1 files changed, 52 insertions, 0 deletions
diff --git a/2048/DEPENDENCIES/gpc_pid.sci b/2048/DEPENDENCIES/gpc_pid.sci
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+++ b/2048/DEPENDENCIES/gpc_pid.sci
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+// 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;