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Apply the fundamental tools of linear control theory to model, analyze, design, and understand the behavior of dynamic production systems
In Control Theory Applications for Dynamic Production Systems: Time and Frequency Methods for Analysis and Design, distinguished manufacturing engineer Dr. Neil A. Duffie delivers a comprehensive explanation of how core concepts of control theorical analysis and design can be applied to production systems. Time-based perspectives on response to turbulence are augmented by frequency-based perspectives, fostering new understanding and guiding design of decision-making. The time delays intrinsic to decision making and decision implementation in production systems are addressed throughout.
Readers will discover methods for calculating time response and frequency response, modeling using transfer functions, assessing stability, and design of decision making for closed-loop production systems. The author has included real-world examples emphasizing the different components of production systems and illustrating how practical results can be quickly obtained using straightforward Matlab programs (which can easily be translated to other platforms).
Avoiding unnecessary theoretical jargon, this book fosters an in-depth understanding of key tools of control system engineering. It offers:
Perfect for production, manufacturing, industrial, and control system engineers, Control Theory Applications for Dynamic Production Systems will also earn a place in the libraries of students taking advanced courses on industrial system digitalization, dynamics, and design.
Neil A. Duffie, PhD, is Professor Emeritus and past Chair of the Department of Mechanical Engineering at the University of Wisconsin-Madison. He is a Past President of SME, recipient of the Frederick W. Taylor Research Medal, and Fellow of ASME, CIRP, and SME. His research is focused on the dynamics of production systems, distributed system control, and manufacturing process automation.
Contents
Preface xi
Acknowledgments xv
1 Introduction 1
1.1 Control System Engineering Software 6
2 Continuous-Time and Discrete-Time Modeling of Production Systems 7
2.1 Continuous-Time Models of Components of Production Systems 9
2.2 Discrete-Time Models of Components of Production Systems 15
2.3 Delay 19
2.4 Model Linearization 22
2.4.1 Linearization Using Taylor Series Expansion – One Independent Variable 23
2.4.2 Linearization Using Taylor Series Expansion – Multiple Independent Variables 25
2.4.3 Piecewise Approximation 26
2.5 Summary 27
3 Transfer Functions and Block Diagrams 29
3.1 Laplace Transform 30
3.2 Properties of the Laplace Transform 33
3.2.1 Laplace Transform of a Function of Time Multiplied by a Constant 33
3.2.2 Laplace Transform of the Sum of Two Functions of Time 33
3.2.3 Laplace Transform of the First Derivative of a Function of Time 33
3.2.4 Laplace Transform of Higher Derivatives of a Function of Time Function 34
3.2.5 Laplace Transform of Function with Time Delay 34
3.3 Continuous-Time Transfer Functions 35
3.4 Z Transform 41
3.5 Properties of the Z Transform 44
3.5.1 Z Transform of a Sequence Multiplied by a Constant 45
3.5.2 Z Transform of the Sum of Two Sequences 45
3.5.3 Z Transform of Time Delay dT 45
3.5.4 Z Transform of a Difference Equation 46
3.6 Discrete-Time Transfer Functions 46
3.7 Block Diagrams 50
3.8 Transfer Function Algebra 53
3.8.1 Series Relationships 53
3.8.2 Parallel Relationships 56
3.8.3 Closed-Loop Relationships 58
3.8.4 Transfer Functions of Production Systems with Multiple Inputs and Outputs 64
3.8.5 Matrices of Transfer Functions 69
3.8.6 Factors of Transfer Function Numerator and Denominator 73
3.8.7 Canceling Common Factors in a Transfer Function 74
3.8.8 Padé Approximation of Continuous-Time Delay 78
3.8.9 Absorption of Discrete Time Delay 79
3.9 Production Systems with Continuous-Time and Discrete-Time Components 81
3.9.1 Transfer Function of a Zero-Order Hold (ZOH) 81
3.9.2 Discrete-Time Transfer Function Representing Continuous-Time Components Preceded by a Hold and Followed by a Sampler 82
3.10 Potential Problems in Numerical Computations Using Transfer Functions 90
3.11 Summary 93
4 Fundamental Dynamic Characteristics and Time Response 95
4.1 Obtaining Fundamental Dynamic Characteristics from Transfer Functions96
4.1.1 Characteristic Equation 96
4.1.2 Fundamental Continuous-Time Dynamic Characteristics 97
4.1.3 Continuous-Time Stability Criterion 100
4.1.4 Fundamental Discrete-Time Dynamic Characteristics 107
4.1.5 Discrete-Time Stability Criterion 111
4.2 Characteristics of Time Response 116
4.2.1 Calculation of Time Response 117
4.2.2 Step Response Characteristics 121
4.3 Summary 127
5 Frequency Response 129
5.1 Frequency Response of Continuous-Time Systems 129
5.1.1 Frequency Response of Integrating Continuous-Time Production Systems or Components 132
5.1.2 Frequency Response of 1st-order Continuous-Time Production Systems or Components 136
5.1.3 Frequency Response of 2nd-order Continuous-Time Production Systems or Components 140
5.1.4 Frequency Response of Delay in Continuous-Time Production Systems or Components 145
5.2 Frequency Response of Discrete-Time Systems 148
5.2.1 Frequency Response of Discrete-Time Integrating Production Systems or Components 149
5.2.2 Frequency Response of Discrete-Time 1st-Order Production Systems or Components 153
5.2.3 Aliasing Errors 156
5.3 Frequency Response Characteristics 158
5.3.1 Zero-Frequency Magnitude (DC Gain) and Bandwidth 158
5.3.2 Magnitude (Gain) Margin and Phase Margin 160
5.4 Summary 165
6 Design of Decision-Making for Closed-Loop Production Systems 167
6.1 Basic Types of Continuous-Time Control 169
6.1.1 Continuous-Time Proportional Control 171
6.1.2 Continuous-Time Proportional Plus Derivative Control 171
6.1.3 Continuous-Time Integral Control 172
6.1.4 Continuous-Time Proportional Plus Integral Control 173
6.2 Basic Types of Discrete-Time Control 173
6.2.1 Discrete-Time Proportional Control 174
6.2.2 Discrete-Time Proportional Plus Derivative Control 175
6.2.3 Discrete-Time Integral Control 175
6.2.4 Discrete-Time Proportional Plus Integral Control 176
6.3 Control Design Using Time Response 176
6.4 Direct Design of Decision-Making 186
6.4.1 Model Simplification by Eliminating Small Time Constants and Delays 194
6.5 Design Using Frequency Response 198
6.5.1 Using the Frequency Response Guidelines to Design Decision-Making 203
6.6 Closed-Loop Decision-Making Topologies 219
6.6.1 PID Control 219
6.6.2 Decision-Making Components in the Feedback Path 221
6.6.3 Cascade Control 226
6.6.4 Feedforward Control 231
6.6.5 Circumventing Time Delay Using a Smith Predictor Topology 238
6.7 Sensitivity to Parameter Variations 244
6.8 Summary 247
7 Application Examples 249
7.1 Potential Impact of Digitalization on Improving Recovery Time in Replanning by Reducing Delays 250
7.2 Adjustment of Steel Coil Deliveries in a Production Network with Inventory Information Sharing 256
7.3 Effect of Order Flow Information Sharing on the Dynamic Behavior of a Production Network 263
7.4 Adjustment of Cross-Trained and Permanent Worker Capacity 275
7.5 Closed-Loop, Multi-Rate Production System with Different Adjustment Periods for WIP and Backlog Regulation 283
7.6 Summary 295
References 296
Bibliography 297
Index 299
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