Book Description :
Genre : Educational, Engineering
Written By : Derek Atherton
Book Size : 8.89 Mb
The book is concerned with the effects of nonlinearity in feedback control systems and techniques which can be used to design feedback loops containing nonlinear elements. After a short introductory chapter on nonlinearity and its possible effects the use of phase plane methods for nonlinear second order systems is discussed. The next three chapters cover the describing function method and its applications in the determination of limit cycles, stability analysis and the prediction of unique nonlinear behaviour such as jump resonance and subharmonic generation. The following chapter shows using the Tsypkin approach how in feedback loops with a relay nonlinearity any limit cycles and their stability can be found exactly. Examples are given which cover some unique forms of limit cycles such as limit cycles with a sliding mode and multipulse limit cycles, which can be caused by resonant plant transfer functions. In recent years with the advent of microprocessor controllers there has been considerable interest in techniques for controller tuning based on limit cycle data and this is the topic covered in the next chapter. The analyses used make use of both the describing function method and the Tsypkin method presented in the previous chapters. The next topic covered is absolute stability methods for a nonlinear feedback loop with a single nonlinearity with emphasis placed on frequency domain methods to allow comparison with describing function results. The final chapter covers some methods for the design of nonlinear systems. The material is of an introductory nature but hopefully gives an overview and provides a basic understanding of various topics, many developed in recent years, and several of which have entire textbooks devoted to them.
Content :
Introduction
What is nonlinearity?
Forms of nonlinearity
Structure and Behaviour
Overview of contents
References
The Phase Plane Method
Introduction
Basic Principles
The Phase Plane for Systems with Linear Segmented Nonlinearities
Conclusions
References
Bibliography
The Describing Function
Introduction
The Sinusoidal Describing Function
Some Properties of the DF
The Evaluation of some DFs
Nonlinear Models and DFs
Harmonic Outputs
Sine plus Bias DF and the IDF
Conclusions
References
Bibliography
Appendix -Tables of Describing Functions
Stability and Limit Cycles using th e DF
Introduction
Limit Cycle Evaluation
Stability of a Predicted Limit Cycle
DF Accuracy
Some Examples of Limit Cycle Evaluation
More than one Nonlinear Element
Applications of SBOF to find Limit Cycles
Conclusions
Bibliography
The SSDF and Harmonically Forced Systems
Introduction
The Cubic Nonlinearity with Two Sinusoidal Inputs
Modified Nonllnearltles and the SSDF
The IDF for Related Signals
More Accurate Determination of Limit Cycles
Closed Loop Frequency Response
Jump Resonance
Conclusions
References
Limit cycles in relay systems
Introduction
The Frequency Domain Approach
Properties and Evaluation of A loci
Solving for Limit Cycles
Limit Cycle Stability
Some Interesting Limit Cycle Problems
Forced oscillations
Conclusions
References
Appendix
Controlle r Tuning from Relay Produ ced Limit Cycles
Introduction
Knowledge from the Limit Cycle
Tuning the Controller
Autotuning using the Relay in Parallel with the Controller
Conclusions
References
Absolute Stability Results
Introduction
Lyapunov's Method
Application of Lyapunov's Method
Definitions and Loop Transformations
Frequency Domain Criteria
Examples
Conclusions
References
Bibliography
Design of Nonlinear Control Systems
Introduction
Linearization
Frequency Response Shaping
Nonlinear Compensation
Compensation using DF Models
Time Optimal Control
Sliding Mode Control
Fuzzy Logic
Neural Networks
Exact Linearization
General Comments
References
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