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% Example 3.32 
% 
% Pole placement -- using place function in MATLAB 
% 
disp('Pole placement -- using place function in MATLAB') 
a=[0 1 0; 0 0 1; 0 -2 -3]; 
b=[0; 0; 1]; 
c=[1 0 0]; 
d=[0]; 
disp('The rank of controllability matrix') 
rc=rank(ctrb(a,b)) 
p=[-2+2*sqrt(3)*i -2-2*sqrt(3)*i -10]; 
k=place(a,b,p) 
a1=a-b*k; 
b1=b*k(1); 
c1=c; d1=d; 
figure(1) 
step(a1,b1,c1,d1) 
title('Step Response of Designed Servo System') 
figure(2) 
[y,x,t]=step(a1,b,c1,d1); 
plot(t,x) 
title('Step Response Curves for x1,x2,x3') 
grid on