[Solved]Consider System Following State Equation A1 T 212 151 X1 2 X1 T 0 01 2 1×2 T X3 T Y T Unit Q37179384

Consider a system with the following state equation a1(t) 21.2 -1.51[x1 [2 x1 (t) [0 0.1 2] 1×2(t) X3(t) y(t) The unit step response is required to have a settling time of less than 2 seconds and a percent overshoot of less than 5%. In addition a zero steady-state error is needed. The goal is to design the state feedback control law in the form of u(t) = Kx(t) + Gr(t) (a) Find the desired region of the S-plane for two dominant closed loop eigenvalues to ensure the settling time and overshoot requirements are satisfied. Pick the desired location of dominant eigenvalues as well as the third eigenvalue. (b) Use MATLAB to find the feedback gain matrix K that places the closed-loop eigenvalues at desired locations selected in part (a). (use place or acker commands) (c) Find the value of G that satisfies the steady-state error requirement (d) With r(t) as the input, use MATLAB to plot the unit step response of the closed-loop ystem and verify that all requirements are satisfied . s Attach your code and MATLAB results. Add explanation/analysis wherever needed. Show transcribed image text Consider a system with the following state equation a1(t) 21.2 -1.51[x1 [2 x1 (t) [0 0.1 2] 1×2(t) X3(t) y(t) The unit step response is required to have a settling time of less than 2 seconds and a percent overshoot of less than 5%. In addition a zero steady-state error is needed. The goal is to design the state feedback control law in the form of u(t) = Kx(t) + Gr(t)
(a) Find the desired region of the S-plane for two dominant closed loop eigenvalues to ensure the settling time and overshoot requirements are satisfied. Pick the desired location of dominant eigenvalues as well as the third eigenvalue. (b) Use MATLAB to find the feedback gain matrix K that places the closed-loop eigenvalues at desired locations selected in part (a). (use place or acker commands) (c) Find the value of G that satisfies the steady-state error requirement (d) With r(t) as the input, use MATLAB to plot the unit step response of the closed-loop ystem and verify that all requirements are satisfied . s Attach your code and MATLAB results. Add explanation/analysis wherever needed.

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Answer to Consider a system with the following state equation a1(t) 21.2 -1.51[x1 [2 x1 (t) [0 0.1 2] 1×2(t) X3(t) y(t) The unit s… . . .