A8 = 8 A9=2

please attach any matlab screenshots for graphs and any code used please answer all parts

[EEE2012-Control] Question 3 The block diagram of a plant is shown in figure 3. Gs(s) x(s) Y(s) Gl(s) Gz(s) G3(s) G4(s) Hz(s) Hz(s) Figure 3 The sub systems have the following transfer functions; Gr(s)=15+8 1 1 G2(s)= (s + 2) G;(s) = (5+4) G4(S) 1 (s2 + 3s +36) (s + 5) G5(s)= (s +ag) Hirag H2=1 a. Use the appropriate Matlab commands to simplify the block diagram and to find the overall transfer function of the plant. (12 marks] b. What are the order and type of the overall system? [2 marks] C. Find the poles and zeros of the system, sketch the pole-zero map and discuss which poles dominate the systems' response. [6 marks] d. Based on the pole-zero map found in c., find a simplified reduced order system model which adequately represents the system dynamics and matches the steady-state performance. State any assumptions you have made. [6 marks] Page 8 of 9 [EEE2012-Control] e. Sketch the initial and simplified system response to a unit step input (superimpose both time domain responses on a single plot) and comment on the validity of the simplified reduced order system model. [6 marks] f. Sketch the root locus of the reduced order system and comment on the system dynamics and stability. [6 marks] g. If a proportional controller is used to control the system, find the closed loop transfer function of the reduced order system with unity feedback and explain if the proportional controller is a suitable choice for the system. [6 marks] h. Sketch the time domain response of the reduced order system in reaction to a unit step input when Kp= 500 and discuss how the time response confirms your answer to part g. [6 marks] END Page 9 of 9