Question

1. Consider the unity feedback system shown in figure 1 with G(S) -2sti a) Determine the closed loop transfer function TF(s) γ(s) R(s) What are the poles and zeros of TF1(s)? [2 marks] b) For TF(s), calculate the DC gain, natural frequency and damping ratio. Classify TF1(s) as underdamped overdamped, critically damped or undamped [3 marks] c) Use the initial value theorem and final value theorem to determine the initial value (Mo) and final value (M) of the [2 marks] d) For the unit step response of TF1(s), calculate the % overshoot, rise time, peak time and settling time. [4 marks] 3 marks] 1 mark] [2 marks] h) Sketch, on an s-plane, the regions that the poles must be in for a system to be stable, have a natural frequency time domain output y(t) to a unit step input TF(s) (s+10) e) Show that TF-(s) is a good approximation to T(anove for A f) Identify the system type of G(s) g) Determine the steady state error of the system shown in figure 1 to a unit step and a unit ramp o, 2 2 rad/s and have a damping ratio /2/2 [3 marks] R(s) + Y(s) Figure 1

Answer 1