Observer-Based Feedback Linearizing Control of an Electromagnetic Suspension

1996 ◽  
Vol 118 (3) ◽  
pp. 615-619 ◽  
Author(s):  
B. C. Fabien
Keyword(s):  
Feedback Controller ◽  
Superior Performance ◽  
Linear Feedback ◽  
Nonlinear Controller ◽  
Electromagnetic Suspension ◽  
Weakly Coupled ◽  
Coupled Riccati Equations ◽  
Linear Feedback Controller ◽  
Lyapunov’S Second Method ◽  
Feedback Linearizable Systems

This paper develops a stabilizing observer-based feedback linearizing controller for a single-axis electromagnetic suspension. The controller uses only the measured output of the system, and is shown to be robust with respect to parameter uncertainty. The controller differs from other robust feedback linearizing controllers that have appeared in recent literature, because it is continuous, and non-adaptive. Lyapunov’s second method is used to prove stability and robustness of the controller. The controller has a simple structure and its gains are determined by solving two weakly coupled Riccati equations. Numerical simulations are performed to compare a linear feedback controller and the observer-based feedback linearizing controller. Results obtained demonstrate that the nonlinear controller yields superior performance when compared with the linear feedback controller. The controller synthesis technique developed in this paper is applicable to other fully feedback linearizable systems, not just electromagnetic suspensions.

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.

Chaotic Control in a Fractional-Order Modified Van Der Pol Oscillator

2011 ◽  
Vol 474-476 ◽  
pp. 83-88
Author(s):  
Xin Gao
Keyword(s):  
Fractional Order ◽  
Feedback Controller ◽  
Van Der Pol Oscillator ◽  
Linear Feedback ◽  
Fractional Order Systems ◽  
Van Der Pol ◽  
Chaotic Control ◽  
Linear Feedback Controller

The dynamics of fractional-order systems have attracted increasing attention in recent years. In this paper, we study the chaotic behaviors in a fractional-order modified van der Pol oscillator. We find that chaos exists in the fractional-order modified van der Pol oscillator with order less than 3. In addition, the lowest order we find for chaos to exist in such system is 2.4. Finally, a simple, but effective, linear feedback controller is also designed to stabilize the fractional order chaotic van der Pol oscillator.

Optimal Linear Feedback Control for a Class of Nonlinear Nonquadratic Non-Gaussian Problems

1991 ◽  
Vol 113 (4) ◽  
pp. 568-574 ◽  
Author(s):  
R. J. Chang
Keyword(s):  
Control System ◽  
Stochastic Systems ◽  
Feedback Controller ◽  
Performance Criteria ◽  
Linear Feedback ◽  
Feedback Gain ◽  
Linear Feedback Controller ◽  
Gaussian Method ◽  
Optimal Linear ◽  
Non Gaussian

An optimal linear feedback controller designed for a class of nonlinear stochastic systems with nonquadratic performance criteria by a non-Gaussian approach is presented. The non-Gaussian method is developed through expressing the unknown stationary output density function as a weighted sum of the Gaussian densities with undetermined parameters. With the aid of a Gaussian-sum density, the optimal feedback gain for a control system with complete state information is derived. By assuming that the separation principle is valid for the class of stochastic systems, a nonlinear precomputed-gain filter is then implemented. The method is illustrated by a Duffing-type control system and the performance of a linear feedback controller designed through both quadratic and nonquadratic performance indices is compared.

A New 6D Hyperchaotic System with Four Positive Lyapunov Exponents Coined

2015 ◽  
Vol 25 (04) ◽  
pp. 1550060 ◽  
Author(s):  
Qigui Yang ◽  
Waleed Mahgoub Osman ◽  
Chuntao Chen
Keyword(s):  
Lyapunov Exponents ◽  
Lorenz System ◽  
Feedback Controller ◽  
Linear Feedback ◽  
Hyperchaotic System ◽  
Nonlinear Feedback ◽  
Dynamical Behaviors ◽  
Linear Feedback Controller ◽  
The Lorenz System ◽  
Hyperbolic Equilibrium

This paper reports the finding of a new six-dimensional (6D) autonomous hyperchaotic system, which is obtained by coupling a 1D linear system and a 5D hyperchaotic system that is constructed by adding a linear feedback controller and a nonlinear feedback controller to the Lorenz system. This hyperchaotic system has very simple algebraic structure but can exhibit complex dynamical behaviors. Of particular interest is that it has a hyperchaotic attractor with four positive Lyapunov exponents and a unique equilibrium in a large range of parameters. Numerical analysis of phase trajectories, Lyapunov exponents, bifurcation, power spectrum and Poincaré projections verifies the existence of the hyperchaotic and chaotic attractors. In addition, stability of the hyperbolic equilibrium is analyzed and two complete mathematical characterizations for 6D Hopf bifurcation are given.

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