initial commit / add all books

55 files changed, 953 insertions, 0 deletions

diff --git a/29/CH12/EX12.1/exa12_1.sce b/29/CH12/EX12.1/exa12_1.sce
new file mode 100755
index 000000000..93f4c7aae
--- /dev/null
+++ b/29/CH12/EX12.1/exa12_1.sce
@@ -0,0 +1,19 @@
+//Caption:transfer_function

+// example 12.1

+//page 515

+// we are solving this problem from signal flow graph approach

+syms G H;

+// forward path denoted by P1,P2 and so on and loop by L1,L2 and so on 

+//path factor by D1,D2 and so on and graph determinant by D

+P1=1*G*1

+P2=1;

+L1=-G;

+L2=-G*H;

+L3=G*H;

+D1=1;

+D2=1;

+D=1-(L1+L2+L3);

+D=simple(D)

+Y=(P1*D1+P2*D2)/D;

+Y=simple(Y);

+disp(Y,"C(s)/R(s)=");
\ No newline at end of file
diff --git a/29/CH12/EX12.10/exa12_10.sce b/29/CH12/EX12.10/exa12_10.sce
new file mode 100755
index 000000000..740a10a74
--- /dev/null
+++ b/29/CH12/EX12.10/exa12_10.sce
@@ -0,0 +1,12 @@
+//Caption:determine_unit_step_response
+//example 12.10
+//page 524
+s=%s;
+syms t;
+CL=sym('1/((s+1)*(s^2+1))')
+disp(CL,"C(s)/R(s)=");
+//for unit step response R(s)=1/s; 
+d=CL*(1/s);
+a=s*d;
+c=ilaplace(d,s,t);
+disp(c,"c(t)=");
\ No newline at end of file
diff --git a/29/CH12/EX12.11/exa12_11.sce b/29/CH12/EX12.11/exa12_11.sce
new file mode 100755
index 000000000..80e747fc4
--- /dev/null
+++ b/29/CH12/EX12.11/exa12_11.sce
@@ -0,0 +1,19 @@
+//Caption:determine_unit_step_and_unit_impulse_response
+//example 12.11
+//page 524
+s=%s;
+syms t;
+G=sym('8/(s+1)');
+H=sym('(1/2*s)');
+CL=G/(1+G*H);
+disp(CL,"C(s)/R(s)=");
+//for unit step response R(s)=1/s; 
+d=CL*(1/s);
+disp(d,"C(s)=");
+c=ilaplace(d,s,t);
+disp(c,"unit step response,c(t)=");
+//for unit impulse response R(s)=1; 
+e=CL*(1);
+disp(e,"C(s)=");
+ct=ilaplace(e,s,t);
+disp(ct,"unit impulse response,c(t)=");
diff --git a/29/CH12/EX12.12/exa12_12.sce b/29/CH12/EX12.12/exa12_12.sce
new file mode 100755
index 000000000..d17a00c7c
--- /dev/null
+++ b/29/CH12/EX12.12/exa12_12.sce
@@ -0,0 +1,29 @@
+//caption:determine_Wn,Wd,zeta_and_steady_state_error

+//example 12_12

+//page 526

+s=%s;

+G=sym('20/(s*(s^2+6*s+6))');

+H=0.25;

+CL=G/(1+G*H);

+CL=simple(CL);

+disp(CL,"C(s)/R(s)=");

+printf("the char. eq is:")

+disp("s^2+s+1=0")

+Wn=sqrt(1)//natural_frequency

+//2*zeta*Wn=1

+zeta=1/(2*Wn);//damping ratio

+d=zeta*Wn;//damping_factor

+z=sqrt(1-zeta^2);

+Wd=Wn*z;//damped_frequency_of_oscillation

+Mp=exp((-zeta*%pi)/z)*100;//%_max.peak_overshoot

+ts=4/(zeta*Wn);//settling_time

+tp=%pi/(Wn*sqrt(1-zeta^2));//peak_time

+tu=2*%pi/(Wn*sqrt(1-zeta^2));//first under shoot

+ti=tu-tp;//time interval between max. and min. values

+disp(Wn,"natural_frequency=");

+disp(zeta,"damping ratio=");

+disp(Wd,"damped_frequency_of_oscillation=");

+disp(Mp,"%_max.peak_overshoot=");

+disp(ts,"settling_time=");

+disp(tp,"peak_time=");

+disp(ti,"time_interval_between_max_and_min_values=");
\ No newline at end of file
diff --git a/29/CH12/EX12.13/exa12_13.sce b/29/CH12/EX12.13/exa12_13.sce
new file mode 100755
index 000000000..fcbe01f99
--- /dev/null
+++ b/29/CH12/EX12.13/exa12_13.sce
@@ -0,0 +1,17 @@
+//caption:determine_Wn,Wd,zeta_and_steady_state_error

+//example 12_13

+//page 527

+syms Kp K Kd T 

+s=%s;

+//exec series.sce;

+//exec parallel.sce;

+a=(Kp+s*Kd)*K

+b=1/(s*(s*T+1))

+G=series(a,b)

+H=1;

+er=1/(1+G*H)

+disp(er,"E(s)/R(s)=");

+R=1/s^2

+E=R*er

+ess=limit(s*E,s,0)

+disp(ess,"steady state error,ess=")

diff --git a/29/CH12/EX12.15/exa12_15.sce b/29/CH12/EX12.15/exa12_15.sce
new file mode 100755
index 000000000..6af9c6d79
--- /dev/null
+++ b/29/CH12/EX12.15/exa12_15.sce
@@ -0,0 +1,25 @@
+//caption:stability_using_Routh-hurwitz_criterion

+//example 12.15

+//page 529

+s=%s;

+syms  K

+G=sym('K/(s*(s^2+s+1)*(s+5)');

+H=1;

+CH=(s*(s^2+s+1)*(s+5)+K)

+disp('=0',CH,"characterstics_eq,CH=")

+c0=coeffs(CH,'s',0);

+c1=coeffs(CH,'s',1);

+c2=coeffs(CH,'s',2);

+c3=coeffs(CH,'s',3);

+c4=coeffs(CH,'s',4);

+b=[c0 c1 c2 c3 c4 ]

+routh=[b([5,3,1]);b([4,2]),0]

+routh=[routh;-det(routh(1:2,1:2)/routh(2,1)),K,0]

+t=routh(2:3,1:2)

+routh=[routh;-det(t)/t(2,1),0,0]

+routh=[routh;K,0,0]

+disp(routh,"routh=")

+disp("for given system to be stable:");

+disp("((5.1*5-6*K)/5.1)>0 and K>0");

+disp("which gives:");

+disp("0<K<4.25");

diff --git a/29/CH12/EX12.16/exa12_16.sce b/29/CH12/EX12.16/exa12_16.sce
new file mode 100755
index 000000000..969f0a12c
--- /dev/null
+++ b/29/CH12/EX12.16/exa12_16.sce
@@ -0,0 +1,25 @@
+//caption:stability_using_Routh-hurwitz_criterion

+//example 12.16

+//page 530

+s=%s;

+syms  K

+CH=s^4+2*s^3+10*s^2+(K-10)*s+K

+disp('=0',CH,"characterstics_eq,CH=")

+c0=coeffs(CH,'s',0);

+c1=coeffs(CH,'s',1);

+c2=coeffs(CH,'s',2);

+c3=coeffs(CH,'s',3);

+c4=coeffs(CH,'s',4);

+b=[c0 c1 c2 c3 c4 ]

+routh=[b([5,3,1]);b([4,2]),0]

+routh=[routh;-det(routh(1:2,1:2)/routh(2,1)),K,0]

+routh(3,1)=simple(routh(3,1))

+t=routh(2:3,1:2)

+l=simple(-det(t)/t(2,1))

+routh=[routh;l,0,0]

+//routh=[routh;K,0,0]

+disp(routh,"routh=")

+disp("for given system to be stable,following condition should be satisfied");

+disp("K<30,K<22.9 and K>13.1,K>0")

+disp("which gives,")

+disp("13.1<K<22.9");

diff --git a/29/CH12/EX12.17/exa12_17.sce b/29/CH12/EX12.17/exa12_17.sce
new file mode 100755
index 000000000..7e9cd520d
--- /dev/null
+++ b/29/CH12/EX12.17/exa12_17.sce
@@ -0,0 +1,27 @@
+//caption:stability_using_Routh-hurwitz_criterion

+//example 12.17

+//page 530

+s=%s;

+syms  K

+G=sym('K/((s^3+3*s+2)*(s^2+6*s+24))');

+H=1;

+CH=((s^3+3*s+2)*(s^2+6*s+24)+K)

+disp('=0',CH,"characterstics_eq,CH=")

+c0=coeffs(CH,'s',0);

+c1=coeffs(CH,'s',1);

+c2=coeffs(CH,'s',2);

+c3=coeffs(CH,'s',3);

+c4=coeffs(CH,'s',4);

+b=[c0 c1 c2 c3 c4 ]

+routh=[b([5,3,1]);b([4,2]),0]

+routh=[routh;-det(routh(1:2,1:2))/routh(2,1),routh(1,3),0]

+routh(3,1)=simple(routh(3,1))

+t=routh(2:3,1:2)

+l=simple(-det(t)/t(2,1))

+routh=[routh;l,0,0]

+//routh=[routh;K,0,0]

+disp(routh,"routh=")

+disp("for given system to be stable,following condition should be satisfied");

+disp("78.84-0.259K>0")

+disp("which gives limiting value of K")

+disp("K<288.9");

diff --git a/29/CH12/EX12.18/exa12_18.sce b/29/CH12/EX12.18/exa12_18.sce
new file mode 100755
index 000000000..c3723ac80
--- /dev/null
+++ b/29/CH12/EX12.18/exa12_18.sce
@@ -0,0 +1,27 @@
+//caption:stability_using_Routh-hurwitz_criterion

+//example 12.18

+//page 531

+s=%s;

+A=s^5+s^4+4*s^3+4*s^2+s+1;

+b=coeff(A)

+n=length(b)

+routh=[b([6 4 2]);b([5 3 1])]

+routh1=routh;

+c=[routh(1,1),routh(1,3);routh(2,1),routh(2,3)]

+routh=[routh;-det(routh(1:2,1:2))/routh(2,1),-det(c)/routh(2,1),0]

+disp("since all elements of third row are zero, so we make auxiliary equation")

+A=sym('s^4+4*s^2+1')//auxiliary equation

+B=diff(A,s)

+routh=[routh1;4,8,0]

+d=[routh(2,1),routh(2,3);routh(3,1),routh(3,3)]

+routh=[routh;-det(routh(2:3,1:2))/routh(3,1),-det(d)/routh(3,1),0]

+routh2=routh

+routh=[routh;-det(routh(3:4,1:2))/routh(4,1),0,0]

+routh=[routh;-det(routh(4:5,1:2))/routh(5,1),0,0];

+disp(routh,"routh=")

+disp("stability is examined as below . since roots of auxiliary eq are also roots of characterstics eq")

+A=s^4+4*s^2+1

+b=roots(A)

+disp("since the equation has non repeating  roots on s plane imaginary axis.hence system  are unstable" )

+

+

diff --git a/29/CH12/EX12.19/exa12_19.sce b/29/CH12/EX12.19/exa12_19.sce
new file mode 100755
index 000000000..d398f99e6
--- /dev/null
+++ b/29/CH12/EX12.19/exa12_19.sce
@@ -0,0 +1,30 @@
+//caption:stability_using_Routh-hurwitz_criterion

+//example 12.19

+//page 531

+s=%s;

+A=s^5+s^4+4*s^3+4*s^2+4*s+4;

+b=coeff(A)

+n=length(b)

+routh=[b([6,4,2]);b([5 3 1])]

+routh1=routh;

+c=[routh(1,1),routh(1,3);routh(2,1),routh(2,3)]

+routh=[routh;-det(routh(1:2,1:2))/routh(2,1),-det(c)/routh(2,1),0]

+disp("since all elements of third row are zero, so we make auxiliary equation")

+A=sym('s^4+4*s^2+4')//auxiliary equation

+B=diff(A,s)

+routh=[routh1;4,8,0]

+d=[routh(2,1),routh(2,3);routh(3,1),routh(3,3)]

+routh=[routh;-det(routh(2:3,1:2))/routh(3,1),-det(d)/routh(3,1),0]

+routh2=routh

+routh=[routh;-det(routh(3:4,1:2))/routh(4,1),0,0]

+disp("since all elements of fifth row are zero, so we make auxiliary equation")

+A=sym('2*s^2+4')//auxiliary equation

+B=diff(A,s)

+routh=[routh2;4,0,0]

+routh=[routh;-det(routh(4:5,1:2))/routh(5,1),0,0];

+disp(routh,"routh=")

+disp("stability is examined as below . since roots of auxiliary eq are also roots of characterstics eq")

+A=s^4+4*s^2+4

+b=roots(A)

+disp("since the equation has multiple roots on s plane imaginary axis.hence system  are unstable" )

+

diff --git a/29/CH12/EX12.2/exa12_2.sce b/29/CH12/EX12.2/exa12_2.sce
new file mode 100755
index 000000000..109549f56
--- /dev/null
+++ b/29/CH12/EX12.2/exa12_2.sce
@@ -0,0 +1,20 @@
+//Caption:transfer_function

+// example 12.2

+//page 516

+// we are solving this problem from signal flow graph approach

+syms G1 G2 G3 G4

+// forward path denoted by P1,P2 and so on and loop by L1,L2 and so on 

+//path factor by D1,D2 and so on and graph determinant by D

+P1=G1;

+P2=G2;

+P3=-G1*G2*G3;

+P4=G1*G2*G4;

+L1=-G1*G2*G3*G4;

+D1=1;

+D2=1;

+D3=1;

+D4=1;

+D=1-(L1);

+Y=(P1*D1+P2*D2+P3*D3+P4*D4)/D;

+Y=simple(Y);

+disp(Y,"C(s)/R(s)=");
\ No newline at end of file
diff --git a/29/CH12/EX12.21/exa12_21.sce b/29/CH12/EX12.21/exa12_21.sce
new file mode 100755
index 000000000..8c306d734
--- /dev/null
+++ b/29/CH12/EX12.21/exa12_21.sce
@@ -0,0 +1,32 @@
+//caption:determine_frequency_of_oscillations

+//example 12.21

+//page 533

+s=%s;

+syms  K

+G=sym('K*(s*(2*s+1))/(s^3+3*s+20)');

+H=1;

+CH=((s^3+3*s+20)+K*(s*(2*s+1)))

+disp('=0',CH,"characterstics_eq,CH=")

+c0=coeffs(CH,'s',0);

+c1=coeffs(CH,'s',1);

+c2=coeffs(CH,'s',2);

+c3=coeffs(CH,'s',3);

+b=[c0 c1 c2 c3]

+routh=[b([4,2]);b([3,1])]

+routh=[routh;-det(routh(1:2,1:2)/routh(2,1)),0]

+routh(3,1)=simple(routh(3,1))

+t=routh(2:3,1:2)

+l=simple(-det(t)/t(2,1))

+routh=[routh;l,0]

+disp(routh,"routh=")

+disp("for sustained oscillations:");

+disp("2*K^2+6*K-20=0")

+disp("which gives K")

+disp("K=2");

+disp("freq of oscillations is calculated by solving equation formed by s^2 row of the routh table")

+K=2

+k=2

+A=2*k*s^2+20

+r=roots(A)

+disp(%i*r(2),"frequency of oscillations=" )

+

diff --git a/29/CH12/EX12.23.i/exa12_23_i.jpg b/29/CH12/EX12.23.i/exa12_23_i.jpg
new file mode 100755
index 000000000..35eb94b06
--- /dev/null
+++ b/29/CH12/EX12.23.i/exa12_23_i.jpg
diff --git a/29/CH12/EX12.23.i/exa12_23_i.sce b/29/CH12/EX12.23.i/exa12_23_i.sce
new file mode 100755
index 000000000..a6d124d50
--- /dev/null
+++ b/29/CH12/EX12.23.i/exa12_23_i.sce
@@ -0,0 +1,23 @@
+//caption:stability_using_Nyquist_criterion
+//example 12_23_i
+//page 535
+clf();
+s=%s;
+s1=-s;
+disp("for K=0.1")
+g=(0.1*(s+10)*(s+40))/(s*(s+1)*(s+4));
+g1=(0.1*(s1+10)*(s1+40))/(s1*(s1+1)*(s1+4));
+GH=syslin('c',g);
+GH1=syslin('c',g1);
+nyquist(GH);
+nyquist(GH1);
+//mtlb_axis([-1.5 0.2 -0.3 0.3]);
+xtitle('Nyquist plot of (0.1*(s+10)*(s+40))/(s*(s+1)*(s+4))')
+figure;
+show_margins(GH,'nyquist')
+disp("since the point(-1+%i0) is  not encircled clockwise by Nyquist plot ,so N=0 and P=0")
+N=0;//no. of encirclement of -1+%i0 by G(s)H(s) plot anticlockwise
+P=0;//no. of poles of G(s)H(s) with positive real part
+Z=P-N;//np.of zeros of 1+G(s)H(s)=0 with positive real part
+disp(Z,"Z=")
+disp("as Z=0,there are no roots of closed loop characterstics eq having positive real part, hence system is stable.")
\ No newline at end of file
diff --git a/29/CH12/EX12.23.i/exa12_23_i_margin.jpg b/29/CH12/EX12.23.i/exa12_23_i_margin.jpg
new file mode 100755
index 000000000..c8103916f
--- /dev/null
+++ b/29/CH12/EX12.23.i/exa12_23_i_margin.jpg
diff --git a/29/CH12/EX12.23.ii/exa12_23_ii.jpg b/29/CH12/EX12.23.ii/exa12_23_ii.jpg
new file mode 100755
index 000000000..35eb94b06
--- /dev/null
+++ b/29/CH12/EX12.23.ii/exa12_23_ii.jpg
diff --git a/29/CH12/EX12.23.ii/exa12_23_ii.sce b/29/CH12/EX12.23.ii/exa12_23_ii.sce
new file mode 100755
index 000000000..8413448ea
--- /dev/null
+++ b/29/CH12/EX12.23.ii/exa12_23_ii.sce
@@ -0,0 +1,20 @@
+//caption:stability_using_Nyquist_criterion
+//example 12_23_ii
+//page 535
+disp("for K=1")
+g=(0.1*(s+10)*(s+40))/(s*(s+1)*(s+4));
+g1=(0.1*(s1+10)*(s1+40))/(s1*(s1+1)*(s1+4));
+GH=syslin('c',g);
+GH1=syslin('c',g1);
+nyquist(GH);
+nyquist(GH1);
+//mtlb_axis([-3 0.5 -0.6 0.6]);
+xtitle('Nyquist plot of (0.1*(s+10)*(s+40))/(s*(s+1)*(s+4))')
+figure;
+show_margins(GH,'nyquist')
+disp("since the point(-1+%i0) is  encircled twice clockwise by Nyquist plot ,so N=2 and P=0(given)")
+N=-2;//no. of encirclement of -1+%i0 by G(s)H(s) plot anticlockwise
+P=0;//no. of poles of G(s)H(s) with positive real part
+Z=P-N;//np.of zeros of 1+G(s)H(s)=0 with positive real part
+disp(Z,"Z=")
+disp("as Z=2,there are two roots of closed loop characterstics eq having positive real part, hence system is unstable.")
diff --git a/29/CH12/EX12.23.ii/exa12_23_ii_margin.jpg b/29/CH12/EX12.23.ii/exa12_23_ii_margin.jpg
new file mode 100755
index 000000000..c8103916f
--- /dev/null
+++ b/29/CH12/EX12.23.ii/exa12_23_ii_margin.jpg
diff --git a/29/CH12/EX12.23.iii/exa12_23_iii.jpg b/29/CH12/EX12.23.iii/exa12_23_iii.jpg
new file mode 100755
index 000000000..0fe49a99c
--- /dev/null
+++ b/29/CH12/EX12.23.iii/exa12_23_iii.jpg
diff --git a/29/CH12/EX12.23.iii/exa12_23_iii.sce b/29/CH12/EX12.23.iii/exa12_23_iii.sce
new file mode 100755
index 000000000..de1fd6f1c
--- /dev/null
+++ b/29/CH12/EX12.23.iii/exa12_23_iii.sce
@@ -0,0 +1,20 @@
+//caption:stability_using_Nyquist_criterion
+//example 12_23_iii
+//page 535
+disp("for K=10")
+g=(10*(s+10)*(s+40))/(s*(s+1)*(s+4));
+g1=(10*(s1+10)*(s1+40))/(s1*(s1+1)*(s1+4));
+GH=syslin('c',g);
+GH1=syslin('c',g1);
+nyquist(GH);
+nyquist(GH1);
+//mtlb_axis([-1.5 0.2 -0.3 0.3]);
+xtitle('Nyquist plot of (0.1*(s+10)*(s+40))/(s*(s+1)*(s+4))')
+figure;
+show_margins(GH,'nyquist')
+disp("since the point(-1+%i0) is encircled once in clockwise and once in anti clockwise direction by Nyquist plot ,so N=0 and P=0")
+N=0;//no. of encirclement of -1+%i0 by G(s)H(s) plot anticlockwise
+P=0;//no. of poles of G(s)H(s) with positive real part
+Z=P-N;//np.of zeros of 1+G(s)H(s)=0 with positive real part
+disp(Z,"Z=")
+disp("as Z=0,there are no roots of closed loop characterstics eq having positive real part, hence system is stable.")
\ No newline at end of file
diff --git a/29/CH12/EX12.23.iii/exa12_23_iii_margin.jpg b/29/CH12/EX12.23.iii/exa12_23_iii_margin.jpg
new file mode 100755
index 000000000..9185b33cd
--- /dev/null
+++ b/29/CH12/EX12.23.iii/exa12_23_iii_margin.jpg
diff --git a/29/CH12/EX12.27/exa12_27.jpg b/29/CH12/EX12.27/exa12_27.jpg
new file mode 100755
index 000000000..a714180f2
--- /dev/null
+++ b/29/CH12/EX12.27/exa12_27.jpg
diff --git a/29/CH12/EX12.27/exa12_27.sce b/29/CH12/EX12.27/exa12_27.sce
new file mode 100755
index 000000000..ebeda64fd
--- /dev/null
+++ b/29/CH12/EX12.27/exa12_27.sce
@@ -0,0 +1,16 @@
+//caption:gain_and_phase_margin
+//example 12_27
+//page543
+clf();
+s=%s;
+s1=-s;
+disp("for K=0.5")
+g=(0.5)/(s*(s+1)^2);
+GH=syslin('c',g);
+nyquist(GH);
+//mtlb_axis([-5 1  -500 500]);
+xtitle('Nyquist plot of (2.5*3)/(s*(0.4*s+1)*(0.2*s+1))')
+pm=p_margin(GH)
+disp(pm,"phase margin=")
+gm=g_margin(GH)
+disp(gm,"gain margin=")
\ No newline at end of file
diff --git a/29/CH12/EX12.3/exa12_3.sce b/29/CH12/EX12.3/exa12_3.sce
new file mode 100755
index 000000000..807177955
--- /dev/null
+++ b/29/CH12/EX12.3/exa12_3.sce
@@ -0,0 +1,20 @@
+//Caption:transfer_function

+// example 12.3

+//page 517

+// we are solving this problem from signal flow graph approach

+syms G1 G2 G3 G4 H2 H1 H3

+// forward path denoted by P1,P2 and so on and loop by L1,L2 and so on 

+//path factor by D1,D2 and so on and graph determinant by D

+P1=G2*G4;

+P2=G2*G3*G4;

+P3=G1*G3*G4;

+L1=-G4*H1;

+L2=-G3*G4*H1*H2;

+L3=-G1*G3*G4*H1*H2*H3

+D1=1;

+D2=1;

+D3=1;

+D=1-(L1+L2+L3);

+Y=(P1*D1+P2*D2+P3*D3)/D;

+Y=simple(Y);

+disp(Y,"C(s)/R(s)=");
\ No newline at end of file
diff --git a/29/CH12/EX12.33/exa12_33.jpg b/29/CH12/EX12.33/exa12_33.jpg
new file mode 100755
index 000000000..953ba9881
--- /dev/null
+++ b/29/CH12/EX12.33/exa12_33.jpg
diff --git a/29/CH12/EX12.33/exa12_33.sce b/29/CH12/EX12.33/exa12_33.sce
new file mode 100755
index 000000000..0f8ba232f
--- /dev/null
+++ b/29/CH12/EX12.33/exa12_33.sce
@@ -0,0 +1,18 @@
+//caption:determine_close_loop_stability

+//example 12_33

+//page 550

+s=%s;

+g=(720*(s+1.25))/(s*(s+10)*(s^2+2*s+9));

+G=syslin('c',g)

+fmin=0.1; 

+fmax=100; 

+bode(G, fmin, fmax) 

+[gm,freqGM]=g_margin(G);

+[pm,freqPM]=p_margin(G);

+show_margins(G);

+disp(gm,"gain_margin=");

+disp((freqGM*2*%pi),"gain_margin_freq=");

+disp(pm,"phase_margin=");

+disp((freqPM*2*%pi),"phase_margin_freq=");

+show_margins(G);

+disp("since gain and phase margin are both negative so system is unstable")

diff --git a/29/CH12/EX12.4/exa12_4.sce b/29/CH12/EX12.4/exa12_4.sce
new file mode 100755
index 000000000..632eb558d
--- /dev/null
+++ b/29/CH12/EX12.4/exa12_4.sce
@@ -0,0 +1,24 @@
+//Caption:transfer_function

+// example 12.4

+//page 518

+// we are solving this problem from signal flow graph approach

+syms G1 G2 

+// forward path denoted by P1,P2 and so on and loop by L1,L2 and so on 

+//path factor by D1,D2 and so on and graph determinant by D

+P1=G1;

+P2=G2;

+P3=G1*G2;

+P4=G1*G2;

+L1=-G1;

+L2=-G2;

+L3=G1*G2;

+L4=-G1*G2;

+L5=-G1*G2;

+D1=1;

+D2=1;

+D3=1;

+D4=1;

+D=1-(L1+L2+L3+L4+L5);

+Y=(P1*D1+P2*D2+P3*D3+P4*D4)/D;

+Y=simple(Y);

+disp(Y,"C(s)/R(s)=");
\ No newline at end of file
diff --git a/29/CH12/EX12.42/exa12_42.jpg b/29/CH12/EX12.42/exa12_42.jpg
new file mode 100755
index 000000000..20058fc5b
--- /dev/null
+++ b/29/CH12/EX12.42/exa12_42.jpg
diff --git a/29/CH12/EX12.42/exa12_42.sce b/29/CH12/EX12.42/exa12_42.sce
new file mode 100755
index 000000000..b35ce3ce3
--- /dev/null
+++ b/29/CH12/EX12.42/exa12_42.sce
@@ -0,0 +1,50 @@
+//caption:root_locus

+//example 12_42

+//page 562

+s=%s;

+syms K;

+GH=K/(s*(s+2)*(s+4))

+//since Mp=40%, so .4=exp((-zeta*%pi)/(sqrt(1-zeta^2))

+zeta=0.3

+//from given data 

+disp("the characterstics eq. is determined as:")

+CH=(s*(s+2)*(s+4))+K

+K=sym('-(s^3+6*s^2+8*s)')

+d=diff(K,s)

+e=-3*s^2-12*s-8 

+r1=roots(e)

+disp(r1,"roots=")

+disp("-0.842 is break away point sinc it lies on root locus")

+CH=sym('s^3+6*s^2+8*s+K');

+disp('=0',CH,"characterstics_eq,CH=")

+c0=coeffs(CH,'s',0);

+c1=coeffs(CH,'s',1);

+c2=coeffs(CH,'s',2);

+c3=coeffs(CH,'s',3);

+b=[c0 c1 c2 c3]

+n=4;

+routh=[b([4,2]);b([3,1])];

+routh=[routh;-det(routh)/routh(2,1),0]

+t=routh(2:3,1:2)

+routh=[routh;-det(t)/t(2,1),0]

+disp(routh,"routh=")

+disp("for given system to be marginally stable:");

+disp("(48-K)=0 ");

+disp("which gives:");

+disp("K=48");

+K=48;

+k=48

+a=6*s^2+48//intersection of root locus with imaginary plane

+r=roots(a)

+g=k/(s*(s+2)*(s+4))

+G=syslin('c',g)

+evans(g,8)

+xgrid(2)

+disp("the line theta=acos(zeta)=72.5 intersects root locus at sa=(-0.5+i1.65)")

+disp("the value of K at s=sa is find to be 14.87 for Mp=40%")

+K=14.87

+ts=4/0.5     //ts=4/(zeta*wn)

+Kv=limit(s*GH,s,0)

+Kv=eval(Kv)

+Kv=float(Kv)

+disp(Kv,"Kv=");

diff --git a/29/CH12/EX12.43/exa12_43.jpg b/29/CH12/EX12.43/exa12_43.jpg
new file mode 100755
index 000000000..77635d7f6
--- /dev/null
+++ b/29/CH12/EX12.43/exa12_43.jpg
diff --git a/29/CH12/EX12.43/exa12_43.sce b/29/CH12/EX12.43/exa12_43.sce
new file mode 100755
index 000000000..7162eba9c
--- /dev/null
+++ b/29/CH12/EX12.43/exa12_43.sce
@@ -0,0 +1,44 @@
+//caption:root_locus_and_value_of_K

+//example 12.43

+//page 564

+s=%s;

+syms K;

+GH=K/(s*(s+2)*(s^2+2*s+2))

+disp("the characterstics eq. is determined as:")

+CH=(s*(s+2)*(s^2+2*s+2))+K

+CH=sym('s^4+4*s^3+6*s^2+4*s+K');

+disp('=0',CH,"characterstics_eq,CH=")

+c0=coeffs(CH,'s',0);

+c1=coeffs(CH,'s',1);

+c2=coeffs(CH,'s',2);

+c3=coeffs(CH,'s',3);

+c4=coeffs(CH,'s',4);

+b=[c0 c1 c2 c3 c4 ]

+routh=[b([5,3,1]);b([4,2]),0]

+routh=[routh;-det(routh(1:2,1:2))/routh(2,1),routh(1,3),0]

+routh(3,1)=simple(routh(3,1))

+t=routh(2:3,1:2)

+l=simple(-det(t)/t(2,1))

+routh=[routh;l,0,0]

+routh=[routh;K,0,0]

+K=sym('s^4+4*s^3+6*s^2+4*s')

+d=diff(K,s)

+e=-(4*s^3+12*s^2+12*s+4)

+r=roots(e)

+disp(routh,"routh=")

+disp("for given system to be marginally stable:");

+disp("((20-4K)/5)=0 ");

+disp("which gives:");

+disp("K=5");

+K=5;

+k=5

+a=5*s^2+5//intersection of root locus with s plane

+r=roots(a)

+disp(r,"intersection point with imaginary axis=")

+g=k/(s*(s+2)*(s^2+2*s+2))

+G=syslin('c',g)

+evans(g,200)

+xgrid(2)

+disp("angle of departure=-90 and +90")

+disp("breakaway point is -1 and +j and -j")

+disp("on solving we find K=1")

diff --git a/29/CH12/EX12.44/exa12_44.jpg b/29/CH12/EX12.44/exa12_44.jpg
new file mode 100755
index 000000000..fb078ee4c
--- /dev/null
+++ b/29/CH12/EX12.44/exa12_44.jpg
diff --git a/29/CH12/EX12.44/exa12_44.sce b/29/CH12/EX12.44/exa12_44.sce
new file mode 100755
index 000000000..038669848
--- /dev/null
+++ b/29/CH12/EX12.44/exa12_44.sce
@@ -0,0 +1,41 @@
+//caption:root_locus_and_value_of_K

+//example 12.44

+//page 565

+s=%s;

+syms K;

+GH=K/((s^2+2*s+5)*(s^2+2*s+2))

+disp("the characterstics eq. is determined as:")

+CH=((s^2+2*s+5)*(s^2+2*s+2))+K

+CH=sym('((s^2+2*s+5)*(s^2+2*s+2))+K');

+disp('=0',CH,"characterstics_eq,CH=")

+c0=coeffs(CH,'s',0);

+c1=coeffs(CH,'s',1);

+c2=coeffs(CH,'s',2);

+c3=coeffs(CH,'s',3);

+c4=coeffs(CH,'s',4);

+b=[c0 c1 c2 c3 c4 ]

+routh=[b([5,3,1]);b([4,2]),0]

+routh=[routh;-det(routh(1:2,1:2))/routh(2,1),routh(1,3),0]

+routh(3,1)=simple(routh(3,1))

+t=routh(2:3,1:2)

+l=simple(-det(t)/t(2,1))

+routh=[routh;l,0,0]

+routh=[routh;K,0,0]

+K=sym('-(s^2+2*s+5)*(s^2+2*s+2)')

+d=diff(K,s)

+e=-(4*s^3+12*s^2+22*s+14)

+r=roots(e)

+disp(routh,"routh=")

+disp("for given system to be marginally stable:");

+disp("((7.5*14-4(K+10)/7.5)=0 ");

+disp("which gives:");

+disp("K=16.25");

+K=16.25;

+k=16.25

+a=7.5*s^2+26.25//intersection of root locus with s plane

+r=roots(a)

+g=k/((s^2+2*s+5)*(s^2+2*s+2))

+G=syslin('c',g)

+evans(g,200)

+xgrid(2)

+disp(r,"the point of intersection of root locus with imaginary axis =")

diff --git a/29/CH12/EX12.45/exa12_45.jpg b/29/CH12/EX12.45/exa12_45.jpg
new file mode 100755
index 000000000..abd65455e
--- /dev/null
+++ b/29/CH12/EX12.45/exa12_45.jpg
diff --git a/29/CH12/EX12.45/exa12_45.sce b/29/CH12/EX12.45/exa12_45.sce
new file mode 100755
index 000000000..6e8c16086
--- /dev/null
+++ b/29/CH12/EX12.45/exa12_45.sce
@@ -0,0 +1,38 @@
+//caption:root_locus_and_value_of_K

+//example 12.45

+//page 567

+s=%s;

+syms K;

+GH=K*(s+1)/(s*(s+2)*(s^2+4*s+8))

+disp("the characterstics eq. is determined as:")

+CH=((s*(s+2)*(s^2+4*s+8)))+K*(s+1)

+CH=sym('((s*(s+2)*(s^2+4*s+8)))+K*(s+1)');

+disp('=0',CH,"characterstics_eq,CH=")

+c0=coeffs(CH,'s',0);

+c1=coeffs(CH,'s',1);

+c2=coeffs(CH,'s',2);

+c3=coeffs(CH,'s',3);

+c4=coeffs(CH,'s',4);

+b=[c0 c1 c2 c3 c4 ]

+routh=[b([5,3,1]);b([4,2]),0]

+routh=[routh;-det(routh(1:2,1:2))/routh(2,1),routh(1,3),0]

+routh(3,1)=simple(routh(3,1))

+t=routh(2:3,1:2)

+l=simple(-det(t)/t(2,1))

+routh=[routh;l,0,0]

+routh=[routh;K,0,0]

+disp(routh,"routh=")

+disp("for given system to be marginally stable:");

+disp("(K^2-28*K-1280)=0 ");

+disp("which gives:");

+disp("K=52.4 and -24.42");

+K=52.4;//considering positive value

+k=52.4

+a=((80-52.4)/6)*s^2+52.4//intersection of root locus with imaginary axis

+r=roots(a)

+g=k*(s+1)/(s*(s+2)*(s^2+4*s+8))

+G=syslin('c',g)

+clf();

+evans(g,10)

+xgrid(2)

+disp(r,"the point of intersection of root locus with imaginary axis =")

diff --git a/29/CH12/EX12.46/exa12_46.jpg b/29/CH12/EX12.46/exa12_46.jpg
new file mode 100755
index 000000000..d42cbae3a
--- /dev/null
+++ b/29/CH12/EX12.46/exa12_46.jpg
diff --git a/29/CH12/EX12.46/exa12_46.sce b/29/CH12/EX12.46/exa12_46.sce
new file mode 100755
index 000000000..6c9c3bd40
--- /dev/null
+++ b/29/CH12/EX12.46/exa12_46.sce
@@ -0,0 +1,41 @@
+//caption:root_locus_and_value_of_K

+//example 12.46

+//page 570

+s=%s;

+syms K;

+GH=K/(s*((s+6)^2))

+disp("the characterstics eq. is determined as:")

+CH=(s*((s+6)^2))+K

+CH=sym('(s*((s+6)^2))+K');

+disp('=0',CH,"characterstics_eq,CH=")

+c0=coeffs(CH,'s',0);

+c1=coeffs(CH,'s',1);

+c2=coeffs(CH,'s',2);

+c3=coeffs(CH,'s',3);

+b=[c0 c1 c2 c3]

+n=4;

+routh=[b([4,2]);b([3,1])];

+routh=[routh;-det(routh)/routh(2,1),0]

+t=routh(2:3,1:2)

+routh=[routh;-det(t)/t(2,1),0]

+K=sym('-(s*((s+6)^2))')

+d=diff(K,s)

+e=3*s^2+24*s+36 

+r1=roots(e)

+disp(r1,"roots=")

+disp("-2 is break away point sinc it lies on root locus")

+disp(routh,"routh=")

+disp("for given system to be marginally stable:");

+disp("(-(K-432)/12)=0 ");

+disp("which gives:");

+disp("K=432");

+K=432;//considering positive value

+k=432

+a=12*s^2+k//intersection of root locus with imaginary axis plane

+r=roots(a)

+g=k/(s*((s+6)^2))

+G=syslin('c',g)

+clf();

+evans(g,5)

+xgrid(2)

+disp(r,"the point of intersection of root locus with imaginary axis =")

diff --git a/29/CH12/EX12.48/exa12_48.jpg b/29/CH12/EX12.48/exa12_48.jpg
new file mode 100755
index 000000000..20058fc5b
--- /dev/null
+++ b/29/CH12/EX12.48/exa12_48.jpg
diff --git a/29/CH12/EX12.48/exa12_48.sce b/29/CH12/EX12.48/exa12_48.sce
new file mode 100755
index 000000000..6b7d805b8
--- /dev/null
+++ b/29/CH12/EX12.48/exa12_48.sce
@@ -0,0 +1,49 @@
+//caption:root_locus_and_value_of_K

+//example 12_48

+//page 574

+s=%s;

+syms K;

+GH=K/(s*(s+2)*(s+4))

+zeta=0.277

+//from given data 

+disp("the characterstics eq. is determined as:")

+CH=(s*(s+2)*(s+4))+K

+K=sym('-(s^3+6*s^2+8*s)')

+d=diff(K,s)

+e=-3*s^2-12*s-8 

+r1=roots(e)

+disp(r1,"roots=")

+disp("-0.85 is break away point sinc it lies on root locus")

+CH=sym('s^3+6*s^2+8*s+K');

+disp('=0',CH,"characterstics_eq,CH=")

+c0=coeffs(CH,'s',0);

+c1=coeffs(CH,'s',1);

+c2=coeffs(CH,'s',2);

+c3=coeffs(CH,'s',3);

+b=[c0 c1 c2 c3]

+n=4;

+routh=[b([4,2]);b([3,1])];

+routh=[routh;-det(routh)/routh(2,1),0]

+t=routh(2:3,1:2)

+routh=[routh;-det(t)/t(2,1),0]

+disp(routh,"routh=")

+disp("for given system to be marginally stable:");

+disp("(48-K)=0 ");

+disp("which gives:");

+disp("K=48");

+K=48;

+k=48

+a=6*s^2+48//intersection of root locus with imaginary plane

+r=roots(a)

+g=k/(s*(s+2)*(s+4))

+G=syslin('c',g)

+evans(g,8)

+xgrid(2)

+disp("the line theta=acos(zeta)=73.9 intersects root locus at sa=(-0.5+i1.66)")

+disp("the value of K at s=sa is find to be 15 for zeta=0.277")

+K=15

+k=15

+disp(r,"the point of intersection of root locus with imaginary axis =")

+g=k/(s*(s+2)*(s+4))

+cl=g/(1+g)

+disp(cl,"C(s)/R(s)=")
\ No newline at end of file
diff --git a/29/CH12/EX12.49/exa12_49.jpg b/29/CH12/EX12.49/exa12_49.jpg
new file mode 100755
index 000000000..66d777f26
--- /dev/null
+++ b/29/CH12/EX12.49/exa12_49.jpg
diff --git a/29/CH12/EX12.49/exa12_49.sce b/29/CH12/EX12.49/exa12_49.sce
new file mode 100755
index 000000000..eb8e50b86
--- /dev/null
+++ b/29/CH12/EX12.49/exa12_49.sce
@@ -0,0 +1,28 @@
+//caption:root_locus_and_value_of_K

+//example 12.49

+//page 576

+s=%s;

+syms K;

+GH=(K*(s+4))/(s+2)^2

+disp("the characterstics eq. is determined as:")

+CH=(s+2)^2+(K*(s+4))

+CH=sym('((s+2)^2)+K*(s+4)');

+disp('=0',CH,"characterstics_eq,CH=")

+K=sym('((s+2)^2/(s+4))')

+d=diff(K,s)

+e=(s+2)*(s+6)

+r1=roots(e)

+disp(r1,"roots=")

+disp("-2 and -6 is break away point")

+g=(s+4)/((s+2)^2)

+G=syslin('c',g)

+clf();

+evans(g,10)

+xgrid(2)

+disp("for wd=2rad/sec,the point on root locus is s=-4+j2")

+disp("the value of K at s=-4+j2 is 4")

+K=4

+k=4

+g=k*(s+4)/((s+2)^2)

+cl=g/(1+g)

+disp(cl,"C(s)/R(s)=")
\ No newline at end of file
diff --git a/29/CH12/EX12.5/exa12_5.sce b/29/CH12/EX12.5/exa12_5.sce
new file mode 100755
index 000000000..0a6904c29
--- /dev/null
+++ b/29/CH12/EX12.5/exa12_5.sce
@@ -0,0 +1,19 @@
+//Caption:transfer_function

+// example 12.5

+//page 518

+// we are solving this problem from signal flow graph approach

+syms G1 G2 G3 G4 G5 H1 H2

+// forward path denoted by P1,P2 and so on and loop by L1,L2 and so on 

+//path factor by D1,D2 and so on and graph determinant by D

+P1=G1*G4*G5;

+P2=G1*G2*G3*G5;

+L1=-G3*G5;

+L2=-G3*G5*H2;

+L3=-G1*G4*G5*H1;

+L4=-G1*G2*G3*G5*H1;

+D1=1;

+D2=1;

+D=1-(L1+L2+L3+L4);

+Y=(P1*D1+P2*D2)/D;

+Y=simple(Y);

+disp(Y,"C(s)/R(s)=");
\ No newline at end of file
diff --git a/29/CH12/EX12.50/exa12_50.jpg b/29/CH12/EX12.50/exa12_50.jpg
new file mode 100755
index 000000000..ed60a3e8f
--- /dev/null
+++ b/29/CH12/EX12.50/exa12_50.jpg
diff --git a/29/CH12/EX12.50/exa12_50.sce b/29/CH12/EX12.50/exa12_50.sce
new file mode 100755
index 000000000..2703a28eb
--- /dev/null
+++ b/29/CH12/EX12.50/exa12_50.sce
@@ -0,0 +1,26 @@
+//caption:root_locus_and_close_loop_transfer_function

+//example 12.50

+//page 578

+s=%s

+K=8

+G=K/(s*(s+4))

+H=1;

+GH=G*H

+G=syslin('c',G)

+evans(G,8)

+xgrid(2)

+CH=s*(s+4)+K

+disp('=0',CH,"characterstics_eq,CH=")

+r=roots(CH)

+disp(r,"the point at which K=8")

+cl=G/(1+GH)

+disp(cl,"C(s)/R(s)=")

+

+

+

+disp("part b")

+g=K/(s+4)

+h=1/s

+gh=g*h

+CL=g/(1+gh)

+disp(CL,"C(s)/R(s)=")

diff --git a/29/CH12/EX12.51/exa12_51.jpg b/29/CH12/EX12.51/exa12_51.jpg
new file mode 100755
index 000000000..8dc2f996f
--- /dev/null
+++ b/29/CH12/EX12.51/exa12_51.jpg
diff --git a/29/CH12/EX12.51/exa12_51.sce b/29/CH12/EX12.51/exa12_51.sce
new file mode 100755
index 000000000..0f03ac36e
--- /dev/null
+++ b/29/CH12/EX12.51/exa12_51.sce
@@ -0,0 +1,14 @@
+//caption:root_locus_and_gain,phase_margin

+//example 12.51

+//page 580

+s=%s;

+K=3.46

+G=K/(s*(s+1)*(s+2))

+G=syslin('c',G)

+clf();

+evans(G,20)

+xgrid(2)

+[gm,freq_gm]=g_margin(G)

+[pm,freq_pm]=p_margin(G)

+disp(gm,"gain_margin=",freq_gm*2*%pi,"gain_margin_freq=")

+disp(pm,"phase_margin=",freq_pm*2*%pi,"phase_margin_freq=")

diff --git a/29/CH12/EX12.54/exa12_54.sce b/29/CH12/EX12.54/exa12_54.sce
new file mode 100755
index 000000000..0a3bdd501
--- /dev/null
+++ b/29/CH12/EX12.54/exa12_54.sce
@@ -0,0 +1,11 @@
+//caption:obtain_state_matrix

+//example 12_54

+//page 583

+s=%s;

+g=5*(s+2)/(s*(s+1)*(s+5));

+CL=syslin('c',g);

+disp(CL,"C(s)/R(s)=");

+SS=tf2ss(CL)

+[Ac,Bc,U,ind]=canon(SS(2),SS(3))

+disp(SS,"state space matrix=")

+disp(Ac,"Ac",Bc,"Bc",U,"U",ind,"ind")
\ No newline at end of file
diff --git a/29/CH12/EX12.55/exa12_55.sce b/29/CH12/EX12.55/exa12_55.sce
new file mode 100755
index 000000000..db018fef6
--- /dev/null
+++ b/29/CH12/EX12.55/exa12_55.sce
@@ -0,0 +1,11 @@
+//caption:obtain_state_matrix

+//example 12_55

+//page 585

+s=%s;

+g=50/(s*(s^2+0.5*s+50));

+CL=syslin('c',g);

+disp(CL,"C(s)/R(s)=");

+SS=tf2ss(CL)

+[Ac,Bc,U,ind]=canon(SS(2),SS(3))

+disp(SS,"state space matrix=")

+disp(Ac,"Ac",Bc,"Bc",U,"U",ind,"ind")
\ No newline at end of file
diff --git a/29/CH12/EX12.56/exa12_56.sce b/29/CH12/EX12.56/exa12_56.sce
new file mode 100755
index 000000000..e7c9302a6
--- /dev/null
+++ b/29/CH12/EX12.56/exa12_56.sce
@@ -0,0 +1,26 @@
+//caption:obtain_state_transistion_matrix

+//example 12_56

+//page 586

+s=%s;

+syms t

+A=[0 1;0 -3]

+[r c]=size(A);//size of matrix A

+p=s*eye(r,c)-A;//s*I-A where I is identity matrix

+q=det(p)//determinant of sI-A

+r=inv(p)//inverse of sI-A

+//for calculating state transistion matrix

+ip=[0 0;0 0]

+i=1;

+j=1;

+for i=1:2

+  for j=1:2

+    if(i==2 & j==1)

+      else

+    ip(i,j)=ilaplace(r(i,j),s,t);

+    j=j+1;

+    end

+  end

+  i=i+1;

+end

+r(2,1)=0

+disp(ip,"state transistion matrix,ip(t)=");
\ No newline at end of file
diff --git a/29/CH12/EX12.57/exa12_57.sce b/29/CH12/EX12.57/exa12_57.sce
new file mode 100755
index 000000000..e647af62c
--- /dev/null
+++ b/29/CH12/EX12.57/exa12_57.sce
@@ -0,0 +1,19 @@
+//caption:obtain_time_response

+//example 12_57

+//page 586

+s=%s;

+syms t

+A=[0 1;-2 -3]

+B=[1 0]'

+x0=[0 0]'

+u=1/(s+1)

+[r c]=size(A);//size of matrix A

+p=s*eye(r,c)-A;//s*I-A where I is identity matrix

+q=det(p)//determinant of sI-A

+r=inv(p)//inverse of sI-A

+m=r*B*(1/(s+1));

+//for calculating zero state response

+x=[0;0]

+x(1,1)=ilaplace(m(1,1),s,t);

+x(2,1)=ilaplace(m(2,1),s,t);

+disp(x,"time response of the system,x(t)=");

diff --git a/29/CH12/EX12.59/exa12_59.sce b/29/CH12/EX12.59/exa12_59.sce
new file mode 100755
index 000000000..f63c58a72
--- /dev/null
+++ b/29/CH12/EX12.59/exa12_59.sce
@@ -0,0 +1,20 @@
+//caption:obtain_time_response

+//example 12_59

+//page 590

+s=%s;

+syms t

+A=[-1 0;1 -1]

+B=[0 1]'

+x0=[1 0]'

+[r c]=size(A);//size of matrix A

+p=s*eye(r,c)-A;//s*I-A where I is identity matrix

+q=det(p)//determinant of sI-A

+r=inv(p)//inverse of sI-A

+m=r*B*(1/s)

+r1=r*x0

+X=r1+m

+//for calculating zero state response

+x=[0;0]

+x(1,1)=ilaplace(X(1,1),s,t);

+x(2,1)=ilaplace(X(2,1),s,t);

+disp(x,"zero input response of the system,x(t)=");

diff --git a/29/CH12/EX12.61/exa12_61.sce b/29/CH12/EX12.61/exa12_61.sce
new file mode 100755
index 000000000..fc81b8e8d
--- /dev/null
+++ b/29/CH12/EX12.61/exa12_61.sce
@@ -0,0 +1,14 @@
+//caption:obtain_transfer_matrix

+//example 12_61

+//page 592

+s=%s;

+syms t

+A=[-1 -1;3 -5]

+B=[1 1]'

+C=[1 2]

+[r c]=size(A);//size of matrix A

+p=s*eye(r,c)-A;//s*I-A where I is identity matrix

+q=det(p)//determinant of sI-A

+r=inv(p)//inverse of sI-A

+G=C*r*B

+disp(G,"transfer_matrix=")
\ No newline at end of file
diff --git a/29/CH12/EX12.7/exa12_7.sce b/29/CH12/EX12.7/exa12_7.sce
new file mode 100755
index 000000000..4f918bd5a
--- /dev/null
+++ b/29/CH12/EX12.7/exa12_7.sce
@@ -0,0 +1,23 @@
+//Caption:determine_peak_time_and_peak_overshoot
+//example 12.7
+//page 520
+s=%s;
+syms t;
+G=sym('(s+2)/(s*(s+1))')//G(s)
+H=1;
+CL=G/(1+G*H);
+disp(CL,"C(s)/R(s)=");
+//for unit step response R(s)=1/s; 
+d=CL*(1/s);
+a=s*d;
+disp(d,"C(s)=");
+c=ilaplace(d,s,t);
+disp(c,"c(t)=");
+//for peak time we get tp=3*%pi/4
+tp=3*%pi/4
+Cmax=1-(exp(-tp)*cos(tp));
+Css=limit(a,s,0);
+disp(Css,"Css=");
+Mp=((Cmax-Css)/Css)*100
+Mp=float(Mp)
+disp(Mp,"peak_overshoot=")
diff --git a/29/CH12/EX12.8/exa12_8.sce b/29/CH12/EX12.8/exa12_8.sce
new file mode 100755
index 000000000..e8d049937
--- /dev/null
+++ b/29/CH12/EX12.8/exa12_8.sce
@@ -0,0 +1,24 @@
+//Caption:time_response_and_peak_overshoot
+//example 12.8
+//page 521
+s=%s;
+syms t;
+num=sym('8*(s+1)');
+den=sym('(s^2+2*s+2)');
+CL=num/den;
+disp(CL,"C(s)/R(s)=");
+//for unit step response R(s)=1/s; 
+d=CL*(1/s);
+disp(d,"C(s)=");
+c=ilaplace(d,s,t);
+disp(c,"c(t)=");
+//for peak time we get tp=%pi/2
+t=%pi/2
+a=s*d;
+a=simple(a)
+Cmax=4*(1+1.414*exp(-t)*sin(t-(%pi/4)))
+Css=limit(a,s,0);
+disp(Css,"Css=");
+Mp=((Cmax-Css)/Css)*100
+Mp=float(Mp)
+disp(Mp,"peak_overshoot=")
diff --git a/29/CH12/EX12.9/exa12_9.sce b/29/CH12/EX12.9/exa12_9.sce
new file mode 100755
index 000000000..77dba4d20
--- /dev/null
+++ b/29/CH12/EX12.9/exa12_9.sce
@@ -0,0 +1,32 @@
+//Caption:determine_peak_overshoot
+//example 12.9
+//page 523
+s=%s;
+syms t K;
+CL=sym('(s+1)/(s^2+2*s+5)');
+CL=K*CL;
+disp(CL,"C(s)/R(s)=")
+//for unit step response R(s)=1/s; 
+d=CL*(1/s)
+Css=limit(s*d,s,0)
+disp(Css,"Css=");
+//since Css=0.8 (given)
+K=0.8*5;
+CL=eval(CL);
+disp(CL,"C(s)/R(s)=");
+//for unit step response R(s)=1/s; 
+d=CL*(1/s)
+disp(d,"C(s)=");
+c=ilaplace(d,s,t);
+disp(c,"c(t)=");
+//for peak time we get tp=0.785
+t=0.785
+a=s*d;
+a=simple(a)
+Cmax=(4/5)*(1-exp(-t)*cos(2*%pi/4)+exp(-t)*2*sin(2*%pi/4))
+Css=limit(a,s,0)
+disp(Css,"Css=");
+Mp=((Cmax-Css)/Css)*100
+Mp=float(Mp)
+disp(Mp,"peak_overshoot=")
+