Essentials of Control Techniques and Theory

by Billingsley; John

• ISBN13: 9781420091236
• ISBN10: 1420091239
• eBook ISBN(s): 9781351834414
• Additional ISBN(s): 9781351834414
• Format: Hardcover
• Copyright: 2009-11-10
• Publisher: CRC Press

Summary

Carefully separating the essential from the ornamental, Essentials of Control Techniques and Theorypresents the nuts and bolts for designing a successful controller. It discusses the theory required to support the art of designing a working controller as well as the various aspects to convince a client, employer, or examiner of your expertise. A Compelling Account of the Basics of Control Theory Control solutions for practicing engineers Using the author#xE2;#xAC;"s own Javascript On-Line Learning Interactive Environment for Simulation (Jollies), the text relies on computer-based graphical analysis methods, such as Nyquist, Nichols, root locus, and phase-plane, to illustrate how useful computer simulation can be for analyzing both linear and nonlinear systems. It explains step-by-step the design and modeling of various control systems, including discrete time systems and an inverted pendulum. Along with offering many web-based simulations, the book shows how mathematics, such as vectors, matrices, and the differential equations that govern state variables, can help us understand the concepts that underpin the controller#xE2;#xAC;"s effects. From frequency domain analysis to time-domain state-space representation, this book covers many aspects of classical and modern control theory. It presents important methods for designing and analyzing linear systems and controllers.

Table of Contents

Preface	p. xi
Author	p. xiii
Essentials of Control Techniques-What You Need to Know
Introduction: Control in a Nutshell; History, Theory, Art, and Practice	p. 3
The Origins of Control	p. 3
Early Days of Feedback	p. 5
The Origins of Simulation	p. 6
Discrete Time	p. 7
Modeling Time	p. 9
Introduction	p. 9
A Simple System	p. 9
Simulation	p. 11
Choosing a Computing Platform	p. 12
An Alternative Platform	p. 15
Solving the First Order Equation	p. 16
A Second Order Problem	p. 19
Matrix State Equations	p. 23
Analog Simulation	p. 24
Closed Loop Equations	p. 26
Simulation with Jollies: JavaScript On-Line Learning Interactive Environment for Simulation	p. 29
Introduction	p. 29
How a Jollies Simulation is Made Up	p. 31
Moving Images without an Applet	p. 35
A Generic Simulation	p. 38
Practical Control Systems	p. 41
Introduction	p. 41
The Nature of Sensors	p. 42
Velocity and Acceleration	p. 44
Output Transducers	p. 44
A Control Experiment	p. 46
Adding Control	p. 49
Introduction	p. 49
Vector State Equations	p. 49
Feedback	p. 52
Another Approach	p. 53
A Change of Variables	p. 55
Systems with Time Delay and the PID Controller	p. 57
Simulating the Water Heater Experiment	p. 60
Systems with Real Components and Saturating Signals-Use of the Phase Plane	p. 63
An Early Glimpse of Pole Assignment	p. 63
The Effect of Saturation	p. 63
Meet the Phase Plane	p. 65
Phase Plane for Saturating Drive	p. 70
Bang-Bang Control and Sliding Mode	p. 74
Frequency Domain Methods	p. 77
Introduction	p. 77
Sine-Wave Fundamentals	p. 78
Complex Amplitudes	p. 79
More Complex Still-Complex Frequencies	p. 81
Eigenfunctions and Gain	p. 81
A Surfeit of Feedback	p. 83
Poles and Polynomials	p. 85
Complex Manipulations	p. 87
Decibels and Octaves	p. 88
Frequency Plots and Compensators	p. 89
Second Order Responses	p. 92
Excited Poles	p. 93
Discrete Time Systems and Computer Control	p. 97
Introduction	p. 97
State Transition	p. 98
Discrete Time State Equations and Feedback	p. 101
Solving Discrete Time Equations	p. 102
Matrices and Eigenvectors	p. 103
Eigenvalues and Continuous Time Equations	p. 104
Simulation of a Discrete Time System	p. 105
A Practical Example of Discrete Time Control	p. 107
And There's More	p. 110
Controllers with Added Dynamics	p. 112
Controlling an Inverted Pendulum	p. 115
Deriving the State Equations	p. 115
Simulating the Pendulum	p. 119
Adding Reality	p. 122
A Better Choice of Poles	p. 123
Increasing the Realism	p. 124
Tuning the Feedback Pragmatically	p. 126
Constrained Demand	p. 127
In Conclusion	p. 129
Essentials of Control Theory-What You Ought to Know
More Frequency Domain Background Theory	p. 133
Introduction	p. 133
Complex Planes and Mappings	p. 134
The Cauchy-Riemann Equations	p. 135
Complex Integration	p. 138
Differential Equations and the Laplace Transform	p. 140
The Fourier Transform	p. 144
More Frequency Domain Methods	p. 147
Introduction	p. 147
The Nyquist Plot	p. 148
Nyquist with M-Circles	p. 151
Software for Computing the Diagrams	p. 153
The "Curly Squares" Plot	p. 154
Completing the Mapping	p. 155
Nyquist Summary	p. 156
The Nichols Chart	p. 156
The Inverse-Nyquist Diagram	p. 158
Summary of Experimental Methods	p. 162
The Root Locus	p. 165
Introduction	p. 165
Root Locus and Mapping	p. 165
A Root Locus Plot	p. 169
Plotting with Poles and Zeroes	p. 172
Poles and Polynomials	p. 173
Compensators and Other Examples	p. 176
Conclusions	p. 178
Fashionable Topics in Control	p. 181
Introduction	p. 181
Adaptive Control	p. 182
Optimal Control	p. 182
Bang-Bang, Variable Structure, and Fuzzy Control	p. 182
Neural Nets	p. 184
Heuristic and Generic Algorithms	p. 184
Robust Control and H-infinity	p. 185
The Describing Function	p. 185
Lyapunov Methods	p. 186
Conclusion	p. 187
Linking the Time and Frequency Domains	p. 189
Introduction	p. 189
State-Space and Transfer Functions	p. 189
Deriving the Transfer Function Matrix	p. 190
Transfer Function and Time Responses	p. 193
Filters in Software	p. 197
Software Filters for Data	p. 199
State Equations in the Companion Form	p. 201
Time, Frequency, and Convolution	p. 205
Delays and the Unit Impulse	p. 205
The Convolution Integral	p. 207
Finite Impulse Response (FIR) Filters	p. 209
Correlation	p. 211
Conclusion	p. 215
More about Time and State Equations	p. 217
Introduction	p. 217
Juggling the Matrices	p. 217
Eigenvectors and Eigenvalues Revisited	p. 218
Splitting a System into Independent Subsystems	p. 221
Repeated Roots	p. 225
Controllability and Observability	p. 227
Practical Observers, Feedback with Dynamics	p. 233
Introduction	p. 233
The Kalman Filter	p. 233
Reduced-State Observers	p. 237
Control with Added Dynamics	p. 242
Conclusion	p. 246
Digital Control in More Detail	p. 247
Introduction	p. 247
Finite Differences-The Beta-Operator	p. 247
Meet the z-Transform	p. 254
Trains of Impulses	p. 252
Some Properties of the z-transform	p. 254
Initial and Final Value Theorems	p. 256
Dead-Beat Response	p. 257
Discrete Time Observers	p. 259
Relationship between z-and Other Transforms	p. 267
Introduction	p. 267
The Impulse Modulator
Cascading Transforms	p. 268
Tables of Transform	p. 271
The Beta and w-Transforms	p. 272
Design Methods for Computer Control	p. 277
Introduction	p. 277
The Digital-to-Analog Convertor (DAC) as Zero Order Hold	p. 277
Quantization	p. 279
A Position Control Example, Discrete Time Root Locus	p. 280
Discrete Time Dynamic Control-Assessing Performance	p. 282
Errors and Noise	p. 289
Disturbances	p. 289
Practical design Considerations	p. 292
Delays and Sample rates	p. 296
Conclusion	p. 297
Optimal Control-Nothing but the Best	p. 299
Introduction: The End Point Problem	p. 299
Dynamic Programming	p. 300
Optimal Control of a Linear System	p. 305
Time Optimal Control of a Second Order System	p. 306
Optimal or Suboptimal?	p. 308
Quadratic Cost Functions	p. 309
In Conclusion	p. 315
Index	p. 317
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