Sliding Mode Hyperplane Research Articles

Adaptive neural-network-based sliding mode control of switching distributed delay systems with Markov jump parameters

This paper is devoted to the issue of observer-based adaptive sliding mode control of distributed delay systems with deterministic switching rules and stochastic jumping process, simultaneously, through a neural network approach. Firstly, relying on the designed Lebesgue observer, a sliding mode hyperplane in the integral form is put forward, on which a desired sliding mode dynamic system is derived. Secondly, in consideration of complexity of real transition rates information, a novel adaptive dynamic controller that fits to universal mode information is designed to ensure the existence of sliding motion in finite-time, especially for the case that the mode information is totally unknown. In addition, an observer-based neural compensator is developed to attenuate the effectiveness of unknown system nonlinearity. Thirdly, an average dwell-time approach is utilized to check the mean-square exponential stability of the obtained sliding mode dynamics, particularly, the proposed criteria conditions are successfully unified with the designed controller in the type of mode information. Finally, a practical example is provided to verify the validity of the proposed method.

Nonsingular Fast Terminal Sliding Mode Control for a Bearingless Induction Motor

In order to solve the problem of the speed response and system buffeting for a bearingless induction motor (BIM), which is subjected to various interferences and uncertainties, as well as the worse convergence performance of linear sliding mode and the singularity of terminal sliding mode, a nonsingular fast terminal sliding mode control strategy is proposed. Taking the power function of system state variables into consideration, the sliding mode hyperplane is designed as a combination of linear and nonsingular terminal sliding modes, which make the approaching speed correlate with the state variables of the system. Meanwhile, the differential sliding surface is constructed, and it is based on the rotational speed and radial displacement error of the BIM. Therefore, current signal and radial force are derived by the synthesis of the equations of electromagnetic torque, motion, and levitation force motion. Compared with the conventional strategies, the convergence speed of system state variables can be accelerated during the whole process, which contributes to operate without chattering and achieve high servo precisions. The theoretical simulation and experimental results indicate that the presented strategy can not only quickly track the given value of speed and radial displacement simultaneously, but also enhance the operation quality and robustness of the system. In addition, the rotor is capable of quickly reaching the steady position and achieving stable suspension.

The stochastic sliding mode variable structure guidance laws based on optimal control theory

A stochastic sliding-mode variable structure guidance law involving optimal control theory is presented for the missile target intercept model, in which state noise, uncertain system parameters, target movement and measured noise are considered. This guidance law synthesizes the merits of optimal guidance law with line-of-sight rate convergence and sliding-mode guidance law with strong robustness. Through theoretic analysis, it is proved that the sliding mode hyperplane is sub-achievable in the closed loop system. The numerical results show the effectiveness of the proposed control algorithm.

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.

Robust discrete adaptive input-output-based sliding mode controller

A robust input-output-based discrete adaptive sliding mode controller is proposed. It combines an integral action, a nonlinear output feedback, an adjustable sliding mode and an adaptive plant parameter estimator. The controller design is carried out via the Lyapunov direct method. A pole assignment procedure is developed for determination of the integral control gain and the coefficients of the sliding mode hyperplane. An on-line update for coefficients of the hyperplane is used to improve control loop behaviour further. Compared with the optimally tuned proportional-integral-derivative (PID) controller, the new controller has increased robustness with regard to the variation in the main process parameters and it has much better set point tracking characteristics. The new controller also exhibits very good disturbance rejection property comparable work or better than to that obtained by the optimally tuned PID controller. Simulation experiments are made to illustrate the quality and robustness of control achieved.

Sliding mode control with time-varying hyperplane for AMB systems

Deals with sliding mode hyperplane design for a class of linear parameter-varying (LPV) plants, the state-space matrices of which are an affine function of time varying physical parameters. The proposed hyperplane, involving a linear matrix inequality (LMI) approach, has continuous dynamics due to scheduling parameters and provides stability and robustness against parametric uncertainties. We have designed a time-varying hyperplane for a rotor-magnetic bearing system with a gyroscopic effect, which can be considered an LPV plant due to parameter dependence on rotational speed. The obtained hyperplane is continuously scheduled with respect to rotational speed. We successfully carried out experiments using a commercially available turbomolecular pump system and results were reasonable and good.

Compensator based output feedback sliding mode controller design

Recent work has shown that the problem of hyperplane design for output feedback sliding mode controllers is equivalent to a static output feedback pole placement problem for a certain subsystem. It is well known that the dimensionality requirements for this type of problem can be obviated by using a dynamic compensator. In this paper, a new parameterization of both the hyperplane and the compensator is proposed. The advantages of this approach are twofold: firstly it becomes straightforward to construct numerical algorithms for dynamic output feedback sliding mode hyperplane design, and secondly it enables an intuitive procedure to be employed for the design of the controller. The resulting control strategy uses only the plant outputs and the compensator states, yet is shown to guarantee the existence of a sliding motion.