Chemical Process Control - a First Course With MATLAB - P. Chau (CRC, 2001) WW.pdf - Matlab - walbo48

Table of Contents

Preface

1. Introduction ............................................................ [ Number of 10-point single-space pages -->] 3

2. Mathematical Preliminaries .................................................................................................. 35

2.1 A simple differential equation model

2.2 Laplace transform

2.3 Laplace transforms common to control problems

2.4 Initial and final value theorems

2.5 Partial fraction expansion

2.5.1 Case 1: p(s) has distinct, real roots

2.5.2 Case 2: p(s) has complex roots

2.5.3 Case 3: p(s) has repeated roots

2.6 Transfer function, pole, and zero

2.7 Summary of pole characteristics

2.8 Two transient model examples

2.8.1 A Transient Response Example

2.8.2 A stirred tank heater

2.9 Linearization of nonlinear equations

2.10 Block diagram reduction

Review Problems

3. Dynamic Response ............................................................................................................. 19

3.1 First order differential equation models

3.1.1 Step response of a first order model

3.1.2 Impulse response of a first order model

3.1.3 Integrating process

3.2 Second order differential equation models

3.2.1 Step response time domain solutions

3.2.2 Time-domain features of underdamped step response

3.3 Processes with dead time

3.4 Higher order processes and approximations

3.4.1 Simple tanks-in-series

3.4.2 Approximation with lower order functions with dead time

3.4.3 Interacting tanks-in-series

3.5 Effect of zeros in time response

3.5.1 Lead-lag element

3.5.2 Transfer functions in parallel

Review Problems

4. State Space Representation ................................................................................................... 18

4.1 State space models

4.2 Relation with transfer function models

4.3 Properties of state space models

4.3.1 Time-domain solution

4.3.2 Controllable canonical form

4.3.3 Diagonal canonical form

Review Problems

5. Analysis of PID Control Systems ........................................................................................ 22

5.1 PID controllers

5.1.1 Proportional control

5.1.2 Proportional-Integral (PI) control

5.1.3 Proportional-Derivative (PD) control

5.1.4 Proportional-Integral-Derivative (PID) control

5.2 Closed-loop transfer functions

5.2.1 Closed-loop transfer functions and characteristic polynomials

5.2.2 How do we choose the controlled and manipulated variables?

5.2.3 Synthesis of a single-loop feedback system

5.3 Closed-loop system response

5.4 Selection and action of controllers

5.4.1 Brief comments on the choice of controllers

Review Problems

6. Design and Tuning of Single-Loop Control Systems ............................................................... 19

6.1 Tuning controllers with empirical relations

6.1.1 Controller settings based on process reaction curve

6.1.2 Minimum error integral criteria

6.1.3 Ziegler-Nichols ultimate-cycle method

6.2 Direct synthesis and internal model control

6.2.1 Direct synthesis

6.2.2 Pole-zero cancellation

6.2.3 Internal model control (IMC)

Review Problems

7. Stability of Closed-loop Systems .......................................................................................... 17

7.1 Definition of Stability

7.2 The Routh-Hurwitz Criterion

7.3 Direct Substitution Analysis

7.4 Root Locus Analysis

7.5 Root Locus Design

7.6 A final remark on root locus plots

Review Problems

8. Frequency Response Analysis ................................................................................................ 29

8.1 Magnitude and Phase Lag

8.1.1 The general analysis

8.1.2 Some important properties

8.2 Graphical analysis tools

8.2.1 Magnitude and Phase Plots

8.2.2 Polar Coordinate Plots

8.2.3 Magnitude vs Phase Plot

8.3 Stability Analysis

8.3.1 Nyquist Stability criterion

8.3.2 Gain and Phase Margins

8.4 Controller Design

8.4.1 How do we calculate proportional gain without trial-and-error?

8.4.2 A final word: Can frequency response methods replace root locus?

Review Problems

9. Design of State Space Systems ............................................................................................. 18

9.1 Controllability and Observability

9.1.1 Controllability

9.1.2 Observability

9.2 Pole Placement Design

9.2.1 Pole placement and Ackermann's formula

9.2.2 Servo systems

9.2.3 Servo systems with integral control

9.3 State Estimation Design

9.3.1 State estimator

9.3.2 Full-order state estimator system

9.3.3 Estimator design

9.3.4 Reduced-order estimator

Review Problems

10. Multiloop Systems ............................................................................................................ 27

10.1 Cascade Control

10.2 Feedforward Control

10.3 Feedforward-feedback Control

10.4 Ratio Control

10.5 Time delay compensation—the Smith predictor

10.6 Multiple-input Multiple-output control

10.6.1 MIMO Transfer functions

10.6.2 Process gain matrix

10.6.3 Relative gain array

10.7 Decoupling of interacting systems

10.7.1 Alternate definition of manipulated variables

10.7.2 Decoupler functions

10.7.3 “Feedforward” decoupling functions

Review Problems

MATLAB Tutorial Sessions

Session 1. Important basic functions ................................................................................... 7

M1.1 Some basic MATLAB commands

M1.2 Some simple plotting

M1.3 Making M-files and saving the workspace

Session 2 Partial fraction and transfer functions..................................................................... 5

M2.1 Partial fractions

M2.2 Object-oriented transfer functions

Session 3 Time response simulation ................................................................................... 4

M3.1 Step and impulse response simulations

M3.2 LTI Viewer

Session 4 State space functions.......................................................................................... 7

M4.1 Conversion between transfer function and state space

M4.2 Time response simulation

M4.3 Transformations

Session 5 Feedback simulation functions ............................................................................. 5

M5.1 Simulink

M5.2 Control toolbox functions

Session 6 Root locus functions.......................................................................................... 7

M6.1 Root locus plots

M6.2 Root locus design graphics interface

M6.3 Root locus plots of PID control systems

Session 7 Frequency response functions............................................................................... 4

M7.1 Nyquist and Nichols Plots

M7.2 Magnitude and Phase Angle (Bode) Plots

References................................................................................................................................1

Homework Problems ............................................................................................................... 31

Part I Basics problems

Part II Intermediate problems

Part III Extensive integrated problems

The best approach to control is to think of it as applied mathematics.

Virtually everything we do in this introductory course is related to the

properties of first and second order differential equations, and with different

techniques in visualizing the solutions.

Chemical Process Control: A First Course with MATLAB

Pao C. Chau

University of California, San Diego

Preface

This is an introductory text written from the perspective of a student. The major concern is not how much

material we cover, but rather, how to present the most important and basic concepts that one should

grasp in a first course. If your instructor is using some other text that you are struggling to understand, we

hope we can help you too. The material here is the result of a process of elimination. The writing and

examples are succinct and self-explanatory, and the style is purposely unorthodox and conversational.

To a great extent, the style, content, and the extensive use of footnotes are molded heavily by questions

raised in class. I left out very few derivation steps. If they were, the missing steps are provided as

hints in the Review Problems at the back of each chapter. I strive to eliminate those “easily obtained”

results that baffle many of us. Most students should be able to read the material on their own. You just

need basic knowledge in differential equations, and it helps if you have taken a course on writing

material balances. With the exception of chapters 4, 9, and 10, which should be skipped in a quarter-

long course, it also helps if you proceed chapter by chapter. The presentation of material is not intended

for someone to just jump right in the middle of the text. We place a very strong emphasis on developing

analytical skills. To keep pace with the modern computer era, we also take a coherent and integrated

approach to using a computational tool. We believe in active learning. When you read the chapters, it

is very important that you have MATLAB with its Control Toolbox to experiment and test the examples

firsthand.

Notes to Instructors

There are probably more introductory texts in control than other engineering disciplines. It is arguable

whether we need another control text. As we move into the era of hundred dollar textbooks, I believe

we can lighten the economic burden, and with the Internet, assemble a new generation of modularized

texts that soften the printing burden by off loading selected material to the Web. Still a key resolve is

to scale back on the scope of a text to the most crucial basics. How much students can, or be enticed to,

learn is inversely proportional to the number of pages that they have to read—akin to diminished

magnitude and increased lag in frequency response. So as textbooks become thicker over the years in

attempts to reach out to students and are excellent resources from the perspective of instructors, these

texts are by no means more effective pedagogical tools. This project was started as a set of review notes

when I found students having trouble identifying the key concepts in these expansive texts. I also found

these texts in many circumstances deter students from active learning and experimenting on their own.

At this point, the contents are scaled down to fit a one-semester course. On a quarter system,

Chapters 4, 9, and 10 can be omitted. With the exception of two chapters (4 and 9) on state space

models, the organization has “evolved” to become very classical. The syllabus is chosen such that

students can get to tuning PID controllers before they lose interest. Furthermore, discrete-time analysis

has been discarded. If there is to be one introductory course in the undergraduate curriculum, it is very

important to provide an exposure to state space models as a bridge to a graduate level course. The last

chapter on mutliloop systems is a collection of topics that are usually handled by several chapters in a

formal text. This chapter is written such that only the most crucial concepts are illustrated and that it

could be incorporated comfortably in a one-semester curriculum. For schools with the luxury of two

control courses in the curriculum, this last chapter should provide a nice introductory transition.

Because the material is so restricted, we emphasize that this is a "first course" textbook, lest a student

might mistakenly ignore the immense expanse of the control field. We also have omitted appendices

and extensive references. As a modularized tool, we use our Web Support to provide references, support

material, and detailed MATLAB plots and results.

Homework problems are also handled differently. At the end of each chapter are short, mostly

derivation type, problems which we call Review Problems. Hints or solutions are provided for these

exercises. To enhance the skill of problem solving, we take the extreme approach, more so than

Stephanopoulos (1984), of collecting major homework problems at the back and not at the end of each

chapter. Our aim is to emphasize the need to understand and integrate knowledge, a virtue that is

endearing to ABET, the engineering accreditation body in the United States. These problems do not even

specify the associated chapter as many of them involve different techniques. A student has to

determine the appropriate route of attack. An instructor may find it aggravating to assign individual

parts of a problem, but when all the parts are solved, we hope the exercise would provide a better

perspective to how different ideas are integrated.

To be an effective teaching tool, this text is intended for experienced instructors who may have a

wealth of their own examples and material, but writing an introductory text is of no interest to them.

The concise coverage conveniently provides a vehicle with which they can take a basic, minimalist set

of chapters and add supplementary material that they deem appropriate. Even without

supplementary material, however, this text contains the most crucial material and there should not be

a need for an additional expensive, formal text.

While the intended teaching style relies heavily on the use of MATLAB , the presentation is very

different from texts which prepare elaborate M-files and even menu-driven interfaces. One of the

reasons why MATLAB is such a great tool is that it does not have a steep learning curve. Students can

quickly experiment on their own. Spoon-feeding with our misguided intention would only destroy the

incentive to explore and learn on one's own. To counter this pitfall, strong emphasis is placed on what

one can accomplish easily with only a few MATLAB statements. MATLAB is introduced as walk-

through tutorials that encourage students to enter commands on their own. As strong advocates of active

learning, we do not duplicate MATLAB results. Students, again, are encouraged to execute the commands

themselves. In case help is needed, our Web Support, however, has the complete set of MATLAB results

and plots. This organization provides a more coherent discourse on how one can make use of different

features of MATLAB , not to mention saving significant printing costs. Finally, we can revise the

tutorials easily to keep up with the continual upgrade of MATLAB . At this writing, the tutorials are

based on MATLAB version 5.3, and the object-oriented functions in the Control Toolbox version 4.2.

Simulink version 3.0 is also utilized, but its scope is limited to simulating more complex control systems.

As a first course text, the development of models is limited to stirred-tanks, stirred tank heater,

and a few other examples that are used extensively and repeatedly throughout the chapters. Our

philosophy is one step back in time. The focus is the theory and the building of a foundation that may

help to solve other problems. The design is also to be able to launch into the topic of tuning controllers

before students may lose interest. The coverage of Laplace transform is not entirely a concession to

remedial mathematics. The examples are tuned to illustrate immediately how pole positions may

relate to time domain response. Furthermore, students tend to be confused by the many different design

methods. As much as I can, especially in the controller design chapters, the same examples are used

throughout. The goal is to help a student understand how the same problem can be solved by different

techniques.

We have given up the pretense that we can cover controller design and still have time to do all

the plots manually. We rely on MATLAB to construct the plots. For example, we take a unique approach

to root locus plots. We do not ignore it like some texts do, but we also do not go into the hand sketching

details. The same can be said with frequency response analysis. On the whole, we use root locus and

Bode plots as computational and pedagogical tools in ways that can help to understand the choice of

different controller designs. Exercises that may help such thinking are in the MATLAB tutorials and

homework problems.

Finally, I have to thank Costas Pozikidris and Florence Padgett for encouragement and support on

this project, Raymond de Callafon for revising the chapters on state space models, and Allan Cruz for

proofreading. Last but not least, Henry Lim combed through the manuscript and made numerous

insightful comments. His wisdom is sprinkled throughout the text.

Web Support ( MATLAB outputs of text examples and MATLAB sessions, references, and supplementary

notes) is available at the CENG 120 homepage. G o to http://courses.ucsd.edu and find CENG 120.

Chemical Process Control - a First Course With MATLAB - P. Chau (CRC, 2001) WW.pdf

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