2 Mathematical Techniques for Control-System Analysis
by Stanley M. Shinners
Modern Control System Theory and Design, 2nd Edition
- Coverpage
- Titlepage
- Copyright
- Dedication
- Contents
- Preface
- 1 General Concept of Control-System Design
- 2 Mathematical Techniques for Control-System Analysis
- 2.1. Introduction
- 2.2. Review of Complex Variables, Complex Functions, and the s Plane
- 2.3. Review of Fourier Series and Fourier Transform
- 2.4. Review of the Laplace Transform
- 2.5. Useful Laplace Transforms
- 2.6. Important Properties of the Laplace Transform
- 2.7. Inversion by Partial Fraction Expansion
- 2.8. Application of MATLAB to Control Systems
- 2.9. Inversion with Partial Fraction Expansion Using MATLAB
- 2.10. Laplace-Transform Solution of Differential Equations
- 2.11. Transfer-Function Concept
- 2.12. Transfer Functions of Common Networks
- 2.13. Transfer Functions of Systems
- 2.14. Signal-Flow Graphs and Mason’s Theorem
- 2.15. Reduction of the Signal-Flow Graph
- 2.16. Application of Mason’s Theorem and the Signal-Flow Graph to Multiple-Feeback Systems
- 2.17. Disturbance Signals in Feedback Control Systems
- 2.18. Operational Amplifiers
- 2.19. Simulation Diagrams
- 2.20. Review of Matrix Algebra
- 2.21. State-Variable Concepts
- 2.22. State-Variable Diagram
- 2.23. Transformation Between the State-Space Form and the Transfer Function Form using MATLAB
- 2.24. Digital Computer Evaluation of the Time Response
- 2.25. Obtaining the Transient Response of Systems Using MATLAB
- 2.26. State Transition Matrix
- 2.27. Total Solution of the State Equation
- 2.28. Evaluation of the State Transition Matrix from an Exponential Series
- 2.29. Summary
- 2.30. Illustrative Problems and Solutions
- Problems
- References
- 3 State Equations and Transfer-Function Representation of Physical Linear Control-System Elements
- 3.1. Introduction
- 3.2. State Equations of Electrical Networks
- 3.4. Transfer-Function and State-Variable Representation of Typical Electromechanical Control-System Devices
- 3.5. Transfer-Function and State-Variable Representation of Typical Hydraulic Devices
- 3.6. Transfer-Function Representation of Thermal Systems
- 3.7. A Generalized Approach for Modeling—the Principles of Conservation and Analogy
- 3.8. Illustrative Problems and Solutions
- Problems
- References
- 4 Second-Order Systems
- 4.1. Introduction
- 4.2. Characteristic Responses of Second-Order Control Systems
- 4.3. Relation Between Location of Roots in the s-Plane and the Transient Response
- 4.4. State-Variable Signal-Flow Graph of a Second-Order System
- 4.5. What is the Best Damping Ratio to Use?
- 4.7. Illustrative Problems and Solutions
- Problems
- References
- 5.1. Introduction
- 5.2. Stability
- 5.3. Sensitivity
- 5.4. Static Accuracy
- 5.5. Transient Response
- 5.6. Performance Indices
- 5.7. Zero-Error Systems
- 5.8. The ITAE Performance Criterion for Optimizing the Transient Response
- 5.9. Other Practical Considerations
- 5.10. Illustrative Problems and Solutions
- Problems
- References
- 6 Techniques for Determining Control-System Stability
- 6.1. Introduction
- 6.2. Determining the Characteristic Equation using Conventional and State-Variable Methods
- 6.3. Routh—Hurwitz Stability Criterion
- 6.4. Mapping Contours From the s-Plane to the F(s)-Plane
- 6.5. Nyquist Stability Criterion
- 6.6. Nyquist Diagrams Using MATLAB
- 6.7. Bode-Diagram Approach
- 6.8. Bode Diagrams Using MATLAB
- 6.9. Digital Computer Programs for Obtaining the Open-Loop and Closed-Loop Frequency Responses and the Time-Domain Response
- 6.10. Nichols Chart
- 6.11. Nichols Chart Using MATLAB
- 6.12. Relationship between Closed-Loop Frequency Response and the Time-Domain Response
- 6.14. Root-Locus Method for Negative-Feedback Systems
- 6.15. Root Locus of Time-Delay Factors
- 6.17. Root-Locus Method for Control Systems Using MATLAB
- 6.18. Digital Computer Program for Obtaining the Root Locus
- 6.20. Comparison of the Nyquist Diagram, Bode Diagram, Nichols Chart, and Root Locus for 12 Commonly Used Transfer Functions
- 6.21. Commercially Available Software Packages for Computer-Aided Control-System Design
- 6.22. What is the “Best” Stability Analysis Technique? Guidelines for using the Analysis Techniques Presented
- 6.23. Illustrative Problems and Solutions
- References
- 7 Linear Control-System Compensation and Design
- 7.2. Cascade-Compensation Techniques
- 7.3. Minor-Loop Feedback-Compensation Techniques
- 7.4. Proportional-Plus-Integral-Plus Derivative (PID) Compensators
- 7.5. Example for the Design of a Second-Order Control System
- 7.6. Compensation and Design using the Bode-Diagram Method
- 7.8. Compensation and Design using the Nichols Chart
- 7.9. Compensation and Design using the Root-Locus Method
- 7.11. Illustrative Problems and Solutions
- Problems
- 8 Modern Control-System Design using State-Space, Pole Placement, Ackermann’s Formula, Estimation, Robust Control, and H∞ Techniques
- 8.1. Introduction
- 8.2. Pole-Placement Design using Linear-State-Variable Feedback
- 8.4. Controllability
- 8.5. Observability
- 8.6. Ackermann’s Formula for Design using Pole Placement
- 8.7. Estimator Design in Conjunction with the Pole Placement Approach using Linear-State-Variable Feedback
- 8.9. Extension of Combined Compensator Design Including a Controller and an Estimator for Systems Containing a Reference Input
- 8.10. Robust Control Systems
- 8.11. An Introduction to H∞ Control Concepts
- 8.13. Linear Algebraic Aspects of Control-System Design Computations
- Problems
- References
- Appendix A Laplace-Transform Table
- Answers to Selected Problems
- Index
-
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