From b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b Mon Sep 17 00:00:00 2001
From: priyanka
Date: Wed, 24 Jun 2015 15:03:17 +0530
Subject: initial commit / add all books

---
 1202/CH22/EX22.4/22_4.png | Bin 0 -> 7134 bytes
 1202/CH22/EX22.4/22_4.sce |  93 ++++++++++++++++++++++++++++++++++++++++++++++
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 create mode 100755 1202/CH22/EX22.4/22_4.png
 create mode 100755 1202/CH22/EX22.4/22_4.sce

(limited to '1202/CH22/EX22.4')

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+clear
+clc
+
+//Example 22.4
+disp('Example 22.4')
+K=[-6 3;12 5];
+tau=[0.67 2;0.67 5];
+s=%s;
+G=K./(1+tau*s);
+delay75=0.75;
+delay1=1;
+RGA=K.*inv(K');
+disp(RGA,"RGA=")
+
+//IMC based tuning
+tauC=[tau(1,1) tau(2,2)];
+Kc=diag(tau./(repmat(tauC,2,1)+[delay75 delay1;delay75 delay1])./K);
+tauI=diag(tau);
+disp(Kc,"Kc=")
+disp(tauI,"tauI=")
+
+//====Making step response models of the continuos transfer functions====//
+Ts=0.05;//Sampling time ie delta_T
+delay75=0.75/Ts;
+delay1=1/Ts;
+N=30/Ts;//Model Order
+s=%s;
+G=syslin('c',diag(matrix(G,1,4)));//Transfer function
+t=0:Ts:N*Ts;
+u_sim=ones(4,length(t));
+u_sim([1 2],1:(delay75))=zeros(2,delay75); //input delay to account for delay in SNP
+u_sim([3 4],1:(delay1))=zeros(2,delay1); //input delay to account for delay in DPM
+S=csim(u_sim,t,G)';//generating step response model for real plant
+//plot(t,S);
+S(1,:)=[];
+//Now we have these step response models for each of the transfer functions
+//[S1 S3
+//S2 S4 
+
+
+
+
+T=50;//Simulation Run Time in minutes
+n=T/Ts*2+1; //no. of discrete points in our domain of analysis
+
+
+//========Set point as -10=============//
+//p is the controller output
+p=zeros(n,2);
+delta_p=zeros(n,2);
+e=zeros(n,2); //errors=(ysp-y) on which PI acts
+ysp=zeros(n,2);
+ysp((n-1)/2+1:n,1)=-10*ones(n-((n-1)/2+1)+1,1);
+
+t=-(n-1)/2*Ts:Ts:(n-1)/2*Ts;
+y=zeros(n,2);
+
+
+for k=(n-1)/2+1:n
+    
+    //Error  e
+    e(k,:)=ysp(k-1,:)-y(k-1,:);
+    delta_e(k,:)=e(k,:)-e(k-1,:);
+
+    //Controller calculation----Digital PID----Eqn 7-28 Pg 136 (Velocity form)
+//    p(k,:)=p(k-1,:)+flipdim([delta_e(k,:)+e(k,:)*diag(Ts./tauI)]*diag(Kc),2);
+    p(k,:)=p(k-1,:)+([delta_e(k,:)+e(k,:)*diag(Ts./tauI)]*diag(Kc));
+    //1-1/2-2 pairing
+    
+    delta_p(k,:)=p(k,:)-p(k-1,:);
+       
+    //Output
+    y(k,1)=[S(1:N-1,1);S(1:N-1,3)]'...
+        *[flipdim(delta_p(k-N+1:k-1,1),1);flipdim(delta_p(k-N+1:k-1,2),1)]...
+        +[S(N,1) S(N,3)]*[p(k-N,1);p(k-N,2)];
+    y(k,2)=[S(1:N-1,2);S(1:N-1,4)]'...
+        *[flipdim(delta_p(k-N+1:k-1,1),1);flipdim(delta_p(k-N+1:k-1,2),1);]...
+        +[S(N,2) S(N,4)]*[p(k-N,1);p(k-N,2)];
+end
+
+
+plot(t',y(:,1),'--',t',y(:,2),':',t',ysp(:,1),'-');
+set(gca(),"data_bounds",[0 50 -20 25]); //putting bounds on display
+l=legend("Mean arterial pressure","Cardiac output",position=1);
+//l.font_size=5;
+xtitle("","Time(min)","$y$");
+a=get("current_axes");
+c=a.y_label;c.font_size=5;
+
+mprintf('\nThere is more interaction in the variables\n...
+than the book claims, hence a mismatch between the result\n...
+and the book\n')
+
-- 
cgit