3. Consider a unity-feedback control system with plant G(s) following figure. 316 and controller C(s), as shown in the Reference Error Controller Plant r(t) e(t) u(t) y(1) C(s) G(s) (a) De oles rela iegr C gain and (b) Саp necessar and sucient. of K nat re (c) Show using the Final Value Theorem that the system with the P controller from (b) can track a init-step reference r(t) = 1 with zero steady-state error lim+o e(t) = 0. (d) Show that it however cannot track a unit-ramp reference r(t) =t with zero steady-state error. Can the error be made arbitrarily small with Kp without losing stability? (e) Can a PI controller C(s) = Kp + AL stabilize the plant G(8) and, at the same time, yield zero steady-state error to both unit-step and unit-ramp references? If so, find the values of Kp and Ki that are necessary and sufficient. Reconsider the unity-feedback control system shown in Problem 3 and let the controller C(s) and plant G(s) be defined as follows. (a) Let C(s) = Kp and G(s) = : Find the value of Kp that yields 10% of overshoot in y(t) when r(t) is a unit-step input. Hint: 2nd-order system. (s+3) (b) Let C(s) = Kp and G(s) = G+US+2+46+5): Sketch the root locus of the open-loop transfer function C(s)G(s) by hand and using MATLAB's rlocus. Derive a condition that Kp must satisfy in order for the closed-loop system to be asymptotically stable. %3D
3. Consider a unity-feedback control system with plant G(s) following figure. 316 and controller C(s), as shown in the Reference Error Controller Plant r(t) e(t) u(t) y(1) C(s) G(s) (a) De oles rela iegr C gain and (b) Саp necessar and sucient. of K nat re (c) Show using the Final Value Theorem that the system with the P controller from (b) can track a init-step reference r(t) = 1 with zero steady-state error lim+o e(t) = 0. (d) Show that it however cannot track a unit-ramp reference r(t) =t with zero steady-state error. Can the error be made arbitrarily small with Kp without losing stability? (e) Can a PI controller C(s) = Kp + AL stabilize the plant G(8) and, at the same time, yield zero steady-state error to both unit-step and unit-ramp references? If so, find the values of Kp and Ki that are necessary and sufficient. Reconsider the unity-feedback control system shown in Problem 3 and let the controller C(s) and plant G(s) be defined as follows. (a) Let C(s) = Kp and G(s) = : Find the value of Kp that yields 10% of overshoot in y(t) when r(t) is a unit-step input. Hint: 2nd-order system. (s+3) (b) Let C(s) = Kp and G(s) = G+US+2+46+5): Sketch the root locus of the open-loop transfer function C(s)G(s) by hand and using MATLAB's rlocus. Derive a condition that Kp must satisfy in order for the closed-loop system to be asymptotically stable. %3D
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
Related questions
Question
Part F and not the matlab part. Thanks
Transcribed Image Text:3. Consider a unity-feedback control system with plant G(s)
following figure.
316 and controller C(s), as shown in the
%3D
Reference
Error Controller
Plant
r(t)
e(t)
u(t)
y(1)
C(s)
G(s)
(a) De
Poles
rela
iegre
-C gain
and
(b) Саp
necessar and sucient.
of K nat re
(c) Show using the Final Value Theorem that the system with the P controller from (b) can track a
init-step reference r(t) = 1 with zero steady-state error lim-oo e(t) = 0.
(d) Show that it however cannot track a unit-ramp reference r(t) =t with zero steady-state error.
Can the error be made arbitrarily small with Kp without losing stability?
(e) Can a PI controller C(s) = Kp + AL stabilize the plant G(8) and, at the same time, yield zero
steady-state error to both unit-step and unit-ramp references? If so, find the values of Kp and
Ki that are necessary and sufficient.
Reconsider the unity-feedback control system shown in Problem 3 and let the controller C(s) and plant
G(s) be defined as follows.
(a) Let C(s) = Kp and G(s) = : Find the value of Kp that yields 10% of overshoot in y(t)
when r(t) is a unit-step input. Hint: 2nd-order system.
(s+3)
(b) Let C(s) = Kp and G(s) = S+21ASL5): Sketch the root locus of the open-loop transfer
function C(s)G(s) by hand and using MATLAB's rlocus. Derive a condition that Kp must
satisfy in order for the closed-loop system to be asymptotically stable.
%3D
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Power System Analysis and Design (MindTap Course …
Electrical Engineering
ISBN:
9781305632134
Author:
J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:
Cengage Learning
Power System Analysis and Design (MindTap Course …
Electrical Engineering
ISBN:
9781305632134
Author:
J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:
Cengage Learning