1.1. Consider the system in the figure below containing second-order dynamics under feedback control with a proportional-derivative (PD) controller. Using any method you choose, show that the proposed PD control system cannot obtain zero offset for changes in the reference signal R(s).. R(s) Kc(1+ KDS) 1 (s+2)² Y(s) 1.2. Consider a first-order plus dead-time model in standard form such that Y(s) Kpe-0s U(s) TS+1 with positive process gain 1.3. Kp > 0. If the system is controlled using a stable PID feedback controller with G₁(s) = Kc (1 + ±1. 1½ + Kas), complete the table below by circling the best answer indicating (i) The sign that is expected for the controller term. (ii) The effect that an increase in the tuning parameter will have on steady-state offset. TI S (iii) What direction you would change the tuning parameter to increase the controller's aggression. (iv) How the tuning parameters will likely need to be changed if any of the process parameters increase. Tuning response to ↑ in process parameter (circle) Tuning Parameter Sign (circle) Effect on SS offset A for more controller "aggression" (circle) (circle) KP 0 τ Proportional, Kc + ↑ (none) ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ Integral, ti ↑ (none) ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ Derivative, KD + ↑ (none) ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ first-order systems under proportional control have extremely fast response times and nearly zero offset as we increase the controller gain Kc → ∞. Succinctly give two reasons why using extremely large values of Kε is not possible in practice.
1.1. Consider the system in the figure below containing second-order dynamics under feedback control with a proportional-derivative (PD) controller. Using any method you choose, show that the proposed PD control system cannot obtain zero offset for changes in the reference signal R(s).. R(s) Kc(1+ KDS) 1 (s+2)² Y(s) 1.2. Consider a first-order plus dead-time model in standard form such that Y(s) Kpe-0s U(s) TS+1 with positive process gain 1.3. Kp > 0. If the system is controlled using a stable PID feedback controller with G₁(s) = Kc (1 + ±1. 1½ + Kas), complete the table below by circling the best answer indicating (i) The sign that is expected for the controller term. (ii) The effect that an increase in the tuning parameter will have on steady-state offset. TI S (iii) What direction you would change the tuning parameter to increase the controller's aggression. (iv) How the tuning parameters will likely need to be changed if any of the process parameters increase. Tuning response to ↑ in process parameter (circle) Tuning Parameter Sign (circle) Effect on SS offset A for more controller "aggression" (circle) (circle) KP 0 τ Proportional, Kc + ↑ (none) ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ Integral, ti ↑ (none) ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ Derivative, KD + ↑ (none) ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ first-order systems under proportional control have extremely fast response times and nearly zero offset as we increase the controller gain Kc → ∞. Succinctly give two reasons why using extremely large values of Kε is not possible in practice.
Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter12: Power System Controls
Section: Chapter Questions
Problem 12.2P
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Please explain step by step in detail. I am most confused about the table. Thank you
Transcribed Image Text:1.1. Consider the system in the figure below containing second-order dynamics under feedback control with a
proportional-derivative (PD) controller. Using any method you choose, show that the proposed PD control
system cannot obtain zero offset for changes in the reference signal R(s)..
R(s)
Kc(1+ KDS)
1
(s+2)²
Y(s)
1.2. Consider a first-order plus dead-time model in standard form such that
Y(s)
Kpe-0s
U(s) TS+1
with positive process gain
1.3.
Kp > 0. If the system is controlled using a stable PID feedback controller with G₁(s) = Kc (1 + ±1. 1½ + Kas),
complete the table below by circling the best answer indicating
(i) The sign that is expected for the controller term.
(ii) The effect that an increase in the tuning parameter will have on steady-state offset.
TI S
(iii) What direction you would change the tuning parameter to increase the controller's aggression.
(iv) How the tuning parameters will likely need to be changed if any of the process parameters increase.
Tuning response to ↑ in
process parameter (circle)
Tuning
Parameter
Sign
(circle)
Effect on
SS offset
A for more
controller
"aggression"
(circle)
(circle)
KP
0
τ
Proportional, Kc
+
↑
(none) ↓
↑
↓
↑
↓
↑
↓
↑
↓
Integral, ti
↑ (none) ↓
↑
↓
↑
↓
↑
↓
↑
↓
Derivative, KD
+
↑ (none) ↓
↑
↓
↑
↓
↑
↓
↑
↓
first-order systems under proportional control have extremely fast response
times and nearly zero offset as we increase the controller gain Kc → ∞. Succinctly give two reasons why using
extremely large values of Kε is not possible in practice.
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