Use ultimate sensitivity tuning to tune the controller gains.
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
Related questions
Question
Use ultimate sensitivity tuning to tune the controller gains.
![**Part 8: PID Controller**
(a) Use ultimate sensitivity tuning to tune the controller gains.
\[ G_c = K_p \left(1 + T_D s + \frac{1}{T_I s}\right) \]
For PID: \( K_p = 0.6K_u \)
\[ T_I = \frac{P_u}{2} \quad T_D = \frac{P_u}{8} \]
**Block Diagram:**
1. Input: \( R(s) \)
2. Summation point (subtracts feedback)
3. Controller \( G_c \)
4. Transfer function block: \(\frac{100}{s^3 + 10s^2 + 61s + 1300} \)
5. Output: \( Y(s) \)
**Parameters:**
- \( K_u = \)
- \( K_D = \)
- \( T_d = \)
- \( P_u = \)
- \( T_i = \)
**Explanation of Diagram:**
The diagram consists of a control loop with a summation point that subtracts feedback \( Y(s) \) from the input \( R(s) \), fed into the controller \( G_c \). The resultant signal is processed through a transfer function represented by a block with the specified equation, and the output is denoted as \( Y(s) \).
The equations and parameters provided are typically used to tune the PID controller parameters based on ultimate sensitivity method, where \( K_p \), \( T_I \), and \( T_D \) define the proportional, integral, and derivative gains.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9048bbbd-0e8a-43c6-a906-7a61c8fe333b%2F92f5997f-174e-4350-b1ea-0979ab7ace7a%2F2lczsyl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Part 8: PID Controller**
(a) Use ultimate sensitivity tuning to tune the controller gains.
\[ G_c = K_p \left(1 + T_D s + \frac{1}{T_I s}\right) \]
For PID: \( K_p = 0.6K_u \)
\[ T_I = \frac{P_u}{2} \quad T_D = \frac{P_u}{8} \]
**Block Diagram:**
1. Input: \( R(s) \)
2. Summation point (subtracts feedback)
3. Controller \( G_c \)
4. Transfer function block: \(\frac{100}{s^3 + 10s^2 + 61s + 1300} \)
5. Output: \( Y(s) \)
**Parameters:**
- \( K_u = \)
- \( K_D = \)
- \( T_d = \)
- \( P_u = \)
- \( T_i = \)
**Explanation of Diagram:**
The diagram consists of a control loop with a summation point that subtracts feedback \( Y(s) \) from the input \( R(s) \), fed into the controller \( G_c \). The resultant signal is processed through a transfer function represented by a block with the specified equation, and the output is denoted as \( Y(s) \).
The equations and parameters provided are typically used to tune the PID controller parameters based on ultimate sensitivity method, where \( K_p \), \( T_I \), and \( T_D \) define the proportional, integral, and derivative gains.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Recommended textbooks for you
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
Industrial Plastics: Theory and Applications
Chemical Engineering
ISBN:
9781285061238
Author:
Lokensgard, Erik
Publisher:
Delmar Cengage Learning
Unit Operations of Chemical Engineering
Chemical Engineering
ISBN:
9780072848236
Author:
Warren McCabe, Julian C. Smith, Peter Harriott
Publisher:
McGraw-Hill Companies, The