Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
A process has the transfer function,

A process has the transfer function,

Introductory Circuit Analysis (13th Edition)
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...
See similar textbooks
icon
Related questions
Question
100%
12.1 A process has the transfer function, \[ G(s) = \frac{K}{(10s + 1)(5s + 1)} \] where \( K \) has a nominal value of \( K = 1 \). PID controller settings are to be calculated using the Direct Synthesis approach with \( \tau_c = 5 \) min. Suppose that these controller constants are employed and that \( K \) changes unexpectedly from 1 to \( 1 + \alpha \). (a) For what values of \( \alpha \) will the closed-loop system be stable? (b) Suppose that the PID controller constants are calculated using the nominal value of \( K = 1 \) but it is desired that the resulting closed-loop system be stable for \( |\alpha| \leq 0.2 \). What is the smallest value of \( \tau_c \) that can be used? (c) What conclusions can be made concerning the effect that the choice of \( \tau_c \) has on the robustness of the closed-loop system to changes in steady-state gain \( K \)?
Transcribed Image Text:12.1 A process has the transfer function, \[ G(s) = \frac{K}{(10s + 1)(5s + 1)} \] where \( K \) has a nominal value of \( K = 1 \). PID controller settings are to be calculated using the Direct Synthesis approach with \( \tau_c = 5 \) min. Suppose that these controller constants are employed and that \( K \) changes unexpectedly from 1 to \( 1 + \alpha \). (a) For what values of \( \alpha \) will the closed-loop system be stable? (b) Suppose that the PID controller constants are calculated using the nominal value of \( K = 1 \) but it is desired that the resulting closed-loop system be stable for \( |\alpha| \leq 0.2 \). What is the smallest value of \( \tau_c \) that can be used? (c) What conclusions can be made concerning the effect that the choice of \( \tau_c \) has on the robustness of the closed-loop system to changes in steady-state gain \( K \)?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Mathematical Modeling of Mechanical System
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
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,
SEE MORE TEXTBOOKS