Design of Linear Feedback Controllers for Dynamic Systems With Hysteresis

2014 ◽  
Vol 22 (4) ◽  
pp. 1268-1280 ◽  
Keyword(s):  
Dynamic Systems ◽  
Linear Feedback ◽  
Feedback Controllers

scholarly journals On the Passivity and Positivity Properties in Dynamic Systems: Their Achievement under Control Laws and Their Maintenance under Parameterizations Switching

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Dynamic Systems ◽  
Transfer Functions ◽  
Dissipation Function ◽  
Linear Feedback ◽  
Feedback Controllers ◽  
Control Laws ◽  
Strict Positivity ◽  
Output Matrix ◽  
Regenerative Systems ◽  
Time Invariant

This paper is devoted to discuss certain aspects of passivity results in dynamic systems and the characterization of the regenerative systems counterparts. In particular, the various concepts of passivity as standard passivity, strict input passivity, strict output passivity, and very strict passivity (i.e., joint strict input and output passivity) are given and related to the existence of a storage function and a dissipation function. Later on, the obtained results are related to external positivity of systems and positivity or strict positivity of the transfer matrices and transfer functions in the time-invariant case. On the other hand, how to achieve or how eventually to increase the passivity effects via linear feedback by the synthesis of the appropriate feed-forward or feedback controllers or, simply, by adding a positive parallel direct input-output matrix interconnection gain is discussed.

scholarly journals Controlled Positive Dynamic Systems with an Entropy Operator: Fundamentals of the Theory and Applications

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2585
Author(s):  
Yuri S. Popkov
Keyword(s):  
Feedback Control ◽  
Dynamic Systems ◽  
Dynamic Properties ◽  
Monotone Operators ◽  
Singular Points ◽  
Program Control ◽  
Linear Feedback ◽  
Economic Systems ◽  
Linear Feedback Control ◽  
Nonzero Equilibrium

Controlled dynamic systems with an entropy operator (DSEO) are considered. Mathematical models of such systems were used to study the dynamic properties in demo-economic systems, the spatiotemporal evolution of traffic flows, recurrent procedures for restoring images from projections, etc. Three problems of the study of DSEO are considered: the existence and uniqueness of singular points and the influence of control on them; stability in “large” of the singular points; and optimization of program control with linear feedback. The theorems of existence, uniqueness, and localization of singular points are proved using the properties of equations with monotone operators and the method of linear majorants of the entropy operator. The theorem on asymptotic stability of the DSEO in “large” is proven using differential inequalities. Methods for the synthesis of quasi-optimal program control and linear feedback control with integral quadratic quality functional, and ensuring the existence of a nonzero equilibrium, were developed. A recursive method for solving the integral equations of the DSEO using the multidimensional functional power series and the multidimensional Laplace transform was developed. The problem of managing regional foreign direct investment is considered, the distribution of flows is modeled by the corresponding DSEO. It is shown that linear feedback control is a more effective tool than program control.

Three-Stage Feedback Controller Design With Applications to a Three Time-Scale System

2016 ◽  
Author(s):  
Verica Radisavljevic-Gajic ◽  
Milos Milanovic
Keyword(s):  
Time Scale ◽  
Controller Design ◽  
Feedback Controller ◽  
Linear Feedback ◽  
Feedback Controllers ◽  
Linear Feedback Controller ◽  
Full State ◽  
Full State Feedback ◽  
A New Technique ◽  
Natural Decomposition

A new technique was presented that facilitates design of independent full-state feedback controllers at the subsystem levels. Different types of local controllers, for example, eigenvalue assignment, robust, optimal (in some sense L1, H2, H∞, ...) may be used to control different subsystems. This feature has not been available for any known linear feedback controller design. In the second part of the paper, we specialize the results obtained to the three time-scale linear systems (singularly perturbed control systems) that have natural decomposition into slow, fast, and very fast subsystems. The proposed technique eliminates numerical ill-condition of the original three-time scale problems.

ON FEEDBACK CONTROL OF CHAOTIC NONLINEAR DYNAMIC SYSTEMS

1992 ◽  
Vol 02 (02) ◽  
pp. 407-411 ◽  
Author(s):  
GUANRONG CHEN ◽  
XIAONING DONG
Keyword(s):  
Feedback Control ◽  
Computer Simulations ◽  
Discrete Time ◽  
Dynamic Systems ◽  
Chaotic Dynamic ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Nonlinear Dynamic Systems ◽  
Feedback Controls ◽  
Feedback Controllers

In this paper, some interesting analysis and simulations on the control of chaotic dynamic systems using conventional feedback control strategies are presented. The typical discrete-time chaotic Lozi system is investigated in some detail. The trajectories of the chaotic Lozi system are controlled to its equilibrium points using conventional feedback controls. Analysis on the design of the feedback controllers and its computer simulations are included.

scholarly journals Hyperchaos Numerical Simulation and Control in a 4D Hyperchaotic System

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Junhai Ma ◽  
Yujing Yang
Keyword(s):  
Lyapunov Exponents ◽  
Equilibrium Points ◽  
Linear Feedback ◽  
Hyperchaotic System ◽  
Bifurcation Diagrams ◽  
Theory Analysis ◽  
Feedback Controllers ◽  
Dynamic Simulations ◽  
Wide Range ◽  
And Control

A hyperchaotic system is introduced, and the complex dynamical behaviors of such system are investigated by means of numerical simulations. The bifurcation diagrams, Lyapunov exponents, hyperchaotic attractors, the power spectrums, and time charts are mapped out through the theory analysis and dynamic simulations. The chaotic and hyper-chaotic attractors exist and alter over a wide range of parameters according to the variety of Lyapunov exponents and bifurcation diagrams. Furthermore, linear feedback controllers are designed for stabilizing the hyperchaos to the unstable equilibrium points; thus, we achieve the goal of a second control which is more useful in application.

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