An electronic PID temperature controller is at steady state with an output of 12 mA. The set point equals the nominal process temperature initially. At t = 0, the set point is increased at the rate of 0.5 mA/min (equivalent to a rate of 2°F/min). If the PID transfer function and current settings are: P'(s) E(s) =Kc1+ C - 1 T₁S + TDS Kc = 2 (dimensionless) tl = 1.5 min TD = 0.5 min (a) Derive an expression for the controller output p(t). (b) Repeat (a) for a PI controller. (c) Plot the two controller outputs in Simulink and qualitatively discuss their differences.
An electronic PID temperature controller is at steady state with an output of 12 mA. The set point equals the nominal process temperature initially. At t = 0, the set point is increased at the rate of 0.5 mA/min (equivalent to a rate of 2°F/min). If the PID transfer function and current settings are: P'(s) E(s) =Kc1+ C - 1 T₁S + TDS Kc = 2 (dimensionless) tl = 1.5 min TD = 0.5 min (a) Derive an expression for the controller output p(t). (b) Repeat (a) for a PI controller. (c) Plot the two controller outputs in Simulink and qualitatively discuss their differences.
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
![**Electronic PID Temperature Controller Analysis**
An electronic PID temperature controller operates at a steady state with an output of 12 mA. Initially, the set point equals the nominal process temperature. At time \( t = 0 \), the set point is increased at a rate of 0.5 mA/min (equivalent to a rate of 2°F/min). The PID transfer function and the current settings are as follows:
\[
\frac{P'(s)}{E(s)} = K_c \left[ 1 + \frac{1}{\tau_I s} + \tau_D s \right]
\]
- **\( K_c \) (Controller Gain):** 2 (dimensionless)
- **\( \tau_I \) (Integral Time):** 1.5 min
- **\( \tau_D \) (Derivative Time):** 0.5 min
**Tasks:**
(a) Derive an expression for the controller output \( p(t) \).
(b) Derive the expression for a PI controller output.
(c) Plot the two controller outputs in Simulink and qualitatively discuss their differences.
This exercise involves understanding the differences between PID and PI controllers and their respective outputs when subjected to a change in the set point. The derived expressions and Simulink plots will aid in visualizing and analyzing these differences.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ef5005f-99e9-4e7d-9469-054276644387%2F9492520e-f77c-40c0-8c1e-c37297cb3945%2Fxqcg4fm_processed.png&w=3840&q=75)
Transcribed Image Text:**Electronic PID Temperature Controller Analysis**
An electronic PID temperature controller operates at a steady state with an output of 12 mA. Initially, the set point equals the nominal process temperature. At time \( t = 0 \), the set point is increased at a rate of 0.5 mA/min (equivalent to a rate of 2°F/min). The PID transfer function and the current settings are as follows:
\[
\frac{P'(s)}{E(s)} = K_c \left[ 1 + \frac{1}{\tau_I s} + \tau_D s \right]
\]
- **\( K_c \) (Controller Gain):** 2 (dimensionless)
- **\( \tau_I \) (Integral Time):** 1.5 min
- **\( \tau_D \) (Derivative Time):** 0.5 min
**Tasks:**
(a) Derive an expression for the controller output \( p(t) \).
(b) Derive the expression for a PI controller output.
(c) Plot the two controller outputs in Simulink and qualitatively discuss their differences.
This exercise involves understanding the differences between PID and PI controllers and their respective outputs when subjected to a change in the set point. The derived expressions and Simulink plots will aid in visualizing and analyzing these differences.
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 5 steps with 5 images
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