Approximation law for discrete-time variable structure control systems

Two approximation laws of sliding mode for discrete-time variable structure control systems are proposed to overcome the limitations of the exponential approximation law and the variable rate approximation law. By applying the proposed approximation laws of sliding mode to discrete-time variable structure control systems, the stability of origin can be guaranteed, and the chattering along the switching surface caused by discrete-time variable structure control can be restrained effectively. In designing of approximation laws, the problem that the system control input is restricted is also considered, which is very important in practical systems. Finally a simulation example shows the effectiveness of the two approximation laws proposed.     

不确定离散切换系统的滑模控制

研究一类不确定离散切换系统的鲁棒滑模控制问题.针对传统变结构控制应用于离散系统时易失去其鲁棒性的问题,提出一种采用带调整参数递归式滑模函数的离散滑模控制策略,改进了离散时间滑模控制系统的趋近律方法,并针对不确定因素的影响设计了无须知道扰动上界的估计器.应用Lyapunov函数给出了离散切换系统的滑动模态可达条件,并设计了离散切换规则.仿真结果表明了所提出设计方法的有效性.     

离散时间系统变结构拟滑模控制改进算法

传统的离散时间变结构控制律均是以等效控制为基础,长期的应用表明这种没计思想欠合理.针对该问题,设计了离散时间系统变结构滑模控制的一种新算法.算法针对前人所提出的控制算法不足之处,对离散时间滑模控制量设计进行了改进.理论分析表明,所提出的控制算法满足离散时间变结构系统到达条件的要求,通过选择合适的滑模切换函数以及控制律参数,保证系统的轨线快速落在滑模面上,有效地缩短了系统状态到达滑动模态的时间,且抖振小.仿真结果表明,使用改进控制算法的系统输出响应优于未改进算法情况,响应速度较快,证明了所提出的算法是可行的、有效的.     

离散时间系统变结构控制的趋近律问题

针对离散系统变结构控制，提出了两个新的滑模趋近律．应用该趋近设计变结构控制系统，其原点的稳定性和系统的平稳性都优于指数趋近律和比例-等速-变速趋近律．通过仿真例子对此进行了验证．     

Variable structure control with sliding mode prediction for discrete-time nonlinear systems

A new variable structure control algorithm based on sliding mode prediction for a class of discrete-time nonlinear systems is presented. By employing a special model to predict future sliding mode value, and combining feedback correction and receding horizon optimization methods which are extensively applied on predictive control strategy, a discrete-time variable structure control law is constructed. The closed-loop systems are proved to have robustness to uncertainties with unspecified boundaries. Numerical simulation and pendulum experiment results illustrate that the closed-loop systems possess desired performance, such as strong robustness, fast convergence and chattering elimination.     

An adaptive reaching law of chattering-free discrete-time sliding mode control for systems with external disturbance

An adaptive reaching law of chattering-free discrete-time sliding mode control is proposed for the systems with external disturbance. An adaptive function is proposed in the reaching law which can increase reaching speed as sliding variable is far away from zero and avoid undesired chattering when sliding variable is close to origin. Moreover, a third-order backward difference of disturbance is added to obtain a narrower quasi-sliding mode band (QSMB). Both the closed-loop system performance and finite reaching steps to achieve the desired QSMB are theoretically analyzed. The simulation results verify the effectiveness of the proposed control strategy.     

Delta 算子不确定系统的滑模变结构控制

研究算子系统滑模变结构控制的综合问题.首先,利用线性矩阵不等式方法给出了切换面存在的充分条件,分析了算子变结构控制系统的到达条件,将连续系统和离散系统统一到算子系统.基于指数趋近律,给出滑模变结构控制一般方法.其次,给出一类算子不确定系统的滑模控制器设计,分析了准滑动模态的渐近稳定性,使得系统具有良好的动态性能.最后,用一个仿真实例说明在采样周期取值非常小的前提下,该方法设计的滑模变结构控制仍具有可行性和有效性.     

一种离散时间系统变结构趋近律

针对一类离散时间系统,提出一种变结构控制设计方法。为了减小离散指数趋近律的抖振现象,本文构造一种趋近律, 利用它设计变结构控制器,能够大幅度削弱抖振,有效地改善控制品质,使系统最终趋于原点,并使系统稳定。给出数值计算和仿真算例。     

On discrete-time variable structure sliding mode control

The purpose of this paper is to show the limitations of discrete-time variable structure sliding mode control and that the equivalent control must be used in order to have sliding in a neighborhood of the switching surface. Conflicting requirements for the sliding mode controller behavior in the continuous and discrete-time domains are revealed and analyzed. A linear control law for an uncertain discrete-time linear plant, with bounded uncertainties, is analyzed and its superiority over nonlinear controllers is demonstrated. The conclusion of the obtained results is that in the discrete-time variable structure sliding mode controller design, unlike in the continuous-time, the designer may have limited flexibility in selecting controller architectures.     

Continuous approximation of variable structure control

A straightforward modification of the theory of ‘sliding’ variable structure control systems is used to design a control law that is a continuous arbitrarily close approximation, within a predefined subspace, to the discontinuous variable structure control law. Linear combinations of eigenvectors, and certain null spaces, are used to analyse the state trajectory under the influence of the continuous control law. Comparisons are drawn and the inherent robustness properties of variable structure control systems are retained, while the undesirable chatter motion of the sliding mode is eliminated. The accuracy of the approximation to the idealized case can easily be calculated. The general results are illustrated by the simulation of a time-invariant fourth-order multivariable system with two controls     

RCMAC-based adaptive control for uncertain nonlinear systems.

An adaptive control system, using a recurrent cerebellar model articulation controller (RCMAC) and based on a sliding mode technique, is developed for uncertain nonlinear systems. The proposed dynamic structure of RCMAC has superior capability to the conventional static cerebellar model articulation controller in an efficient learning mechanism and dynamic response. Temporal relations are embedded in RCMAC by adding feedback connections in the association memory space so that the RCMAC provides a dynamical structure. The proposed control system consists of an adaptive RCMAC and a compensated controller. The adaptive RCMAC is used to mimic an ideal sliding mode controller, and the compensated controller is designed to compensate for the approximation error between the ideal sliding mode controller and the adaptive RCMAC. The online adaptive laws of the control system are derived based on the Lyapunov stability theorem, so that the stability of the system can be guaranteed. In addition, in order to relax the requirement of the approximation error bound, an estimation law is derived to estimate the error bound. Finally, the simulation and experimental studies demonstrate the effectiveness of the proposed control scheme for the nonlinear systems with unknown dynamic functions.     

非线性变结构控制系统的综合

本文讨论了非线性变结构控制系统的综合问题,提出了滑动模态补偿器的概念.利用本 文方法,使用变结构系统理论设计含有参数变化的非线性系统成为可能,控制的设计在某些情 况下也相当简单.     

不确定Delta算子系统的滑模软切换控制

针对一类带有内部参数摄动和外部扰动的快速采样控制系统,基于sigmoid函数提出了一种Delta算子S-变速趋近律方法,并设计了不确定Delta算子系统的滑模软切换控制器。基于Delta算子采样原理,将连续时间系统和离散时间系统的软切换控制器设计统一到Delta算子系统。基于Delta算子S-变速趋近律方法设计的闭环快速采样滑模软切换控制器能够在限制时刻内到达切换面,削弱了系统颤振。从仿真实例可以看出,该滑模软切换控制器的稳定性和平稳性优于传统指数趋近律情形,整个动态过程具有良好的完全鲁棒性。     

滑模预测离散变结构控制

研究了不确定离散时间系统的变结构控制设计问题,提出了基于滑模预测思想的离散变结构控制系统设计新思路.该方法综合考虑抖振、鲁棒性以及控制量约束等指标要求,利用当前及过去时刻的滑模信息预测未来时刻的滑模动态,实现了滚动优化求解.仿真结果表明,该方法可有效消除抖振现象,并能够保证闭环系统的鲁棒稳定性.     

Adaptive switching gain for a discrete-time sliding mode controller

Sliding mode control is a well-known technique capable of making the closed loop system robust with respect to certain kinds of parameter variations and unmodelled dynamics. The sliding mode control law consists of a continuous component which is based on the model knowledge and discontinuous component which is based on the model uncertainty. This paper extends two known adaption laws for the switching gain for continuous-time sliding mode controllers to the multiple input case. Because these adaption laws have some fundamental problems in discrete-time, we introduce a new adaption law specifically designed for discrete-time sliding mode controllers.     

不确定MIMO线性系统的全局快速终端滑模控制

针对一类不确定多输入多输出(MIMO)线性系统,提出一种全局快速终端滑模变结构控制方案.通过对系统进行特殊的非奇异状态变换,设计了相应的非线性终端滑模超曲面及变结构控制律,使得系统状态在有限时间内收敛到终端滑模面上,随后保持在滑模面上并按全局快速终端滑模规律运动,以较普通终端滑模更快的收敛速度在有限时间内到达平衡点.仿真结果证明了该方法的有效性.     

基于变速趋近律的机电伺服系统自适应滑模控制

针对带有摩擦力矩、负载力矩以及扰动力矩等不确定性的机电伺服系统,提出一种基于变速趋近律的自适应滑模控制方法.首先,构造双曲正切型辅助函数并设计新的变速趋近律,用以调节滑模变量的收敛速度,使其在到达减速点之前具有较快的收敛速度,而在到达减速点以后则能有效削弱抖振.在此基础上,构造自适应滑模控制器,保证系统位置输出能够快速稳定地跟踪期望轨迹.同时,设计参数更新律估计不确定项平方的上界,确保控制信号的连续性和减小控制信号抖振.基于李雅普诺夫稳定性定理给出误差收敛性分析,并给出仿真对比验证所提出方法的有效性.     

广义非线性系统的变结构控制理论

利用几何方法,从广义非线性系统本身出发,研究了广义非线性控制的变化结构控制理论,给出了系统存在变结构控制的充分实际没动模式的近似定理。从所得结论可知,滑动条件仅能保证实际滑动模的慢变状态赵近于理想滑动模的慢变状态,而不能保证实际滑动模的状态趋近于理想滑动模的快变状态,研究正常非线性系统的方法已不能简单地被利用到广义非线性系统。     

Binary ABR flow control over ATM networks with uncertainty using discrete-time variable structure controller

A binary available bit rate （ABR） scheme based on discrete-time variable structure control （DVSC） theory is proposed to solve the problem of asynchronous transfer mode （ATM） networks congestion in this paper. A discrete-time system model with uncertainty is introduced to depict the time-varying ATM networks. Based on the system model, an asymptotically stable sliding surface is designed by linear matrix inequality （LMI）. In addition, a novel discrete-time reaching law that can obviously reduce chatter is also put forward. The proposed discrete-time variable structure controller can effectively constrain the oscillation of allowed cell rate （ACR） and the queue length in a router. Moreover, the controller is self-adaptive against the uncertainty in the system. Simulations are done in different scenarios. The results demonstrate that the controller has better stability and robustness than the traditional binary flow controller, so it is good for adequately exerting the simplicity of binary flow control mechanisms.     

新的离散时间系统变结构趋近律

针对离散时间系统变结构控制的设计问题进行了研究。为了改善离散指数趋近律的趋近过程,提出了一种新的趋近律,利用该趋近律设计的变结构控制器,不仅能够大幅度削弱抖振,使系统运动最终趋于原点不存在稳态振荡,而且能使系统的准滑动模态保持步步穿越切换面的基本属性,有效地改善了趋近过程,提高了控制品质。仿真分析验证了该方法的合理性与有效性。