Zhiyu Xi

Piecewise Integral Sliding-Mode Control for T–S Fuzzy Systems

This paper addresses the issue of piecewise integral sliding-mode control (ISMC) for the Takagi-Sugeno (T-S) fuzzy systems. ISMC is chosen to stabilize the T-S fuzzy system because of its superior capability in treating uncertainties. Individual integral sliding surfaces are designed in different operating regions of the T-S fuzzy system. Conditions on the existence of the sliding mode in the associated region are given. The chattering phenomenon around region boundaries is analyzed, and the prevention of such chattering is discussed. An illustrative example is finally given to show the efficiency of the proposed method.

A new design of robust H∞ sliding mode control for uncertain stochastic T-S fuzzy time-delay systems.

In this paper, a novel dynamic sliding mode control scheme is proposed for a class of uncertain stochastic nonlinear time-delay systems represented by Takagi-Sugeno fuzzy models. The key advantage of the proposed scheme is that two very restrictive assumptions in most existing sliding mode control approaches for stochastic fuzzy systems have been removed. It is shown that the closed-loop control system trajectories can be driven onto the sliding surface in finite time almost certainly. It is also shown that the stochastic stability of the resulting sliding motion can be guaranteed in terms of linear matrix inequalities; moreover, the sliding-mode controller can be obtained simultaneously. Simulation results illustrating the advantages and effectiveness of the proposed approaches are also provided.

Robust

This paper addresses the sliding-mode control (SMC) design problem for a class of uncertain nonlinear systems that can be represented by Takagi-Sugeno (T-S) fuzzy models. We propose a novel dynamic sliding-mode control scheme for T-S fuzzy models, aiming to eliminate the restrictive assumption that all subsystems share a common input matrix, which is required in most existing fuzzy SMC approaches. Sufficient conditions for the reachability of the sliding surface and asymptotic stability of the sliding motion are formulated in the form of linear matrix inequalities. Finally, simulation results that illustrate the advantages and effectiveness of the proposed approaches are provided.

{\mathscr H}_{\infty }

This paper addresses piecewise sliding-mode control for Takagi-Sugeno (T-S) fuzzy models. A novel sliding-mode control (SMC) design approach is developed which is based on individual sliding surface in each local region of the T-S fuzzy systems. Conditions of existence of sliding mode in the associated region are given. The chattering effect around region boundaries is analyzed, and prevention of such chattering is discussed. Two illustrative examples are finally given to illustrate the effectiveness and performance of the proposed controller.

Control of T–S Fuzzy Time-Delay Systems via a New Sliding-Mode Control Scheme

Many control methods have been applied to the ball and beam system. In this paper, simulation and on-line control results are presented. The system will be identified as a Hammerstein model. A non-minimal state space model is used to derive a nonlinear model predictive control algorithm. The results indicate that a Hammerstein model provides an accurate description of this nonlinear system. When the nonlinearity is successfully compensated for a high-gain linear controller yields good performance.

Piecewise Sliding-Mode Control for T–S Fuzzy Systems

This paper addresses a terminal sliding mode control method for nonlinear discrete time systems. A sequence of nonlinear sliding manifolds is designed. After the last one in this sequence is forced to the vicinity of the origin by a reaching controller, the rest are proved to stay bounded under the influence of a power rule. Allowing for the characteristics of discrete time sliding mode, the sizes of the quasi sliding bands are studied. An illustrative example is given at the end to prove the efficacy of proposed methods.

Ball and Beam System - Nonlinear MPC Using Hammerstein Model

This paper addresses a terminal sliding mode control method for linear discrete time systems affected by uncertainties. A nonlinear sliding manifold is designed. A terminal sliding mode controller is designed to drive the sliding variable to the vicinity of the origin. The bound within which the sliding variable stays eventually is found. How the state variables behave subsequently is also analysed. All the above analysis are based on the assumption that the uncertainty is unknown but bounded. An illustrative example is given at the end to prove the efficacy of the proposed methods.

On discrete time terminal sliding mode control for nonlinear systems with Uncertainty

Many control methods have been applied to the ball and beam system. In this paper, simulation and on-line control results are presented. For MPC controllers designed using a NMSS model, a time delay is introduced into the predictive model to account for aspects of system behavior. A non-minimal state-space model is used to derive a model-predictive controller. The results indicate that high-gain control coupled with model-following and feedforward action provides a linear controller robust against the systems typical non-linearities and disturbances.

On discrete time terminal sliding mode control for linear systems with uncertainty

This paper addresses higher order sliding mode control for continuous linear systems. We propose a new method of reaching control design while the sliding surface and equivalent control can be designed conventionally. The high order derivatives of the sliding surface and the sliding surface itself are forced to zero in an n-th order sliding mode scheme. This is realized by an optimization based on the prediction of the derivatives. An illustrative example-inverted pendulum is given at the end.