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

Question

yingyu hua 2023-11-1

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https://ww2.mathworks.cn/matlabcentral/answers/2041481-the-discrepancy-between-continuous-and-discrete-lqr-response-for-the-same-state-space-system

回答： yingyu hua 2023-11-1

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!