Control Theory Applications for Dynamic Production Systems Time and Frequency Methods for Analysis and Design
Neil A. DuffieUniversity of WisconsinMadison, Wisconsin
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To Hans-Peter Wiendahl (1938–2019)
Contents 1
Cover
5
Preface
7 1 Introduction1.1 Control System Engineering Software 8 2 Continuous-Time and Discrete-Time Modeling of Production Systems2.1 Continuous-Time Models of Components of Production Systems2.2 Discrete-Time Models of Components of Production Systems2.3 Delay2.4 Model Linearization2.4.1 Linearization Using Taylor Series Expansion – One Independent Variable2.4.2 Linearization Using Taylor Series Expansion – Multiple Independent Variables2.4.3 Piecewise Approximation2.5 Summary 9 3 Transfer Functions and Block Diagrams3.1 Laplace Transform3.2 Properties of the Laplace Transform3.2.1 Laplace Transform of a Function of Time Multiplied by a Constant3.2.2 Laplace Transform of the Sum of Two Functions of Time3.2.3 Laplace Transform of the First Derivative of a Function of Time3.2.4 Laplace Transform of Higher Derivatives of a Function of Time Function3.2.5 Laplace Transform of Function with Time Delay3.3 Continuous-Time Transfer Functions3.4 Z Transform3.5 Properties of the Z Transform3.5.1 Z Transform of a Sequence Multiplied by a Constant3.5.2 Z Transform of the Sum of Two Sequences3.5.3 Z Transform of Time Delay dT3.5.4 Z Transform of a Difference Equation3.6 Discrete-Time Transfer Functions3.7 Block Diagrams3.8 Transfer Function Algebra3.8.1 Series Relationships3.8.2 Parallel Relationships3.8.3 Closed-Loop Relationships3.8.4 Transfer Functions of Production Systems with Multiple Inputs and Outputs3.8.5 Matrices of Transfer Functions3.8.6 Factors of Transfer Function Numerator and Denominator3.8.7 Canceling Common Factors in a Transfer Function3.8.8 Padé Approximation of Continuous-Time Delay3.8.9 Absorption of Discrete Time Delay3.9 Production Systems with Continuous-Time and Discrete-Time Components3.9.1 Transfer Function of a Zero-Order Hold (ZOH)3.9.2 Discrete-Time Transfer Function Representing Continuous-Time Components Preceded by a Hold and Followed by a Sampler3.10 Potential Problems in Numerical Computations Using Transfer Functions3.11 Summary 10 4 Fundamental Dynamic Characteristics and Time Response4.1 Obtaining Fundamental Dynamic Characteristics from Transfer Functions4.1.1 Characteristic Equation4.1.2 Fundamental Continuous-Time Dynamic Characteristics4.1.3 Continuous-Time Stability Criterion4.1.4 Fundamental Discrete-Time Dynamic Characteristics4.1.5 Discrete-Time Stability Criterion4.2 Characteristics of Time Response4.2.1 Calculation of Time Response4.2.2 Step Response Characteristics4.3 Summary
