Control Systems Design

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Control Systems Design

Control Systems Design

The Control systems design are all around us. They may be found in our homes, automobiles, industries, and communication and transportation networks, to name a few. Control is becoming increasingly mission essential; if the control fails, processes will fail. Control has been and will continue to be crucial in the design of experimental apparatus and instruments used in fundamental sciences. Control principles also have an influence on disciplines as diverse as economics, biology, and medicine.

Like many other branches of engineering science, control has developed in the same pattern as the natural sciences. Although there are strong similarities between the natural sciences and the engineering sciences, it is important that realize that there are some fundamental differences.

Natural science is motivated by the desire to comprehend natural occurrences. As a result, there has been a significant emphasis on investigation and separation of certain phenomena, often known as reductionism. One of the primary goals of natural science is to discover fundamental rules that explain nature. Engineering science is motivated by the desire to comprehend, develop, and construct man-made technological systems. This puts a greater focus on interaction and design. Interaction is a crucial component of almost all man-made systems.

One of the primary goals of natural science is to discover fundamental rules that explain nature. Engineering science is motivated by the desire to comprehend, develop, and construct man-made technological systems. This puts a greater focus on interaction and design. Interaction is a crucial component of almost all man-made systems. As a result, it is critical to replace reductionism with a holistic systems perspective. Technical systems are growing increasingly complex, posing problems akin to natural systems.

 

Contents

  1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2 A Brief History . . . . . . . . . . . . . . . . . . . . . . . . 9

1.3 Process Control . . . . . . . . . . . . . . . . . . . . . . . . 14

1.4 Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . 17

1.5 Robotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.6 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.7 Aeronautics . . . . . . . . . . . . . . . . . . . . . . . . . . 25

1.8 Electronics and Communication . . . . . . . . . . . . . . 28

1.9 Automotive . . . . . . . . . . . . . . . . . . . . . . . . . . 34

1.10 Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

1.11 Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . 39

1.12 Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

1.13 Biology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

1.14 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

  1. Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.2 Simple Forms of Feedback . . . . . . . . . . . . . . . . . 46

2.3 Representation of Feedback Systems . . . . . . . . . . . 49

2.4 Properties of Feedback . . . . . . . . . . . . . . . . . . . 58

2.5 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

2.6 Open and Closed Loop Systems . . . . . . . . . . . . . . 66

2.7 Feedforward . . . . . . . . . . . . . . . . . . . . . . . . . . 68

2.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

  1. Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.2 Two Views on Dynamics . . . . . . . . . . . . . . . . . . . 72

3.3 Ordinary Differential Equations . . . . . . . . . . . . . . 77

3.4 Laplace Transforms . . . . . . . . . . . . . . . . . . . . . 82

3.5 Frequency Response . . . . . . . . . . . . . . . . . . . . . 90

3.6 State Models . . . . . . . . . . . . . . . . . . . . . . . . . 117

3.7 Linear TimeInvariant

3.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

  1. Simple Control Systems . . . . . . . . . . . . . . . . . . . . . 144

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 144

4.2 Cruise Control . . . . . . . . . . . . . . . . . . . . . . . . 145

4.3 Bicycle Dynamics . . . . . . . . . . . . . . . . . . . . . . . 149

4.4 Control of First Order Systems . . . . . . . . . . . . . . . 154

4.5 Control of Second Order Systems . . . . . . . . . . . . . 162

4.6 Control of Systems of High Order* . . . . . . . . . . . . 168

4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

  1. Feedback Fundamentals . . . . . . . . . . . . . . . . . . . . . 177

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 177

5.2 The Basic Feedback Loop . . . . . . . . . . . . . . . . . . 178

5.3 The Gang of Six . . . . . . . . . . . . . . . . . . . . . . . 181

5.4 Disturbance Attenuation . . . . . . . . . . . . . . . . . . 188

5.5 Process Variations . . . . . . . . . . . . . . . . . . . . . . 191

5.6 When are Two Processes Similar? . . . . . . . . . . . . . 197

5.7 The Sensitivity Functions . . . . . . . . . . . . . . . . . . 200

5.8 Reference Signals . . . . . . . . . . . . . . . . . . . . . . 203

5.9 Fundamental Limitations . . . . . . . . . . . . . . . . . . 207

5.10 Electronic Amplifiers . . . . . . . . . . . . . . . . . . . . . 211

5.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

  1. PID Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 216

6.2 The Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 217

6.3 Filtering and Set Point Weighting . . . . . . . . . . . . . 219

6.4 Different Parameterizations . . . . . . . . . . . . . . . . 222

6.5 Windup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

6.6 Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

6.7 Computer Implementation . . . . . . . . . . . . . . . . . 237

6.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

  1. Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 252

7.2 Stability and Robustness to Process Variations . . . . . 252

7.3 Disturbances . . . . . . . . . . . . . . . . . . . . . . . . . 256

7.4 Reference Signals . . . . . . . . . . . . . . . . . . . . . . 259

7.5 Specifications Based on Optimization . . . . . . . . . . . 262

7.6 Properties of Simple Systems . . . . . . . . . . . . . . . . 263

7.7 Poles and Zeros . . . . . . . . . . . . . . . . . . . . . . . . 267

7.8 Relations Between Specifications . . . . . . . . . . . . . . 268

7.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

  1. Feedforward Design . . . . . . . . . . . . . . . . . . . . . . . 270

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 270

8.2 Disturbance attenuation . . . . . . . . . . . . . . . . . . . 270

8.3 System inverses . . . . . . . . . . . . . . . . . . . . . . . 273

8.4 Response to Reference Inputs . . . . . . . . . . . . . . . 274

8.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

  1. State Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . 278

9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 278

9.2 State Feedback . . . . . . . . . . . . . . . . . . . . . . . . 280

9.3 Observers . . . . . . . . . . . . . . . . . . . . . . . . . . . 290

9.4 Output Feedback . . . . . . . . . . . . . . . . . . . . . . . 298

9.5 Comparison with PID Control . . . . . . . . . . . . . . . 303

9.6 Disturbance Models . . . . . . . . . . . . . . . . . . . . . 308

9.7 Reference Signals . . . . . . . . . . . . . . . . . . . . . . 312

9.8 An Example . . . . . . . . . . . . . . . . . . . . . . . . . . 317

9.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 329

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330

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