the discrepancy between continuous and discrete LQR response for the same state space system

Hi

I have a continuous state space system: dx=Ag*x+Bu*u+Bg*Xr; y=Cy*X+Dyu*u+Dy*Xr; Xr is the excitation, u is the LQR control force, y is the state vector. Xr is the excitation sampled by0.01s.

In the program, first the continuous LQR control force is derived by the lqr command; the continuous state vector"statecon" preserves the continuous LQR response. Then the continous system is discretized by 0.01s and the discrete LQR is derived by dlqr/lqrd command, the state vector xx2 is for the discrete LQR response.

I compared the discrete and continuous response , 4 elements and the control force, it turns out the continuous and discrete system has quite different response, except the 2nd state (figure1).

I am expecting the discrete response are very close to the continuous one, I wonder if the program is accurate or I made a mistake? should the discrete system deviate from the continuous system so much?

Thanks for your advice in advance!

Answer 1

[yingyu hua]

Please run the differentofdiscreteLQRandconLQR.m file