Design of uncertain multi-input systems with state delay and input deadzone nonlinearity via sliding mode control

The problem of robust stabilization of a class of uncertain multi-input time-delayed systems with deadzone nonlinearity in the actuator is considered. To achieve a stable uncertain multi-input system, sliding mode control (SMC) is adopted in the controller design. The proposed controller guarantees the global reaching condition of the sliding mode in the uncertain multi-input system. In the sliding mode, the investigated time-delayed systems with deadzone nonlinearity still possess the insensitivity to the uncertainties and/or disturbances, which can be seen in the systems with linear inputs. In addition, the proposed controller can work effectively for systems no matter whether sector nonlinearity and/or deadzone exists in the actuator or not. However, such property cannot be obtained by the controller design through traditional SMC for the systems without input nonlinearity. Besides, the traditional SMC controller might produce limit cycles once the system contains deadzone in the input. Furthermore, the presented controller ensures the system trajectories globally exponentially converged in the sliding mode. Finally, two examples are illustrated to demonstrate the effectiveness of the proposed sliding mode controller.     

一类非线性系统时变滑模变结构控制

针对参数不确定性非线系统,分析了在未知扰动下的输出调节问题,提出了基于李亚普诺夫稳定性理论意义下的时变滑模变结构控制律,该控制律能保证系统误差的快速收敛性及对外部扰动和参数不确定性的不敏感性,最后给出的仿真实例实证实了理论分析结果的正确性。     

一类具有变时滞不确定分布参数系统的滑动模控制

研究一类不确定变时滞分布参数系统的滑动模控制问题．首先设计一种无记忆功能的变结构控制器;然后分析了在滑动模切换面上滑动模控制系统关于不确定量的不变性特征;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．研究表明,所设计的控制器结构简单．容易实现．     

一类不确定混沌系统的模糊滑模控制与同步

针对一类具有不确定项的二阶连续时间混沌系统的定值跟踪控制和自混沌同步及异结构混沌同步问题,提出了一种模糊滑模变结构控制方法,设计了模糊滑模变结构控制器,并从理论上证明了控制系统的稳定性.在该控制器的作用下,可以实现两个相同或不同结构的混沌系统的控制与同步,且不受不确定性的影响,具有很强的鲁棒性.定值跟踪和同步控制的仿真结果表明,该控制器是有效的.     

不确定Willis脑动脉瘤系统的自适应模糊滑模控制

研究了具有不确定项的非线性Willis环上脑动脉瘤系统的混沌控制和同步问题,提出了一种自适应模糊滑模变结构控制方法,设计了模糊滑模变结构控制器及自适应控制律,并从理论上证明了控制系统的稳定性。在该控制器的作用下,受控Willis脑动脉瘤系统能够达到任意目标轨道,且不受不确定性的影响,具有很强的鲁棒性。定值跟踪和同步控制的仿真结果表明了控制器的有效性。     

动态不确定多输入多输出系统的变结构鲁棒控制

本文仅利用输入输出数据给出了一种动态不确定多输入多输出系统的变结构控制器设计机制，控制系统的设计中引入了一个严格正实的模型．应用适当逻辑切换的状态变量滤波器实现变结构控制．证明了所提方案能保证全局输出有界稳定并能实现滑模控制和渐近跟踪参考模型的输出．该设计方案对结构不确定性具有一定的鲁棒性．仿真结果表明了所提方案的有效性．     

时滞关联大系统的分散变结构自适应控制

针对一类满足匹配条件的不确定性时滞关联大系统,提出了一种基于Lyapunov稳定性理论的分散变结构自适应控制方案.通过引入积分滑模和能在线估计不确定性扰动与时滞关联的界的自适应算法,保证了闭环系统的渐近稳定性,实现了系统的鲁棒自适应控制.所提出的方案具有较强的工程实用性.算例仿真的结果表明了该控制方案的可行性.     

一类非匹配不确定非线性系统的鲁棒跟踪控制制

针对一类半严格反馈型不确定非线性系统,提出一种鲁棒反演滑模变结构控制方法.采用反演控制方法设计了使前n-1阶子系统稳定的虚拟控制律,抑制非匹配不确定性的影响;在第n步设计了一种连续可导的滑模变结构控制律,消除控制抖振,实现了对存在未知不确定性及扰动系统的鲁棒输出跟踪.通过Lyapunov定理证明了闭环系统所有信号最终有界.仿真结果验证了该方法的有效性.     

On the convergence properties of a 2-sliding control algorithm for non-linear uncertain systems

The second order sliding mode control of uncertain dynamical systems can be expressed in terms of the stabilization of uncertain second-order non-linear systems with incomplete state availability. The existence of the solution strictly depends on the assumptions made on the uncertainties, and global results are not always attainable. In this paper the class of systems for which a suitable variable structure control algorithm ensures finite time global convergence to the sliding manifold is identified. Simulation results highlight the effectiveness of the proposed method.     

基于云模型的变桨距系统积分滑模控制

针对具有参数变化和外加干扰的变桨距风力发电系统,提出了一种基于云模型的积分滑模控制。在滑模控制中引入误差项的积分,并用状态量代替误差的导数,消除传统滑模控制需要期望输出信号导数已知的假设;利用云模型的不确定性推理方法,动态地调节切换增益;利用积分的方法对切换增益进行估计,估计出系统中不确定因素的界,有效地削弱系统的抖振。仿真结果表明:该控制器用于风速高于额定风速以上的变桨距控制系统中,具有较好的控制品质,对系统参数的不确定和外部干扰具有很强的鲁棒性。     

基于Backstepping的倒立摆鲁棒跟踪控制

针对内部参数不确定及存在外部干扰的非线性倒立摆系统,提出了基于Backstepping方法的滑模变结构控制律,并且采用RBF神经网络逼近系统不确定非线性函数,同时引入滑模误差对其神经网络权值进行在线自适应调整,使神经网络的逼近速度加快,改善了动态性能.该控制律能保证倒立撰轨迹跟踪误差的快速收敛性以及对外部扰动和内部参数不确定的不敏感性,最后给出的仿真实例证明了该理论分析结果的正确性,控制效果良好.     

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.     

一种基于指数趋近律的非线性系统变结构轨迹跟踪控制新方法

针对多输入多输出二阶不确定非线性机械系统中轨迹跟踪控制的问题,提出一种新的基于指数趋近律的滑模变结构控制方法,用于提高系统的平稳性和快速性。在滑模变结构控制器设计过程中采用一种新的指数趋近律以改进闭环系统的暂态和稳态响应性能,使系统跟踪误差收敛速度加快,特别是减少轨迹跟踪误差到达滑模面的时间,同时提高了系统轨迹跟踪过程的平稳性。通过采用边界层方法消除滑模控制输入抖振问题,避免控制过程中执行器的频繁切换,进一步提高所提出滑模控制器在实际系统中的实用性。基于李雅普诺夫稳定性理论证明了闭环系统的稳定性和跟踪误差的收敛性。数值仿真验证了所提出的控制方法的有效性。     

Dynamic output feedback sliding mode design for a class of linear unmatched uncertain systems

This paper investigates the output feedback stabilization problem for a class of multi-input/multi-output (MIMO) systems with matched/unmatched uncertainties by the variable structure system (VSS) with a new sliding mode control. In dynamic systems, a new idea of a sliding sector that consists of two sets of switching surfaces is proposed. A new invariance condition is derived such that the reduced-order system in the new sliding mode is completely invariant to both matched and unmatched uncertainties. Additionally, to demonstrate the effectiveness of the proposed scheme and to reduce the drawbacks of conventional VSS design, a modified dynamic variable structure controller using only the output variables is applied to perform the sliding mode. Furthermore, a stability analysis of the overall system is also provided. Finally, an example is given to illustrate the effectiveness of the control scheme.     

具有非线性时变滑模面的变结构控制系统设计

以二阶系统为研究对象,提出一种具有非线性连续时变滑模面的变结构控制器设计方法.用该方法设计的变结构控制系统,系统的初始状态位于滑模面上,通过滑模面斜率的连续变化,能消除系统状态变量到达滑模面的过程,极大地提高对参数摄动和外部干扰的鲁棒性,应用Lyapunov法证明时变滑模面的存在,计算机仿真结果证明该方法的正确性.     

Design of large-scale time-delayed systems with dead-zone input via variable structure control

To deal with time delay in the interconnection and dead-zone nonlinearity in the input, a new decentralized variable structure control (DVSC) law is proposed for a class of uncertain large-scale system (LSS) in this paper. The developed DVSC for the interconnected systems is realized independently through the delay terms. The applied control effort of the DVSC law is always out of the dead-band to eliminate the effects arisen from the dead-zone nonlinearity in the input function. In the sliding mode, it can be seen that the invariance condition also holds. It is worth noting that the traditional large-scale time-delayed system is only a special case in this work. Illustrative examples are given to verify the validity of the developed controller.     

非线性相似组合系统的鲁棒输出跟踪控制*

研究一类具有相似结构的非线性不确定组合系统的分散输出跟踪控制问题,利用的相似结构,提出一种设计具有相似结构的分散滑模控制器的方法,所设计的控制器,对于所有允许的不确定性,均使系统输出渐近跟踪所给定的参考输出。     

线性时滞中立型控制系统的滑动模补偿器方法

利用变结构控制理论，提出了线性不确定系数时滞中立型控制系统的一种新方法－－滑动模补偿器法。即当系统具有不确定系数时，引进一个滑动模补偿器，实现了完全的模型跟踪从而克服了用常规方法确定滑动曲面时所遇到的若干困难，为说明此法的设计技巧，给出了一个数值仿真例子。     

电液伺服系统的多滑模鲁棒自适应控制

针对一类参数与外负载非匹配不确定的非线性高阶系统,提出了一种基于逐步递推方法的多滑模鲁棒自适应控制策略.应用逐步递推的多滑模控制方法简化了高阶系统的控制问题,同时在自适应控制中加入鲁棒控制的方法,以消除不确定性对控制性能的影响.首先利用逐步递推方法与状态反馈精确线性化理论,得出确定系统的多滑模控制器设计方法;然后基于Lyapunov稳定性分析方法,给出不确定系统的参数自适应律,及鲁棒自适应控制器的设计方法.本文把该控制策略应用到电液伺服系统的位置跟踪控制中,仿真结果显示,该控制方法具有较强的鲁棒性及良好的跟踪效果.     

Sliding mode learning control of non‐minimum phase nonlinear systems

In this paper, a novel robust sliding mode learning control scheme is developed for a class of non‐minimum phase nonlinear systems with uncertain dynamics. It is shown that the proposed sliding mode learning controller, designed based on the most recent information of the stability status of the closed‐loop system, is capable of adjusting the control signal to drive the sliding variable to reach the sliding surface in finite time and remain on it thereafter. The closed‐loop dynamics including both observable and non‐observable ones are then guaranteed to asymptotically converge to zero in the sliding mode. The developed learning control method possesses many appealing features including chattering‐free characteristic, strong robustness with respect to uncertainties. More importantly, the prior information of the bounds of uncertainties is no longer required in designing the controller. Numerical examples are presented in comparison with the conventional sliding mode control and backstepping control approaches to illustrate the effectiveness of the proposed control methodology. Copyright © 2015 John Wiley & Sons, Ltd.