Assume that the process is described by the transfer function H(z) =z - 0.5/z² - 1 The reference model is specified as Hm(z)=1/z^2 a) Design a controller in the form of R(q)u(k) = T(q)uc(k) — S(q)y(k) to make the closed-loop transfer function match the reference model as close as possible. Also try to make the controller reject constant disturbance. b) Design a two-degree-of-freedom controller in the form ofu(k) =ufb(k) +uff(k)where the feedback control signal uƒó(k) is generated by the feedbackcontrollerS(z)Ugs(=) = 5(-) Y (2)R(z)and the feed-forward control signal uƒƒ(k) is produced by the feed-forward controllerUƒƒ(z) = Hƒƒ(z)Uc(z)Design the feedback controller and feed-forward controller properly tofollow the same reference model and to reject constant disturbance.

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