Answer Happy

Question 4-(30pts) Assume that a system has open loop poles at the origin and at -1. We want to design a PD compensator which achieves a settling time of 4s and an O.S% of 16.3. If the proposed PD compensator is in cascade form and has a zero at-4, a) Show using Root Locus that the proposed controller can indeed achieve these performance goals. b) Show that the required feedback gain is 1. Question 5 (30pts). The state space model of a DC motor is given by the equations: *-44)-8* --. Where the states x-[x1,x2] correspond to angular displacement and velocity respectively and V is the voltage input Determine the controllability and observability of the system and design a full state feedback controller that will place the closed loop poles at -1 and make the system critically damped. Question 6 (20pt): For the closed system transfer function given below, determine for which values of k the system will be stable using the Routh Hurwitz method. k s+10s +31s+ 30+ k