Her-Terng Yau

Control of chaos in Lorenz system

Abstract A strategy is proposed to control Lorenz chaos, whereby a sliding surface is assigned such that a sliding mode motion occurs when the proposed control law is applied. The results show that only part of the system state can be regulated arbitrarily, due to the structure of the Lorenz system and the applied control variable. The paper also provides a further discussion on the resulting system behavior, which is not addressed in the literature.

Chaos synchronization of different chaotic systems subjected to input nonlinearity

Abstract In this paper, a unified mathematical expression describing a class of synchronization systems is presented, for which the problem of chaos synchronization between different chaotic systems with input nonlinearity has been studied. Based on Lyapunov stability theory, a sliding mode controller and some generic sufficient conditions for global asymptotic synchronization are designed such that the error dynamics of two different chaotic motions satisfy stability in the Lyapunov sense in spite of the input nonlinearity. This technique is applied to achieve chaos synchronization of three pairs of different chaotic systems (Lorenz–Chen, Chen–Liu, and Liu–Lorenz) in drive–response structure. The numerical simulation results demonstrate the validity and feasibility of the proposed controller.

SLIDING MODE CONTROL OF CHAOTIC SYSTEMS WITH UNCERTAINTIES

A sliding mode hyperplane design for a class of chaotic systems with uncertainties is considered in this paper. The concept of extended systems is used such that continuous control input is obtained using a sliding mode design scheme. It is guaranteed that under the proposed control law, uncertain chaotic systems can asymptotically track target orbits. The converging speed of error states can be arbitrarily set by assigning the corresponding dynamics to the sliding surfaces. Illustrative examples of a controlled uncertain Duffing–Holmes system are presented.

Design of sliding mode controller for Lorenz chaotic system with nonlinear input

Abstract In this paper, a sliding mode controller is presented to control Lorenz chaos subject to sector nonlinear input. The proposed control law is robust against both the uncertainty in system parameters and external disturbance. Simulation results show that the system state can be regulated to a specified point in the state space. It is also seen that the system still possesses the advantage of fast response and good transient performance even though the control input is nonlinear.

Identification and Compensation of Nonlinear Friction Characteristics and Precision Control for a Linear Motor Stage

The main goal of this investigation is to improve the tracking accuracy of the stage of a linear motor. A DC brushless linear motor is used to actuate a gantry stage to perform printing. To compensate for the tracking error of the gantry stage that is associated with nonlinear friction, the dynamics of the nonlinear static friction are formulated using the Hsieh-Pan model. Particle swarm optimization (PSO), genetic algorithm, and real-coded genetic algorithm-based optimization problems are investigated to evaluate the parameters of the nonlinear friction model. The use of PSO-based optimization to tune the parameters of a disturbance-observer-based variable structure controller is also discussed to improve the tracking response. To check the consistency of the proposed controller, it is implemented in real time and an improved positional accuracy better than 0.1 μm is readily achieved.

Chaos in the imbalance response of a flexible rotor supported by oil film bearings with non-linear suspension

The dynamics of flexible rotors associated with fluid film bearings have been studied since the 1950s. Most of the literature has assumed rigid, undamped bearing support with linear elastic restoring force. For a more precise description of fluid film bearing-rotor systems, a non-linearly supported model is proposed in this paper, where a linear damping force and a non-linear elastic restoring force are assumed. Numerical results show that due to non-linear factors, though the dynamic equations of the bearing center and the rotor center are coupled, the trajectory of the rotor center demonstrates steady-state symmetric motion even when the trajectory of the bearing center is in a state of disorder. Poincaré maps, bifurcation diagrams, and power spectra are used to analyze the behavior of the bearing center in the horizontal and vertical directions under different operating conditions. The fractal dimension concept is used to determine whether the system is in a state of chaotic motion. Numerical results find that the dimension of the bearing center trajectory is fractal and greater than two in some operating conditions, indicating that the system is in a state of chaotic motion. Chaotic behavior was found in an intermediate speed range, disappearing at higher speeds. It is suggested that this is a characteristic of all fluid film systems. It is suggested that a number of existing life-critical fluid film bearing systems are possibly being operated in this chaotic region and that such systems should be reevaluated in terms of this new observation.

Nonlinear analysis and control of the uncertain micro-electro-mechanical system by using a fuzzy sliding mode control design

This study analyzes the chaotic behavior of a micromechanical resonator with electrostatic forces on both sides and investigates the control of chaos. A phase portrait, maximum Lyapunov exponent and bifurcation diagram are used to find the chaotic dynamics of this micro-electro-mechanical system (MEMS). To suppress chaotic motion, a robust fuzzy sliding mode controller (FSMC) is designed to turn the chaotic motion into a periodic motion even when the MEMS has system uncertainties.

SYNCHRONIZATION CONTROL FOR A CLASS OF CHAOTIC SYSTEMS WITH UNCERTAINTIES

This paper investigates the chaos synchronization problem for a class of uncertain master-slave chaotic systems. Based on the variable structure control theory, a strategy is proposed to guarantee the occurrence of a sliding mode motion of error states when the proposed control law is applied. As expected, the error state is able to drive to zero with match external uncertainties or into a predictable neighborhood of zero with mismatch external uncertainties. Furthermore, a modified continuous sliding mode controller is also proposed to avoid the chattering. Examples of Lorenz system and Chuas circuit are presented to demonstrate the obtained results.

Using Self-Synchronization Error Dynamics Formulation Based Controller for Maximum Photovoltaic Power Tracking in Micro-Grid Systems

This paper proposes a self-synchronization error dynamics formulation based controller for maximum photovoltaic power tracking (MPPT) of a photovoltaic (PV) array. The output power conversion of a PV array depends on atmospheric conditions, such as the solar radiation and ambient temperature, and its conversion efficiency is low. Therefore, a MPPT controller is necessary for a PV conversion system, in order to improve the output power. A PV cell is a p-n semiconductor junction. Photon motion, temperature, or electricity conduction cause anomalous diffusion phenomena in inhomogeneous media. In order to describe nonlinear-characteristics, fractional-order calculus can be used to express the dynamic behaviors using fractional-order incremental conductance and to adjust the terminal voltage to the maximum power point. Inspired by the synchronization of Sprott system, a voltage detector is formulated to trace the desired voltage and to control the duty cycle of a boost converter. For a small photovoltaic system, the numerical experiments demonstrate that the proposed method can reduce the tracking time and can improve the conversion efficiency.

Generalized Projective Synchronization for the Horizontal Platform Systems via an Integral-type Sliding Mode Control

In this paper, an integral-type sliding mode controller design for generalized projective synchronization of two horizontal platform systems (HPS) is considered. The concept of extend systems is used such that continuous control input is obtained using a sliding mode design scheme. Based on the Lyapunov stability theorem, control laws are derived. It is guaranteed that under the proposed control law, an uncertain slave chaotic HPS can asymptotically track a master chaotic HPS. The converging speed of error states can be arbitrarily set by assigning the corresponding dynamics to the sliding surfaces. Numerical simulations are shown to verify the results and this control law can be applied to another chaotic system of the same design scheme.