Techniques of Model Based Control
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Summary
For upper-level undergraduate and graduate level Chemical Engineering courses
in process control as well as professional Instrument and Control Engineers,
Systems Engineers, Process Engineers, and Chemical Engineers interested in developing
a better understanding of the concepts used in model-based control.
A comprehensive introduction to the concepts, techniques, and applications
of model-based process control that presents the process control problem as
a subset of overall plant operations problem rather than as a separate discipline.
In addition, the approaches presented in the book are motivated by their use
in solving practical problems, thus emphasizing methods rather than theory.
The examples used to illustrate these methods and the MATLAB software that is
included are further intended to assist the reader in the design and tuning
of actual control systems.
Features
Comprehensive introduction to model-based control—And its relation to
classical control methods.
Provides an understanding of the theory behind the methods used in process control
through an in-depth analysis of model-based control techniques.
Powerful techniques of advanced control—Including easy-to-use methods for
incorporating process uncertainty into control system design and tuning.
Introduces advanced methods and offers new insights into the techniques of model
based control needed to solve tough control problems.
MATLAB software—Containing .m files.
Helps students solve exercise problems while it reinforces concepts through
practice problems and allows for hands-on training of control system tuning,
design, and evaluation.
Table of Contents
Preface
Acknowledgements.
1. Introduction.
Nature of The Process Control Problem. Overview of Model Based Process Control.
Summary.
2. Continuous-Time Models.
Introduction. Process Model Representations. Time Domain Models. Laplace Domain
Models. FOPDT Models and Model Identification.
3. One-Degree of Freedom Internal Model Control.
Introduction. Properties of IMC. IMC Designs for No Disturbance Lag. Design
for Processes with No Zeros Near the Imaginary Axis or in the Right Half of
the s-Plane. Design for Processes with Zeros Near the Imaginary Axis. Design
for Processes with Right Half Plane Zeros. Problems with Mathematically Optimal
Controllers. Modifying the Process to Improve Control System Performance. Software
Tools for IMC Design. Summary.
4. Two-Degree of Freedom Internal Model Control.
Introduction. Structure of Two-Degree of Freedom IMC. Design for Stable Processes.
Design for Unstable Processes. Software Tools For 2DF IMC Designs. Summary.
5. Model State Feedback Implementations of IMC Systems.
Motivation. MSF Implementation of 1DF IMC. SIMULINK Realization of MSF Implementation
of IMC. Finding A Safe Lower Bound on the MSF Filter Time Constant. MSF Implementation
of 2DF IMC. Summary.
6. PI and PID Parameters From IMC Designs.
Introduction. The PID Controller. PID Parameters from IMC Controllers. Algorithms
and Software For Computing PID Parameters. Accommodating Negative Integral and
Derivative Time Constants. 2DF PID Parameters from 2DF IMC. Saturation Compensation.
Summary.
7. Tuning and Synthesis of 1DF IMC for Uncertain Processes.
Introduction. Process Uncertainty Descriptions. Mp Tuning. Conditions For Existence
of Solutions to The Mp Tuning Problem. Mp Synthesis. Software for Mp Tuning
and Synthesis. Summary.
8 Tuning and Synthesis of 2DF IMC for Uncertain Processes.
Introduction. Mp Tuning for Stable Overdamped Uncertain Processes. Mp Synthesis
for Stable Overdamped Processes. Mp Tuning for Underdamped and Unstable Processes.
Mp Synthesis for Underdamped and Unstable Processes. Summary.
9. Feedforward Control.
Introduction. Controller Design when Perfect Compensation is Possible. Controller
Design when Perfect Compensation is Not Possible. Controller Design for Uncertain
Processes. Summary.
10. Cascade Control.
Introduction. Cascade Structures and Controller Designs. Saturation Compensation.
Summary.
11. Output Constraint Control (Override Control).
Introduction. Override and Cascade Control Structures. Cascade Constraint Control.
Summary.
12. Single Variable Inferential Control.
Introduction. Classical Control Strategies. Inferential Control. Summary.
13. Inferential Estimation Using Multiple Measurements.
Introduction. Derivation of the Steady State Estimator. Selection of Secondary
Measurements. Adding Dynamic Compensation to the Estimator. Optimal Estimation.
Summary.
14. Discrete-Time Models.
The Z-Tranform Representation. Models of Computer-Controlled Systems. Discrete-Time
FIR Models. Discrete-Time FSR Models. Summary.
15. Identification: Basic Concepts.
Introduction. Least-Squares Estimation of Parameters. Properties of The Least-Squares
Estimator. General Procedure For Process Identification. Summary.
16. Identification: Advanced Concepts.
Design of Input Signals: PRBS Signals. Noise Prefiltering. Modifications To
The Basic Least-Squares Identification. Multiple Input Multiple Output Systems.
A Comprehensive Example. Effect of Prefilter on Parameter Estimates. Software
for Identification. Summary.
17. Basic Model Predictive Control.
Introduction. SISO MPC. Unconstrained Multivariable Systems. State Space Formulation
of Unconstrained MPC. Summary.
18. Advanced Model Predictive Control.
Incorporating Constraints. Incorporating Economic Objectives: The LP-MPC Algorithm.
Extension to Nonlinear Systems. Extension to Batch Processes. Summary.
19. Inferential MPC.
Inferential Model Predictive Control. Simple Regression Estimators. Data-Driven
Dynamic Estimators. Nonlinear Data-Driven Estimators. Summary.
Appendices.
A. Review of Basic Concepts.
Block Diagrams. Laplace Trasnform and Transfer Functions. P, PI, and PID Controller
Transfer Functions. Stability of Systems. Stability of Closed Loop Systems.
Controller Tuning. Regulatory Issues Introduced by Constraints.
B. Frequency Response Analysis.
Introduction. Frequency Response From Transfer Functions. Disturbance Suppression
in SISO Systems: Effect of Constraints. Stability In The Frequency Domain. Closed
Loop Frequency Response Characteristics.
C: Review of Linear Least-Squares Regression.
Derivation of The Linear Least-Squares Estimate. Properties of The Linear Least-Squares
Estimate. Measures of Model Fit. Robustness. Principal Component Regression.
D: Random Variables and Random Processes.
Introduction To Random Variables. Random Processes and White Noise. Spectral
Decomposition of Random Processes. Multidimensional Random Variables.
E: MATLAB and Control Toolbox Tutorial.
MATLAB Resources. Basic Commands. Control System Toolbox Tutorial.
F: SIMULINK Tutorial.
Basics. Laplace Transform Models. Simulation of Discrete Systems Using SIMULINK.
G: Tutorial on IMCTUNE Software.
Introduction. Getting Started on 1DF Systems. Menu Bar for 1DF Systems. Getting
Started on 2DF Systems. Menu Bar for 2DF Systems. Getting Started on Cascade
Systems. Menu Bar for Cascade Systems.
H: Identification Software.
Introduction. POLYID: Description. MODELBUILDER. PIDTUNER.
I: SIMULINK Models for Case Studies.
Naphtha Cracker. Shell Heavy Oil Fractionator. Temperature and Level Control
in a Mixing Tank. Pressure and Level Control Experiment. Temperature and Level
Control. Heat Exchanger. The Tennessee Eastman Project.
Preface
Preface
The design and tuning of any control systemis always based on a model of the
process to be controlled. For example, when an engineertunes a PID control system
online the controller gain and the integral and derivative timeconstants obtained
from the tuning depend on the local behavior of the process, and this lo-calbehavior
could, if desired, be well approximated by a mathematical model. It turns out,however,
that even in the prosaic task of tuning a PID controller, much better control
systembehavior can be obtained if the local mathematical model of the process
is actually obtained,and the PID tuning is based on that model (see Chapter
6 on PID tuning). The foregoing notwithstanding, in this text the term model-based
controller is used primarily to mean controlsystems that explicitly embed a
process model in the control algorithm. In particular, weconsider control algorithms
such as internal model control (IMC), inferential control (IC)and model-predictive
control (such as dynamic matrix control or DMC), which have foundapplications
in the process industry over the last few decades.
The book focuses on techniques. By this we mean how the algorithms are designedand
applied. There is less emphasis on the underlying theory. We have also used
simple ex-amplesto illustrate the concepts. More complex and realistic examples
are provided in thetext as case study projects.
We have written the text with two types of audience in mind. One is the typical
industrialpractitioner engaged in the practice of process control and interested
in learning thebasics behind various controller tuning methods as well as advanced
control strategies beyondtraditional PID feedback control. Our aim is to provide
sufficient understanding of themethodologies of model-based control to enable
the engineer to determine where and when such control strategies can offer substantial
improvement in control as well as how to implementand maintain such strategies.
The second audience that we have in mind is studentsin senior or graduate level
advanced process control courses. For such students, we havetried to provide
homework exercises and suggested projects to enhance the learning process.It
is assumed throughout that the student has convenient access to modern computing
systemsalong with the necessary software. Most of the problems and examples
cannot be carriedout without the use of such tools.
Chapter 1 gives an overview of the hierarchical approach to process control.
Chapter 2reviews the various types of models used in process control with emphasis
on continuoustime models. Chapter 3 gives the development of the basic model-based
control structure(IMC). The latter two chapters form the basis of the further
developments in both continuousand discrete time implementations.
From this point on the reader can take two possible paths: the first path focuses
on thedevelopment of theory and structures for continuous-time implementation
using the IMCstructure. The second path focuses on discrete-time (computer-based)
implementation ofmodel-based control.
Chapters 4 through 13 cover the first path. Chapter 4 focuses on simultaneous
setpointand disturbance rejection using a two-degree of freedom control structure.
Chapter 5 showshow to handle control effort constraints using model state feedback.
Chapter 6 shows therelationship between classical PID controllers and the internal
model control structure.Chapter 7 shows how to design one-degree of freedom
controllers in the presence of modeluncertainty. Chapter 8 shows how to tune
two-degree of freedom controllers. Chapters 9through 11 focus on multiloop control
structures such as feedforward, cascade, and constraintcontrol. Chapter 12 discusses
control using secondary measurements (called inferentialcontrol). Chapter 13
extends the concepts of Chapter 12 to inferential control using multiplesecondary
measurements using disturbance estimation methods.
Chapters 14 through 19 cover the second path dealing with discrete-time computer
implementationof model-based controllers. Chapter 14 introduces the models used
in discrete-timerepresentation and Chapters 15 and 16 discuss algorithms used
to identify such modelsfrom plant test data. Chapters 17 and 18 discuss the
computer implementation of model-basedcontrol using the model-predictive control
framework. Chapter 19 extends this to inferentialcontrol using secondary measurements.
As an aid to the various possible readers, we have provided an extensive set
of appendicesthat contain the background material necessary for the material
in the main body ofthe text. We have indicated at the beginning of each chapter
the prerequisite material, and wesuggest that the appropriate appendices be
reviewed prior to reading the chapter. The followingmaterial is reviewed:
Laplace transforms and block diagrams.
Frequency response methods.
Linear least square regression.
Probability theory and random variables.
MATLAB and SIMULINK software.
We have used the MATLAB/SIMULINK software system as the platform uponwhich to
develop software that provides added functionality and a convenient interface
forsolving otherwise complex problems. Among the reasons for this choice is
that theMATLAB platform provides the tools required to implement and test various
control conceptswith relatively little effort required to learn how to use the
software. However, there is other software that provides similar functionality,
and the reader is encouraged to use which-evertools are most comfortable.
The website (http://www.phptr.com/brosilow/) associated with this text contains
the following material:
* IMCTUNE:
A user-friendly interface to a set of MATLAB m-files that enables the reader
to design and tune both IMC and PID controllers for single loop, feedforward
and cascade control systems. In addition to MATLAB and SIMULINK, IMCTUNE requires
the Control System and Optimization toolboxes in addition toA user-friendly
interface to a set of MATLAB m-files that enables the MATLAB 5.3.1 or later
versions.
* MODELBUILDER:
A set of MATLAB m-files to generate both discrete time and continuous time process
models from input/output data. Requires the Identification Toolbox.
* PIDTUNER:
A set of MATLAB m-files that implement and test classical PID tuning. Requires
the Control System Toolbox.
* SIMULINK case study models:
MATLAB/SIMULINK models of a number ofprocess systems including the Shell fractionation
column, a Naphtha cracker simulator and the Tennessee Eastman problem. These
models can be used in course projects.
* Microsoft PowerPoint slides
containing the text material.
* MATLAB m-files, mat-files and data files, SIMULINK mdl-files
and MicrosoftWord files related to the examples and exercises in the text. These
files are identified by chapter and example number. The * .mat files for the
examples in Chapters 3 through 11 are associated with IMCTUNE.
* Syllabi
used by the authors in their respective undergraduate and graduate courses.
The reader is strongly encouraged to download the software listed above and
to useit to reproduce results of examples in the text, and to solve the problems
at the end of thechapters. Our experience with teaching using this text material
indicates that hands-on exercisesusing simulated processes is important to get
a good understanding of the concepts.
Hence the reader is strongly urged to experiment with the software. We have
provided anumber of exercises that require computer implementation and testing
of the concepts.While the normal reader will have had an introductory course
in process control, itis possible to use at least parts of this text in an introductory
course. For example, ColemanBrosilow has used Chapters 3, 5, 6, 7, and parts
of 9 and 10 in a first undergraduate course in process control for more than
ten years. Babu Joseph has been using the Appendix mate-rialin the laboratory
sessions associated with the undergraduate course. The entire materialin this
book can be included in a graduate course on process control. However, the bookshould
be supplemented with some additional material on multivariable control.
The SIMULINK case studies provide comprehensive test beds for implementingand
testing the various concepts and algorithms presented in the text. The visual
feedbackprovided by the simulation case studies is valuable in understanding
the performance andlimitations of the control algorithms. Experience with the
simulated examples can smooththe transition to real-world applications.
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