*(t) (t) 1 0 y(t) = [O 1]x(t) ) 01( [1 ]xce) + (!] uce O h [1 0 x(kh+h) (kh h 1h y(kh) = [01]x(kh) A 1+2]x02) + (4) u(kh

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T T 1 0 Y T O 1 X T 01 1 Xce Uce O H 1 0 X Kh H Kh H 1h Y Kh 01 X Kh A 1 2 X02 4 U Kh 1 (82.42 KiB) Viewed 28 times

*(t) (t) 1 0 y(t) = [O 1]x(t) ) 01( [1 ]xce) + (!] uce O h [1 0 x(kh+h) (kh h 1h y(kh) = [01]x(kh) A 1+2]x02) + (4) u(kh) 2 = c) Let h = 1. Design for the discretized system a state feedback control law of the form u[k] = myref – Lx[k] = where m is constant Yref is the reference and La gain vector. Assume that the states are measurable, the desired closed loop poles are 0.5 0.5 and the static gain of the closed loop system is 1. d) Suppose now that only the input u and output y are measured (i.e., 21 is not measured). Design a discrete-time controller to the process, which consists of a combination of state feedback and state observer as u[k] = myref = Lk[k] The desired closed loop poles due to state feedback are, as before, 0.5 = 20.5 and the observer has the dead-beat characteristics. Choose the pre- compensator coefficient m such that the output of the controlled process follows the reference. Verify the performance