不确定奇异系统的变结构控制

针对一类不确定奇异线性系统，利用线性矩阵不等式（LMI）方法获得了滑模运动渐近稳定的充分条件，给出了变结构控制器的设计方法，该方法保证系统状态轨线经有限时间到达滑模面，并在其上实现滑模运动。滑模运动正则、无脉冲模、渐近稳定。     

非完整移动机器人编队的滑模控制

提出了一个非线性滑模控制器,协调一组非完整移动机器人以取得合乎要求的编队．考虑了两个机器人组成的领航者—跟随者机器人模型,通过滑模控制使它们沿预定的轨迹运动并保持预定的相对距离、方位角及运动方向．运用传统的李亚普诺夫理论研究了闭环系统的稳定性．在合理的假设下,从理论上证明了存在有界干扰情形下机器人编队的渐近稳定性,即所设计的滑模控制器使得相对距离误差、方位角误差及运动方向误差渐近稳定．最后,给出了两台机器人情形的数值仿真例子来验证该方法的有效性．     

基于模糊双曲模型的积分滑模控制

针对一般形式的非线性系统,提出一种基于模糊双曲模型(FHM)的积分滑模控制器设计方法.利用模糊双曲模型来表述这类连续非线性系统.构建出积分滑模面,利用线性矩阵不等式(LMI)方法得到滑模动态渐近稳定的充分条件.设计了积分滑模控制器,保证了系统的状态轨迹能够在有限时间内到达滑模面上并且保持在它上面运动.仿真结果表明了该方法的有效性.     

基于非光滑线性Lipschitz连续平面的滑模控制设计

利用Ｆｉｌｉｐｐｏｖ解、Ｃｌａｒｋｅ广义梯度和非光滑Ｌｙａｐｕｎｏｖ稳定理论,对一类滑模面设计为非光滑线性Ｌｉｐｓｃｈｉｔｚ连续平面的二阶系统滑模控制问题进行深入讨论．首先设计控制律,使闭环系统在有限时间内能够到达所设计的滑模面;然后证明系统在滑模面上的运动是渐近稳定的．放宽了对滑模控制中滑模面设计的要求,提高了所提出设计方法的灵活性,有利于改善系统性能．仿真结果验证了所提出设计方法的正确性和有效性．     

一类具有连续分布时滞的抛物型系统的无记忆滑模控制器设计

研究了一类具有连续分布时滞的抛物型系统的滑模控制问题.首先,通过构造辅助函数与使用矩阵范数不等式设计了无记忆功能的滑模控制器;其次,给出了滑模运动方程指数渐近稳定的充分条件;最后给出了从任意初始位置出发的轨线到达滑动模态区的时间估计.仿真结果说明了本文方法的有效性.     

基于非光滑线性Ｌｉｐｓｃｈｉｔｚ连续平面的滑模控制设计

利用Ｆｉｌｉｐｐｏｖ解、Ｃｌａｒｋｅ广义梯度和非光滑Ｌｙａｐｕｎｏｖ稳定理论,对一类滑模面设计为非光滑线性Ｌｉｐｓｃｈｉｔｚ连续平面的二阶系统滑模控制问题进行深入讨论．首先设计控制律,使闭环系统在有限时间内能够到达所设计的滑模面;然后证明系统在滑模面上的运动是渐近稳定的．放宽了对滑模控制中滑模面设计的要求,提高了所提出设计方法的灵活性,有利于改善系统性能．仿真结果验证了所提出设计方法的正确性和有效性．

     

滑模控制一类非线性分布式时滞系统

针对一类状态不可测的非线性不确定分布式时滞系统, 给出了系统滑动模态鲁棒渐近稳定的充分条件. 设计了一类滑模观测器, 同时采用线性矩阵不等式的处理方法给出了该观测器存在的充分条件. 再应用滑模控制的趋近率方法和基于观测器所得到的估计状态, 综合了一类滑模控制器. 该控制器同时保证了估计状态下的滑模面和估计误差状态下的滑模面的渐近可达性.     

不确定统一混沌系统平衡点的渐近稳定

研究不确定统一混沌系统平衡点的渐近稳定问题.利用滑模控制理论,给出了此类系统的滑模控制器的设计新方法和控制律算法.该控制器使得误差空间任一点出发的运动都在有限时间到达滑动模态,并沿切换面渐近到达原点,以达到将统一混沌系统控制到平衡点的目的.与现有文献所得结论相比,该文所设计的控制器算法具有抖振小、平稳性好和保守性小等优点.运动方程分析和仿真结果都验证了结论的有效性.     

不确定线性2-D 离散系统的鲁棒滑模控制

针对不确定线性离散二维（2-D）系统,研究了其鲁棒稳定性、鲁棒镇定和鲁棒滑模控制问题.基于线性矩阵不等式的方法推导了该系统鲁棒渐近稳定的充分条件,并给出了系统状态反馈镇定器和理想滑动模态存在的充分条件.改进了离散时间滑模控制系统的趋近律方法,使得状态能够到达滑模面上产生理想的滑动模态,并将其推广应用到2-D离散系统中,综合了一类滑模控制器保证闭环系统鲁棒渐近稳定.仿真实例证实了该设计方法的有效性.     

一类不确定广义时滞系统的H∞自适应控制

针对一类具有外部扰动的不确定广义时滞系统,首先,设计一个积分型滑模面函数,基于Lyapunov稳定性理论,并结合线性矩阵不等式等技术,给出该滑动模态方程鲁棒渐近稳定的一个充分性判据;然后,通过设计一个新型的自适应滑模控制器,使得该闭环系统的状态可在有限时间内到达滑模面并作滑动运动;最后,通过一个数值仿真例子验证所提出的方法是有效可行的.     

Robust Stabilization of Uncertain Fuzzy Systems Using Variable Structure System Approach

Based on the variable structure system (VSS) theory, we develop a fuzzy control system design method for a class of uncertain nonlinear multivariable systems that can be represented by a Takagi-Sugeno fuzzy model. We make the first attempt to relax the restrictive assumption that each nominal local system model shares the same input channel, which is required in the traditional VSS-based fuzzy control design methods. As the local controller we use a sliding mode controller with a switching feedback control term. In terms of linear matrix inequalities (LMIs), we derive a sufficient condition for the existence of linear sliding surfaces guaranteeing asymptotic stability of the reduced-order equivalent sliding mode dynamics. We present an LMI characterization of such sliding surfaces. We also give an LMI-based algorithm to design the switching feedback control term so that a stable sliding motion is induced in finite time. Finally, we give a numerical design example.     

An LMI-based variable structure control for a class of uncertain singular Markov switched systems

An H-infinifty variable structure control is presented for singular Markov switched systems with mismatched norm-bounded uncertainties and mismatched norm-bounded external disturbances. It is shown that the sliding mode dynamics on the given switching surface is regular, impulse-free, and stochastically stable and satisfies H-infinity performance. A variable structure controller is designed to guarantee that the system trajectory converges to the linear switching surface in some finite time. Finally, a numerical example is solved to show the effectiveness and validness of the theoretical results.     

An LMI-based variable structure control for a class of uncertain singular Markov switched systems

An H-infinifty variable structure control is presented for singular Markov switched systems with mismatched norm-bounded uncertainties and mismatched norm-bounded external disturbances. It is shown that the sliding mode dynamics on the given switching surface is regular, impulse-free, and stochastically stable and satisfies H-infinity performance. A variable structure controller is designed to guarantee that the system trajectory converges to the linear switching surface in some finite time. Finally, a numerical example is solved to show the effectiveness and validness of the theoretical results.     

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.     

Discrete-time sliding mode control of flexible rotor-magnetic bearing systems

This paper is concerned with the computer-based sliding mode control of flexible rotor—magnetic bearing systems (FR-MBS). The plant dynamics consisting of actuator dynamics and flexible rotor dynamics are described. The reduced-order model for controller design is given by eliminating higher-order modes of the mechanical and electrical magnetic interaction system. A discrete-time sliding mode controller with a new robust reduced-order variable structure system (VSS) observer is proposed and its robust performance is evaluated with several simulations based on a calculation model. This digital controller is implemented to replace a linear analogue PID compensator. Levitation tests using the proposed digital controller are performed and compared with those of the PID compensator. The unstable modes can be easily controlled with the good stability and the spillover phenomena due to ignored higher-order modes are not generated. It is indicated that the discrete-time sliding mode control has robustness to the model parameter variations and external disturbances. Using the discrete time sliding mode controller with the reduced-order VSS observer, the test rig of the magnetic bearing system can be successfully rotated in a speed range of 0–35 000 rpm, which includes the first critical shaft frequency of the flexible rotor.     

The variable structure controller design for a class of nonlinear uncertain systems based on robust observer

The variable structure controller is designed for a class of nonlinear uncertain time-delay system by using robust observer, and incorporating H-infinity control technique, the controller can guarantee the H-infinity performance of sliding mode dynamics and satisfy the reaching condition, which also does not require uncertainties to satisfy matching condition and linear boundary condition. The simulation example is given to illustrate the method.     

A robust MIMO terminal sliding mode control scheme for rigidrobotic manipulators

In this paper, a robust multi-input/multi-output (MIMO) terminal sliding mode control technique is developed for n-link rigid robotic manipulators. It is shown that an MIMO terminal switching plane variable vector is first defined, and the relationship between the terminal switching plane variable vector and system error dynamics is established. By using the MIMO terminal sliding mode technique and a few structural properties of rigid robotic manipulators, a robust controller can then be designed so that the output tracking error can converge to zero in a finite time, and strong robustness with respect to large uncertain dynamics can be guaranteed. It is also shown that the high gain of the terminal sliding mode controllers can be significantly reduced with respect to the one of the linear sliding mode controller where the sampling interval is nonzero     

机器人离散滑模变结构—PI控制器

本文采用离散滑模变结构控制方法，针对机器人提出了一种滑模变结构——ＰＩ控制方案，给出了该控制方案滑模存在条件及控制器设计方案。该控制器将离散滑模变结构控制和ＰＩ控制两者的优点有机地结合起来，理论分析和仿真结果表明该控制器能使机器人在各种复杂非线性动力学情况下具有良好的性能指标。这种控制器输出切换小，可以投入应用。     

基于输出反馈的直升机变结构控制律设计

针对直升机的小扰动模型,设计了静态输出反馈滑模控制器（SOFSMC）。利用参考模型,实现了直升机的相关动态指标。针对滑模面的设计问题,将其等价地转化为一组双线性矩阵不等式（BLMI）,并采用迭代线性矩阵不等式（ILMI）技术来求解。针对控制律的综合问题,给出了一种基于单位向量法的控制律,并通过引入线性反馈来保证系统进入滑动模态后线性控制部分与标称系统的线性控制部分的一致性。仿真结果验证了该方法的有效性。     

基于滑模变结构的轮式机器人运动误差控制器设计

面对当前使用的基于黎卡提微分方程、综合位姿误差控制优化仿真方法受到不确定性因素干扰,导致控制误差较大的问题,提出了基于滑模变结构的轮式机器人运动误差控制器设计。使用双框架陀螺仪,为控制器提供电力。采用FB900C/E 角位变送器,将交流信号转换为角位移输出。使用TMS320F2812的DSP控制器,负责控制整个控制器的数据传输以及电平转换。充分考虑相变量输入的n阶线形数据,设计滑模变结构控制律,计算滑模变结构控制滑动面。在滑模变结构模态控制阶段,构建滑模变结构模态控制阶段的运动方程矩阵。对滑模切换面强制状态点运动,通过控制目标实现稳定控制。对DSP程序控制流程进行设计,将基于滑模变结构的误差控制结果传递到电位器上,并将运行数据发送到主机,由此完成轮式机器人运动误差控制。由实验结果可知,该控制器通过自适应调整参数后,滑模抖振得到明显消除,且最大控制误差为0.01rad,具有精准控制效果。