ans =

-0.7727 1.1364

0.2273 -0.3636

0.5000 -0.5000

-0.4091 0.4545

1.6364 -1.8182

-0.1818 0.0909

» Nx = ans(1:4,:)

Nx =

-0.7727 1.1364

0.2273 -0.3636

0.5000 -0.5000

-0.4091 0.4545

» Nu = ans(5:6,:)

Nu =

1.6364 -1.8182

-0.1818 0.0909

» yref = [4;6]

yref =

4

6

» K

K =

0 0 0 0

14.1500 -17.2500 53.0000 -57.7500

» t=[0:100]/20;

» a=A-B*K;

» u=((Nu+K*Nx)*yref*ones(1,length(t)))';

» [y,x] = lsim(a,B,C,[0 0;0 0],u,t);

» plot(t,x)

» grid

» title('Response of states'); xlabel('Time (sec.)'); ylabel('x(t)');

» plot(t,y)

» grid

» title('Output Response'); xlabel('Time (sec.)'); ylabel('y(t)');

» %look at decoupled states:

» [p,l]=eig(a);

» z = inv(v)*x';

» zss=max(max(abs(z)));

» ts = 4/5

ts =

0.8000

» plot(t,abs(z),[0 5],zss*[.98 .98],[0 5],zss*[1.02 1.02],[ts ts],[0 1.02*zss])

» grid

» title('Response of decoupled states'); xlabel('Time (sec.)'); ylabel('z(t)');

» %now let Nu = 0:

» Nu=[0 0;0 0];

» u=((Nu+K*Nx)*yref*ones(1,length(t)))';

» [y,x] = lsim(a,B,C,[0 0;0 0],u,t);

» plot(t,x)

» grid

» title('Response of states (Nu=0)'); xlabel('Time (sec.)'); ylabel('x(t)');

» plot(t,y)

» grid