Time response for optimal tracking problem

[sbashrawi]

Homework Statement

Hi guys
I want to know how to plot time responce for optimal tracking problem.
I have the following information
state equation
dx = AX+Bu
Y =Cx
want to track a comand z= [z1;z2] constant
I know that we need to find the feedback gain by
sys= ss(A,B,C,D)
[K,S,E] = lqr(sys,Q,R)
the initial condition is given
closed loop matrix is given by A_closed = A - B*K

HOw can I use these information: A_cloosed, Z , initial contion to plot the time response
in matalb ?

Any help please

Homework Equations

The Attempt at a Solution

 

[Valkarie]

Assuming you are familiar with the MATLAB syntax, you can use the following commands to plot the time response of your system.First, define the system: sys = ss(A,B,C,D);Next, calculate the feedback gain K: [K,S,E] = lqr(sys,Q,R);After that, calculate the closed loop matrix A_closed: A_closed = A - B*K;Then, define the state space model with the initial condition: x0 = [x10;x20]; % initial conditionmodel = ss(A_closed,B,C,D,x0);Finally, plot the time response: t = 0:0.01:10; % time vectorz = [z1;z2]; % command signal[y,t] = lsim(model,z,t);plot(t,y);