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% Example 3.47 
% 
% Design of quadratic optimal regulator system 
% 
a=-diag([0.2 0.5 14.3 33.3 10])+diag([0.5 1.6 85.8 100],1); 
b=[0 0 0 0 30]'; 
c=[1 0 0 0 0]; d=[0]; 
q=diag([1 1 1 1 1]); r=1; 
[k,p,e]=lqr(a,b,q,r); 
disp(' The optimal feedback gain matrix k is') 
k 
 
% 
% Step response 
% 
% The close loop state system is denoted as (ac,bc,cc,dc) 
% 
k1=k(1); 
ac=a-b*k; 
bc=b*k1; 
cc=c; dc=d; 
figure(1) 
step(ac,bc,cc,dc) 
title('Step Response of Quadratic Optimal Control system') 
xlabel('Sec') 
ylabel('Output y=x1') 
figure(2) 
[y,x,t]=step(ac,bc,cc,dc); 
plot(t,x,'y') 
title('Step Response Curves for x1,x2,x3,x4,x5') 
xlabel('Sec') 
ylabel('x1,x2,x3,x4,x5')