Suppose the open-loop plant, and the controller, s+1 P(s): s(s + 10) C(s) = k are structured in a unity feedback control scheme. Assume k > 0. a) b) d) Find the closed-loop transfer function G(s) from r to y as a ratio of polynomials in s: Sketch the desired pole region if the closed-loop step response is to satisfy: tr < 0.6s Mp < 43.1% Determine which element of the specification (t, or Mp) will always be satisfied regard- less of the value of k. You must justify your answer. HINT: Consider the poles of G(s). r(t) = t. Determine the steady-state error e(0) for tracking when the reference is a ramp input