Suwat Kuntanapreeda

Robust synchronization of fractional-order unified chaotic systems via linear control

A new scheme for accomplishing synchronization between two fractional-order unified chaotic systems is proposed in this paper. The scheme does not require that the nonlinear dynamics of the synchronization error system must be eliminated. Moreover, the parameter of the systems does not have to be known. A controller is a linear feedback controller, which is simple in implementation. It is designed based on an LMI condition. The LMI condition guarantees that the synchronization between the slave system and the master system is achieved. Numerical simulations are performed to demonstrate the effectiveness of the proposed scheme.

Robust stabilization of fractional-order chaotic systems with linear controllers: LMI-based sufficient conditions

This paper is concerned with the problem of robust state feedback controller design to suppress fractional-order chaotic systems. A general class of fractional-order chaotic systems is considered and it is assumed that the systems’ equations depend on bounded uncertain parameters. We transform the chaotic system equations into linear interval systems, and a sufficient stabilizability condition is derived in terms of linear matrix inequality (LMI). Then, an appropriate feedback gain is introduced to bring the chaotic states to the origin. Such design will result in a simple but effective controller. Several numerical simulations have been carried out to verify the effectiveness of the theoretic results.

OUTPUT FEEDBACK CONTROL OF UNIFIED CHAOTIC SYSTEMS BASED ON FEEDBACK PASSIVITY

Recently, the concept of feedback passivity-based control has drawn attention to chaos control. In all existing papers, the implementations of passivity-based control laws require the system states for feedback. In this paper, a passivity-based control law which only requires the knowledge of the system output is proposed. Simulation results are provided to show the effectiveness of the proposed solution.

Synchronization of chaotic systems with unknown parameters using adaptive passivity-based control

Abstract This paper investigates the problem of complete synchronization of chaotic systems with unknown parameters. An adaptive control scheme based on a feedback passivity approach is proposed. The convergence of the synchronization error is guaranteed. The unified chaotic and hyperchaotic Lu systems are taken as illustrative examples. The feasibility and effectiveness of the proposed scheme are demonstrated through numerical simulations.

Improving Delay-Margin of Noncollocated Vibration Control of Piezo-Actuated Flexible Beams via a Fractional-Order Controller

Noncollocated control of flexible structures results in nonminimum-phase systems because the separation between the actuator and the sensor creates an input-output delay. The delay can deteriorate stability of closed-loop systems. This paper presents a simple approach to improve the delay-margin of the noncollocated vibration control of piezo-actuated flexible beams using a fractional-order controller. Results of real life experiments illustrate efficiency of the controller and show that the fractional-order controller has better stability robustness than the integer-order controller.

Nonlinear extended output feedback control for CSTRs with van de Vusse reaction

Abstract This paper developed an output-feedback control system for regulation of continuous stirred tank reactors (CSTRs) with van de Vusse reaction. The reactors are often used as benchmark representatives of nonminimum-phase processes. Control of such nonlinear processes is difficult because they exhibit the inverse response. Linear controllers usually give unsatisfactory results in this case and thus nonlinear control approaches are more suitable. The proposed control system consists of a nonlinear observer and an extended nonlinear state feedback controller. The extension consists in adding the integrator to the controller for improving steady state performance of the control system. Stability of the control system including the observer dynamics is guaranteed, thanks to the existence of an input-to-state Lyapunov function. Simulation studies are conducted to illustrate the effectiveness of the proposed control system and its robustness.

Adaptive Vibration Control of Piezoactuated Euler-Bernoulli Beams Using Infinite-Dimensional Lyapunov Method and High-Order Sliding-Mode Differentiation

This paper presents an adaptive control scheme to suppress vibration of flexible beams using a collocated piezoelectric actuator-sensor configuration. A governing equation of the beams is modelled by a partial differential equation based on Euler-Bernoulli theory. Thus, the beams are infinite-dimensional systems. Whereas conventional control design techniques for infinite-dimensional systems make use of approximated finite-dimensional models, the present adaptive control law is derived based on the infinite-dimensional Lyapunov method, without using any approximated finite-dimension model. Thus, the stability of the control system is guaranteed for all vibration modes. The implementation of the control law requires a derivative of the sensor output for feedback. A high-order sliding mode differentiation technique is used to estimate the derivative. The technique features robust exact differentiation with finite-time convergence. Numerical simulation and experimental results illustrate the effectiveness of the controller.

Traction Control of Electric Vehicles Using Sliding-Mode Controller with Tractive Force Observer

Traction control is an important element in modern vehicles to enhance drive efficiency, safety, and stability. Traction is produced by friction between tire and road, which is a nonlinear function of wheel slip. In this paper, a sliding-mode control approach is used to design a robust traction controller. The control objective is to operate vehicles such that a desired wheel slip ratio is achieved. A nonlinearity observer is employed to estimate tire tractive forces, which are used in the control law. Simulation and experimental results have illustrated the success of the proposed observer-based controller.

An Observer-Based Neural Network Controller for Chaotic Lorenz System

The paper proposes an alternative control design for the chaotic Lorenz system based on neural networks. The controller is a feedforward neural network trained by a model reference technique. Implementation of the control design requires system states for feedback, while in most of practical applications only the system output is available. To overcome this problem, a nonlinear observer is used to estimate the states of the system. Simulation results have illustrated the feasibility and effectiveness of the proposed observer-based neural network controller.

SIMPLE LMI-BASED SYNCHRONIZATION OF FRACTIONAL-ORDER CHAOTIC SYSTEMS

This paper presents a simple scheme for synchronization of fractional-order chaotic systems. The scheme utilizes a recently developed LMI (Linear matrix inequality) stabilization theorem for fractional-order linear interval systems to design a linear controller. In contrast to existing schemes in the literature, the present scheme is straightforward and does not require that nonlinear parts of synchronization error dynamics are cancelled by the controller. The fractional-order Rossler, Lorenz, and hyperchaotic Chen systems are used as demonstrative examples. Numerical results illustrate the effectiveness of the present scheme.