不确定离散时间系统积分滑模保性能控制

针对不确定离散时间系统,研究其积分滑模（ＩＳＭ）保性能控制的设计问题．将最优保性能积分滑模面设计问题,转化为一个具有线性矩阵不等式（ＬＭＩ）约束的目标函数凸优化问题,给出了最优保性能积分滑模面存在的充分条件,并结合干扰估计器设计相应的保性能控制器．与传统滑模控制相比较,积分滑模保性能控制系统具有全阶滑动模态,系统的鲁棒性得到加强,消除了控制抖振和稳态抖振．仿真结果验证了该方法的有效性．     

不确定离散时间系统的复合非线性反馈积分滑模控制

针对不确定离散时间系统,提出一种基于离散复合非线性反馈的积分滑模(DCNF-ISM)控制策略,并将该算法应用于扰动下的磁盘跟踪问题.该算法由离散复合非线性反馈(DCNF)控制律与积分滑模(ISM)控制律两部分组成,其中DCNF控制律用于保证系统具有较好瞬态性能,基于改进的离散趋近律设计的ISM控制律用于保证系统鲁棒性.基于Lyapunov稳定性理论对本文提出的控制策略的稳定性进行了推导证明,证明了离散时间系统的一致最终有界性.仿真结果表明,本文提出的控制策略能保证系统在扰动下仍然能够精确跟踪给定的参考信号,与传统的DCNF控制相比,该算法能够保证系统具有响应速度快超调量小、鲁棒性强等优点.     

不确定离散时间系统的滑模可靠控制

存在状态时滞的不确定离散时间系统的的滑模可靠控制问题,其中,被控系统执行器可能发生部分故障.通过构造一种拟积分型切换面,可以保证系统状态轨迹从开始时刻就位于切换面上.利用Lyapunov稳定性理论和线性矩阵不等式技术给出了滑模动态系统渐近稳定的充分条件.而且,所设计的滑模控制律可以保证在执行器故障影响下的滑动模态仍然是可达的.数值仿真验证了本文设计方法的有效性.     

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.     

一类非线性不确定系统的高阶积分自适应滑模控制

为有效改善传统积分滑模在一类非线性不确定系统的应用中存在的抖振问题,结合有限时间收敛理论、高阶积分滑模理论和自适应控制理论,提出了一种高阶积分自适应滑模控制方法;该方法通过选取有限时间收敛反馈量和设计高阶积分滑模面,不仅确保了系统状态误差在有限时间内的收敛性,而且还保证了系统具备对不确定性干扰的抑制能力;同时,当系统的不确定项的边界范围无法预先确定时,采用自适应方法对滑模控制的趋近速率进行估计;仿真结果表明所提方法能够有效抑制非线性不确定系统的抖动,并具有较高的控制精度.     

一类非线性不确定系统的自适应积分滑模控制

针对一类具有不确定参数的复杂非线性系统,提出了一种自适应积分滑模控制方法。控制器的设计分两步进行：首先,基于被控对象模型构造一个简化子系统,设计出该子系统的一个全局渐近稳定控制律;然后构造一个积分滑模面,设计自适应积分滑模补偿器以处理系统中含有不确定参数的部分,保证了滑模面的可达性和原系统的闭环稳定性。补偿后,系统的完整自适应控制律由简化子系统的控制律加补偿控制器两部分组成。所提设计方法简单,便于工程实现。最后,通过仿真结果验证了设计方案的有效性。     

一类不确定非线性系统的改进积分型滑模控制

针对一类不确定非线性系统的传统滑模控制,推导了滑模误差和稳态误差的范围．为了减小系统的稳态误差,同时防止积分饱和,设计了一种改进积分型滑模面．在边界层外,通过调节因子对积分项进行削弱,以防止在初始误差较大的条件下积分饱和引起的超调较大和调节时间较长的问题;在边界层内,采用传统积分以减小系统稳态误差．理论分析和仿真研究表明了所提改进积分型滑模控制方法的有效性．     

基于干扰观测器的离散滑模控制算法

为了降低离散滑模控制过程中的抖振,减轻控制器的负担,提高控制精度,针对线性参数不确定性离散系统,构造了一种基于干扰观测器的离散滑模控制算法,并给出了稳定性证明.理论分析和数值仿真均表明,该算法可以实现对干扰高精度的实时估计;切换函数最终将收敛于与干扰变化率和系统采样时间有关的小范围.数值仿真还表明,用幂次函数代替算法中的符号函数或饱和函数后,可以彻底消除控制器输出和切换函数中的高频抖振,这对于提高实际工程应用中控制器的寿命和改善系统的控制性能具有重要的意义.     

基于干扰补偿趋近律的离散滑模多周期重复控制

针对离散时间系统的多周期干扰抑制问题,提出一种离散滑模多周期重复控制器设计方法.利用非线性幂次函数设计新型离散趋近律,将周期差分等效干扰以加权形式嵌入到趋近律中,构造带干扰补偿作用的离散趋近律,并据此设计离散滑模多周期重复控制器.为了进行控制器参数整定和表征闭环系统的收敛性能,推导准滑模域边界层的表达式.所提出控制方法既能够消除多周期干扰信号,也能够减小准滑模域边界层.数值仿真验证了所提出控制方法的有效性.     

一类不确定离散时间系统的最优鲁棒控制

本文针对一类含有不确定因素的离散单输入系统,采用李雅普诺夫第二种方法设计了一种鲁棒控制器.这个控制器是系统状态的线性函数,并且被证明当矩阵Q给定时,它是最优的.文末给出了仿真例子.     

带有非线性不确定奇异系统的积分滑模控制

针对一类含有非线性不确定的奇异系统, 提出了一种面向性能的鲁棒控制器. 控制器由3部分组成: 积分滑模控制、附加的非线性控制及复合非线性反馈控制. 积分滑模控制可将匹配不确定完全抵消并使系统轨迹进入理想滑模; 附加的非线性控制用来抑制理想滑动模态上非匹配不确定对系统稳定性和性能的影响; 复合非线性反馈控制则保证闭环系统输出按性能要求渐近地跟踪参考输入信号. 最后通过算例说明所提算法的有效性.     

基于幂次函数的离散滑模控制算法

利用幂次函数构造一种新的趋近律离散滑模控制算法,并给出了无抖振的理论证明.对于标称系统,该算法可使切换函数无抖振、无正负交替地快速趋近于零;对于满足匹配条件的不确定性系统,可使切换函数无抖振、单调地收敛于与外干扰相关的某一数值.利用倒立摆模型进行了数值仿真,结果表明,控制器的输出、切换函数、被控系统的输出均不存在抖振现象,而且被控系统表现出了良好的动态品质.     

Robust tracking and model following of uncertain dynamic systems via discrete-time integral sliding mode control

A discrete-time integral sliding mode control scheme is proposed to realize the problem of robust tracking and modeling following for a class of uncertain linear systems. It will be shown that the proposed scheme guarantees the stability of closed-loop system and achieves zero-tracking error in the presence of parameter uncertainties and external disturbances. The selection of switching surface and the existence of sliding mode are two important issues, which have been addressed. This scheme assures robustness against system uncertainties and disturbances. Chattering phenomenon and reaching phase are eliminated. Moreover, the knowledge of upper bound of uncertainties is not required. Both the theoretical analysis and illustrative example demonstrate the validity of the proposed scheme. Recommended by Editorial Board member Ju Hyun Park under the direction of Editor Young IL Lee. Ming-Chang Pai received the M.S. and Ph.D. degrees in Mechanical Engineering in 1994 and 1998 from Pennsylvania State University, State College, P.A.. He is currently an Associate Professor in the Department of Automation Engineering at Nan-Kai University of Technology. His research interests are in mechatronics, robots, robust control and nonlinear control.     

无抖振离散滑模趋近律

针对离散滑模趋近律形式多样且容易产生高频抖振的问题,提出了离散滑模趋近律的一般形式,并给出了无抖振的到达条件及其理论证明,从一般意义上为离散滑模趋近律的设计提供了理论依据。针对满足匹配条件的不确定系统,给出了切换函数收敛域的推导方法,推导了无抖振的最小收敛域。以典型的高氏指数趋近律为例,利用无抖振的到达条件,对其一般形式进行了无抖振改进,验证了所提出方法的有效性。     

非匹配离散系统无抖振鲁棒准滑模控制

研究离散准滑动模态的鲁棒性恢复和抖振削弱问题。针对一类同时含有匹配建模误差和非匹配外界干扰不确定离散系统,设计一种基于解耦干扰补偿器的鲁棒准滑模控制方案。为保证系统的鲁棒性,针对非匹配外界干扰设计一种改进的解耦干扰补偿器,估计误差有界收敛。通过引入幂次函数设计鲁棒离散准滑模控制器,消除系统抖振,给出切换函数准滑模带,并证明了闭环系统离散准滑动模态的稳定可达性。最后通过仿真验证了所提出控制方案的有效性。     

Adaptive sliding mode control for a class of uncertain discrete-time systems using multi-rate output measurement

This article is concerned with the design of an adaptive sliding mode control (SMC) for a class of uncertain discrete-time systems using the multi-rate output measurement. The states of the discrete-time systems are assumed to be taken in the multi-rate output measurement by the contamination with measurement noise. The uncertainties are assumed not to satisfy the matching condition, and are expressed in a parameterised form. A least squares estimator (LSE) to take the estimates for the un-measurable states and the uncertainties is designed in a batch form by using the noisy multi-rate output measurement. The proposed adaptive SMC is designed by using the sliding surface expressed as the linear state function and the estimates obtained from the LSE. It is proved that the estimation errors converge to zero as time tends to infinite, and the states of the system are bounded under the action of the proposed adaptive SMC. The effectiveness of the proposed method is indicated through the simulation experiment in a simple system.     

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.     

Output feedback sliding mode control under networked environment

This article considers the problem of sliding mode output feedback control for networked control systems (NCSs). The key idea is to make use of not only the current and previous measurements, but also previous inputs for the reconstruction of the state variables. Using this idea, sliding mode controllers are designed for systems with constant or time-varying network delay. The approach is not only more practical but also easy to implement. To illustrate this, the design technique is applied to an inverted pendulum system.     

Composite disturbance-observer-based control and terminal sliding mode control for non-linear systems with disturbances

A novel type of control scheme combining the disturbance-observer-based control (DOBC) with terminal sliding mode (TSM) control is proposed for a class of multiple-input–multiple-output (MIMO) continuous non-linear systems subject to disturbances. The disturbances are supposed to include two parts. One in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modelling perturbations. The other is supposed to have the bounded H ₂ norm. The disturbance observers based on regional pole placement and D-stability theory are presented, which can be constructed separately from the controller design. By integrating DOBC with TSM control laws, the disturbances can be rejected and attenuated, simultaneously, and the desired dynamic performances can be guaranteed for non-linear systems in finite time with known and unknown non-linear dynamics, respectively. Two simulation examples for a flight control system and a hard disk drive actuator are given respectively to demonstrate the effectiveness of the proposed control schemes compared with the previous schemes.