Nonlinear Control Systems by Zoran Vukić, Ljubomir Kuljača, Dali Đonlagić, Sejid Tešnjak

By Zoran Vukić, Ljubomir Kuljača, Dali Đonlagić, Sejid Tešnjak

This article emphasizes classical equipment and provides crucial analytical instruments and techniques for the development and improvement of better layout tools in nonlinear keep an eye on. It bargains engineering tactics for the frequency area, in addition to solved examples for transparent figuring out of regulate functions within the commercial, electric, method, production, and car industries. The authors talk about houses of nonlinear structures, balance, linearization equipment, working modes and dynamic research equipment, section trajectories in dynamic research of nonlinear platforms, and harmonic linearization in dynamic research of nonlinear keep watch over platforms working in stabilization mode.Properties of nonlinear structures, balance, linearization tools, working modes and dynamic research tools, part trajectories in dynamic research of nonlinear platforms, harmonic linearization in dynamic research of nonlinear keep an eye on structures working in stabilization mode, harmonic linearization in dynamic research of nonlinear regulate structures in monitoring mode of operation, functionality estimation of nonlinear regulate method temporary responses, describing functionality technique in fuzzy regulate structures. Appendices: harmonic linearization, Popov diagrams.

Table of Contents:

Series Introduction
Preface
Properties of Nonlinear Systems
Problems within the thought of Nonlinear Systems
Basic Mathematical and Structural types of Nonlinear Systems
Basic particular homes of Nonlinear Systems
Stability and Equilibrium States
Basic houses of Nonlinear Functions
Typical Nonlinear Elements
Nonlinear components with Single-Valued non-stop Characteristics
Nonlinear parts with Single-Valued Discontinuous Characteristics
Nonlinear parts with Double-Valued Characteristics
Nonlinear components with Multi-Valued Characteristics
Atypical (Non-Standard) Nonlinear Elements
Basic Nonlinearity Classes
Conclusion
Stability
Equilibrium States and ideas of Stability
Stability of a Nonlinear process in line with balance of the Linearized System
Lyapunov Stability
Definitions of Stability
Lyapunov Direct Method
Absolute Stability
Absolute balance of Equilibrium States of an Unforced procedure (Popov Criterion)
Geometrical Interpretation of Popov Criterion
Absolute balance with volatile Linear Part
Examples of picking Absolute balance through the use of Popov Plot
Absolute balance of an Unforced procedure with Time-Varying Nonlinear Characteristic
Absolute balance of pressured Nonlinear Systems
Absolute balance of pressured Nonlinear structures with an risky Linear Part
Conclusion
Linearization Methods
Graphical Linearization Methods
Algebraic Linearization
Analytical Linearization strategy (Linearization within the neighborhood of the working Point)
Evaluation of Linearization Coefficients through Least-Squares Method
Harmonic Linearization
Describing Function
Statistical Linearization
Combined (Dual-Input) Describing Functions
Conclusion
Operating Modes and Dynamic research Methods
Operating Modes of Nonlinear regulate Systems
Self-Oscillations
Forced Oscillations
Effects of High-Frequency Signal---Dither
Methods of Dynamic research of Nonlinear Systems
Phase Trajectories in Dynamic research of Nonlinear Systems
Phase Plane
Phase Trajectories of Linear Systems
Phase Trajectories of Nonlinear Systems
Methods of Defining part Trajectories
Estimation of balance and function by way of section Trajectories
Examples of program of assorted how you can receive part Trajectories
Conclusion
Harmonic Linearization in Dynamic research of Nonlinear keep an eye on platforms working in Stabilization Mode
Describing functionality in Dynamic research of Unforced Nonlinear keep an eye on Systems
Analysis of Symmetrical Self-Oscillations
Analytical balance Criterion of Self-Oscillations
Determination of Symmetrical Self-Oscillations
Asymmetrical Self-Oscillations---Systems with Asymmetrical Nonlinear Static Characteristic
Asymmetrical Self-Oscillations---Systems with Symmetrical Nonlinear Characteristic
Reliability of the Describing functionality Method
Forced Oscillations of Nonlinear Systems
Symmetrical pressured Oscillations
Asymmetrical compelled Oscillations
Resonance Jump
Conclusion
Harmonic Linearization in Dynamic research of Nonlinear keep watch over structures in monitoring Mode of Operation
Vibrational Linearization with Self-Oscillations
Dynamic research of Nonlinear keep an eye on platforms in monitoring Mode of Operation with pressured Oscillations
Performance Estimation of Nonlinear keep watch over approach temporary Responses
Determining Symmetrical brief Responses close to Periodic Solutions
Performance Diagrams of Nonlinear procedure temporary Responses
Describing functionality approach in Fuzzy keep watch over Systems
Basics of Fuzzy Logic
Introduction
Fuzzy units Fundamentals
Crisp and Fuzzy units and Their club Functions
Fuzzy Set Parameter Presentation
Basic Operation on Fuzzy units up to the mark Systems
Language Variable Operators
General Language Variable Operators
Fuzzy Relations
Fuzzy Relational Equations
Use of Language Variables and Language Expressions
Fuzzification
Language Description of the approach via IF-THEN Rules
Language Description of the approach with Fuzzy choice Making
Defuzzification or Fuzzy Set Adjustment (Calculating Crisp Output Values)
Describing functionality of SISO Fuzzy Element
Stability research of a Fuzzy keep watch over System
Influence of Fuzzy Regulator on Resonance Jump
Appendix A Harmonic Linearization
Appendix B Popov Diagrams
Bibliography
Index

Show description

Read Online or Download Nonlinear Control Systems PDF

Best control systems books

Modeling and Control of Complex Physical Systems: The Port-Hamiltonian Approach

Strength alternate is a tremendous origin of the dynamics of actual platforms, and, as a result, within the examine of complicated multi-domain structures, methodologies that explicitly describe the topology of strength exchanges are instrumental in structuring the modeling and the computation of the system's dynamics and its keep watch over.

Intelligent Diagnosis and Prognosis of Industrial Networked Systems (Automation and Control Engineering)

In an period of extensive festival the place plant working efficiencies needs to be maximized, downtime as a result of equipment failure has develop into extra high priced. to chop working expenditures and raise sales, industries have an pressing have to expect fault development and closing lifespan of commercial machines, strategies, and structures.

Fault Detection and Diagnosis in Engineering Systems

That includes a model-based method of fault detection and analysis in engineering platforms, this ebook includes up to date, functional details on fighting product deterioration, functionality degradation and significant equipment harm. ;College or college bookstores may perhaps order 5 or extra copies at a unique pupil cost.

Additional info for Nonlinear Control Systems

Example text

10 the trajec­ tory of such system is shown for the same initial conditions as in previous case (point A) where the behavior ofthe system is chaotic. 6 (point B) the system settles to the stable limit cycle outside the chaotic attractor region. Here one can observe qualitatively completely different behaviors ofthe nonlinear :,ystem which depend only on initial conditions. 4 = Stability and Equilibrium States Very often the dynamic behavior of a system is characterized by the phrase "the system is stable".

L 6d): 11 = Copyright © 2003 by Marcel Dekker, Inc. , (c) (d) (e) Figure 1 . 1 6: Nonlinear characteristic of the type dead zone. Copyright © 2003 by Marcel Dekker, Inc. 31 Properties of Nonlinear Systems x (a) (b) Figure 1 . 17 : Nonlinear characteristic of the type saturation. Saturation (limiter). Figure l . 1 7a shows the static characteristic of the nonlin­ earity of the type saturation (limiter). Similar characteristics are in practically all types of amplifiers (electronic, electromechanic, pneumatic, hydraulic, combined ones) where the limited output power cannot follow large input signals.

A= A-1 ,2 = Copyright © 2003 by Marcel Dekker. Inc. 20 Chapter I to Fig. 7a - stable for both branches. If the bifurcation points exist in a nonlinear control system, it is important to know the regions of structural stability in the parameter plane and in the phase plane and it is necessary to ensure that the parameters and the states of the system remain within these regions. Structural instability can be expected with control systems whose objects (processes) are nonlinear, with certain types of adaptive control systems, and generally with the systems whose action and reaction forces cannot reach the equilibrium state.

Download PDF sample

Rated 4.81 of 5 – based on 45 votes