 1; Tc = 1; C = 0; D = 1;
+st = 1; st1 = 0;
+t_init = 0; t_final = 20;
+
+// u1: -4 to 11
+// y1: 0 to 1.4
+exec('cosfil_ip.sci',-1);
+[Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+[Np,Rcp] = cosfil_ip(N,Rc); // N/Rc
+[Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+[Cp,Dp] = cosfil_ip(C,D); // C/D
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y="217.0"/></SplitBlock><ControlPort dataType="UNKNOW_TYPE" id="6e4925f9:1460474cdcb:-7ae8" ordering="1" parent="6e4925f9:1460474cdcb:-7ae9" style="ControlPort;align=center;verticalAlign=top;spacing=10.0;rotation=90;flip=false;mirror=false" visible="0"><mxGeometry as="geometry" height="8.0" width="8.0" x="-4.0" y="-8.0"/></ControlPort><CommandPort dataType="UNKNOW_TYPE" id="6e4925f9:1460474cdcb:-7ae7" ordering="1" parent="6e4925f9:1460474cdcb:-7ae9" style="CommandPort;align=center;verticalAlign=bottom;spacing=10.0;rotation=90;flip=false;mirror=false" visible="0"><mxGeometry as="geometry" height="8.0" width="8.0" x="-4.0" y="7.0"/></CommandPort><CommandPort dataType="UNKNOW_TYPE" id="6e4925f9:1460474cdcb:-7ae6" ordering="2" parent="6e4925f9:1460474cdcb:-7ae9" style="CommandPort;align=center;verticalAlign=bottom;spacing=10.0;rotation=90;flip=false;mirror=false" visible="0"><mxGeometry as="geometry" height="8.0" width="8.0" x="-4.0" y="7.0"/></CommandPort><CommandControlLink id="6e4925f9:1460474cdcb:-7ae5" parent="-7476484f:145f8cd2a3c:-7be9" source="6e4925f9:1460474cdcb:-7aee" target="6e4925f9:1460474cdcb:-7ae8"><mxGeometry as="geometry"><Array as="points" scilabClass="ScilabList"/></mxGeometry></CommandControlLink><CommandControlLink id="6e4925f9:1460474cdcb:-7aea" parent="-7476484f:145f8cd2a3c:-7be9" source="6e4925f9:1460474cdcb:-7ae6" target="6285486a:14602f0faf7:-7e0f"><mxGeometry as="geometry"><mxPoint as="sourcePoint" x="430.0" y="350.0"/><mxPoint as="targetPoint" x="350.0" y="220.0"/><Array as="points" scilabClass="ScilabList"><mxPoint x="350.0" y="220.0"/><mxPoint x="350.0" y="320.0"/><mxPoint x="430.0" y="320.0"/></Array></mxGeometry></CommandControlLink><SplitBlock id="6e4925f9:1460474cdcb:-7ae2" interfaceFunctionName="CLKSPLIT_f" ordering="31" parent="-7476484f:145f8cd2a3c:-7be9" simulationFunctionType="DEFAULT" style="CLKSPLIT_f;flip=false;mirror=false"><mxGeometry as="geometry" height="7.0" width="7.0" x="307.0" 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\ No newline at end of file diff --git a/2048/CH7/EX7.7/type_test.sce b/2048/CH7/EX7.7/type_test.sce new file mode 100755 index 000000000..1539de5e9 --- /dev/null +++ b/2048/CH7/EX7.7/type_test.sce @@ -0,0 +1,49 @@ +// Illustration of system type, as explained in Example 7.10 on page 275.
+// 7.7
+
+exec('rowjoin.sci',-1);
+exec('zpowk.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+exec('indep.sci',-1);
+exec('t1calc.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('clcoef.sci',-1);
+exec('colsplit.sci',-1);
+exec('seshft.sci',-1);
+exec('left_prm.sci',-1);
+exec('cindep.sci',-1);
+exec('xdync.sci',-1);
+exec('pp_pid.sci',-1);
+exec('cosfil_ip.sci');
+
+// Plant
+B = 1; A = [1 -1]; zk = [0 1]; Ts = 1; k = 1;
+// Value of k absent in original code
+// Specify closed loop characteristic polynomial
+phi = [1 -0.5];
+
+// Design the controller
+reject_ramps = 1;
+ if reject_ramps == 1,
+ Delta = [1 -1]; // to reject ramps another Delta
+ else
+ Delta = 1; // steps can be rejected by plant itself
+ end
+[Rc,Sc] = pp_pid(B,A,k,phi,Delta);
+
+// parameters for simulation using stb_disc.mdl
+Tc = Sc; gamm = 1; N = 1;
+C = 0; D = 1; N_var = 0;
+st = 1; t_init = 0; t_final = 20;
+
+[Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+[Rcp1,Rcp2] = cosfil_ip(1,Rc); // 1/Rc
+[Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+[Bp,Ap] = cosfil_ip(B,A); // B/A
+[zkp1,zkp2] = cosfil_ip(zk,1); // zk/1
+[Cp,Dp] = cosfil_ip(C,D); // C/D
+
+// Give appropriate path
+//xcos('stb_disc.xcos');
diff --git a/2048/CH7/EX7.7/u1_7_7.png b/2048/CH7/EX7.7/u1_7_7.png Binary files differnew file mode 100755 index 000000000..53d0282ed --- /dev/null +++ b/2048/CH7/EX7.7/u1_7_7.png diff --git a/2048/CH7/EX7.7/y1_7_7.png b/2048/CH7/EX7.7/y1_7_7.png Binary files differnew file mode 100755 index 000000000..fb134c666 --- /dev/null +++ b/2048/CH7/EX7.7/y1_7_7.png diff --git a/2048/CH7/EX7.8/abex.sce b/2048/CH7/EX7.8/abex.sce new file mode 100755 index 000000000..5e6806220 --- /dev/null +++ b/2048/CH7/EX7.8/abex.sce @@ -0,0 +1,23 @@ +// Solution to Aryabhatta's identity, presented in Example 7.12 on page 293.
+// 7.8
+
+exec('indep.sci',-1);
+exec('rowjoin.sci',-1);
+exec('polsize.sci',-1);
+exec('makezero.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('seshft.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('xdync.sci',-1);
+
+N = convol([0 1],[1 1]);
+D = convol([1 -4],[1 -1]);
+dN = 2; dD = 2;
+C = [1 -1 0.5];
+dC = 2;
+[Y,dY,X,dX,B,dB,A,dA] = xdync(N,dN,D,dD,C,dC)
+
diff --git a/2048/CH7/EX7.9/data01.sce b/2048/CH7/EX7.9/data01.sce new file mode 100755 index 000000000..c72c576d4 --- /dev/null +++ b/2048/CH7/EX7.9/data01.sce @@ -0,0 +1,27 @@ +// Left coprime factorization as discussed in Example 7.13 on page 295.
+// 7.9
+
+exec('rowjoin.sci',-1);
+exec('makezero.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('polsize.sci',-1);
+exec('seshft.sci',-1);
+exec('indep.sci',-1);
+exec('move_sci.sci',-1);
+exec('t1calc.sci',-1);
+exec('left_prm.sci',-1);
+
+D = [1 0 0 0 0 0
+0 1 0 1 0 0
+0 0 1 1 1 0];
+N = [
+1 0 0
+0 1 0
+0 0 1];
+dD = 1;
+dN = 0;
+[B,dB,A,dA] = left_prm(N,dN,D,dD)
+
+
+
diff --git a/2048/CH8/EX8.1/disc2.sce b/2048/CH8/EX8.1/disc2.sce new file mode 100755 index 000000000..240c2ed86 --- /dev/null +++ b/2048/CH8/EX8.1/disc2.sce @@ -0,0 +1,7 @@ +// Continuous to discrete time transfer function
+// 8.1
+
+exec('tf.sci');
+
+sys = tf(10,[5 1]);
+sysd = ss2tf(dscr(sys,0.5));
diff --git a/2048/CH9/EX9.1/ball_basic.sce b/2048/CH9/EX9.1/ball_basic.sce new file mode 100755 index 000000000..a77321e8b --- /dev/null +++ b/2048/CH9/EX9.1/ball_basic.sce @@ -0,0 +1,67 @@ +// Pole placement controller for magnetically suspended ball problem, discussed in Example 9.3 on page 331.
+// 9.1
+
+exec('myc2d.sci',-1);
+exec('desired.sci',-1);
+exec('zpowk.sci',-1);
+exec('polsplit2.sci',-1);
+exec('polsize.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('polmul.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('xdync.sci',-1);
+exec('left_prm.sci',-1);
+exec('rowjoin.sci',-1);
+exec('pp_basic.sci',-1);
+exec('polyno.sci',-1);
+exec('cosfil_ip.sci',-1);
+
+// Magnetically suspended ball problem
+// Operating conditions
+M = 0.05; L = 0.01; R = 1; K = 0.0001; g = 9.81;
+
+//Equilibrium conditions
+hs = 0.01; is = sqrt(M*g*hs/K);
+
+// State space matrices
+a21 = K*is^2/M/hs^2; a23 = - 2*K*is/M/hs; a33 = - R/L;
+b3 = 1/L;
+a1 = [0 1 0; a21 0 a23; 0 0 a33];
+b1 = [0; 0; b3]; c1 = [1 0 0]; d1 = 0;
+
+// Transfer functions
+G = syslin('c',a1,b1,c1,d1); Ts = 0.01;
+[B,A,k] = myc2d(G,Ts);
+
+//polynomials are returned
+[Ds,num,den] = ss2tf(G);
+num = clean(num); den = clean(den);
+
+// Transient specifications
+rise = 0.15; epsilon = 0.05;
+phi = desired(Ts,rise,epsilon);
+
+// Controller design
+[Rc,Sc,Tc,gamm] = pp_basic(B,A,k,phi);
+
+// Setting up simulation parameters for basic.xcos
+st = 0.0001; // desired change in h, in m.
+t_init = 0; // simulation start time
+t_final = 0.5; // simulation end time
+
+// Setting up simulation parameters for c_ss_cl.xcos
+N_var = 0; xInitial = [0 0 0]; N = 1; C = 0; D = 1;
+
+[Tc1,Rc1] = cosfil_ip(Tc,Rc); // Tc/Rc
+[Sc2,Rc2] = cosfil_ip(Sc,Rc); // Sc/Rc
+
+[Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+[Np,Rcp] = cosfil_ip(N,Rc); // 1/Rc
+[Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+[Cp,Dp] = cosfil_ip(C,D); // C/D
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\ No newline at end of file diff --git a/2048/CH9/EX9.1/u1_c_ss_cl.png b/2048/CH9/EX9.1/u1_c_ss_cl.png Binary files differnew file mode 100755 index 000000000..94481d0b2 --- /dev/null +++ b/2048/CH9/EX9.1/u1_c_ss_cl.png diff --git a/2048/CH9/EX9.1/y1_c_ss_cl.png b/2048/CH9/EX9.1/y1_c_ss_cl.png Binary files differnew file mode 100755 index 000000000..117ffd2ab --- /dev/null +++ b/2048/CH9/EX9.1/y1_c_ss_cl.png diff --git a/2048/CH9/EX9.10/ibm_pp.sce b/2048/CH9/EX9.10/ibm_pp.sce new file mode 100755 index 000000000..d4798e0c0 --- /dev/null +++ b/2048/CH9/EX9.10/ibm_pp.sce @@ -0,0 +1,52 @@ +// Pole placement controller IBM Lotus Domino server, discussed in Example 9.9 on page 341.
+// 9.10
+
+exec('desired.sci',-1);
+exec('pp_im.sci',-1);
+exec('zpowk.sci',-1);
+exec('cosfil_ip.sci',-1);
+exec('polsplit3.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('polmul.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('polyno.sci',-1);
+
+// Control of IBM lotus domino server
+// Transfer function
+B = 0.47; A = [1 -0.43]; k = 1;
+[zk,dzk] = zpowk(k);
+
+// Transient specifications
+rise = 10; epsilon = 0.01; Ts = 1;
+phi = desired(Ts,rise,epsilon);
+
+// Controller design
+Delta = [1 -1]; // internal model of step used
+[Rc,Sc,Tc,gamm] = pp_im(B,A,k,phi,Delta);
+
+// Simulation parameters for stb_disc.xcos
+st = 1; // desired change
+t_init = 0; // simulation start time
+t_final = 40; // simulation end time
+C = 0; D = 1; N_var = 0;
+
+[Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+[Rcp1,Rcp2] = cosfil_ip(1,Rc); // 1/Rc
+[Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+[Bp,Ap] = cosfil_ip(B,A); // B/A
+[zkp1,zkp2] = cosfil_ip(zk,1); // zk/1
+[Cp,Dp] = cosfil_ip(C,D); // C/D
+
+
+
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\ No newline at end of file diff --git a/2048/CH9/EX9.11/motor.sce b/2048/CH9/EX9.11/motor.sce new file mode 100755 index 000000000..ba3adb8cd --- /dev/null +++ b/2048/CH9/EX9.11/motor.sce @@ -0,0 +1,52 @@ +// Pole placement controller for motor problem, discussed in Example 9.10 on page 343.
+// 9.11
+
+exec('desired.sci',-1);
+exec('pp_im.sci',-1);
+exec('myc2d.sci',-1);
+exec('cosfil_ip.sci',-1);
+exec('polsplit3.sci',-1);
+exec('zpowk.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('polyno.sci',-1);
+
+// Motor control problem
+// Transfer function
+a1 = [-1 0; 1 0]; b1 = [1; 0]; c1 = [0 1]; d1 = 0;
+G = syslin('c',a1,b1,c1,d1); Ts = 0.25;
+[B,A,k] = myc2d(G,Ts);
+
+// Transient specifications
+rise = 3; epsilon = 0.05;
+phi = desired(Ts,rise,epsilon);
+
+// Controller design
+Delta = 1; // No internal model of step used
+[Rc,Sc,Tc,gamm] = pp_im(B,A,k,phi,Delta);
+
+// simulation parameters for c_ss_cl.xcos
+st = 1; //desired change in position
+t_init = 0; //simulation start time
+t_final = 10; //simulation end time
+xInitial = [0 0]; //initial conditions
+N = 1; C = 0; D = 1; N_var = 0;
+
+[Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+[Np,Rcp] = cosfil_ip(N,Rc); // 1/Rc
+[Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+[Cp,Dp] = cosfil_ip(C,D); // C/D
+
+
+
diff --git a/2048/CH9/EX9.11/u1_c_ss_cl.png b/2048/CH9/EX9.11/u1_c_ss_cl.png Binary files differnew file mode 100755 index 000000000..f67d5358d --- /dev/null +++ b/2048/CH9/EX9.11/u1_c_ss_cl.png diff --git a/2048/CH9/EX9.11/y1_c_ss_cl.png b/2048/CH9/EX9.11/y1_c_ss_cl.png Binary files differnew file mode 100755 index 000000000..2796e8183 --- /dev/null +++ b/2048/CH9/EX9.11/y1_c_ss_cl.png diff --git a/2048/CH9/EX9.12/polsplit3.sci b/2048/CH9/EX9.12/polsplit3.sci new file mode 100755 index 000000000..caffc7509 --- /dev/null +++ b/2048/CH9/EX9.12/polsplit3.sci @@ -0,0 +1,33 @@ +// Procedure to split a polynomial into good and bad factors, as discussed in Sec. 9.5. The factors that have roots outside unit circle or with negative real parts are defined as bad.
+// 9.12
+
+// function [goodpoly,badpoly] = polsplit3(fac,a)
+// Splits a scalar polynomial of z^{-1} into good and bad
+// factors. Input is a polynomial in increasing degree of
+// z^{-1}. Optional input is a, where a <= 1.
+// Factors that have roots outside a circle of radius a or
+// with negative roots will be called bad and the rest
+// good. If a is not specified, it will be assumed as 1.
+
+function [goodpoly,badpoly] = polsplit3(fac,a)
+if argn(2) == 1, a = 1; end
+if a>1 error('good polynomial also is unstable'); end
+fac1 = poly(fac(length(fac):-1:1),'z','coeff');
+rts = roots(fac1);
+rts = rts(length(rts):-1:1);
+
+// extract good and bad roots
+badindex = mtlb_find((abs(rts)>=a-1.0e-5)|(real(rts)<-0.05));
+badpoly = coeff(poly(rts(badindex),'z'));
+goodindex = mtlb_find((abs(rts)<a-1.0e-5)&(real(rts)>=-0.05));
+goodpoly = coeff(poly(rts(goodindex),'z'));
+
+// scale by equating the largest terms
+[m,index] = max(abs(fac));
+goodbad = convol(goodpoly,badpoly);
+goodbad = goodbad(length(goodbad):-1:1);
+factor1 = fac(index)/goodbad(index);
+goodpoly = goodpoly * factor1;
+goodpoly = goodpoly(length(goodpoly):-1:1);
+badpoly = badpoly(length(badpoly):-1:1);
+endfunction;
diff --git a/2048/CH9/EX9.13/pp_im2.sci b/2048/CH9/EX9.13/pp_im2.sci new file mode 100755 index 000000000..61ba58d1b --- /dev/null +++ b/2048/CH9/EX9.13/pp_im2.sci @@ -0,0 +1,31 @@ +// Pole placement controller without intra sample oscillations, as discussed in Sec. 9.5.
+// 9.13
+
+// function [Rc,Sc,Tc,gamma,phit] = pp_im2(B,A,k,phi,Delta,a)
+// 2-DOF PP controller with internal model of Delta and without
+// hidden oscillations
+
+function [Rc,Sc,Tc,gamm,phit] = pp_im2(B,A,k,phi,Delta,a)
+
+if argn(2) == 5, a = 1; end
+dphi = length(phi)-1;
+
+// Setting up and solving Aryabhatta identity
+[Ag,Ab] = polsplit3(A,a); dAb = length(Ab) - 1;
+[Bg,Bb] = polsplit3(B,a); dBb = length(Bb) - 1;
+
+[zk,dzk] = zpowk(k);
+
+[N,dN] = polmul(Bb,dBb,zk,dzk);
+dDelta = length(Delta)-1;
+[D,dD] = polmul(Ab,dAb,Delta,dDelta);
+
+[S1,dS1,R1,dR1] = xdync(N,dN,D,dD,phi,dphi);
+
+// Determination of control law
+Rc = convol(Bg,convol(R1,Delta)); Sc = convol(Ag,S1);
+Tc = Ag; gamm = sum(phi)/sum(Bb);
+
+// Total characteristic polynomial
+phit = convol(phi,convol(Ag,Bg));
+endfunction;
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\ No newline at end of file diff --git a/2048/CH9/EX9.14/sigurd.sce b/2048/CH9/EX9.14/sigurd.sce new file mode 100755 index 000000000..f02beb607 --- /dev/null +++ b/2048/CH9/EX9.14/sigurd.sce @@ -0,0 +1,66 @@ +// Controller design for the case study presented in Example 9.12 on page 347.
+// 9.14
+
+exec('tf.sci',-1);
+exec('desired.sci',-1);
+exec('zpowk.sci',-1);
+exec('myc2d.sci',-1);
+exec('polsplit3.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('pp_im2.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('cosfil_ip.sci',-1);
+
+num = 200;
+den = convol([0.05 1],[0.05 1]);
+den = convol([10 1],den);
+G = tf(num,den); Ts = 0.025;
+num = G('num'); den = G('den');
+// iodel = 0;
+[B,A,k] = myc2d(G,Ts);
+[zk,dzk] = zpowk(k); //int1 = 0;
+
+// Transient specifications
+a = 0.9; rise = 0.24; epsilon = 0.05;
+phi = desired(Ts,rise,epsilon);
+
+// Controller design
+Delta = [1 -1]; // internal model of step is present
+[Rc,Sc,Tc,gamm] = pp_im2(B,A,k,phi,Delta,a);
+
+// margin calculation
+Lnum = convol(Sc,convol(B,zk));
+Lden = convol(Rc,A);
+L = tf(Lnum,Lden,Ts);
+Gm = g_margin(L); //---- Does not match --------------- (in dB)
+Pm = p_margin(L); //---- Convergence problem --------------- (in degree)
+
+num1 = 100; den1 = [10 1];
+Gd = tf(num1,den1); //-------
+[C,D,k1] = myc2d(Gd,Ts);
+[zk,dzk] = zpowk(k);
+C = convol(C,zk);
+
+// simulation parameters g_s_cl2.xcos ------------
+N = 1;
+st = 1; // desired change in setpoint
+st1 = 0; // magnitude of disturbance
+t_init = 0; // simulation start time
+t_final = 1.5; // simulation end time
+
+[Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+[Np,Rcp] = cosfil_ip(N,Rc); // N/Rc
+[Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+[Cp,Dp] = cosfil_ip(C,D); // C/D
+
diff --git a/2048/CH9/EX9.14/u1_g_s_cl2.png b/2048/CH9/EX9.14/u1_g_s_cl2.png Binary files differnew file mode 100755 index 000000000..f88b50eba --- /dev/null +++ b/2048/CH9/EX9.14/u1_g_s_cl2.png diff --git a/2048/CH9/EX9.14/y1_g_s_cl2.png b/2048/CH9/EX9.14/y1_g_s_cl2.png Binary files differnew file mode 100755 index 000000000..98461c5e6 --- /dev/null +++ b/2048/CH9/EX9.14/y1_g_s_cl2.png diff --git a/2048/CH9/EX9.15/g_s_cl3.xcos b/2048/CH9/EX9.15/g_s_cl3.xcos new file mode 100755 index 000000000..9d6266ea3 --- /dev/null +++ b/2048/CH9/EX9.15/g_s_cl3.xcos @@ -0,0 +1 @@ +<?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1" finalIntegrationTime="5.0" title="g_s_cl3"><!--Xcos - 1.0 - scilab-5.4.1 - 20130329 1751--><mxGraphModel as="model"><root><mxCell id="7b254bcc:14613988545:-7cfd"/><mxCell id="7b254bcc:14613988545:-7cfe" parent="7b254bcc:14613988545:-7cfd"/><BasicBlock blockType="h" id="7b254bcc:14613988545:-79fb" interfaceFunctionName="STEP_FUNCTION" ordering="1" 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\ No newline at end of file diff --git a/2048/CH9/EX9.15/sigurd_his.sce b/2048/CH9/EX9.15/sigurd_his.sce new file mode 100755 index 000000000..d53f3c500 --- /dev/null +++ b/2048/CH9/EX9.15/sigurd_his.sce @@ -0,0 +1,64 @@ +// Evaluation of continuous time controller for the case study presented in Example 9.13 on page 349.
+// 9.15
+
+clear
+exec('tf.sci',-1);
+exec('myc2d.sci',-1);
+exec('zpowk.sci',-1);
+exec('cosfil_ip.sci',-1);
+exec('polyno.sci',-1);
+
+num = 200;
+den = convol([0.05 1],[0.05 1]);
+den = convol([10 1],den);
+G = tf(num,den); Ts = 0.005;
+[B,A,k] = myc2d(G,Ts);
+[zk,dzk] = zpowk(k); //int = 0;
+
+// Sigurd's feedback controller'
+numb = 0.5*convol([1 2],[0.05 1]);
+denb = convol([1 0],[0.005 1]);
+Gb = tf(numb,denb);
+[Sb,Rb,kb] = myc2d(Gb,Ts);
+[zkb,dzkb] = zpowk(kb);
+Sb = convol(Sb,zkb);
+
+// Sigurd's feed forward controller'
+numf = [0.5 1];
+denf = convol([0.65 1],[0.03 1]);
+Gf = tf(numf,denf);
+[Sf,Rf,kf] = myc2d(Gf,Ts);
+[zkf,dzkf] = zpowk(kf);
+Sf = convol(Sf,zkf);
+
+// Margins
+simp_mode(%f);
+L = G*Gb;
+Gm = g_margin(L); // ------
+Pm = p_margin(L); // ------
+Lnum = convol(Sb,convol(zk,B));
+Lden = convol(Rb,A);
+L = tf(Lnum,Lden,Ts);
+DGm = g_margin(L); // ------
+DPm = p_margin(L); // ------
+
+// Noise
+num1 = 100; den1 = [10 1];
+
+// simulation parameters for
+// entirely continuous simulation: g_s_cl3.xcos
+// hybrid simulation: g_s_cl6.xcos
+st = 1; // desired change in setpoint
+st1 = 0;
+t_init = 0; // simulation start time
+t_final = 5; // simulation end time
+
+num = polyno(num,'s'); den = polyno(den,'s');
+Numb = polyno(numb,'s'); Denb = polyno(denb,'s');
+Numf = polyno(numf,'s'); Denf = polyno(denf,'s');
+Num1 = polyno(num1,'s'); Den1 = polyno(den1,'s');
+
+[Sbp,Rbp] = cosfil_ip(Sb,Rb);
+[Sfp,Rfp] = cosfil_ip(Sf,Rf);
+
+
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\ No newline at end of file diff --git a/2048/CH9/EX9.16/type_2DOF.sce b/2048/CH9/EX9.16/type_2DOF.sce new file mode 100755 index 000000000..3ba0f297d --- /dev/null +++ b/2048/CH9/EX9.16/type_2DOF.sce @@ -0,0 +1,42 @@ +// System type with 2-DOF controller. It is used to arrive at the results Example 9.14.
+// 9.16
+
+exec('polsplit3.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+exec('pp_im.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('seshft.sci',-1);
+exec('zpowk.sci',-1);
+exec('cosfil_ip.sci',-1);
+exec('polyno.sci',-1);
+
+B = 1; A = [1 -1]; k = 1; zk = zpowk(k); Ts = 1;
+phi = [1 -0.5];
+
+Delta = 1; // Choice of internal model of step
+[Rc,Sc,Tc,gamm] = pp_im(B,A,k,phi,Delta);
+
+// simulation parameters for stb_disc.xcos
+st = 1; // desired step change
+t_init = 0; // simulation start time
+t_final = 20; // simulation end time
+xInitial = [0 0];
+C = 0; D = 1; N_var = 0;
+
+[Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+[Rcp1,Rcp2] = cosfil_ip(1,Rc); // 1/Rc
+[Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+[Bp,Ap] = cosfil_ip(B,A); // B/A
+[zkp1,zkp2] = cosfil_ip(zk,1); // zk/1
+[Cp,Dp] = cosfil_ip(C,D); // C/D
+
diff --git a/2048/CH9/EX9.17/dof_choice.sce b/2048/CH9/EX9.17/dof_choice.sce new file mode 100755 index 000000000..a44b0a70d --- /dev/null +++ b/2048/CH9/EX9.17/dof_choice.sce @@ -0,0 +1,58 @@ +// Illustrating the benefit of cancellation. It is used to arrive at the results of Example 9.15.
+// 9.17
+
+exec('pp_im.sci',-1);
+exec('pp_pid.sci',-1);
+exec('zpowk.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('polyno.sci',-1);
+exec('cosfil_ip.sci',-1);
+
+
+// test problem to demonstrate benefits of 2_dof
+// Ts = 1; B = [1 0.9]; A = conv([1 -1],[1 -0.8]); k = 1;
+Ts = 1; k = 1;
+B = convol([1 0.9],[1 -0.8]); A = convol([1 -1],[1 -0.5]);
+
+// closed loop characteristic polynomial
+phi = [1 -1 0.5];
+
+Delta = 1; // Choice of internal model of step
+control = 1;
+if control == 1, // 1-DOF with no cancellation
+ [Rc,Sc] = pp_pid(B,A,k,phi,Delta);
+ Tc = Sc; gamm = 1;
+else // 2-DOF
+ [Rc,Sc,Tc,gamm] = pp_im(B,A,k,phi,Delta);
+end
+
+// simulation parameters for stb_disc.mdl
+[zk,dzk] = zpowk(k);
+st = 1; // desired step change
+t_init = 0; // simulation start time
+t_final = 20; // simulation end time
+xInitial = [0 0];
+C = 0; D = 1; N_var = 0;
+
+[Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+[Rcp1,Rcp2] = cosfil_ip(1,Rc); // 1/Rc
+[Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+[Bp,Ap] = cosfil_ip(B,A); // B/A
+[zkp1,zkp2] = cosfil_ip(zk,1); // zk/1
+[Cp,Dp] = cosfil_ip(C,D); // C/D
+
+
+
+
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\ No newline at end of file diff --git a/2048/CH9/EX9.18/ibm_pp_sat.sce b/2048/CH9/EX9.18/ibm_pp_sat.sce new file mode 100755 index 000000000..21ab344c3 --- /dev/null +++ b/2048/CH9/EX9.18/ibm_pp_sat.sce @@ -0,0 +1,84 @@ +// Anti windup control (AWC) of IBM Lotus Domino server, studied in Example 9.16 on page 357. It can be used for the follwoing situations: with and without saturation, and with and without AWC.
+// 9.18
+
+exec('pp_im2.sci',-1);
+exec('desired.sci',-1);
+exec('zpowk.sci',-1);
+exec('cosfil_ip.sci',-1);
+exec('polsplit3.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('polyno.sci',-1);
+exec('cindep.sci',-1);
+exec('poladd.sci',-1);
+
+// Transfer function
+B = 0.47; A = [1 -0.43]; k = 1;
+[zk,dzk] = zpowk(k);
+
+// Transient specifications
+rise = 10; epsilon = 0.01; Ts = 1;
+phi = desired(Ts,rise,epsilon);
+
+// Controller design
+delta = [1 -1]; // internal model of step used
+[Rc,Sc,Tc,gamm,F] = pp_im2(B,A,k,phi,delta);
+
+// Study of Antiwindup Controller
+
+key = x_choose(['Simulate without any saturation limits';
+ 'Simulate saturation, but do not use AWC';
+ 'Simulate saturation with AWC in place';
+ 'Simulate with AWC, without saturation limits'],...
+ ['Please choose one of the following']);
+
+if key ==0
+ disp('Invalid choice');
+ return;
+elseif key == 1
+ U = 2; L = -2; P = 1; F = Rc; E = 0; PSc = Sc; PTc = Tc;
+elseif key == 2
+ U = 1; L = -1; P = 1; F = Rc; E = 0; PSc = Sc; PTc = Tc;
+else
+ if key == 3 // Antiwindup controller and with saturation
+ U = 1; L = -1;
+ elseif key == 4 // Antiwindup controller, but no saturation
+ U = 2; L = -2;
+ end
+ P = A;
+ dF = length(F) - 1;
+ PRc = convol(P,Rc); dPRc = length(PRc) - 1;
+ [E,dE] = poladd(F,dF,-PRc,dPRc);
+ PSc = convol(P,Sc); PTc = convol(P,Tc);
+end
+
+// Setting up simulation parameters for stb_disc_sat
+t_init = 0; // first step begins
+st = 1; // height of first step
+t_init2 = 500; // second step begins
+st2 = -2; // height of second step
+t_final = 1000; // simulation end time
+st1 = 0; // no disturbance input
+C = 0; D = 1; N_var = 0;
+
+[PTcp1,PTcp2] = cosfil_ip(PTc,1); // PTc/1
+[Fp1,Fp2] = cosfil_ip(1,F); // 1/F
+[Ep,Fp] = cosfil_ip(E,F); // E/F
+[PScp1,PScp2] = cosfil_ip(PSc,1); // PSc/1
+[Bp,Ap] = cosfil_ip(B,A); // B/A
+[zkp1,zkp2] = cosfil_ip(zk,1); // zk/1
+[Cp,Dp] = cosfil_ip(C,D); // C/D
+
+
+
+
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\ No newline at end of file diff --git a/2048/CH9/EX9.19/pid_neg.sce b/2048/CH9/EX9.19/pid_neg.sce new file mode 100755 index 000000000..ef7886892 --- /dev/null +++ b/2048/CH9/EX9.19/pid_neg.sce @@ -0,0 +1,52 @@ +// Demonstration of usefulness of negative PID parameters, discussed in Example 9.17 on page 361.
+// 9.19
+
+exec('iodelay.sci',-1);
+exec('delc2d.sci',-1);
+exec('desired.sci',-1);
+exec('pp_pid.sci',-1);
+exec('cosfil_ip.sci',-1);
+exec('tf.sci',-1);
+exec('flip.sci',-1);
+exec('zpowk.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+
+// Discretize the continuous plant
+num = 1; den = [2 1]; tau = 0.5;
+G1 = tf(num,den);
+G = iodelay(G1,tau);
+Ts = 0.5;
+[B,A,k] = delc2d(G,G1,Ts);
+
+// Specify transient requirements
+epsilon = 0.05; rise = 5;
+phi = desired(Ts,rise,epsilon);
+
+// Design the controller
+Delta = [1 -1];
+[Rc,Sc] = pp_pid(B,A,k,phi,Delta);
+
+// parameters for simulation using g_s_cl
+Tc = Sc; gamm = 1; N = 1;
+C = 0; D = 1; N_var = 0;
+st = 1; t_init = 0; t_final = 20;
+
+[Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+[Np,Rcp] = cosfil_ip(N,Rc); // N/Rc
+[Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+[Cp,Dp] = cosfil_ip(C,D); // C/D
+Num = numer(G1);
+Den = denom(G1);
+
diff --git a/2048/CH9/EX9.19/u1_9_19.png b/2048/CH9/EX9.19/u1_9_19.png Binary files differnew file mode 100755 index 000000000..9785bf16f --- /dev/null +++ b/2048/CH9/EX9.19/u1_9_19.png diff --git a/2048/CH9/EX9.19/y1_9_19.png b/2048/CH9/EX9.19/y1_9_19.png Binary files differnew file mode 100755 index 000000000..aa2fa15bb --- /dev/null +++ b/2048/CH9/EX9.19/y1_9_19.png diff --git a/2048/CH9/EX9.2/myc2d.sci b/2048/CH9/EX9.2/myc2d.sci new file mode 100755 index 000000000..1644cddfe --- /dev/null +++ b/2048/CH9/EX9.2/myc2d.sci @@ -0,0 +1,20 @@ +// Discretization of continuous transfer function. The result is numerator and denominator in powers of z^{-1} and the delay term k.
+// 9.2
+// function [B,A,k] = myc2d(G,Ts)
+// Produces numerator and denominator of discrete transfer
+// function in powers of z^{-1}
+// G is continuous transfer function; time delays are not allowed
+// Ts is the sampling time, all in consistent time units
+
+function [B,A,k] = myc2d(G,Ts)
+H = ss2tf(dscr(G,Ts));
+num1 = coeff(H('num'));
+den1 = coeff(H('den'));//-------------
+A = den1(length(den1):-1:1);
+num2 = num1(length(num1):-1:1); //flip
+nonzero = find(num1);
+first_nz = nonzero(1);
+B = num2(first_nz:length(num2)); //-------------
+k = length(den1) - length(num1);
+endfunction
+
diff --git a/2048/CH9/EX9.20/pp_pid.sci b/2048/CH9/EX9.20/pp_pid.sci new file mode 100755 index 000000000..7071ab671 --- /dev/null +++ b/2048/CH9/EX9.20/pp_pid.sci @@ -0,0 +1,15 @@ +// Solution to Aryabhatta's identity arising in PID controller design, namely Eq. 9.37 on page 363.
+// 9.20
+
+function [Rc,Sc] = pp_pid(B,A,k,phi,Delta)
+
+// Setting up and solving Aryabhatta identity
+dB = length(B) - 1; dA = length(A) - 1;
+[zk,dzk] = zpowk(k);
+[N,dN] = polmul(B,dB,zk,dzk);
+dDelta = length(Delta)-1;
+[D,dD] = polmul(A,dA,Delta,dDelta);
+dphi = length(phi)-1;
+[Sc,dSc,R,dR] = xdync(N,dN,D,dD,phi,dphi);
+Rc = convol(R,Delta);
+endfunction;
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\ No newline at end of file diff --git a/2048/CH9/EX9.21/motor_pd.sce b/2048/CH9/EX9.21/motor_pd.sce new file mode 100755 index 000000000..8408bc3d0 --- /dev/null +++ b/2048/CH9/EX9.21/motor_pd.sce @@ -0,0 +1,69 @@ +// DC motor with PID control, tuned through pole placement technique, as in Example 9.18.
+// 9.21
+
+exec('desired.sci',-1);
+exec('pp_pid.sci',-1);
+exec('cosfil_ip.sci',-1);
+exec('pd.sci',-1);
+exec('polyno.sci',-1);
+exec('myc2d.sci',-1);
+exec('zpowk.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+
+// Motor control problem
+// Transfer function
+
+a = [-1 0; 1 0]; b = [1; 0]; c = [0 1]; d = 0;
+G = syslin('c',a,b,c,d); Ts = 0.25;
+[B,A,k] = myc2d(G,Ts);
+[Ds,num,den] = ss2tf(G);
+
+// Transient specifications
+rise = 3; epsilon = 0.05;
+phi = desired(Ts,rise,epsilon);
+
+// Controller design
+Delta = 1; //No internal model of step used
+[Rc,Sc] = pp_pid(B,A,k,phi,Delta);
+
+// continuous time controller
+[K,taud,N] = pd(Rc,Sc,Ts);
+numb = K*[1 taud*(1+1/N)]; denb = [1 taud/N];
+numf = 1; denf = 1;
+
+// simulation parameters
+st = 1; // desired change in position
+t_init = 0; // simulation start time
+t_final = 20; // simulation end time
+st1 = 0;
+
+// continuous controller simulation: g_s_cl3.xcos
+num1 = 0; den1 = 1;
+
+// discrete controller simulation: g_s_cl2.xcos
+// u1: -0.1 to 0.8
+// y1: 0 to 1.4
+C = 0; D = 1; N = 1; gamm = 1; Tc = Sc;
+
+[Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+[Np,Rcp] = cosfil_ip(N,Rc); // N/Rc
+[Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+[Cp,Dp] = cosfil_ip(C,D); // C/D
+Numb = polyno(numb,'s');
+Denb = polyno(denb,'s');
+Numf = polyno(numf,'s');
+Denf = polyno(denf,'s');
+Num1 = polyno(num1,'s');
+Den1 = polyno(den1,'s');
diff --git a/2048/CH9/EX9.21/u1_g_s_cl2.png b/2048/CH9/EX9.21/u1_g_s_cl2.png Binary files differnew file mode 100755 index 000000000..862f872a9 --- /dev/null +++ b/2048/CH9/EX9.21/u1_g_s_cl2.png diff --git a/2048/CH9/EX9.21/y1_g_s_cl2.png b/2048/CH9/EX9.21/y1_g_s_cl2.png Binary files differnew file mode 100755 index 000000000..9f0ce2178 --- /dev/null +++ b/2048/CH9/EX9.21/y1_g_s_cl2.png diff --git a/2048/CH9/EX9.22/pd.sci b/2048/CH9/EX9.22/pd.sci new file mode 100755 index 000000000..110401281 --- /dev/null +++ b/2048/CH9/EX9.22/pd.sci @@ -0,0 +1,14 @@ +// PD control law from polynomial coefficients, as explained in Sec. 9.8.
+// 9.22
+
+function [K,taud,N] = pd(Rc,Sc,Ts)
+
+// Both Rc and Sc have to be degree one polynomials
+
+s0 = Sc(1); s1 = Sc(2);
+r1 = Rc(2);
+K = (s0+s1)/(1+r1);
+N = (s1-s0*r1)/r1/(s0+s1);
+taudbyN = -Ts*r1/(1+r1);
+taud = taudbyN * N;
+endfunction;
diff --git a/2048/CH9/EX9.3/polsplit2.sci b/2048/CH9/EX9.3/polsplit2.sci new file mode 100755 index 000000000..524c35442 --- /dev/null +++ b/2048/CH9/EX9.3/polsplit2.sci @@ -0,0 +1,36 @@ +// Procedure to split a polynomial into good and bad factors, as discussed in Sec. 9.2.
+// 9.3
+// function [goodpoly,badpoly] = polsplit2(fac,a)
+// Splits a scalar polynomial of z^{-1} into good and bad
+// factors.
+// Input is a polynomial in increasing degree of z^{-1}
+// Optional input is a, where a <= 1.
+// Factor that has roots of z^{-1} outside a is called
+// good and the rest bad.
+// If a is not specified, it will be assumed as 1-1.0e-5
+
+function [goodpoly,badpoly] = polsplit2(fac,a)
+if argn(2) == 1, a = 1-1.0e-5; end
+if a>1 error('good polynomial is unstable'); end
+fac1 = poly(fac(length(fac):-1:1),'z','coeff');
+rts1 = roots(fac1);
+rts = rts1(length(rts1):-1:1);
+
+// extract good and bad roots
+badindex = find(abs(rts)>=a); // mtlb_find has been replaced by find
+badpoly = coeff(poly((rts(badindex)),"z","roots"));
+goodindex = find(abs(rts)<a); // mtlb_find has been replaced by find
+goodpoly = coeff(poly(rts(goodindex),"z","roots"));
+
+// scale by equating the largest terms
+[m,index] = max(abs(fac));
+goodbad = convol(goodpoly,badpoly);
+goodbad1 = goodbad(length(goodbad):-1:1);//--
+factor1 = fac(index)/goodbad1(index);//--
+goodpoly = goodpoly * factor1;
+goodpoly = goodpoly(length(goodpoly):-1:1);
+badpoly = badpoly(length(badpoly):-1:1);
+endfunction;
+
+
+
diff --git a/2048/CH9/EX9.4/desired.sci b/2048/CH9/EX9.4/desired.sci new file mode 100755 index 000000000..d84e6c918 --- /dev/null +++ b/2048/CH9/EX9.4/desired.sci @@ -0,0 +1,11 @@ +// Calculation of desired closed loop characteristic polynomial, as discussed in Sec. 7.7.
+// 9.4
+
+// function [phi,dphi] = desired(Ts,rise,epsilon)
+// Based on transient requirements,
+// calculates closed loop characteristic polynomial
+
+function [phi,dphi] = desired(Ts,rise,epsilon)
+Nr = rise/Ts; omega = %pi/2/Nr; rho = epsilon^(omega/%pi);
+phi = [1 -2*rho*cos(omega) rho^2]; dphi = length(phi)-1;
+endfunction;
diff --git a/2048/CH9/EX9.5/pp_basic.sci b/2048/CH9/EX9.5/pp_basic.sci new file mode 100755 index 000000000..c8fb0a356 --- /dev/null +++ b/2048/CH9/EX9.5/pp_basic.sci @@ -0,0 +1,26 @@ +// Design of 2-DOF pole placement controller, as discussed in Sec. 9.2.
+// 9.5
+
+// function [Rc,Sc,Tc,gamma] = pp_basic(B,A,k,phi)
+// calculates pole placement controller
+
+
+function [Rc,Sc,Tc,gamm] = pp_basic(B,A,k,phi)
+
+// Setting up and solving Aryabhatta identity
+[Ag,Ab] = polsplit2(A); dAb = length(Ab) - 1;
+[Bg,Bb] = polsplit2(B); dBb = length(Bb) - 1;
+
+[zk,dzk] = zpowk(k);
+
+[N,dN] = polmul(Bb,dBb,zk,dzk);
+dphi = length(phi) - 1;
+
+[S1,dS1,R1,dR1] = xdync(N,dN,Ab,dAb,phi,dphi);
+
+// Determination of control law
+Rc = convol(Bg,R1); Sc = convol(Ag,S1);
+Tc = Ag; gamm = sum(phi)/sum(Bb);
+
+endfunction;
+
diff --git a/2048/CH9/EX9.6/zpowk.sci b/2048/CH9/EX9.6/zpowk.sci new file mode 100755 index 000000000..4b5b43e8d --- /dev/null +++ b/2048/CH9/EX9.6/zpowk.sci @@ -0,0 +1,7 @@ +// Evaluates z^-k.
+// 9.6
+
+function [zk,dzk] = zpowk(k)
+zk = zeros(1,k+1); zk(1,k+1) = 1;
+dzk = k;
+endfunction
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\ No newline at end of file diff --git a/2048/CH9/EX9.7/u1_stb_disc.png b/2048/CH9/EX9.7/u1_stb_disc.png Binary files differnew file mode 100755 index 000000000..da873794a --- /dev/null +++ b/2048/CH9/EX9.7/u1_stb_disc.png diff --git a/2048/CH9/EX9.7/unstb.sce b/2048/CH9/EX9.7/unstb.sce new file mode 100755 index 000000000..b360cf96b --- /dev/null +++ b/2048/CH9/EX9.7/unstb.sce @@ -0,0 +1,56 @@ +// Simulation of closed loop system with an unstable controller, as discussed in Example 9.5 on page 335.
+// 9.7
+
+exec('desired.sci',-1);
+exec('zpowk.sci',-1);
+exec('polmul.sci',-1);
+exec('polsplit2.sci',-1);
+exec('polsize.sci',-1);
+exec('xdync.sci',-1);
+exec('rowjoin.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('cindep.sci',-1);
+exec('seshft.sci',-1);
+exec('cosfil_ip.sci',-1);
+exec('pp_basic.sci',-1);
+
+Ts = 1; B = [1 -3]; A = [1 2 -8]; k = 1;
+// Since k=1, tf is of the form z^-1
+[zk,dzk] = zpowk(k); // int1 = 0;//---- int1
+
+// Transient specifications
+rise = 10; epsilon = 0.1;
+phi = desired(Ts,rise,epsilon);
+
+// Controller design
+[Rc,Sc,Tc,gamm] = pp_basic(B,A,k,phi);
+
+// simulation parameters for basic_disc.xcos
+//While simulating for t_final = 100, set the limit of Y axis of each scope
+//u1: -0.2 to 3
+//y1: -0.1 to 1.2
+st = 1.0; // Desired change in setpoint
+t_init = 0; // Simulation start time
+t_final = 1000; // Simulation end time
+
+// Simulation parameters for stb_disc.xcos
+N_var = 0; C = 0; D = 1; N = 1;
+
+[Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+[Rcp1,Rcp2] = cosfil_ip(1,Rc); // 1/Rc
+[Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+[Bp,Ap] = cosfil_ip(B,A); // B/A
+[zkp1,zkp2] = cosfil_ip(zk,1); // zk/1
+[Cp,Dp] = cosfil_ip(C,D); // C/D
+
+[Tcp,Rcp] = cosfil_ip(Tc,Rc); // Tc/Rc
+[Scp_b,Rcp_b] = cosfil_ip(Sc,Rc); // Sc/Rc
+
+
+
diff --git a/2048/CH9/EX9.7/y1_stb_disc.png b/2048/CH9/EX9.7/y1_stb_disc.png Binary files differnew file mode 100755 index 000000000..d0c820764 --- /dev/null +++ b/2048/CH9/EX9.7/y1_stb_disc.png diff --git a/2048/CH9/EX9.8/pp_im.sci b/2048/CH9/EX9.8/pp_im.sci new file mode 100755 index 000000000..f1a512fea --- /dev/null +++ b/2048/CH9/EX9.8/pp_im.sci @@ -0,0 +1,25 @@ +// Pole placement controller using internal model principle, as discussed in Sec. 9.4.
+// 9.8
+
+// function [Rc,Sc,Tc,gamma,phit] = pp_im(B,A,k,phi,Delta)
+// Calculates 2-DOF pole placement controller.
+
+function [Rc,Sc,Tc,gamm] = pp_im(B,A,k,phi,Delta)
+
+// Setting up and solving Aryabhatta identity
+[Ag,Ab] = polsplit3(A); dAb = length(Ab) - 1;
+[Bg,Bb] = polsplit3(B); dBb = length(Bb) - 1;
+
+[zk,dzk] = zpowk(k);
+
+[N,dN] = polmul(Bb,dBb,zk,dzk);
+dDelta = length(Delta)-1;
+[D,dD] = polmul(Ab,dAb,Delta,dDelta);
+dphi = length(phi)-1;
+
+[S1,dS1,R1,dR1] = xdync(N,dN,D,dD,phi,dphi);
+
+// Determination of control law
+Rc = convol(Bg,convol(R1,Delta)); Sc = convol(Ag,S1);
+Tc = Ag; gamm = sum(phi)/sum(Bb);
+endfunction;
diff --git a/2048/CH9/EX9.9/ball_im.sce b/2048/CH9/EX9.9/ball_im.sce new file mode 100755 index 000000000..fc863c277 --- /dev/null +++ b/2048/CH9/EX9.9/ball_im.sce @@ -0,0 +1,60 @@ +// Pole placement controller, with internal model of a step, for the magnetically suspended ball problem, as discussed in Example 9.8 on page 339.
+// 9.9
+
+// PP control with internal model for ball problem
+exec('desired.sci',-1);
+exec('pp_im.sci',-1);
+exec('myc2d.sci',-1);
+exec('polsplit3.sci',-1);
+exec('zpowk.sci',-1);
+exec('rowjoin.sci',-1);
+exec('left_prm.sci',-1);
+exec('t1calc.sci',-1);
+exec('indep.sci',-1);
+exec('cindep.sci',-1);
+exec('seshft.sci',-1);
+exec('makezero.sci',-1);
+exec('move_sci.sci',-1);
+exec('colsplit.sci',-1);
+exec('clcoef.sci',-1);
+exec('polmul.sci',-1);
+exec('polsize.sci',-1);
+exec('xdync.sci',-1);
+exec('cosfil_ip.sci',-1);
+exec('polyno.sci',-1);
+
+// Operating conditions
+M = 0.05; L = 0.01; R = 1; K = 0.0001; g = 9.81;
+
+// Equilibrium conditions
+hs = 0.01; is = sqrt(M*g*hs/K);
+
+// State space matrices
+a21 = K*is^2/M/hs^2; a23 = - 2*K*is/M/hs; a33 = - R/L;
+b3 = 1/L;
+a1 = [0 1 0; a21 0 a23; 0 0 a33];
+b1 = [0; 0; b3]; c1 = [1 0 0]; d1 = 0;
+
+// Transfer functions
+G = syslin('c',a1,b1,c1,d1); Ts = 0.01; [B,A,k] = myc2d(G,Ts);
+
+// Transient specifications
+rise = 0.1; epsilon = 0.05;
+phi = desired(Ts,rise,epsilon);
+
+// Controller design
+Delta = [1 -1]; //internal model of step used
+[Rc,Sc,Tc,gamm] = pp_im(B,A,k,phi,Delta);
+
+// simulation parameters for c_ss_cl.xcos
+st = 0.0001; //desired change in h, in m.
+t_init = 0; // simulation start time
+t_final = 0.5; //simulation end time
+xInitial = [0 0 0];
+N = 1; C = 0; D = 1; N_var = 0;
+
+[Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+[Np,Rcp] = cosfil_ip(N,Rc); // 1/Rc
+[Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+[Cp,Dp] = cosfil_ip(C,D); // C/D
+
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\ No newline at end of file diff --git a/2048/CH9/EX9.9/u1_c_ss_cl.png b/2048/CH9/EX9.9/u1_c_ss_cl.png Binary files differnew file mode 100755 index 000000000..0b8f48204 --- /dev/null +++ b/2048/CH9/EX9.9/u1_c_ss_cl.png diff --git a/2048/CH9/EX9.9/y1_c_ss_cl.png b/2048/CH9/EX9.9/y1_c_ss_cl.png Binary files differnew file mode 100755 index 000000000..72457a329 --- /dev/null +++ b/2048/CH9/EX9.9/y1_c_ss_cl.png diff --git a/2048/DEPENDENCIES/armac1.sci b/2048/DEPENDENCIES/armac1.sci new file mode 100755 index 000000000..75b8ee7c3 --- /dev/null +++ b/2048/DEPENDENCIES/armac1.sci @@ -0,0 +1,17 @@ +// Scilab description of an ARMAX process
+// Form:
+// A(q) y(t) = [B(q)/F(q)] u(t-nk) + [C(q)/D(q)] e(t)
+
+// [A(q)*F(q)*D(q)] y(t) = [B(q)*D(q)] u(t-nk) + [C(q)*F(q)]e(t)
+// A1(q) = [A(q)*F(q)*D(q)]
+// B1(q) = [B(q)*D(q)]
+// D1(q) = [C(q)*F(q)]
+
+function process_ar = armac1(a,b,c,d,f,sig)
+ny = 1; nu =1;
+a1 = convol(convol(a,f),d);
+b1 = convol(b,d);
+d1 = convol(c,f);
+process_ar = armac(a1,b1,d1,ny,nu,sig);
+
+endfunction;
diff --git a/2048/DEPENDENCIES/arx.sci b/2048/DEPENDENCIES/arx.sci new file mode 100755 index 000000000..038217da2 --- /dev/null +++ b/2048/DEPENDENCIES/arx.sci @@ -0,0 +1,110 @@ +// ARX model parameter estimation
+// Computes Covariance matrix
+// Computes Noisevariance of a process
+
+function [thetaN,covt,nvar,res] = arx(data,na,nb,nk)
+az = max(na,nb+nk-1);
+zer = zeros(az,1);
+zd = data;
+// Zeros appended
+zd1(:,1) = [zer; zd(:,1)];
+zd1(:,2) = [zer; zd(:,2)];
+[r,c] = size(zd1);
+t = az+1:r;
+yt = zd1(:,1); ut = zd1(:,2);
+yt1 = yt'; ut1 = ut'; // row vector
+len1 = length(yt1);
+yt2 = zeros(1,len1-az); ut2 = zeros(1,len1-az);
+
+// arx(Data,[na nb nk])
+ for i=1:na
+ yt2 = [yt2; -yt1(t-i)];
+ end;
+ for i=nk:nb+nk-1
+ ut2 = [ut2; ut1(t-i)];
+ end;
+[r1_a,c1_a] = size(yt2); [r2_a,c2_a] = size(ut2);
+phit = [yt2(2:r1_a,:); ut2(2:r2_a,:)];
+m1 = phit*phit';
+[qm,rm] = qr(m1);
+m2 = phit*zd(:,1);
+thetaN = inv(rm)*qm'*m2;
+// thetaN = inv(m1)*m2;
+// thetaN = m1\m2;
+
+[r1,c1] = size(thetaN);
+a = thetaN(1:na); b = thetaN(na+1:r1);
+
+// Sum of squared residuals
+
+yhat = phit'*thetaN;
+res = zd(:,1) - yhat;
+N = length(res);
+q = rank(phit);
+ssr = res'*res;
+sig2 = ssr/(N-q);
+nvar = sqrt(sig2);
+cov = inv(m1);
+covt = diag(cov);
+
+a = thetaN(1:na); b = thetaN(na+1:r1);
+cova = covt(1:na); covb = covt(na+1:r1);
+x = poly(0,'x');
+disp('Discrete time model: A(x)y(t) = B(x)u(t) + e(t)');
+A = poly([1 a'],'x','coeff');
+cov_a = [0 cova'];
+b1 = zeros(1,nk);
+B = poly([b1 b'],'x','coeff');
+cov_b = covb';
+
+
+
+//////////////////////////////////////
+//////////////////////////////////////
+
+////////// Model Display /////////////
+
+function disp_mod(N,covN)
+len = length(covN);
+B1 = pol2str(N);
+ind = strindex(B1,['+','-']);
+ind = ind - 1;
+B2 = strsplit(B1,ind);
+covB = string(covN);
+
+ if ascii(B2(1)) == 32
+ B2 = B2(2:len+1);
+ end;
+
+ B3(1) = ' ';
+ for i=1:len
+ B3(i) = strsubst(B2(i),'*x','(+-' + covB(i) + ')*x');
+ end;
+
+ B4 = B3(1);
+
+ for i=2:len
+ B4 = B4 + ' ' + B3(i);
+ end;
+
+disp(B4);
+endfunction;
+//////////////////////////////////////
+//////////////////////////////////////
+
+ if na==0
+ disp('A(x) = 1');
+ else
+ disp('A(x) = ');
+ disp_mod(A,cov_a);
+ end;
+
+ if nb~=0
+ disp('B(x) = ');
+ disp_mod(B,cov_b);
+ end;
+
+
+
+endfunction;
+
diff --git a/2048/DEPENDENCIES/ch_pol.sci b/2048/DEPENDENCIES/ch_pol.sci new file mode 100755 index 000000000..fa5fa8af2 --- /dev/null +++ b/2048/DEPENDENCIES/ch_pol.sci @@ -0,0 +1,10 @@ +// function [phi,psi] = ch_pol(N,epsilon)
+// Returns desired characteristic polynomial and numerator
+// N = rise time in number of sample times
+// epsilon = overshoot as a fraction of ss gain
+
+function [phi,psi] = ch_pol(N,epsilon)
+omega = %pi/2/N; r = epsilon^(omega/%pi);
+phi = [1 -2*r*cos(omega) r^2];
+psi = [1-r*cos(omega) (r^2-r*cos(omega))];
+endfunction;
diff --git a/2048/DEPENDENCIES/cindep.sci b/2048/DEPENDENCIES/cindep.sci new file mode 100755 index 000000000..3ffd243d4 --- /dev/null +++ b/2048/DEPENDENCIES/cindep.sci @@ -0,0 +1,35 @@ +// function b = cindep( S,gap)
+// Used in XD + YN = C. All rows except the last of are assumed to
+// be independent. The aim is to check if the last row is dependent on the
+// rest and if so how. The coefficients of dependence are sent in b.
+function b = cindep( S,gap)
+
+if argn(2) == 1
+ gap = 1.0e8;
+end
+eps = 2.2204e-016;
+[rows,cols] = size(S);
+if rows > cols
+ ind = 0;
+else
+ sigma = svd(S);
+ len = length(sigma);
+ if (sigma(len)/sigma(1) <= (eps*max(i,cols)))
+ ind = 0; //not independent
+ else
+ if or(sigma(1:len-1) ./sigma(2:len)>=gap)
+ ind = 0; // not dependent
+ else
+ ind = 1; //independent
+ end
+ end
+end
+if ind
+ b = [];
+else
+ b = S(rows,:)/S(1:rows-1,:);
+ b = makezero(b,gap);
+end
+endfunction
+
+
diff --git a/2048/DEPENDENCIES/clcoef.sci b/2048/DEPENDENCIES/clcoef.sci new file mode 100755 index 000000000..249a5370e --- /dev/null +++ b/2048/DEPENDENCIES/clcoef.sci @@ -0,0 +1,25 @@ +// H. Kwakernaak, July, 1990
+// Modified by Kannan Moudgalya in Nov. 1992
+
+function [P,degP] = clcoef(Q,degQ)
+
+[rQ,cQ] = polsize(Q,degQ);
+
+if and(and(Q==0))
+ P = zeros(rQ,cQ);
+ degP = 0;
+else
+ P = Q; degP = degQ; rP = rQ; cP = cQ;
+ j = degP+1;
+ while j >= 0
+ X = P(:,(j-1)*cP+1:j*cP)
+ if max(sum(abs(X'))) < (1e-8)*max(sum(abs(P)))
+ P = P(:,1:(j-1)*cP);
+ degP = degP-1;
+ else
+ j = 0;
+ end
+ j = j-1;
+ end
+end
+endfunction
diff --git a/2048/DEPENDENCIES/colsplit.sci b/2048/DEPENDENCIES/colsplit.sci new file mode 100755 index 000000000..ec4cafecc --- /dev/null +++ b/2048/DEPENDENCIES/colsplit.sci @@ -0,0 +1,36 @@ +// colsplit
+// The command
+// [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+// produces two polynomial matrix P1 and P2. P1 consists of the first
+// p1 columns of P and P2 consists of the remaining p2 columns of P.
+
+// H. Kwakernaak, July, 1990
+
+
+function [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+if isempty(P)
+ P1 = []; P2 = [];
+ degP1 = 0; degP2 = 0;
+ return;
+end
+
+[rP,cP] = polsize(P,degP);
+if p1 < 0 | p1 > cP | p2 < 0 | p2 > cP | p1+p2 ~= cP
+ error('colsplit: Inconsistent numbers of columns');
+end
+rP1 = rP; rP2 = rP; cP1 = p1; cP2 = p2;
+degP1= degP; degP2 = degP;
+
+if p1 == 0
+ P1 == []; P2 = P;
+elseif p2 == 0
+ P1 = P; P2 = [];
+else
+ P1 = zeros(rP1,(degP1+1)*cP1); P2 = zeros(rP2,(degP2+1)*cP2);
+ for i = 1:degP+1
+ P1(:,(i-1)*cP1+1:i*cP1) = P(:,(i-1)*cP+1:(i-1)*cP+cP1);
+ P2(:,(i-1)*cP2+1:i*cP2) = P(:,(i-1)*cP+cP1+1:i*cP);
+ end
+end
+endfunction;
diff --git a/2048/DEPENDENCIES/cosfil_ip.sci b/2048/DEPENDENCIES/cosfil_ip.sci new file mode 100755 index 000000000..b16ba4b27 --- /dev/null +++ b/2048/DEPENDENCIES/cosfil_ip.sci @@ -0,0 +1,15 @@ +// Input arguments are co efficients of numerator and denominator
+// polynomials in ascending powers of z^-1
+
+// Scicos/Xcos blocks need input polynomials
+// with positive powers of z
+
+function [nume,deno] = cosfil_ip(num,den)
+exec('polyno.sci',-1);
+[Nn,Nd] = polyno(num,'z');
+[Dn,Dd] = polyno(den,'z');
+nume = Nn*Dd;
+deno = Nd*Dn;
+
+endfunction;
+
diff --git a/2048/DEPENDENCIES/covar_m.sci b/2048/DEPENDENCIES/covar_m.sci new file mode 100755 index 000000000..bd84831b2 --- /dev/null +++ b/2048/DEPENDENCIES/covar_m.sci @@ -0,0 +1,46 @@ +//User defined equivalent function to Matlab covar function
+//For discrete time domain only
+//Uses Lyapunov's equation for computation
+//W: noise intensity (scalar)
+//Matlab result for unstable systems:
+//Warning: Unstable models have infinite covariance
+
+function P = covar_m(sys,W)
+a = roots(sys('den'));
+b = length(a);
+c = abs(a) > 1;
+if b ~= 0 then
+ for i = 1:b
+ if c(i) == %t then
+ disp('Warning: System being unstable has infinite covariance');
+ P = %inf;
+ else
+ s = tf2ss(sys);
+ [A,B,C,D] = s(2:5);
+ //Sylvester and Lyapunov solver
+ task = 2; flag = [1 0]; tran = 1;
+ Q1 = -B*W*B';
+ Q = linmeq(task,A,Q1,flag,tran)
+ P = C*Q*C' + D*W*D';
+ end;
+ end;
+else
+ s = tf2ss(sys);
+ [A,B,C,D] = s(2:5);
+ //Sylvester and Lyapunov solver
+ task = 2; flag = [1 0]; tran = 1;
+ Q1 = -B*W*B';
+ Q = linmeq(task,A,Q1,flag,tran)
+ P = C*Q*C' + D*W*D';
+end;
+endfunction;
+
+//if d==0 | c==%f
+// disp('Calc');
+//else
+// disp('Unstable');
+//end;
+// Above logic can also solve our purpose
+// But it gives incorrect answer if roots are [1 -1 1] or
+// [1 -1 -1] ....
+
diff --git a/2048/DEPENDENCIES/covf.sci b/2048/DEPENDENCIES/covf.sci new file mode 100755 index 000000000..2cf7e74d6 --- /dev/null +++ b/2048/DEPENDENCIES/covf.sci @@ -0,0 +1,30 @@ +// z: [y u] (Column matrix)
+// ---- ----
+// | |
+// | ryy(0) ryy(1) ... ryy(len) |
+// | |
+// v = | ruy(0) ruy(1) ... ruy(len) |
+// | |
+// | ryu(0) ryu(1) ... ryu(len) |
+// | |
+// | ruu(0) ruu(1) ... ruu(len) |
+// | |
+// ---- ----
+// No. of lags
+
+function v = covf(z,n)
+[r c] = size(z);
+y1 = z(:,1);
+u1 = z(:,2);
+ if n>r
+ // disp('Incorrect number of lags');
+ n = r;
+ else
+ r = n;
+ end;
+ryu = corr(y1,u1,r);
+ruy = corr(u1,y1,r);;
+ryy = corr(y1,r);
+ruu = corr(u1,r);
+v = [ryy; ruy; ryu; ruu]
+endfunction;
diff --git a/2048/DEPENDENCIES/cra.sci b/2048/DEPENDENCIES/cra.sci new file mode 100755 index 000000000..be0d6e2f2 --- /dev/null +++ b/2048/DEPENDENCIES/cra.sci @@ -0,0 +1,50 @@ +
+// [ir,r,cl] = cra(z,M,n)
+// M: No. of lags
+// n: Order of pre whitening filter
+// z is of the form:
+// z = [y u]
+// y and u are column matrices
+
+function [ir,r,cl] = cra(z,varargin)
+len = length(varargin);
+
+ if len==0,M = 20;n = 10;
+ elseif len==1,M = varargin(1);n=10;
+ else M = varargin(1);n = varargin(2);
+ end;
+
+[ro,co] = size(z);
+
+a1 = armax1(n,-1,0,z(:,2)',zeros(1,ro));
+[A,B,D] = arma2p(a1);
+a11 = coeff(A);
+z22(1,:) = filt(a11,1,z(:,1)');
+z22(2,:) = filt(a11,1,z(:,2)');
+Covr = covf(z22',M+1);
+scir=Covr(4,1);
+sccf=sqrt(Covr(1,1)*Covr(4,1));
+
+ir = Covr(2,:)'/scir;
+
+r(:,1) = -M:M;
+r(:,2) = [Covr(1,M+1:-1:1) Covr(1,2:M+1)]'
+r(:,3) = [Covr(4,M+1:-1:1) Covr(4,2:M+1)]'
+rhoyu = Covr(3,:)'/sccf;
+rhouy = Covr(2,:)'/sccf;
+r(:,4) = [rhoyu(M+1:-1:1); rhouy(2:M+1)];
+
+sdreu=2.58*sqrt(r(:,3)'*r(:,2))/scir/sqrt(ro)*ones(2*M+1,1);
+cl=sdreu(1);
+
+timeax=[0:length(ir)-1];
+plot(timeax,ir,'bo');
+plot2d3(timeax,ir,style = 2);
+plot(timeax,cl*ones(1,length(ir)),'b-.');
+plot(timeax,-cl*ones(1,length(ir)),'b-.');
+xtitle('Impulse response estimate','Lags');
+xgrid();
+
+endfunction;
+
+
diff --git a/2048/DEPENDENCIES/deconvol.sci b/2048/DEPENDENCIES/deconvol.sci new file mode 100755 index 000000000..b3bc8b632 --- /dev/null +++ b/2048/DEPENDENCIES/deconvol.sci @@ -0,0 +1,21 @@ +function q = deconvol(b,a)
+
+ if a(1) == 0
+ error('1st coefficient of A must be nonzero');
+ end;
+
+exec('filt.sci',-1);
+
+nb = length(b); na = length(a);
+
+ if na>nb
+ q = 0;
+ else
+ q = filt(b,a,[1 zeros(1,nb-na)]);
+ end;
+q = clean(q);
+endfunction;
+
+
+
+
diff --git a/2048/DEPENDENCIES/delc2d.sci b/2048/DEPENDENCIES/delc2d.sci new file mode 100755 index 000000000..c038b64b2 --- /dev/null +++ b/2048/DEPENDENCIES/delc2d.sci @@ -0,0 +1,48 @@ +// Discretizing a tf with delay
+// Exact solution
+// Applicable for a 1st order system
+
+// Ref.: pg.287,Digital Control,Prof.Kannan Moudgalya
+
+// D: Delay
+// TF: e^(-Ds) OR e^(-Ds)
+// ------------ ------------ (gen.)
+// tau*s + 1 tau*s + a
+
+//D = kTs + D' (gen.)
+// G: TF with delay component
+// G1: TF with zero delay
+// Required because G cannot be directly used in Scilab
+// Coefficients are returned for ascending powers of z^-1
+
+function [B,A,k1] = delc2d(G,G1,Ts)
+D = G.iodelay;
+d = coeff(G1('den'));
+ if d(1) == 1
+ tau = d(2);
+ mu = 1;
+ else
+ tau = d(2)/d(1);
+ mu = 1/d(1);
+ end;
+
+k = floor(D/Ts);
+Dpri = D - k*Ts;
+Dis = ((%z*(1 - (exp(-(Ts - Dpri)/tau)) ) )+ (exp(-(Ts - Dpri)/tau) - exp(-Ts/tau) ))/ ((%z^(k+1))*(%z - exp(-Ts/tau)))
+Dis1 = Dis*mu;
+disp('Warning: Exact discretization of first order system only');
+k1 = degree(Dis1('den')) - degree(Dis1('num'));
+B = coeff(Dis1('num'));
+A = coeff(Dis1('den'));
+B = flip(B);
+A = flip(A);
+endfunction;
+
+
+
+
+
+
+
+
+
diff --git a/2048/DEPENDENCIES/ext.sci b/2048/DEPENDENCIES/ext.sci new file mode 100755 index 000000000..469e68f2a --- /dev/null +++ b/2048/DEPENDENCIES/ext.sci @@ -0,0 +1,14 @@ +// function [B,degB] = ext(A,degA,k,l)
+// EXTRACTS THE (k,l) ELEMENT OF A polynomial matrix A into B
+
+function [B,degB] = ext(A,degA,k,l)
+
+[rA,cA] = polsize(A,degA);
+degB = degA;
+B = zeros(1,degB+1);
+for m = 0:degB
+ B(1,m+1) = A(k,(m*cA)+l);
+end
+
+[B,degB] = clcoef(B,degB);
+endfunction;
diff --git a/2048/DEPENDENCIES/filt.sci b/2048/DEPENDENCIES/filt.sci new file mode 100755 index 000000000..335a18626 --- /dev/null +++ b/2048/DEPENDENCIES/filt.sci @@ -0,0 +1,28 @@ +// Filters a data sequence using a digital filter
+// a(1)*y(n) = b(1)*x(n) + b(2)*x(n-1) + ... + b(nb+1)*x(n-nb)
+// - a(2)*y(n-1) - ... - a(na+1)*y(n-na)
+
+// x: input signal
+// x has maximum length
+function y = filt(b,a,x)
+l = length(a);
+m = length(b);
+n = length(x);
+b = [b zeros(1,n-m)];
+a = [a zeros(1,n-l)];
+
+y1(1) = b(1)*x(1);
+y2(1) = 0;
+y = y1 + y2;
+y = y/a(1);
+ for i=2:n
+ y1 = b(1:i) .* x(i:-1:1);
+ z1 = sum(y1);
+ y2 = a(2:i).*y(i-1:-1:1);
+ z2 = sum(y2);
+ y3 = z1 - z2;
+ y3 = y3/a(1);
+ y = [y y3];
+ end;
+
+endfunction;
diff --git a/2048/DEPENDENCIES/indep.sci b/2048/DEPENDENCIES/indep.sci new file mode 100755 index 000000000..860abae31 --- /dev/null +++ b/2048/DEPENDENCIES/indep.sci @@ -0,0 +1,38 @@ +// function b = indep(S,gap)
+// determines the first row that is dependent on the previous rows of S.
+// The coefficients of dependence is returned in b
+function b = indep( S,gap)
+
+if argn(2) == 1
+ gap = 1.0e8;
+ end
+[rows,cols] = size(S);
+ind = 1;
+i = 2;
+eps = 2.2204e-016;
+while ind & i <= rows
+ sigma = svd(S(1:i,:));
+ len = length(sigma);
+ if(sigma(len)/sigma(1) < (eps*max(i,cols)))
+ ind =0;
+ else
+ shsig = [sigma(2:len);sigma(len)];
+ if or( (sigma ./shsig) > gap)
+ ind = 0;
+ else
+ ind = 1;
+ i = i+1;
+ end
+ end
+
+end
+if ind
+ b =[];
+
+else
+ c = S(i,:)/S(1:i-1,:);
+ c = makezero(c,gap);
+ b = [-c 1];
+end
+endfunction
+
diff --git a/2048/DEPENDENCIES/iodelay.sci b/2048/DEPENDENCIES/iodelay.sci new file mode 100755 index 000000000..1b70d6265 --- /dev/null +++ b/2048/DEPENDENCIES/iodelay.sci @@ -0,0 +1,360 @@ +function Hd=iodelay(H,d)
+// Author: Serge Steer, Copyright INRIA
+ if or(size(H.num)<>size(d)) then error('Dimension mismatch'),end
+ Hd=mlist(['rd','H','iodelay'],H,d)
+endfunction
+
+//element wise product overloading functions
+function H=%rd_x_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],H1.H.*H2.H,H1.iodelay+ H2.iodelay)
+endfunction
+function H=%rd_x_r(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],H1.H.*H2,H1.iodelay)
+endfunction
+function H=%r_x_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],H1.*H2.H,H2.iodelay)
+endfunction
+function H=%rd_x_s(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],H1.H.*H2,H1.iodelay)
+endfunction
+function H=%s_x_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],H1.*H2.H,H2.iodelay)
+endfunction
+
+//column concatenation overloading functions
+function H=%rd_c_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],[H1.H H2.H],[H1.iodelay,H2.iodelay])
+endfunction
+function H=%rd_c_r(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],[H1.H H2],[H1.iodelay,zeros(H2.num)])
+endfunction
+function H=%r_c_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],[H1 H2.H],[zeros(H1.num),H2.iodelay])
+endfunction
+function H=%rd_c_s(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],[H1.H H2],[H1.iodelay,zeros(H2.num)])
+endfunction
+function H=%s_c_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],[H1 H2.H],[zeros(H1.num),H2.iodelay])
+endfunction
+
+//row concatenation overloading functions
+function H=%rd_f_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],[H1.H;H2.H],[H1.iodelay;H2.iodelay])
+endfunction
+function H=%rd_f_r(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],[H1.H;H2],[H1.iodelay;zeros(H2.num)])
+endfunction
+function H=%r_f_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],[H1;H2.H],[zeros(H1.num);H2.iodelay])
+endfunction
+function H=%rd_f_s(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],[H1.H;H2],[H1.iodelay;zeros(H2.num)])
+endfunction
+function H=%s_f_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],[H1;H2.H],[zeros(H1.num);H2.iodelay])
+endfunction
+
+//matrix product overloading functions
+function H=%rd_m_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D1=H1.iodelay
+ D2=H2.iodelay
+ D=D1*D2;
+ for k=1;size(D2,2)
+ for l=1:size(D1,1)
+ d=D1(l,:)+(D2(:,k)')
+ if or(d(1)<>d) then error('Delays mismatched'),end
+ D(l,k)=d
+ end
+ end
+ H=mlist(['rd','H','iodelay'],H1.H*H2.H,D)
+endfunction
+function H=%rd_m_r(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D1=H1.iodelay
+ for l=1:size(D1,1)
+ if or(D1(l,1)<>D1(l,:)) then error('Delays mismatched'),end
+ end
+ H=mlist(['rd','','iodelay'],H1.H*H2,D1)
+endfunction
+function H=%rd_m_s(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D1=H1.iodelay
+ for l=1:size(D1,1)
+ if or(D1(l,1)<>D1(l,:)) then error('Delays mismatched'),end
+ end
+ H=mlist(['rd','H','iodelay'],H1.H*H2,D1)
+endfunction
+function H=%r_m_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D2=H2.iodelay
+ for l=1:size(D2,2)
+ if or(D2(1,l)<>D2(:,l)) then error('Delays mismatched'),end
+ end
+ H=mlist(['rd','H','iodelay'],H1*H2.H,D2)
+endfunction
+function H=%s_m_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D2=H2.iodelay
+ for l=1:size(D2,2)
+ if or(D2(1,l)<>D2(:,l)) then error('Delays mismatched'),end
+ end
+ H=mlist(['rd','H','iodelay'],H1*H2.H,D2)
+endfunction
+
+//Addition overloading functions
+function H=%rd_a_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D1=H1.iodelay
+ D2=H2.iodelay
+ if or(D1<>D2) then error('Delay mismatch'),end
+ H=mlist(['rd','H','iodelay'],H1.H+H2.H,D1)
+endfunction
+function H=%rd_a_r(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D1=H1.iodelay
+ if or(D1<>0) then error('Delay mismatch'),end
+ H=mlist(['rd','H','iodelay'],H1.H+H2,D1)
+endfunction
+function H=%rd_a_s(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D1=H1.iodelay
+ if or(D1<>0) then error('Delay mismatch'),end
+ H=mlist(['rd','H','iodelay'],H1.H+H2,D1)
+endfunction
+function H=%r_a_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D2=H2.iodelay
+ if or(D2<>0) then error('Delay mismatch'),end
+ H=mlist(['rd','H','iodelay'],H1+H2.H,D2)
+endfunction
+
+//Substraction overloading functions
+function H=%rd_a_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D1=H1.iodelay
+ D2=H2.iodelay
+ if or(D1<>D2) then error('Delay mismatch'),end
+ H=mlist(['rd','H','iodelay'],H1.H-H2.H,D1)
+endfunction
+function H=%rd_a_r(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D1=H1.iodelay
+ if or(D1<>0) then error('Delay mismatch'),end
+ H=mlist(['rd','H','iodelay'],H1.H-H2,D1)
+endfunction
+function H=%rd_a_s(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D1=H1.iodelay
+ if or(D1<>0) then error('Delay mismatch'),end
+ H=mlist(['rd','H','iodelay'],H1.H-H2,D1)
+endfunction
+function H=%r_a_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D2=H2.iodelay
+ if or(D2<>0) then error('Delay mismatch'),end
+ H=mlist(['rd','H','iodelay'],H1-H2.H,D2)
+endfunction
+
+//extraction overloading functions
+function H=%rd_e(varargin)
+// Author: Serge Steer, Copyright INRIA
+ H=varargin($)
+ Hh= H.H;Hh.num=Hh.num(varargin(1:$-1));Hh.den=Hh.den(varargin(1:$-1));
+ H.H=Hh
+ H.iodelay=H.iodelay(varargin(1:$-1))
+endfunction
+
+//insertion overloading functions
+function H=%rd_i_rd(varargin)
+// Author: Serge Steer, Copyright INRIA
+ H=varargin($)
+ Hfrom=varargin($-1)
+
+ Hh= H.H
+ Hh.num(varargin(1:$-2))=Hfrom.H.num
+ Hh.den(varargin(1:$-2))=Hfrom.H.den
+ H.H=Hh
+ H.iodelay(varargin(1:$-2))=Hfrom.iodelay
+endfunction
+function H=%r_i_rd(varargin)
+// Author: Serge Steer, Copyright INRIA
+ H=varargin($)
+ Hfrom=varargin($-1)
+
+ Hh= H.H
+ Hh.num(varargin(1:$-2))=Hfrom.num
+ Hh.den(varargin(1:$-2))=Hfrom.den
+ H.H=Hh
+ H.iodelay(varargin(1:$-2))=zeros(Hfrom.num)
+endfunction
+function H=%s_i_rd(varargin)
+// Author: Serge Steer, Copyright INRIA
+ H=varargin($)
+ Hfrom=varargin($-1)
+
+ Hh= H.H
+ Hh.num(varargin(1:$-2))=Hfrom
+ Hh.den(varargin(1:$-2))=ones(Hfrom)
+ H.H=Hh
+ H.iodelay(varargin(1:$-2))=zeros(Hfrom)
+endfunction
+function H=%rd_i_r(varargin)
+// Author: Serge Steer, Copyright INRIA
+ Hh=varargin($)
+ Hfrom=varargin($-1)
+ Hh.num(varargin(1:$-2))=Hfrom.H.num
+ Hh.den(varargin(1:$-2))=Hfrom.H.den
+ D=zeros(Hh.num)
+ D(varargin(1:$-2))=Hfrom.iodelay
+ H=mlist(['rd','H','iodelay'],Hh,D)
+endfunction
+function H=%rd_i_s(varargin)
+// Author: Serge Steer, Copyright INRIA
+ num=varargin($);den=ones(num)
+ Hfrom=varargin($-1)
+
+ num(varargin(1:$-2))=Hfrom.H.num
+ den(varargin(1:$-2))=Hfrom.H.den
+ D=zeros(num)
+ D(varargin(1:$-2))=Hfrom.iodelay
+ H=mlist(['rd','H','iodelay'],rlist(num,den,'c'),D)
+endfunction
+
+//transpostion overloading function
+function H=%rd_t(H)
+// Author: Serge Steer, Copyright INRIA
+ H.H=H.H'
+ H.iodelay=H.iodelay'
+endfunction
+
+//string overloading function
+function txt=%rd_string(H)
+// Author: Serge Steer, Copyright INRIA
+ r=H.H
+ N=string(r.num)
+ D=string(r.den)
+ ln=max(matrix(length(N),2,-1),'r')
+ ld=max(matrix(length(D),2,-1),'r')
+ l=max(ln,ld)
+ [m,n]=size(r.num);
+ S=emptystr(m,n)
+
+ kz=find(H.iodelay==0);//zero delay entries
+ w='exp('+string(-H.iodelay)+'*s)*';w(kz)='';
+
+ for i=1:m*n
+ s=2*i-1:2*i
+ pw=part(' ',1:length(w(i)))
+ N(s)=pw+part(' ',1:(l(i)-ln(i))/2)+N(s)
+ D(s)=pw+part(' ',1:(l(i)-ld(i))/2)+D(s)
+ S(i) =w(i)+part('-',ones(1,l(i)))
+ end
+ txt=emptystr(5*m,n);
+ txt(1:5:$,:)=N(1:2:$,:)
+ txt(2:5:$,:)=N(2:2:$,:)
+ txt(3:5:$,:)=S(1:$,:)
+ txt(4:5:$,:)=D(1:2:$,:)
+ txt(5:5:$,:)=D(2:2:$,:)
+endfunction
+
+
+//Display overloading function
+function %rd_p(H)
+// Author: Serge Steer, Copyright INRIA
+//used to display rational fraction with complex coefficients
+//The real case is hard coded
+// Copyright INRIA
+ T=string(H)
+ l=max(length(T),'r')
+ Te=emptystr(size(T,1),1)
+ for k=1:size(T,2)
+ Te=Te+part(T(:,k),1:l(k)+1)+' '
+ end
+ mprintf("%s\n",Te)
+endfunction
+
+
+//frequency response computation overloading
+function [frq,repf,splitf]=repfreq(varargin)
+// Author: Serge Steer, Copyright INRIA
+ H=varargin(1)
+ autolib.repfreq
+ if typeof(H)=='rd' then
+ D=H.iodelay
+ varargin(1)=H.H
+ [frq,repf,splitf]=repfreq(varargin(:))
+
+ w=-2*%i*%pi*frq;
+ for k=1:size(D,'*')
+ repf(k,:)=repf(k,:).*exp(D(k)*w)
+ end
+ else
+ [frq,repf,splitf]=repfreq(varargin(:))
+ end
+endfunction
+
+//bode plot computation overloading
+function bode(varargin)
+// Author: Serge Steer, Copyright INRIA
+ H=varargin(1)
+ xdesslib.bode
+ if typeof(H)=='rd' then
+ if type(varargin($))==10 then //a comment
+ cm=varargin($);varagin($)=null()
+ else
+ cm=''
+ end
+ D=H.iodelay
+ varargin(1)=H.H
+ [frq,repf,splitf]=repfreq(varargin(1:$))
+ w=-2*%i*%pi*frq;
+ for k=1:size(D,'*')
+ repf(k,:)=repf(k,:).*exp(D(k)*w)
+ end
+ bode(frq,repf)
+ else
+ bode(varargin(:))
+ end
+endfunction
+
+//nyquist plot computation overloading
+function nyquist(varargin)
+// Author: Serge Steer, Copyright INRIA
+ H=varargin(1)
+ xdesslib.nyquist
+ if typeof(H)=='rd' then
+ if type(varargin($))==10 then //a comment
+ cm=varargin($);varagin($)=null()
+ else
+ cm=''
+ end
+ D=H.iodelay
+ varargin(1)=H.H
+ [frq,repf,splitf]=repfreq(varargin(1:$))
+ w=-2*%i*%pi*frq;
+ for k=1:size(D,'*')
+ repf(k,:)=repf(k,:).*exp(D(k)*w)
+ end
+ nyquist(frq,repf)
+ else
+ nyquist(varargin(:))
+ end
+endfunction
+
diff --git a/2048/DEPENDENCIES/l2r.sci b/2048/DEPENDENCIES/l2r.sci new file mode 100755 index 000000000..26e61e0c8 --- /dev/null +++ b/2048/DEPENDENCIES/l2r.sci @@ -0,0 +1,13 @@ +// function [Rnum,Rnumdeg,Rden,Rdendeg] = l2r(N,degN,D,degD)
+// given Numerator and Denominator polynomial matrices in left form,
+// not necessarily coprime, finds right coprime factorisation.
+
+function [Rnum,Rnumdeg,Rden,Rdendeg] = l2r(N,degN,D,degD)
+
+[N,degN] = transp(N,degN);
+[D,degD] = transp(D,degD);
+
+[Rnum,Rnumdeg,Rden,Rdendeg] = left_prm(N,degN,D,degD);
+[Rnum,Rnumdeg] = transp(Rnum,Rnumdeg);
+[Rden,Rdendeg] = transp(Rden,Rdendeg);
+endfunction;
diff --git a/2048/DEPENDENCIES/label.sci b/2048/DEPENDENCIES/label.sci new file mode 100755 index 000000000..fd7639958 --- /dev/null +++ b/2048/DEPENDENCIES/label.sci @@ -0,0 +1,23 @@ +// Updated (9-12-06)
+// Input arguments:title, xlabel, ylabel and their font sizes
+
+function label(tname,tfont,labelx,labely,xyfont)
+a = get("current_axes")
+xtitle(tname,labelx,labely)
+xgrid
+t = a.title;
+t.font_size = tfont; //Title font size
+t.font_style = 2; //Title font style
+t.text = tname;
+
+u = a.x_label;
+u.font_size = xyfont; //Label font size
+u.font_style = 2; //Label font style
+
+v = a.y_label;
+v.font_size = xyfont; //Label font size
+v.font_style = 2; //Label font style
+
+// a.label_font_size = 3;
+
+endfunction;
diff --git a/2048/DEPENDENCIES/left_prm.sci b/2048/DEPENDENCIES/left_prm.sci new file mode 100755 index 000000000..cd0ffcbf7 --- /dev/null +++ b/2048/DEPENDENCIES/left_prm.sci @@ -0,0 +1,89 @@ +// function [B,degB,A,degA,Y,degY,X,degX] = ...
+// left_prm(N,degN,D,degD,job,gap)
+//
+// does three different things according to integers that 'job' takes
+// job = 1.
+// this is the default. It is always done for all jobs.
+// -1 -1 -1
+// Given ND , returns coprime B and A where ND = A B
+// It is enough if one sends the first four input arguments
+// If gap is required to be sent, then one can send either 1 or a null
+// entry for job
+// job = 2.
+// first solve for job = 1 and then solve XA + YB = I
+// job = 3.
+// used in solving XD + YN = C
+// after finding coprime factorization, data are returned
+//
+// convention: the variable with prefix deg stand for degrees
+// of the corresponding polynomial matrices
+//
+// input:
+// N: right fraction numerator polynomial matrix
+// D: right fraction denominator polynomial matrix
+// N and D are not neccessarily coprime
+// gap: variable used to zero entries; default value is 1.0e+8
+//
+// output
+// b and A are left coprime num. and den. polynomial matrices
+// X and Y are solutions to Aryabhatta identity, only for job = 2
+
+function [B,degB,A,degA,Y,degY,X,degX] = left_prm(N,degN,D,degD,job,gap)
+if argn(2) == 4 | argn(2) == 5
+ gap = 1.0e8 ;
+end
+// pause
+if argn(2) == 4,
+job = 1; end
+[F,degF] = rowjoin(D,degD,N,degN);
+[Frows,Fbcols] = polsize(F,degF); // Fbcols = block columns
+Fcols = Fbcols * (degF+1) ; // actual columns of F
+T1 = [];pr =[];degT1 = 0; T1rows = 0;shft = 0;
+S=F; sel = ones(Frows,1); T1bcols =1;
+abar = (Fbcols + 1):Frows; // a_super_bar of B-C.Chang
+while isempty(T1) | T1rows < Frows - Fbcols
+ Srows = Frows*T1bcols; // max actual columns of result
+ [T1,T1rows,sel,pr] = ...
+ t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap);
+ [T1rows,T1cols] = size(T1);
+ if T1rows < Frows - Fbcols
+ T1 = [T1 zeros(T1rows,Frows)];
+ T1bcols = T1bcols + 1; // max. block columns of result
+ degT1 = degT1 + 1; // degree of result
+ shft = shft +Fbcols;
+ S = seshft(S,F,shft);
+ sel = [sel;sel(Srows-Frows+1:Srows)];
+ rowvec = (T1bcols-1)*Frows+(Fbcols+1):T1bcols * Frows;
+ abar = [abar rowvec]; // A_super_bar of B-C.chang
+ end
+end
+
+[B,degB,A,degA] = colsplit(T1,degT1,Fbcols,Frows-Fbcols);
+[B,degB] = clcoef(B,degB);
+B = -B;
+[A,degA] = clcoef(A,degA);
+// pause
+if job == 2
+ S = S(mtlb_logical(sel),:); // columns
+ [redSrows,Scols] = size(S);
+ C = [eye(Fbcols,Fbcols) zeros(Fbcols,Scols-Fbcols)]; // append with zeros
+ T2 = C/S;
+ T2 = makezero(T2,gap);
+ T2 = move_sci(T2,find(sel),Srows);
+ [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows - Fbcols);
+ [X,degX] = clcoef(X,degX);
+ [Y,degY] = clcoef(Y,degY);
+elseif job == 3
+ Y = S;
+ degY = sel;
+ X = degT1;
+ degX = Fbcols;
+else
+ if job ~= 1
+ error('Message from left_prm:no legal job number specified')
+ end
+end
+endfunction
+
+
+
diff --git a/2048/DEPENDENCIES/makezero.sci b/2048/DEPENDENCIES/makezero.sci new file mode 100755 index 000000000..82644a6ba --- /dev/null +++ b/2048/DEPENDENCIES/makezero.sci @@ -0,0 +1,19 @@ +// function B = makezero(B,gap)
+// where B is a vector and gap acts as a tolerance
+
+function B = makezero(B,gap)
+
+if argn(2) == 1
+ gap = 1.0e8;
+end
+temp = B(find(B)); // non zero entries of B
+temp = -gsort(-abs(temp),'g','d'); // absolute values sorted in descending order
+len = length(temp);
+ratio = temp(1:len-1) ./temp(2:len); // each ratio >1
+min_ind = min(find(ratio>gap));
+if ~isempty(min_ind)
+ our_eps = temp(min_ind+1);
+ zeroind = find(abs(B)<=our_eps);
+ B(zeroind) = zeros(1,length(zeroind));
+end
+endfunction
diff --git a/2048/DEPENDENCIES/move_sci.sci b/2048/DEPENDENCIES/move_sci.sci new file mode 100755 index 000000000..6bd822942 --- /dev/null +++ b/2048/DEPENDENCIES/move_sci.sci @@ -0,0 +1,13 @@ +// function result = move_sci(b,nonred,max_sci)
+// Moves matrix b to matrix result with the information on where to move,
+// decided by the indices of nonred.
+// The matrix result will have as many rows as b has and max number of columns.
+// b is augumented with zeros to have nonred number of columns;
+// The columns of b put into those of result as decided by nonred.
+
+function result = move_sci(b,nonred,max_sci)
+[brows,bcols] = size(b);
+b = [b zeros(brows,length(nonred)-bcols)];
+result = zeros(brows,max_sci);
+result(:,nonred') = b;
+endfunction
diff --git a/2048/DEPENDENCIES/oe.sci b/2048/DEPENDENCIES/oe.sci new file mode 100755 index 000000000..767bd39d0 --- /dev/null +++ b/2048/DEPENDENCIES/oe.sci @@ -0,0 +1,146 @@ +
+// OE Model parameter estimation
+
+///////////////////////////////////////
+/////////// ARX Model /////////////////
+
+
+function [thetaN_arx,covt_arx,nvar,res] = arxc(data,na,nb,nk)
+az = max(na,nb+nk-1);
+zer = zeros(az,1);
+zd = data;
+// Zeros appended
+zd1(:,1) = [zer; zd(:,1)];
+zd1(:,2) = [zer; zd(:,2)];
+[r,c] = size(zd1);
+t = az+1:r;
+yt = zd1(:,1); ut = zd1(:,2);
+yt1 = yt'; ut1 = ut'; // row vector
+len1 = length(yt1);
+yt2 = zeros(1,len1-az); ut2 = zeros(1,len1-az);
+
+// arx(Data,[na nb nk])
+ for i=1:na
+ yt2 = [yt2; -yt1(t-i)];
+ end;
+ for i=nk:nb+nk-1
+ ut2 = [ut2; ut1(t-i)];
+ end;
+[r1,c1] = size(yt2); [r2,c2] = size(ut2);
+phit = [yt2(2:r1,:); ut2(2:r2,:)];
+m1 = phit*phit';
+[qm,rm] = qr(m1);
+m2 = phit*zd(:,1);
+thetaN_arx = inv(rm)*qm'*m2;
+// thetaN_arx = inv(m1)*m2;
+// thetaN_arx = m1\m2;
+
+[r11,c11] = size(thetaN_arx);
+a = thetaN_arx(1:na); b = thetaN_arx(na+1:r11);
+
+// Sum of squared residuals
+
+yhat = phit'*thetaN_arx;
+res = zd(:,1) - yhat;
+N = length(res);
+q = rank(phit);
+ssr = res'*res;
+sig2 = ssr/(N-q);
+nvar = sqrt(sig2);
+cov_arx = inv(m1);
+covt_arx = diag(cov_arx);
+endfunction;
+///////////////////////////////
+//////////////////////////////
+
+///////////////////////////////////////
+////////// Model Display /////////////
+
+function disp_mod(N1,covN1)
+len = length(covN1);
+B1 = pol2str(N1);
+ind = strindex(B1,['+','-']);
+ind = ind - 1;
+B2 = strsplit(B1,ind);
+covB = string(covN1);
+
+ if ascii(B2(1)) == 32
+ B2 = B2(2:len+1);
+ end;
+
+ B3(1) = ' ';
+ for i=1:len
+ B3(i) = strsubst(B2(i),'*x','(+-' + covB(i) + ')*x');
+ end;
+
+ B4 = B3(1);
+
+ for i=2:len
+ B4 = B4 + ' ' + B3(i);
+ end;
+
+disp(B4);
+endfunction;
+///////////////////////////////////////
+///////////////////////////////////////
+
+function [thetaN_oe,covN_oe,nvar,resid] = oe(zd,nb,nf,nk)
+
+[thetaN,covfN,nvar,res] = arxc(zd,nf,nb,nk);
+[r1,c1] = size(thetaN);
+yt = zd(:,1);
+m=50;
+ if nf==0
+ thetaN_oe = thetaN;
+ covN_oe = covfN;
+ else
+ for k=1:m
+ a = thetaN(1:nf);
+ b = thetaN(nf+1:r1);
+ A = [1 a']; // Filter
+ y = yt(1:length(u))';
+ yf = deconvol(y,A);
+ uf = deconvol(u,A);
+ zf = [yf(1:length(uf))' uf'];
+ zdf = detrend(zf,'constant');
+ [thetaNf,covf_a,nvar,resid] = arxc(zdf,nf,nb,nk)
+ thetaN = thetaNf;
+ a1 = thetaN(1:nf);
+ b = (norm(a-a1))/norm(a1);
+ if b<0.005
+ break;
+ end;
+ end;
+ thetaN_oe = thetaN;
+ covN_oe = covf_a;
+ end;
+[rt,ct] = size(thetaN_oe);
+f_oe = [1 thetaN_oe(1:nf)']; b1 = zeros(1,nk);
+b_oe = [b1 thetaN_oe(nf+1:rt)'];
+cov_f = covN_oe(1:nf); cov_b = covN_oe(nf+1:rt);
+
+x = poly(0,'x');
+ if nf ==0
+ disp('Discrete time model: y(t) = B(x)u(t) + e(t)');
+ else
+ disp('Discrete time model: y(t) = [B(x)/F(x)]u(t) + e(t)');
+ end;
+
+F = poly(f_oe,'x','coeff');
+cov_f1 = [0 cov_f'];
+B = poly( b_oe,'x','coeff');
+cov_b1 = cov_b';
+
+ if nb==0
+ error('All B parameters are zero');
+ else
+ disp('B(x) = ');
+ disp_mod(B,cov_b);
+ end;
+
+ if nf~=0
+ disp('F(x) = ');
+ disp_mod(F,cov_f1);
+ end;
+endfunction;
+
diff --git a/2048/DEPENDENCIES/plotacf.sci b/2048/DEPENDENCIES/plotacf.sci new file mode 100755 index 000000000..a36f8caff --- /dev/null +++ b/2048/DEPENDENCIES/plotacf.sci @@ -0,0 +1,39 @@ +// Procedure to plot the ACF, as discussed in Sec. 6.4.3. An example usage is given in 6.5.
+// 6.6
+
+// PLOTACF: Plots normalized autocorrelation function
+//
+// USAGE:: [acf]=plotacf(x,errlim,len,print_code)
+//
+// WHERE:: acf = autocorrelation values
+// x = time series data
+// errlim > 0; error limit = 2/sqrt(data_len)
+// len = length of acf that need to to be plotted
+// NOTE: if len=0 then len=data_length/2;
+// print_code = 0 ==> does not plot OR ELSE plots
+//
+// Pranob Banerjee
+
+function [x]=plotacf(y,errlim,len,code)
+exec('normacf.sci',-1);
+exec('label.sci',-1)
+x = normacf(y);
+l = length(y);
+
+r=l:2*(l-1); lim=2/sqrt(l); rl=1:length(r) ;
+N=length(rl); x=x(r);
+if len>0 & len<N, rl=1:len; x=x(rl); N=len; end;
+if(code > 0 )
+ if(errlim > 0 )
+ rl=rl-1;
+ plot(rl,x,rl,x,'o' , rl,lim*ones(N,1),'--', ...
+ rl,-lim*ones(N,1),'--')
+ xgrid
+ else
+ plot(rl,x)
+ end
+end;
+a = gca();
+a.data_bounds = [0 min(min(x),-lim-0.1); len-1 1.1];
+label(' ',4,'Lag','ACF',4)
+endfunction;
diff --git a/2048/DEPENDENCIES/pol2cart.sci b/2048/DEPENDENCIES/pol2cart.sci new file mode 100755 index 000000000..b12dbc32e --- /dev/null +++ b/2048/DEPENDENCIES/pol2cart.sci @@ -0,0 +1,6 @@ +// Polar to cartesian co ordinate conversion
+
+function [x,y] = pol2cart(theta,r)
+x = r*cos(theta);
+y = r*sin(theta);
+endfunction;
diff --git a/2048/DEPENDENCIES/poladd.sci b/2048/DEPENDENCIES/poladd.sci new file mode 100755 index 000000000..79fcdabed --- /dev/null +++ b/2048/DEPENDENCIES/poladd.sci @@ -0,0 +1,16 @@ +function [C,degC] = poladd(A,degA,B,degB)
+[rA,cA] = polsize(A,degA);
+[rB,cB] = polsize(B,degB);
+if cA ~= cB | rA ~= rB
+ error('poladd: Inconsistent dimensions');
+end
+
+degC = max(degA,degB);
+if degC >= degA
+ A = [A zeros(rA,(degC-degA)*cA)];
+end
+if degC >= degB
+ B = [B zeros(rB,(degC-degB)*cB)];
+end
+C = A+B;
+endfunction;
diff --git a/2048/DEPENDENCIES/polmul.sci b/2048/DEPENDENCIES/polmul.sci new file mode 100755 index 000000000..67e4adb9a --- /dev/null +++ b/2048/DEPENDENCIES/polmul.sci @@ -0,0 +1,34 @@ +// polmul
+// The command
+// [C,degA] = polmul(A,degA,B,degB)
+// produces the polynomial matrix C that equals the product A*B of the
+// polynomial matrices A and B.
+//
+// H. Kwakernaak, July, 1990
+
+
+function [C,degC] = polmul(A,degA,B,degB)
+[rA,cA] = polsize(A,degA);
+[rB,cB] = polsize(B,degB);
+if cA ~= rB
+ error('polmul: Inconsistent dimensions of input matrices');
+end
+
+degC = degA+degB;
+C = [];
+for k = 0:degA+degB
+ mi = 0;
+ if k-degB > mi
+ mi = k-degB;
+ end
+ ma = degA;
+ if k < ma
+ ma = k;
+ end
+ Ck = zeros(rA,cB);
+ for i = mi:ma
+ Ck = Ck + A(:,i*cA+1:(i+1)*cA)*B(:,(k-i)*cB+1:(k-i+1)*cB);
+ end
+ C = [C Ck];
+end
+endfunction
diff --git a/2048/DEPENDENCIES/polsize.sci b/2048/DEPENDENCIES/polsize.sci new file mode 100755 index 000000000..7c0c8a463 --- /dev/null +++ b/2048/DEPENDENCIES/polsize.sci @@ -0,0 +1,15 @@ +// function [rQ,cQ] = polsize(Q,degQ)
+// FUNCTION polsize TO DETERMINE THE DIMENSIONS
+// OF A POLYNOMIAL MATRIX
+//
+// H. Kwakernaak, August, 1990
+
+function [rQ,cQ] = polsize(Q,degQ)
+
+[rQ,cQ] = size(Q); cQ = cQ/(degQ+1);
+if abs(round(cQ)-cQ) > 1e-6
+ error('polsize: Degree of input inconsistent with number of columns');
+else
+ cQ = round(cQ);
+end
+endfunction
diff --git a/2048/DEPENDENCIES/polyno.sci b/2048/DEPENDENCIES/polyno.sci new file mode 100755 index 000000000..e54960cdb --- /dev/null +++ b/2048/DEPENDENCIES/polyno.sci @@ -0,0 +1,30 @@ +// Updated(1-8-07)
+// Operations:
+// Polynomial definition
+// Flipping of coefficients
+// Variables ------- passed as input argument (either 's' or 'z')
+// Both num and den are used mostly used in scicos files,
+// to get rid of negative powers of z
+
+// Polynomials with powers of s need to
+// be flipped only
+
+function [polynu,polyde] = polyno(zc,a)
+zc = clean(zc);
+polynu = poly(zc(length(zc):-1:1),a,'coeff');
+ if a == 'z'
+ polyde = %z^(length(zc) - 1);
+ else
+ polyde = 1;
+ end
+
+// Scicos(4.1) Filter block shouldn't have constant/constant
+ if type(polynu)==1 & type(polyde)==1
+ if a == 'z'
+ polynu = %z; polyde = %z;
+ else
+ polynu = %s; polyde = %s;
+ end;
+ end;
+
+endfunction
diff --git a/2048/DEPENDENCIES/putin.sci b/2048/DEPENDENCIES/putin.sci new file mode 100755 index 000000000..706898856 --- /dev/null +++ b/2048/DEPENDENCIES/putin.sci @@ -0,0 +1,22 @@ +// function [A,degA] = putin(A,degA,B,degB,i,j)
+// PUTS IN THE POLYNOMIAL B INTO THE MATRIX A AT (i,j)TH POSITION
+// Modified by Kannan Moudgalya on 8 November 1992
+
+function [A,degA] = putin(A,degA,B,degB,i,j)
+
+[rA,cA] = polsize(A,degA);
+if degB > degA
+ A = [A zeros(rA,(degB-degA)*cA)];
+ degA = degB;
+end
+
+for k = 0:degB
+ A(i,(k*cA)+j) = B(1,k+1);
+end
+if degA > degB
+ for k = degB+1:degA
+ A(i,(k*cA)+j) = 0;
+ end
+ [A,degA] = clcoef(A,degA);
+end
+endfunction;
diff --git a/2048/DEPENDENCIES/respol.sci b/2048/DEPENDENCIES/respol.sci new file mode 100755 index 000000000..c62c7e05e --- /dev/null +++ b/2048/DEPENDENCIES/respol.sci @@ -0,0 +1,112 @@ +// Computation of residues
+// 4.5
+// Numerator and denominator coefficients
+// are passed in decreasing powers of z(say)
+
+function [res,pol,q] = respol(num,den)
+len = length(num);
+if num(len) == 0
+ num = num(1:len-1);
+end
+
+[resi,q] = pfe(num,den);
+res = resi(:,2);
+res = int(res) + (clean(res - int(res),1.d-04));
+pol = resi(:,1);
+pol = int(pol) + (clean(pol - int(pol),1.d-04));
+endfunction;
+
+///////////////////////////////////////////////////
+// Partial fraction expansion
+
+function [resid1,q] = pfe(num,den)
+x = poly(0,'x');
+s = %s;
+
+exec flip.sci;
+
+num2 = flip(num);
+den2 = flip(den);
+num = poly(num2,'s','coeff');
+den = poly(den2,'s','coeff');
+[fac,g] = factors(den);
+polf = polfact(den);
+n = 1;
+
+r = clean(real(roots(den)),1.d-5);
+//disp(r);
+l = length(r);
+r = gsort(r,'g','i');
+r = [r; 0];
+j = 1;
+t1 = 1; q = [];
+rr = 0;
+rr1 = [0 0];
+m = 1;
+
+ for i = j:l
+ if abs(r(i)- r(i+1)) < 0.01 then
+ r(i);
+ r(i+1);
+ n = n+1;
+ m = n;
+ //pause
+ t1 = i;
+ //disp('Repeated roots')
+ else
+ m = n;
+ //pause
+ n = 1;
+ end
+ i;
+ if n == 1 then
+ rr1 = [rr1; r(i) m];
+ //pause
+ end;
+ j = t1 + 1;
+ end;
+rr2 = rr1(2:$,:);
+[r1,c1] = size(rr2);
+den1 = 1;
+
+for i = 1:r1
+ den1 = den1 * ((s-rr2(i,1))^(rr2(i,2)));
+end;
+[rem,quo] = pdiv(num,den);
+q = quo;
+if quo ~= 0
+ num = rem;
+end
+
+tf = num/den1;
+res1 = 0;
+res3 = [s 0];
+res5 = [0 0];
+for i = 1:r1
+ j = rr2(i,2) + 1;
+ tf1 = tf; //strictly proper
+ k = rr2(i,2);
+ tf2 = ((s-rr2(i,1))^k)*tf1;
+ rr2(i,1);
+ res1 = horner(tf2,rr2(i,1));
+ res2 = [(s - rr2(i,1))^(rr2(i,2)) res1];
+ res4 = [rr2(i,1) res1];
+ res3 = [res3; res2];
+ res5 = [res5; res4];
+ res = res1;
+ for m = 2:j-1
+ k;
+ rr2(i,1);
+ tf1 = derivat(tf2)/factorial(m-1); //ith derivative
+ res = horner(tf1,rr2(i,1));
+ res2 = [(s - rr2(i,1))^(j-m) res];
+ res4 = [rr2(i,1) res];
+ res5 = [res5; res4];
+ res3 = [res3; res2];
+ tf2 = tf1;
+ end;
+end;
+resid = res3(2:$,:); //with s terms
+resid1 = res5(2:$,:); //only poles(in decreasing no. of repetitions)
+endfunction;
+////////////////////////////////////////////////////////////
diff --git a/2048/DEPENDENCIES/rowjoin.sci b/2048/DEPENDENCIES/rowjoin.sci new file mode 100755 index 000000000..c305183cf --- /dev/null +++ b/2048/DEPENDENCIES/rowjoin.sci @@ -0,0 +1,31 @@ +// function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+// MATLAB FUNCTION rowjoin TO SUPERPOSE TWO POLYNOMIAL
+// MATRICES
+
+// H. Kwakernaak, July, 1990
+
+function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+[rP1,cP1] = polsize(P1,degP1);
+[rP2,cP2] = polsize(P2,degP2);
+if cP1 ~= cP2
+ error('rowjoin: Inconsistent numbers of columns');
+end
+
+rP = rP1+rP2; cP = cP1;
+if degP1 >= degP2
+ degP = degP1;
+else
+ degP = degP2;
+end
+
+if isempty(P1)
+ P = P2;
+elseif isempty(P2)
+ P = P1;
+else
+ P = zeros(rP,(degP+1)*cP);
+ P(1:rP1,1:(degP1+1)*cP1) = P1;
+ P(rP1+1:rP,1:(degP2+1)*cP2) = P2;
+end
+endfunction
diff --git a/2048/DEPENDENCIES/seshft.sci b/2048/DEPENDENCIES/seshft.sci new file mode 100755 index 000000000..e69cdf5b3 --- /dev/null +++ b/2048/DEPENDENCIES/seshft.sci @@ -0,0 +1,22 @@ +// function C = seshft(A,B,N)
+//given A and B matrices, returns C = [<-A-> 0
+// 0 <-B->] with B shifted east by N cols
+
+function C = seshft(A,B,N)
+[Arows,Acols] = size(A);
+[Brows,Bcols] = size(B);
+if N >= 0
+ B = [zeros(Brows,N) B];
+ Bcols = Bcols + N;
+elseif N < 0
+ A = [zeros(Arows,abs(N)) A];
+ Acols = Acols +abs(N);
+end
+ if Acols < Bcols
+ A = [A zeros(Arows,Bcols-Acols)];
+ elseif Acols > Bcols
+ B = [B zeros(Brows,Acols-Bcols)];
+ end
+ C = [A
+ B];
+endfunction
diff --git a/2048/DEPENDENCIES/stem.sci b/2048/DEPENDENCIES/stem.sci new file mode 100755 index 000000000..3042267fb --- /dev/null +++ b/2048/DEPENDENCIES/stem.sci @@ -0,0 +1,20 @@ +// Stem plot
+// Updated (1-12-06)
+function stem(x,y,xy)
+if argn(2) == 2
+xy = 5;
+end;
+set("figure_style","new")
+plot2d3(x,y,style=2);
+//plot2d4(x,y,style=-9); // default mark foreground colour: black
+// Can be used instead of xpoly
+// But default values cannot be changed
+xpoly(x,y,"marks");
+p=get("hdl");
+p.mark_size_unit = 'point';
+p.mark_size = xy;
+p.mark_style = 9;
+p.mark_foreground = 2;
+p.mark_background = 2;
+endfunction;
+
diff --git a/2048/DEPENDENCIES/t1calc.sci b/2048/DEPENDENCIES/t1calc.sci new file mode 100755 index 000000000..a9a265ba9 --- /dev/null +++ b/2048/DEPENDENCIES/t1calc.sci @@ -0,0 +1,35 @@ +// function [T1,T1rows,sel,pr] = ...
+// t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+// calculates the coefficient matrix T1
+// redundant row information is kept in sel: redundant rows are marked
+// with zeros. The undeleted rows are marked with ones.
+
+function [T1,T1rows,sel,pr] = t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+b = 1; // vector of primary red.rows
+
+while (T1rows < Frows - Fbcols) & or(sel==1) & ~isempty(b)
+ S = clean(S);
+ b = indep(S(mtlb_logical(sel),:),gap); // send selected rows of S
+ if ~isempty(b)
+ b = clean(b);
+ b = move_sci(b,find(sel),Srows);
+ j = length(b);
+ while ~(b(j) & or(abar==j)) // pick largest nonzero entry
+ j = j-1; // of coeff. belonging to abar
+ if ~j
+ fprintf('\nMessage from t1calc, called from left_prm\n\n')
+ error('Denominator is noninvertible')
+ end
+ end
+ if ~or(j<pr & pmodulo(pr,Frows) == pmodulo(j,Frows)) // pr(2),pr(1)
+ T1 = [T1; b]; // condition is not violated
+ T1rows = T1rows +1; // accept this vector
+ end // else don't accept
+ pr = [pr; j]; // update prime red row info
+ while j <= Srows
+ sel(j) = 0;
+ j = j + Frows;
+ end
+ end
+end
+endfunction
diff --git a/2048/DEPENDENCIES/tf.sci b/2048/DEPENDENCIES/tf.sci new file mode 100755 index 000000000..bba921d14 --- /dev/null +++ b/2048/DEPENDENCIES/tf.sci @@ -0,0 +1,33 @@ +//User defined function
+//Forms a transfer function
+//Scilab: Co efficients are given in increasing power of variable
+//Matlab: Co efficients are given in decreasing power of variable
+//Hence co efficients are flipped here
+
+//Input arguments: (1) Numerator co efficients(decreasing order)
+//(2) Denominator co efficients
+//(3) Variable to specify domain
+
+// Updated (30-11-06)
+// System is continuous => a is not passed
+// System is discrete => a = -1
+// System is discretized (sampled system) => a = Ts
+// Uses syslin
+
+function trfu = tf(num,den,a)
+ if argn(2) == 2
+ d = 'c';
+ elseif a == -1
+ d = 'd';
+ else
+ d = a
+ end;
+num = clean(num);
+den = clean(den);
+num1 = poly(num(length(num):-1:1),'x','coeff');
+den1 = poly(den(length(den):-1:1),'x','coeff');
+trfu = syslin(d,num1,den1);
+endfunction;
+
+
+
diff --git a/2048/DEPENDENCIES/transp.sci b/2048/DEPENDENCIES/transp.sci new file mode 100755 index 000000000..39854c9ce --- /dev/null +++ b/2048/DEPENDENCIES/transp.sci @@ -0,0 +1,17 @@ +// function [P,degP] = transp(Q,degQ)
+// MATLAB FUNCTION transp TO TRANSPOSE
+// A POLYNOMIAL MATRIX
+
+// H. Kwakernaak, July, 1990
+
+function [P,degP] = transp(Q,degQ)
+
+[rQ,cQ] = polsize(Q,degQ);
+
+rP = cQ; cP = rQ; degP = degQ;
+P = zeros(rP,(degP+1)*cP);
+for i = 1:degP+1
+ P(:,(i-1)*cP+1:i*cP) = Q(:,(i-1)*cQ+1:i*cQ)';
+end
+
+endfunction;
diff --git a/2048/DEPENDENCIES/xdync.sci b/2048/DEPENDENCIES/xdync.sci new file mode 100755 index 000000000..e082e587f --- /dev/null +++ b/2048/DEPENDENCIES/xdync.sci @@ -0,0 +1,37 @@ +// function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+// given coefficient matrix in T1, primary redundant row information sel,
+// solves XD + YN = C
+
+// calling order changed on 16 April 2005. Old order:
+// function [B,degB,A,degA,Y,degY,X,degX] = xdync(N,degN,D,degD,C,degC,gap)
+
+function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+if argn(2) == 6
+ gap = 1.0e+8;
+end
+
+[F,degF] = rowjoin(D,degD,N,degN);
+
+[Frows,Fbcols] = polsize(F,degF); //Fbcols = block columns
+
+[B,degB,A,degA,S,sel,degT1,Fbcols] = left_prm(N,degN,D,degD,3,gap);
+//if issoln(D,degD,C,degC,B,degB,A,degA)
+ [Crows,Ccols] = size(C);
+ [Srows,Scols] = size(S);
+ S = clean(S);
+ S = S(mtlb_logical(sel),:);
+ T2 =[];
+
+ for i = 1:Crows,
+ Saug = seshft(S,C(i,:),0);
+ b = cindep(Saug);
+ b = move_sci(b,find(sel),Srows);
+ T2 =[T2; b];
+ end
+
+ [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows-Fbcols);
+
+ [X,degX] = clcoef(X,degX);
+ [Y,degY] = clcoef(Y,degY);
+ Y = clean(Y); X = clean(X);
+endfunction
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