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+clear
+clc
+
+//Example 20.4
+disp('Example 20.4')
+
+J=15;
+Ts=1;//Sampling time ie delta_T
+N=80;//Model Order
+s=%s;
+G=syslin('c',5/(15*s+1));//Transfer function
+t=0:Ts:N*Ts;
+u_sim=ones(1,length(t));
+u_sim(1:3)=[0 0 0]; //input delay to account for 2 min delay in G
+S=csim(u_sim,t,G)';//generating step response model for real plant
+//plot(t,S);
+S(1)=[];
+T=100;//simulation time
+
+n=T/Ts*2+1; //no. of discrete points in our domain of analysis
+//Input initialization T min is the Time for simulation
+//We take a few u values in negative time to facilitate 
+//usage of step response model
+u=zeros(n,1);
+d=zeros(n,1);
+delta_u=zeros(n,1);
+delta_u(101+2)=1; //Step change at t=2 min
+u=cumsum(delta_u);
+delta_d=zeros(n,1);
+delta_d(101+8)=0.15;//disturbance t=8 min
+d=cumsum(delta_d);
+
+yhat=zeros(n,1); //J step ahead predictions
+ytilda=zeros(n,1); //J step ahead predictions corrected
+b=zeros(n,1); //corrections
+
+t=-(n-1)/2:Ts:(n-1)/2;
+
+for k=(n-1)/2+1-J:n-J
+    yhat(k+J)=S(1:N-1)'*flipdim(delta_u(k+J-N+1:k+J-1),1)+S(N)*u(k+J-N);
+    //Predicted y  Eqn 20-10
+    y(k+J)=S(1:N-1)'*flipdim(delta_u(k+J-N+1:k+J-1),1)+S(N)*u(k+J-N)+...
+            S(1:N-1)'*flipdim(delta_d(k+J-N+1:k+J-1),1)+S(N)*d(k+J-N);
+    //Actual values of the process
+    b(k+J)=y(k)-yhat(k); //Note that there is a delay in corrections
+    //which is opposite of prediction
+end
+ytilda=b+yhat;//calculation of corrected y
+plot(t,y,'-',t,yhat,'-.',t,ytilda,'--');
+set(gca(),"data_bounds",[0 100 0 6]); //putting bounds on display
+l=legend("y","$\hat y$","$\tilde y$",position=4);
+l.font_size=5;
+xtitle("Example 20.4","Time(min)","$y$");
+a=get("current_axes");
+c=a.y_label;c.font_size=5;
+
+
+//======Part b=====//
+G2=syslin('c',4/(20*s+1));//Transfer function
+t2=0:Ts:N*Ts;
+u_sim=ones(1,length(t2));
+u_sim(1:3)=[0 0 0]; //input delay to account for 2 min delay in G
+S2=csim(u_sim,t2,G2)';//generating step response model for model
+//plot(t2,S);
+S2(1)=[];
+
+yhat=zeros(n,1); //J step ahead predictions
+ytilda=zeros(n,1); //J step ahead predictions corrected
+b=zeros(n,1); //corrections
+
+for k=(n-1)/2+1-J:n-J
+    yhat(k+J)=S2(1:N-1)'*flipdim(delta_u(k+J-N+1:k+J-1),1)+S2(N)*u(k+J-N);
+    //Predicted y  Eqn 20-10
+    y(k+J)=S(1:N-1)'*flipdim(delta_u(k+J-N+1:k+J-1),1)+S(N)*u(k+J-N)+...
+            S(1:N-1)'*flipdim(delta_d(k+J-N+1:k+J-1),1)+S(N)*d(k+J-N);
+    //Actual values of the process
+    b(k+J)=y(k)-yhat(k); //Note that there is a delay in corrections
+    //which is opposite of prediction
+end
+ytilda=b+yhat;//calculation of corrected y
+scf();
+plot(t,y,'-',t,yhat,'-.',t,ytilda,'--');
+set(gca(),"data_bounds",[0 100 0 6]); //putting bounds on display
+l=legend("y","$\hat y$","$\tilde y$",position=4);
+l.font_size=5;
+xtitle("Example 20.4","Time(min)","$y$");
+a=get("current_axes");
+c=a.y_label;c.font_size=5;
+
+
+