Control Theory Applications for Dynamic Production Systems

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.

• Preface xiAcknowledgments xv1 Introduction 11.1 Control System Engineering Software 62 Continuous-Time and Discrete-Time Modeling of Production Systems 72.1 Continuous-Time Models of Components of Production Systems 92.2 Discrete-Time Models of Components of Production Systems 152.3 Delay 192.4 Model Linearization 222.4.1 Linearization Using Taylor Series Expansion – One Independent Variable 232.4.2 Linearization Using Taylor Series Expansion – Multiple Independent Variables 252.4.3 Piecewise Approximation 262.5 Summary 273 Transfer Functions and Block Diagrams 293.1 Laplace Transform 303.2 Properties of the Laplace Transform 333.2.1 Laplace Transform of a Function of Time Multiplied by a Constant 333.2.2 Laplace Transform of the Sum of Two Functions of Time 333.2.3 Laplace Transform of the First Derivative of a Function of Time 333.2.4 Laplace Transform of Higher Derivatives of a Function of Time Function 343.2.5 Laplace Transform of Function with Time Delay 343.3 Continuous-Time Transfer Functions 353.4 Z Transform 413.5 Properties of the Z Transform 443.5.1 Z Transform of a Sequence Multiplied by a Constant 453.5.2 Z Transform of the Sum of Two Sequences 453.5.3 Z Transform of Time Delay dT 453.5.4 Z Transform of a Difference Equation 463.6 Discrete-Time Transfer Functions 463.7 Block Diagrams 503.8 Transfer Function Algebra 533.8.1 Series Relationships 533.8.2 Parallel Relationships 563.8.3 Closed-Loop Relationships 583.8.4 Transfer Functions of Production Systems with Multiple Inputs and Outputs 643.8.5 Matrices of Transfer Functions 693.8.6 Factors of Transfer Function Numerator and Denominator 733.8.7 Canceling Common Factors in a Transfer Function 743.8.8 Padé Approximation of Continuous-Time Delay 783.8.9 Absorption of Discrete Time Delay 793.9 Production Systems with Continuous-Time and Discrete-Time Components 813.9.1 Transfer Function of a Zero-Order Hold (ZOH) 813.9.2 Discrete-Time Transfer Function Representing Continuous-Time Components Preceded by a Hold and Followed by a Sampler 823.10 Potential Problems in Numerical Computations Using Transfer Functions 903.11 Summary 934 Fundamental Dynamic Characteristics and Time Response 954.1 Obtaining Fundamental Dynamic Characteristics from Transfer Functions 964.1.1 Characteristic Equation 964.1.2 Fundamental Continuous-Time Dynamic Characteristics 974.1.3 Continuous-Time Stability Criterion 1004.1.4 Fundamental Discrete-Time Dynamic Characteristics 1074.1.5 Discrete-Time Stability Criterion 1114.2 Characteristics of Time Response 1164.2.1 Calculation of Time Response 1174.2.2 Step Response Characteristics 1214.3 Summary 1275 Frequency Response 1295.1 Frequency Response of Continuous-Time Systems 1295.1.1 Frequency Response of Integrating Continuous-Time Production Systems or Components 1325.1.2 Frequency Response of 1st-order Continuous-Time Production Systems or Components 1365.1.3 Frequency Response of 2nd-order Continuous-Time Production Systems or Components 1405.1.4 Frequency Response of Delay in Continuous-Time Production Systems or Components 1455.2 Frequency Response of Discrete-Time Systems 1485.2.1 Frequency Response of Discrete-Time Integrating Production Systems or Components 1495.2.2 Frequency Response of Discrete-Time 1st-Order Production Systems or Components 1535.2.3 Aliasing Errors 1565.3 Frequency Response Characteristics 1585.3.1 Zero-Frequency Magnitude (DC Gain) and Bandwidth 1585.3.2 Magnitude (Gain) Margin and Phase Margin 1605.4 Summary 1656 Design of Decision-Making for Closed-Loop Production Systems 1676.1 Basic Types of Continuous-Time Control 1696.1.1 Continuous-Time Proportional Control 1716.1.2 Continuous-Time Proportional Plus Derivative Control 1716.1.3 Continuous-Time Integral Control 1726.1.4 Continuous-Time Proportional Plus Integral Control 1736.2 Basic Types of Discrete-Time Control 1736.2.1 Discrete-Time Proportional Control 1746.2.2 Discrete-Time Proportional Plus Derivative Control 1756.2.3 Discrete-Time Integral Control 1756.2.4 Discrete-Time Proportional Plus Integral Control 1766.3 Control Design Using Time Response 1766.4 Direct Design of Decision-Making 1866.4.1 Model Simplification by Eliminating Small Time Constants and Delays 1946.5 Design Using Frequency Response 1986.5.1 Using the Frequency Response Guidelines to Design Decision-Making 2036.6 Closed-Loop Decision-Making Topologies 2196.6.1 PID Control 2196.6.2 Decision-Making Components in the Feedback Path 2216.6.3 Cascade Control 2266.6.4 Feedforward Control 2316.6.5 Circumventing Time Delay Using a Smith Predictor Topology 2386.7 Sensitivity to Parameter Variations 2446.8 Summary 2477 Application Examples 2497.1 Potential Impact of Digitalization on Improving Recovery Time in Replanning by Reducing Delays 2507.2 Adjustment of Steel Coil Deliveries in a Production Network with Inventory Information Sharing 2567.3 Effect of Order Flow Information Sharing on the Dynamic Behavior of a Production Network 2637.4 Adjustment of Cross-Trained and Permanent Worker Capacity 2757.5 Closed-Loop, Multi-Rate Production System with Different Adjustment Periods for WIP and Backlog Regulation 2837.6 Summary 295References 296Bibliography 297Index 299