A second-degree process is controlled using a closed-loop feedback control system and a PI controller. Using the transfer functions given below: Gp(s) = 2 (4s + 1)(s + 1) 1 (s + 1)² G₂ (s) = Ge(s) = 1 Ga(s) a) Produce the transfer function of the closed loop system for setpoint change. b) Derive the transfer function of the closed loop system for the disruptive effect. c) Kc values that ensure the stable operation of the control system in the case when ti = 4 determine. Can setting K to very large values lead this closed loop control system to an unstable state? d) Determine the dynamic behavior of the control system in the case when Kc=2 and ti= 4 (over- damped, critically damped, underdamped). If the control system is underdamped, calculate the damping coefficient.

A second-degree process is controlled using a closed-loop feedback control system and a PI controller. Using the transfer functions given below: Gp(s) = 2 (4s + 1)(s + 1) 1 (s + 1)² G₂ (s) = Ge(s) = 1 Ga(s) a) Produce the transfer function of the closed loop system for setpoint change. b) Derive the transfer function of the closed loop system for the disruptive effect. c) Kc values that ensure the stable operation of the control system in the case when ti = 4 determine. Can setting K to very large values lead this closed loop control system to an unstable state? d) Determine the dynamic behavior of the control system in the case when Kc=2 and ti= 4 (over- damped, critically damped, underdamped). If the control system is underdamped, calculate the damping coefficient.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

A second-degree process is controlled using a closed-loop feedback control system and a Pl
controller. Using the transfer functions given below:
Gp (s)
2
(4s + 1)(s + 1)
Ga(s) = (s + 1)
G₂ (s) = G(s) = 1
a) Produce the transfer function of the closed loop system for setpoint change.
b) Derive the transfer function of the closed loop system for the disruptive effect.
c) Kc values that ensure the stable operation of the control system in the case when ti = 4
determine. Can setting K to very large values lead this closed loop control system to an unstable
state?
3 b
d) Determine the dynamic behavior of the control system in the case when Kc=2 and Ti= 4 (over-
damped, critically damped, underdamped). If the control system is underdamped, calculate the
damping coefficient.

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