Digital Control Systems

1 Introduction.- A Fundamentals.- 2 Control with Digital Computers (Process Computers, Microcomputers).- 3 Fundamentals of Linear Sampled-data Systems (Discrete-time Systems).- 3.1 Discrete-time Signals.- 3.1.1 Discrete Functions, Difference Equations.- 3.1.2 Impulse Trains.- 3.1.3 Fourier-Transform of the Impulse Train.- 3.2 Laplace-transformation of Discrete-time Functions and Shannon's Sampling Theorem.- 3.2.1 Laplace-transformation.- 3.2.2 Shannon's Sampling Theorem.- 3.2.3 Holding Element.- 3.2.4 Frequency Response of Sampled Systems.- 3.3 z-Transform.- 3.3.1 Introduction of z-Transform.- 3.3.2 z-Transform Theorems.- 3.3.3 Inverse z-Transform.- 3.4 Convolution Sum and z-Transfer Function.- 3.4.1 Convolution Sum.- 3.4.2 Pulse Transfer Function and z-Transfer-Function.- 3.4.3 Properties of the z-Transfer Functions and Difference Equations.- 3.5 Poles and Zeros, Stability.- 3.5.1 Location of Poles in the z-Plane.- 3.5.2 Stability Condition.- 3.5.3 Stability Analysis through Bilinear Transformation.- 3.5.4 Schur-Cohn-Jury Criterion.- 3.5.5 Location of Zeros in the z-Plane.- 3.6 State Variable Representation.- 3.6.1 The Vector Difference Equation Based on Vector Differential Equation.- 3.6.2 The Vector Difference Equation Based on Difference Equation.- 3.6.3 Canonical Forms.- 3.6.4 Processes with Deadtime.- 3.6.5 Solution of Vector Difference Equation.- 3.6.6 Determination of the z-Transfer Function.- 3.6.7 Determination of the Impulse Response.- 3.6.8 Controllability and Observability.- 3.7 Mathematical Models of Processes.- 3.7.1 Basic Types of Technical Processes.- 3.7.2 Determination of the Process Model-Modelling and Identification.- 3.7.3 Calculation of z-Transfer Functions from s-Transfer Functions.- 3.7.4 Simplification of Process Models for Discrete-time Signals.- B Control-Systems for Deterministic Disturbances.- 4 Deterministic Control Systems.- 5 Parameter-optimized Controllers.- 5.1 Discretizing the Differential Equations of Continuous PID-Controllers.- 5.2 Parameter-optimized Discrete Control Algorithms of Low-Order.- 5.2.1 Control Algorithms of First and Second Order.- 5.2.2 Control Algorithms with Prescribed Initial Manipulated Variable.- 5.2.3 PID-Control Algorithm through z-Transformation.- 5.3 Modifications to Discrete PID-Control Algorithms.- 5.3.1 Different Evaluation of Control Variable and Reference Variable.- 5.3.2 Different Discretizations of the Derivative Term.- 5.3.3 Delayed Differential Term.- 5.4 Design Through Numerical Parameter Optimization.- 5.4.1 Numerical Parameter Optimization.- 5.4.2 Simulation Results for PID-Control Algorithms.- 5.5 PID-Controller Design Through Pole-Assignment, Compensation and Approximation.- 5.5.1 Pole-assignment Design.- 5.5.2 Design as a Cancellation Controller.- 5.5.3 Design of PID-Controllers Through Approximation of other Controllers.- 5.6 Tuning Rules for Parameter-optimized Control Algorithms.- 5.6.1 Tuning Rules for Modified PID-controllers.- 5.6.2 Tuning Rules Based on Measured Step Functions.- 5.6.3 Tuning Rules with Oscillation Tests.- 5.7 Choice of Sample Time for Parameter-optimized Control Algorithms.- 5.8 Supplementary Functions of Digital PID-Controllers.- 6 General Linear Controllers and Cancellation Controllers.- 6.1 General Linear Controllers.- 6.1.1 General Linear Controller Design for Specified Poles.- 6.1.2 General Linear Controller Design Through Parameter Optimization.- 6.2 Cancellation Controllers.- 7 Controllers for Finite Settling Time.- 7.1 Deadbeat Controller Without Prescribed Manipulated Variable.- 7.2 Deadbeat Controller with Prescribed Manipulated Variable.- 7.3 Choice of the Sample Time for Deadbeat Controllers.- 7.4 Approximation Through PID-Controllers.- 8 State Controller and State Observers.- 8.1 Optimal State Controllers for Initial Values.- 8.2 Optimal State Controllers for External Disturbances.- 8.3 State Controllers with a Given Characteristic Equation.- 8.4 Modal State Control.- 8.5 State Controllers for Finite Settling Time (Deadbeat).- 8.6 State Observers.- 8.7 State Controllers with Observers.- 8.7.1 An Observer for Initial Values.- 8.7.2 Observer for External Disturbances.- 8.7.3 Introduction of Integral Action Elements into the State Controller.- 8.7.4, Measures to Minimize Observer Delays.- 8.8 State Observer of Reduced-Order.- 8.9 State Variable Reconstruction.- 8.10 Choice of Weighting Matrices and Sample Time.- 8.10.1 Weighting Matrices for State Controllers and Observers.- 8.10.2 Choice of the Sample Time.- 9 Controllers for Processes with Large Deadtime.- 9.1 Models for Processes with Deadtime.- 9.2 Deterministic Controllers for Deadtime Processes.- 9.2.1 Processes with Large Deadtime and Additional Dynamics.- 9.2.2 Pure Deadtime Processes.- 9.3 Comparison of the Control Performance and the Sensitivity of Different Controllers for Deadtime Processes.- 10 Sensitivity and Robustness with Constant Controllers.- 10.1 On the Sensitivity of Closed-loop Systems.- 10.2 Insensitive Control Systems.- 10.2.1 Insensitivity through Additional Dynamic Feedback.- 10.2.2 Insensitivity through Variation of the Design of General Controllers.- 10.3 On the Robustness of Control Systems.- 10.4 Robust Control Systems.- 11 Comparison of Different Controllers for Deterministic Disturbances.- 11.1 Comparison of Controller Structures, Poles and Zeros.- 11.1.1 General Linear Controller for Specified Poles.- 11.1.2 Low Order Parameter-optimized Controllers.- 11.1.3 General Cancellation Controller.- 11.1.4 Deadbeat Controller.- 11.1.5 Predictor Controller.- 11.1.6 State Controller.- 11.2 Characteristic Values for Performance Comparison.- 11.3 Comparison of the Performance of the Control Algorithms.- 11.4 Comparison of the Dynamic Control Factor.- 11.5 Conclusions for the Application of Control Algorithms.- Appendix A.- A1 Tables of z-Transforms and Laplace-Transforms.- A2 Table of Some Transfer Elements with Continuous and Sampled Systems.- A3 Test Processes for Simulation.- A4 On the Differentiation of Vectors and Matrices.- Appendix B.- Problems.- Appendix C.- Results of the Problems.- References.