Given a Bode diagram of a dynamic system, shown in Fig. 4: (a) Find the transfer function of the system G(s) (asymptotes are drawn for you and their slopes are indicated) T (b) Derive the open-loop system response to a harmonic input 2 cos 10t+- (c) Assuming a negative unity feedback configuration: Determine the gain and phase margins of the system Is the system closed-loop stable? Verify your answer using Nyquist plot (use software to generate Nyquist plot and explain how it confirms your conclusion of closed-loop stability/instability) (d) Assuming a proportional controller with gain Kp and negative unity feedback configuration: Can the system be destabilized by a finite gain proportional controller? If yes, find the gain K, that destabilizes the system. If not, explain why not. (e) Find Kp for the system to have a phase margin 20⁰ (f) What is the system phase margin when Kp = 10? At this value of Kp: What is the steady-state error of the closed-loop system to a step input of magnitude A? ● ● ● What is the steady-state error of the closed-loop system to a ramp input of magnitude A? NOTE: parts (b), (c), (e), (f) need to be solved graphically

Given a Bode diagram of a dynamic system, shown in Fig. 4: (a) Find the transfer function of the system G(s) (asymptotes are drawn for you and their slopes are indicated) T (b) Derive the open-loop system response to a harmonic input 2 cos 10t+- (c) Assuming a negative unity feedback configuration: Determine the gain and phase margins of the system Is the system closed-loop stable? Verify your answer using Nyquist plot (use software to generate Nyquist plot and explain how it confirms your conclusion of closed-loop stability/instability) (d) Assuming a proportional controller with gain Kp and negative unity feedback configuration: Can the system be destabilized by a finite gain proportional controller? If yes, find the gain K, that destabilizes the system. If not, explain why not. (e) Find Kp for the system to have a phase margin 20⁰ (f) What is the system phase margin when Kp = 10? At this value of Kp: What is the steady-state error of the closed-loop system to a step input of magnitude A? ● ● ● What is the steady-state error of the closed-loop system to a ramp input of magnitude A? NOTE: parts (b), (c), (e), (f) need to be solved graphically

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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