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Control System Design Guide
Using Your Computer to Understand and Diagnose Feedback Controllers
By George Ellis
Butterworth-Heinemann
Copyright © 2012 Elsevier Inc.
All right reserved.
ISBN: 978-0-12-385921-1
Chapter One
Introduction to Controls Chapter Outline 1.1 Visual ModelQ Simulation Environment 4 1.1.1 Installation of Visual ModelQ 4 1.1.2 Errata 4 1.2 The Control System 5 1.2.1 The Controller 5 1.2.2 The Machine 6 1.3 The Controls Engineer 6
Control theory is used for analysis and design of feedback systems, such as those that regulate temperature, fluid flow, motion, force, voltage, pressure, tension, and current. Skillfully used, control theory can guide engineers in every phase of the product and process design cycle. It can help engineers predict performance, anticipate problems, and provide solutions.
Colleges teach controls with little emphasis on day-to-day problems. The academic community focuses on mathematical derivations and on the development of advanced control schemes; it often neglects the methods that are commonly applied in industry. Students can complete engineering programs that include courses on controls and still remain untutored on how to design, model, build, tune, and troubleshoot a basic control system. The unfortunate result is that many working engineers lay aside analysis when they practice their profession, relying instead on company history and trial-and-error methods.
This book avoids the material and organization of most control theory textbooks. For example, design guidelines are presented throughout; these guidelines are a combination of industry-accepted practices and warnings against common pitfalls. Nontraditional subjects, such as filters and modeling, are presented here because they are essential to understanding and implementing control systems in the workplace. The focus of each chapter is to teach how to use controls to improve a working machine or process.
The wide availability of personal computers and workstations is an important advance for control system designers. Many of the classical control methods, such as the root locus method, are graphical rather than analytical. Their creators sought to avoid what was then the overwhelming number of computations required for analytical methods. Fortunately, these calculations no longer present a barrier. Virtually every personal computer can execute the calculations required by analytical methods. With this in mind, the principles and methods presented herein are essentially analytical, and the arithmetic is meant to be carried out by a computer.
1.1 Visual ModelQ Simulation Environment
Most engineers understand the foundations of control theory. Concepts such as transfer functions, block diagrams, the s-domain, and Bode plots are familiar to most of us. But how should working engineers apply these concepts? As in most disciplines, they must develop intuition, and this requires fluency in the basics. In order to be fluent, you must practice.
When studying control system techniques, finding equipment to practice on is often difficult. As a result, designers often rely on computer simulations. To this end, the author developed, as a companion to this book, Visual ModelQ, a stand-alone, graphical, PC-based simulation environment. The environment provides time-domain and frequency-domain analysis of analog and digital control systems. Dozens of Visual ModelQ models were developed for this book. These models are used extensively in the chapters that follow. Readers can run these experiments to verify results and then modify parameters and other conditions to experiment with the concepts of control systems.
Visual ModelQ is written to teach control theory. It makes convenient those activities that are necessary for studying controls. Control law gains are easy to change. Plots of frequency-domain response (Bode plots) are run with the press of a button. The models in Visual ModelQ run continuously, just as real-time controllers do. The measurement equipment runs independently, so you can change parameters and see the effects immediately.
1.1.1 Installation of Visual ModelQ
Visual ModelQ is available at qxdesign.com. The unregistered version is available free of charge. The unregistered version can execute all the models used in this book. Readers may elect to register their copies of Visual ModelQ at any time; see qxdesign.com for details.
Visual ModelQ runs on PCs using Windows XP and Windows 7. Download the installation package for Visual ModelQ V7.0 or later; the files are typically installed to C:\Program Files\QxDesign, Inc\VisualModelQ7.0. Visual ModelQ installs with both a User's Manual and a Reference Manual. After installation, read the User's Manual. Note that you can access the Reference Manual by pressing the F1 key. Finally, check qxdesign.com from time to time for updated software.
1.1.2 Errata
Check qxdesign.com for errata. It is the author's intention to regularly update the Web page as corrections become known.
1.2 The Control System
The general control system, as shown in Figure 1.1, can be divided into the controller and the machine. The controller can be divided into the control laws and the power converter. The machine may be a temperature bath, a motor, or, as in the case of a power supply, an inductor/ capacitor circuit. The machine can also be divided into two parts: the plant and the feedback device (s). The plant receives two types of signals: a controller output from the power converter and one or more disturbances. Simply put, the goal of the control system is to drive the plant in response to the command while overcoming disturbances.
1.2.1 The Controller
The controller incorporates both control laws and power conversion. Control laws, such as proportional-integral-differential (PID) control, are familiar to control engineers. The process of tuning — setting gains to attain desired performance — amounts to adjusting the parameters of the control laws. Most controllers let designers adjust gains; the most flexible controllers allow the designer to modify the control laws themselves. When tuning, most control engineers focus on attaining a quick, stable command response. However, in some applications, rejecting disturbances is more important than responding to commands. All control systems should demonstrate robust performance because even nearly identical machines and processes vary somewhat from one to the other, and they change over time. Robust operation means control laws must be designed with enough margin to accommodate reasonable changes in the plant and power converter.
Virtually all controllers have power converters. The control laws produce information, but power must be applied to control the plant. The power converter can be driven by any available power source, including electric, pneumatic, hydraulic, or chemical power.
1.2.2 The Machine
The machine is made of two parts: the plant and the feedback. The plant is the element or elements that produce the system response. Plants are generally passive, and they usually dissipate power. Examples of plants include a heating element and a motor coupled to its load.
Control systems need feedback because the plant is rarely predictable enough to be controlled open loop — that is, without feedback. This is because most plants integrate the power converter output to produce the system response. Voltage is applied to inductors to produce current; torque is applied to inertia to produce velocity; pressure is applied to produce fluid flow. In all these cases, the control system cannot control the output variable directly but must provide power to the machine as physics allows and then monitor the feedback to ensure that the plant is on track.
1.3 The Controls Engineer
The focal task of many controls engineers is system integration and commissioning. The most familiar part of this process is tuning the control loops. This process can be intimidating. Often dozens of parameters must be fine-tuned to ensure that the system meets the specification. Sometimes that specification is entirely formal, but more often it is a combination of formal requirements and know-how gained with years of experience. Usually, experienced engineers are required to judge when a system is performing well enough to meet the needs of the application.
For some control systems, each installation may require days or weeks to be correctly commissioned. In a complex machine such as a rolling mill, that process can take months. Each section of the machine must be carefully tuned at the site. So even after the design of the machine is complete, the expertise of a controls engineer is required each time a unit is installed.
Although most controls engineers focus on installation, their job should begin when the machine is designed. Many companies fail to take advantage of their controls experts early in a project; this is short-sighted. A controls engineer may suggest an improved feedback device or enhancements to a machine that will help overcome a stubborn problem. Ideally, the project manager will solicit this input early, because changes of this nature are often difficult to make later.
The controls engineer should also contribute to the selection of the controller. There are many controls-oriented factors that should be taken into account. Does the controller implement familiar control laws? For digital controllers, is the processor fast enough for the needs of the application? Is the complexity/ease-of-use appropriate for the support team and for the customer base? The selection and specification of a controller involves input from many perspectives, but some questions can be answered best by a skilled controls engineer.
What is the role for control theory in the daily tasks of controls engineers? At its root, control theory provides understanding and, with that, intuition. Should the company purchase the controller that runs four times faster even though it costs 25% more? Should they invest in machine changes, and what will be the expected improvement from those efforts? How much will the better feedback device help a noise problem? Understanding controls doesn't guarantee that the engineer will have the correct answer. But a firm grasp on the practical side of controls will provide correct answers more often and thus position the controls engineer to provide leadership in process and product development and support.
Chapter Two
The Frequency Domain
Chapter Outline 2.1 The Laplace Transform 10 2.2 Transfer Functions 10 2.2.1 What is s? 11 2.2.1.1 DC Gain 12 2.2.2 Linearity, Time Invariance, and Transfer Functions 12
2.3 Examples of Transfer Functions 13 2.3.1 Transfer Functions of Controller Elements 13 2.3.1.1 Integration and Differentiation 13 2.3.1.2 Filters 13 2.3.1.3 Control Laws 14 2.3.1.4 Compensators 14 2.3.1.5 Delays 14 2.3.2 Transfer Functions of Power Conversion 14 2.3.3 Transfer Functions of Physical Elements 15 2.3.4 Transfer Functions of Feedback 16
2.4 Block Diagrams 17 2.4.1 Combining Blocks 17 2.4.1.1 Simplifying a Feedback Loop 17 2.4.2 Mason's Signal Flow Graphs 18 2.4.2.1 Step-by-Step Procedure 19
2.5 Phase and Gain 21 2.5.1 Phase and Gain from Transfer Functions 22 2.5.2 Bode Plots: Phase and Gain versus Frequency 23
2.6 Measuring Performance 24 2.6.1 Command Response 24 2.6.2 Stability 27 2.6.3 Time Domain versus Frequency Domain 28
2.7 Questions 28
(Continues...)
Excerpted from Control System Design Guide by George Ellis Copyright © 2012 by Elsevier Inc.. Excerpted by permission of Butterworth-Heinemann. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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