Answer Happy

Question 2 (10 +10 +10+15 = 45 marks) E(S) Ge(s) C(s) R(S) G(s) Figure 2: Unity feedback control system for Question 2 For the unity feedback control system shown in Figure 2, Q= 983 2 G(S) $(5+1)(5+ (a+4) a) Determine the phase margin, the gain crossover frequency, the gain margin, the phase crossover frequency of the system when Gc(s)=1; (10 marks) b) Design a proportional controller Gc(s)=K so that a phase margin of 50° is achieved. Determine the system bandwidth for this design; (10 marks) c) Determine the velocity error constant Kr and the steady state error of the system with a unit ramp input when Gc(s)=1; (10 marks) d) Design a lag compensator so that the closed-loop system satisfies the following specifications: i. ii. iii. the steady-state velocity error constant has a value of Kv=5; A gain-crossover angular frequency of not more than 1 rad/s; a phase margin of 40°. (15 marks)