Consider the linear system whose open-loop dynamics are described by the transfer function: G(s)=(s+4)(s+3)(s1) The system is subject to an unmeasured disturbance dg(t)=k+sin(4t+) where k, and are unknown constants. a) Using pole placement, design a biproper controller that stabilizes the closed-loop control system and achieves zero steady-state output error. Consider a closed-loop characteristic polynomial of the form: Acl(s)=(s+4)(s+3)(s+1)(s+2)r where r is an integer to be assigned in the design of the controller. b) Compute the resulting sensitivity function S(s) and evaluate its value at s=0,s=1 and s=4i c) Compute the complementary sensitivity function T(s). Evaluate the poles and zeros of T(s). d) Compute the amplitude ratio of T(s). Provide a sketch of the amplitude plot of the Bode plot of T(s). Approximate the frequency at which the maximum amplitude ratio occurs