Discrete-time Sliding Mode Control Method Research Articles

Adaptive Dynamic Model-Based Path Following Controller Design for an Unmanned Surface Vessel

Abstract The effective design of a path following controller for Unmanned Surface Vessels (USVs) under uncertain influences induced by various factors such as environmental disturbances is a challenging task. In this study, we propose to ful?lling this task through taking benefits from an online parameter identi?cation technique, the discrete-time sliding mode control (DSMC) method, and the improved line of sight (LOS) algorithm. The Particle Swarm Optimization algorithm (PSO) was adopted to provide initial settings for the straightforward online identification method, i.e., the Forgetting Factor Recursive Least Square method (FFRLS). In order to handle the time-varying sideslip angle of a ship that exists in reality due to environmental disturbances, a multi-model course control scheme is proposed to improve the control performance. For this control scheme, a flexible selection mechanism in-between a heading angle or a course angle tracking controller based on the DSMC method is designed. A solution to ?xing the tracking deviation problem of the LOS guidance law is investigated for which the gradient descent method is introduced. A series of experiments are carried out at sea with a USV called Orca to verify and validate the proposed hybrid path following approach. The results showed that tracking errors mainly induced by environmental disturbances existed but the maximum magnitude among them was small enough and remaining within the acceptable range especially from the marine engineering point of view. These results, to a high degree, validated the robustness and precision of the proposed controller.

Discrete-Time Predictive Sliding Mode Control for a Constrained Parallel Micropositioning Piezostage

This article proposes a new discrete-time predictive sliding mode control (DPSMC) for a parallel micropositioning piezostage to improve the motion accuracy in the presence of cross-coupling hysteresis nonlinearities and input constraints. Unlike the traditional linear discrete-time sliding mode control (DSMC), the proposed DPSMC is chattering free and has a faster convergence rate thanks to the design of a nonlinear discrete-time fast integral terminal sliding mode surface. Moreover, by combining with the receding horizon optimization, the sliding mode state is predicted to follow the expected trajectory of a predefined continuous sliding mode reaching law, which also allows the proposed controller to explicitly deal with constraints. The stability of the closed-loop system is analyzed under the model disturbances and constraints, and proves that the proposed DPSMC can offer a smaller quasi-sliding mode bandwidth than the traditional DSMC. The effectiveness of the proposed controller is validated by a series of numerical simulations and experiments. Results demonstrate the advantages of proposed DPSMC over the traditional DSMC method.

Gained switching-based fuzzy sliding mode control for a discrete-time underactuated robotic system with uncertainties

This study proposes a gained switching-based discrete-time sliding mode control method to address the chattering issue in disturbed discrete-time systems, which suffer from various unknown uncertainties. Through the new structure of the designed reaching law, the proposed method can effectively increase the convergence speed while guaranteeing chattering-free control. The performance of controlling underactuated robotic systems can be further improved by the adoption of fuzzy logic to perform adaptive online hyper-parameter tuning. In addition, an underactuated robotic system with uncertainties is studied to validate the effectiveness of the proposed reaching law. Results reveal the dynamic performance and robustness of the proposed reaching law in the studied system and prove the proposed method’s superiority over other state-of-the-art methods.

Sliding mode based-variable selective control for robust tracking of uncertain Internet-based systems

In this research, the robust control of uncertain linear Internet-based systems has been studied. In this way, an event-triggered strategy has been used to reduce the amount of communication between the plant and the remote controller. The proposed control strategy also ensures stability, robustness and output tracking against the model uncertainties and communication network negative effects. For this purpose, a new sliding surface is designed for linear Internet-based systems by solving a set of linear matrix inequalities which is achieved using the Lyapunov’s stability theorem. Accordingly, corresponding to a range of expected time delays, a discrete-time sliding mode control method is used to design some control signals. The proposed method can cope with relatively large network delays and packet dropouts. The asymptotic stability and robustness of the closed-loop system are also evaluated. Simulation studies on four well-known benchmark problems demonstrate the effectiveness of the proposed method with respect to the model uncertainty and also band-limited communication networks.

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Ramp metering is one of the most efficient and widely used control methods for an intelligent transportation management system on a freeway. Its objective is to control and upgrade freeway traffic by regulating the number of vehicles entering the freeway entrance ramp, in such a way that not only the alleviation of the congestion but also the smoothing of the traffic flow around the desired density level can be achieved for the maintenance of the maximum mainline throughput. When the cycle of the signal detection is larger than that of the system process, the density tracking problem needs to be considered in the form of the discrete-time system. Therefore, a discrete-time sliding mode control method is proposed for the ramp metering problem in the presence of both input constraint in the on-ramp and exogenous disturbance in the off-ramp considering the random behavior of the driver. Simulations were performed using a validated second-order macroscopic traffic flow model in Matlab environment and the simulation results indicate that proposed control method can achieve better performance than previously well-known ALINEA strategy in the sense that mainstream flow throughput is maximized and congestion is alleviated even in the presence of input constraint and exogenous disturbance.

Chattering-free discrete-time sliding mode control

To avoid the chattering problem in the reaching-law-based discrete-time sliding mode control (DSMC) and the generation of over-large control action in the equivalent-control-based DSMC, a new DSMC method based on non-smooth control is proposed in this paper. Since there is no use of any switching term in the proposed DSMC, it is a chattering-free SMC method. Meanwhile, it is shown that the newly proposed non-smooth control-based DSMC can guarantee the same level of accuracy for the sliding mode motion as that of an equivalent control-based DSMC. To demonstrate the effectiveness of the proposed approach, a simulation example is presented.

A New Discrete-time Sliding Mode Control Method Based on Restricted Variable Trending Law

摘要: 考虑惯性执行器输出速度有限的实际,引入趋近律变化速率的控制函数,设计了一种新的无抖振离散滑模变速趋近律算法. 首次提出了通过设计趋近律变化速率来构造离散滑模趋近律的思想,使得控制器的物理意义更加明显,设计更加灵活和简单.对于标称系统, 该算法可以使切换函数在有限时间内快速无抖振地收敛至零;对于满足匹配条件的不确定系统,切 换函数能够收敛至与不确定性及控制参数相关的某一数值,通过设置控制参数,可使这一数值任意小. 关键词: 趋近律 / 无抖振 / 离散 / 滑模控制 / 约束

The Discrete-Time Sliding Mode Control with Computation Time Delay for Repeatable Run-Out Compensation of Hard Disk Drives

The presented is a study on the problem of disturbance rejection, specifically the periodic disturbance, by applying discrete-time sliding mode control method. For perturbations such as modeling errors and external disturbances, their compensation is formulated using the designed sliding mode control. To eliminate the effect of these perturbations, the convergence rate between the disturbance and their compensation has been shaped by an additional parameter. Decoupling of the resultant perturbation estimation dynamics from the closed loop dynamics is achieved. Computation time delay is also presented to address the perturbation effects. The approach developed ensures the robustness of the sliding mode dynamics to parameter uncertainties and exogenous disturbances, in addition to the complete rejection of the periodic disturbance component. Satisfactory simulation results as well as experimental ones have been achieved based on a fast servo system of a modern hard disk drive to illustrate the validity of the controller for repeatable run-out (RRO) compensation.

Discrete-time sliding mode control for uncertain systems with state and input delays

This article presents a discrete-time sliding mode control method for the robust stabilisation of linear uncertain multi-input discrete-time systems with state and input delays. The systems are assumed to have structured mismatched time-varying parameter uncertainties. A specified switching surface is proposed and a sliding mode controller is derived to ensure the existence of the quasi-sliding mode. Based on the improved Lyapunov function and linear matrix inequality technique, delay-independent sufficient conditions for the design of a stable switching surface are given and the stability of the overall closed-loop system is guaranteed. Neither chattering phenomenon will occur nor the knowledge of upper bound of uncertainties is required. Finally, simulation results demonstrate the efficacy of the proposed control methodology.

Discrete-time sliding-mode controller for dual-stage systems—A hierarchical approach

A discrete-time hierarchical sliding-mode control scheme for a dual-stage tracking control system with bounded parameter variation and external disturbance is proposed in this study. This scheme is capable of performing a positioning servo control task that requires driving both coarse tracking and fine tracking stages simultaneously. The desired tracking performances, both the coarse tracking and fine tracking, are ensured. The settling time of the controlled system could be pre-specified by selecting a sliding hyperplane. Furthermore, explicit conditions, involving inequality constraints on the controller parameters, to ensure a one-sided behavior, quasi-sliding mode and chattering-alleviated performance with uncertainty and/or external perturbation of known bounds of the plant are derived. Experimental studies on the design of a track-seeking controller for an optical pick-up head is conducted to further illustrate its feasibility and effectiveness. The experimental results also demonstrate that the proposed scheme provides better performance than a discrete-time sliding mode control method with controller switching method.

Robust Control of a Spindle-Magnetic Bearing System Using Sliding-Mode Control and Variable Structure System Disturbance Observer

This paper is concerned with the design and control of flexible rotor magnetic bearing systems using the discrete time sliding-mode control method. The plant dynamics, consisting of actuator dynamics and flexible rotor dynamics, are described in detail. A variable structure system (VSS) disturbance observer, with which the state vector and disturbance can be estimated simultaneously, is investigated to compensate the mismatched disturbance load on the rotor. A new discrete time sliding-mode servocontroller that can attenuate the chattering phenomenon is proposed using the VSS observer. The usefulness of the proposed controller is demonstrated through computer simulations and experiments for a spindle-magnetic bearing system under external disturbances and modeling uncertainties.