Problem 5. (10 points) Consider the system (k+1) = ör(k) +Tu(k) + I'w(k), y(k) = Hc(k) (1) where x(k) state vector, u(k)

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Problem 5 10 Points Consider The System K 1 Or K Tu K I W K Y K Hc K 1 Where X K State Vector U K 1 (46.17 KiB) Viewed 59 times

Problem 5. (10 points) Consider the system (k+1) = ör(k) +Tu(k) + I'w(k), y(k) = Hc(k) (1) where x(k) state vector, u(k) control input, w(k) disturbance, and y(k) system output. Assume that reference input is r(k), define e(k) = y(k) – r(k), and control is given by u(k) = -K11/(k) - Kr(k) + N r(k) (2) with the integral term 21(k+ 1) = x1(k) +ek) (3) ) Derive the closed-loop system state-space model in the form of X(k+1) = P_X(k) + cor(k) + Ivw(k), y(k) = H X(k) by finding the expressions of co, IcoT, and H., where X(k) = (x1(k), 27 (k)T is the , Heo [] augmented state vector.