Sheng-Dong Xu

T-S fuzzy controllers for nonlinear interconnected systems with multiple time delays

This paper investigates the effectiveness of a passive tuned mass damper (TMD) and fuzzy controller in reducing the structural responses subject to the external force. In general, TMD is good for linear systems. We proposed here an approach of Takagi-Sugeno (T-S) fuzzy controller to deal with the nonlinear system. To overcome the effect of modeling error between nonlinear multiple time-delay systems and T-S fuzzy models, a robustness design of fuzzy control via model-based approach is proposed in this paper. A stability criterion in terms of Lyapunovs direct method is derived to guarantee the stability of nonlinear multiple time-delay interconnected systems. Based on the decentralized control scheme and this criterion, a set of model-based fuzzy controllers is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time-delay interconnected system and the H/sup /spl infin// control performance is achieved at the same time. Finally, the proposed methodology is illustrated by an example of a nonlinear TMD system.

Study of VSC Reliable Designs With Application to Spacecraft Attitude Stabilization

This brief investigates variable structure reliable control (VSRC) issues of a set of second-order nonlinear systems and their application to spacecraft attitude stabilization. Both passive and active reliable designs are presented. To achieve the active task, an observer to identify faults as they occur in the spacecraft actuators is also presented. These VSRC laws do not require the solution of a Hamilton-Jacobi (HJ) equation, which is essential in the optimal approaches such as linear quadratic Riccati (LQR) and Hinfin reliable designs. As a matter of fact, this approach can relax the computational burden for solving the HJ equation. Simulation results regarding spacecraft attitude stabilization with comparisons among the VSRCs and the LQR reliable designs are also given. It is shown from these simulations that the active VSRC is the most flexible, robust and effective method because it does not need to prespecify susceptible actuators and because it allows more space for the control parameter adjustment

APPLICATION AND ROBUSTNESS DESIGN OF FUZZY CONTROLLER FOR RESONANT AND CHAOTIC SYSTEMS WITH EXTERNAL DISTURBANCE

A robustness design of fuzzy control via model-based approach is proposed in this paper to overcome the effect of approximation error between nonlinear system and Takagi-Sugeno (T-S) fuzzy model. T-S fuzz model is used to model the resonant and chaotic systems and the parallel distributed compensation (PDC) is employed to determine structures of fuzzy controllers. Linear matrix inequality (LMI) based design problems are utilized to find common definite matrices P and feedback gains K satisfying stability conditions derived in terms of Lyapunov direct method. Finally, the effectiveness and the feasibility of the proposed controller design method is demonstrated through numerical simulations on the chaotic and resonant systems.

A Study of T–S Model-Based SMC Scheme With Application to Robot Control

In light of the remarkable benefits and numerous applications of the Takagi-Sugeno (T-S) fuzzy system modeling method and the sliding mode control (SMC) technique, this paper aims to study the design of robust controllers for a set of second-order systems using a combination of these two approaches. The combined scheme is shown to have the merits of both approaches. It alleviates not only the online computational burden by using the T-S fuzzy system model to approximate the original nonlinear one (since most of the system parameters of the T-S model can be computed offline) but also preserves the advantages of rapid response and robustness characteristic of the classic SMC schemes. Moreover, the combined scheme does not need to online compute any nonlinear term of the original dynamics, and the increase in the number of fuzzy rules does not create extra online computational burdens for the scheme. The proposed analytical results are also applied to the control of a two-link robot manipulator and compared with the results using classic SMC design. Simulation results demonstrate the benefits of the proposed scheme.

Reliable Control of Nonlinear Systems via Variable Structure Scheme

This study proposes a class of variable structure stabilizing laws which make the closed-loop system be capable of tolerating the abnormal operation of actuators within a pre-specified subset of actuators. The ranges of acceptable change in control gain magnitude that preserves systems stability are estimated for the whole set of actuators. These ranges are shown to be able to be made larger than those obtained by linear quadratic regulator (LQR) reliable design (Veillette, 1995, and Liang, 2000) by the choice of control parameters. Besides, this approach does not need the solution of Hamilton-Jacobi (HJ) equation or inequality, which is essential for optimal approaches such as LQR and H infin reliable designs. As a matter of fact, this approach can also relax the computational burden for solving the HJ equation or inequality

Robustness Design of Fuzzy Control for Nonlinear Multiple Time-Delay Large-Scale Systems via Neural-Network-Based Approach

The stabilization problem is considered in this correspondence for a nonlinear multiple time-delay large-scale system. First, the neural-network (NN) model is employed to approximate each subsystem. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of each NN model. According to the LDI state-space representation, a robustness design of fuzzy control is proposed to overcome the effect of modeling errors between subsystems and NN models. Next, in terms of Lyapunovs direct method, a delay-dependent stability criterion is derived to guarantee the asymptotic stability of nonlinear multiple time-delay large-scale systems. Finally, based on this criterion and the decentralized control scheme, a set of fuzzy controllers is synthesized to stabilize the nonlinear multiple time-delay large-scale system.

Robust Control of the Robot Manipulator via an Improved Sliding Mode Scheme

In this paper, an improved sliding mode control (SMC) scheme, reformed from the conventional SMC approaches, is developed for position tracking of a robot manipulator with parameter uncertainties and external disturbances. The improved SMC scheme, which uses saturation-type SMC laws, is shown to be able to surpass the level of uniformly ultimate boundedness to achieve asymptotic stability. In addition, the presented first-order SMC laws are continuous; as a result, this scheme can also alleviate the undesirable chattering behavior that is characteristic of sign-type SMC laws. Simulation results demonstrate the benefits of the proposed scheme.

LQG optimal control of discrete stochastic systems under parametric and noise uncertainties

In this paper, the linear-quadratic-Gaussian (LQG) optimal control problem is considered and a robust minimax controller composed of the Kalman filter and the optimal regulator is synthesized to guarantee the asymptotic stability of the discrete time-delay systems under both parametric uncertainties and uncertain noise covariances. Designed procedures are finally elaborated with an illustrative example.

Decentralized Stabilization of Neural Network Linearly Interconnected Systems via T-S Fuzzy Control

The stabilization problem is considered in this study for a neuralnetwork (NN) linearly interconnected system that consists of a number of NN models. First, a linear difference inclusion (LDI) state-space representation is established for the dynamics of each NN model. Then, based on the LDI state-space representation, a stability criterion in terms of Lyapunov’s direct method is derived to guarantee the asymptotic stability of closed-loop NN linearly interconnected systems. Subsequently, according to this criterion and the decentralized control scheme, a set of Takagi-Sugeno (T-S) fuzzy controllers is synthesized to stabilize the NN linearly interconnected system. Finally, a numerical example with simulations is given to demonstrate the concepts discussed throughout this paper. DOI: 10.1115/1.2234492

Application of VSC reliable design to spacecraft attitude tracking

This study investigates variable structure reliable control issues of nonlinear systems and its applications to spacecraft attitude tracking problems. The proposed passive reliable control laws must know in advance which group of actuators is allowed to fail. These reliable controllers need not the solution of Hamilton-Jacobi (HJ) equation or inequality that are essentials in optimal approaches such as LQR and H/sub /spl infin// reliable designs. As a matter of fact, this approach is able to relax the computational load in computing the solution of HJ equation. The proposed reliable designs are also applied to spacecraft attitude tracking problems to explain their effectiveness and benefits. Finally, simulation results and comparisons between LQR and variable structure control (VSC) reliable designs are presented to illustrate the merits of the proposed scheme. Although the proposed design is a passive one, it may provide a guideline for active design when a fault detection and diagnosis (FDD) scheme is available.