Chattering in sliding mode control systems with boundary layer approximation of discontinuous control

It has been a widely accepted notion that approximation of discontinuous control by certain continuous function in a boundary layer results in chattering elimination in sliding mode control systems. It is shown through three different types of analysis that in the presence of parasitic dynamics, this approach to chattering elimination would work only if the slope of the continuous nonlinear function within the boundary layer is low enough, which may result in the deterioration of performance of the system. A few examples are provided. An approach to robust stability of linear systems from the consideration of the saturating control is proposed.     

Chattering reduction of sliding mode control by low‐pass filtering the control signal

The conventional approach to reducing control signal chattering in sliding mode control is to use the boundary layer design. However, when there is high‐level measurement noise, the boundary layer design becomes ineffective in chattering reduction. This paper, therefore, proposes a new design for chattering reduction by low‐pass filtering the control signal. The new design is non‐trivial since it requires estimation of the sliding variable via a disturbance estimator. The new sliding mode control has the same performance as the boundary layer design in noise‐free environments, and outperforms the boundary layer design in noisy environments. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

基于滑模变结构的倒立摆系统稳定控制

利用滑模变结构控制对一级倒立摆系统进行了有效控制.首先对一级倒立摆系统的模型进行线性化处理,再利用滑模变结构控制方法对此模型中摆的镇定、台车位置的调节和系统参数不确定性设计了具体的控制规律,并使用饱和函数的方法抑制系统的抖振.最后在Matlab/Simulink上进行了仿真实验,实验结果说明滑模变结构控制方法是有效的.     

滑模变结构控制理论及其算法研究与进展

针对近年来滑模变结构控制的发展状况,将滑模变结构控制分为18个研究方向,即滑模控制的消除抖振问题、准滑动模态控制、基于趋近律的滑模控制、离散系统滑模控制、自适应滑模控制、非匹配不确定性系统滑模控制、时滞系统滑模控制、非线性系统滑模控制、Terminal滑模控制、全鲁棒滑模控制、滑模观测器、神经网络滑模控制、模糊滑模控制、动态滑模控制、积分滑模控制和随机系统的滑模控制等.对每个方向的研究状况进行了分析和说明.最后对滑模控制的未来发展作了几点展望.     

On adaptive sliding mode control without switching gain overestimation

This paper presents some further results on adaptive sliding mode control (ASMC) for a class of nonlinear systems with bounded uncertain parameters. Given a large initial tracking error, current ASMC design generally produces an unnecessarily large switching gain, consequently leading to a serious chattering problem or a large‐amplitude control jump for the continuous counterpart. To solve such an overadaptation problem, the switching gain adaptation mechanism is first analyzed in this paper, and the adaptation induced by the initial tracking error is suggested to be removed. Then, by exploiting the global sliding mode feature of time‐varying sliding mode control and integral sliding mode control, we present two effective methodologies for ASMC design. The proposed ASMC algorithms ensure that there is no overestimation of the switching gain and the system response is not slowed down when a small switching gain is generated. The validity of the proposed methods is verified by both theoretical analysis and simulation results. Copyright © 2012 John Wiley & Sons, Ltd.     

多关节机器人的神经滑模控制

针对含有建模误差和不确定干扰的多关节机械臂轨迹跟踪控制,提出了一种神经滑模控制方法。该方法采用全局快速终端滑模面保证了系统状态能够在有限时间内到达滑模面和平衡点。采用径向基函数神经网络自适应地补偿系统的建模误差和外界干扰,保证了滑模控制在滑模面的运动。利用李亚普诺夫稳定性判据推导出了控制器的控制律和神经网络的目标函数,通过神经网络的在线学习,削弱了滑模控制的抖振。仿真结果表明了其有效性。     

建筑结构基于RBF神经网络的离散滑模控制研究

抖振问题是离散滑模控制在实际系统中应用的突出障碍.根据神经网络控制的优点,采用一种基于RBF神经网络的离散滑模控制方法对地震作用下建筑结构的振动控制问题进行了研究.根据离散系统建模技术,得到了离散时间形式的状态方程,同时给出了确定切换面的方法,并推导了控制律的表达式.以一个三层剪切型建筑结构模型为例来验证所提出的离散滑模控制方法的有效性.算例分析结果表明:本文所提出的控制方法能够有效地减小结构的地震峰值响应,同时达到了削弱控制系统抖振的目的.     

Chattering free adaptive fuzzy terminal sliding mode control for second order nonlinear system

A novel fuzzy terminal sliding mode control （FTSMC） scheme is proposed for position tracking of a class of second-order nonlinear uncertain system. In the proposed scheme, we integrate input-output linearization technique to cancel the nonlinearities. By using a function-augmented sliding hyperplane, it is guaranteed that the output tracking error converges to zero in finite time which can be set arbitrarily. The proposed scheme eliminates reaching phase problem, so that the closed-loop system always shows invariance property to parameter uncertainties. Fuzzy logic systems are used to approximate the unknown system functions and switch item. Robust adaptive law is proposed to reduce approximation errors between true nonlinear functions and fuzzy systems, thus chattering phenomenon can be eliminated. Stability of the proposed control scheme is proved and the scheme is applied to an inverted pendulum system. Simulation studies are provided to confirm performance and effectiveness of the proposed control approach.     

Chattering free adaptive fuzzy terminal sliding mode control for second order nonlinear system

A novel fuzzy terminal sliding mode control (FTSMC) scheme is proposed for position tracking of a class of second-order nonlinear uncertain system. In the proposed scheme, we integrate input-output linearization technique to cancel the nonlinearities. By using a function-augmented sliding hyperplane, it is guaranteed that the output tracking error converges to zero in finite time which can be set arbitrarily. The proposed scheme eliminates reaching phase problem, so that the closed-loop system always shows invariance property to parameter uncertainties. Fuzzy logic systems are used to approximate the unknown system functions and switch item. Robust adaptive law is proposed to reduce approximation errors between true nonlinear functions and fuzzy systems, thus chattering phenomenon can be eliminated. Stability of the proposed control scheme is proved and the scheme is applied to an inverted pendulum system. Simulation studies are provided to confirm performance and effectiveness of the proposed control approach.     

带有干扰观测器的高超声速飞行器滑模控制

针对高超声速飞行器非线性和易受干扰影响的特点,提出了带有扩张状态干扰观测器的连续滑模控制方法.在对飞行器非线性模型做线性化处理的基础上,设计了一种连续时间滑模控制器.该控制器在对不确定性和未知动态保持鲁棒性的基础上,消除了传统滑模中存在的抖振现象.对系统中存在的外加干扰,设计了扩张状态干扰观测器.将外加干扰作为系统的一个状态变量被估计出来,再将估计值用作滑模控制器的补偿量,进而达到消除外干扰的目的.在高超声速飞行器巡航飞行状态的基础上进行了仿真.仿真结果表明,所提出的方案能够满足控制要求.     

An LTR-observer-based dynamic sliding mode control for chattering reduction

Two important approaches to alleviation of control chattering in sliding mode control are the boundary layer control (BLC) and the dynamic sliding mode control (DSMC). The DSMC is superior to the BLC since in DSMC chattering is alleviated without sacrificing the control accuracy. However, the design of DSMC is more challenging because its sliding variable contains an unknown system uncertainty. This paper proposes a robust two-dimensional LTR observer for estimation of the state-dependent uncertainty in the sliding variable. This paper also shows, via simulation examples, that the DSMC can better reduce chattering than the BLC especially in noisy environments.     

串联机器人的双模糊自适应滑模控制

提出了一种串联机器人的改进控制算法。采用一自适应模糊控制器,根据滑模到达条件对滑模切换增益进行估算,消除滑模控制中输出力矩的抖振现象,增强其对不确定性因素的适应能力。采用另一自适应模糊控制器对指数趋近律系数进行修正,改善由于大范围初始位姿产生的偏差而引起的大力矩和速度跳变问题。该方法无需确定被控对象的具体数学模型,具有强鲁棒性和高跟踪精度。基于Lyapunov方法进行了稳定性证明,保证控制系统的稳定性与收敛性。实验结果表明,该方法应用于串联机器人,跟踪效果良好并产生了平滑的力矩输出和速度输出。     

Chattering suppression methods in sliding mode control systems

The implementation of sliding mode control is often irritated by high frequency oscillations known as “chattering” in system outputs issued by dynamics from actuators and sensors ignored in system modeling. This paper provides analysis of chattering in such systems with unmodeled based on the Lyapunov theory and the describing function method. It also describes various approaches to reduce chattering including methods based on relay control gain adaptation. And for those systems to which the methods are not applicable, chattering frequency control using hysteresis loop will be provided.     

多输入不确定系统的平滑非奇异终端滑模控制

研究多输入通道的参数摄动和外部扰动对控制系统输入输出和内部状态稳定性的影响. 采用两次模型变换实现输入输出和内部状态解耦, 运用Lyapunov 稳定定理建立系统收敛区域与不确定项范围的数学关系. 提出一种平滑非奇异终端滑模控制方法, 引入虚拟控制项以增加系统的相对阶, 利用鲁棒微分器合理提取微分信号, 实现系统的无抖振滑模控制. 仿真研究表明了所提出方法的有效性.     

Sliding mode control of boost and buck‐boost power converters using the dynamic sliding manifold

Non‐minimum phase tracking control is studied for boost and buck‐boost power converters. A sliding mode control algorithm is developed to track directly a causal voltage tracking profile given by an exogenous system. The approximate causal output non‐minimum phase asymptotic tracking in non‐linear boost and buck‐boost power converters is addressed via sliding mode control using a dynamic sliding manifold (DSM). Use of DSM allows the stabilization of the internal dynamics when the output tracking error tends asymptotically to zero in the sliding mode. The sliding mode controller with DSM links features of conventional sliding mode control (insensitivity to matched non‐linearities and disturbances) and a conventional dynamic compensator (accommodation to unmatched disturbances). Numerical examples demonstrate the effectiveness of the sliding mode controller even for a known time‐varying load. Copyright © 2003 John Wiley & Sons, Ltd.     

Position control of synchronous motor drive by modified adaptive two-phase sliding mode controller

A modified adaptive two-phase sliding mode controller for the synchronous motor drive that is highly robust to uncertain-ties and external disturbances is proposed in this paper. The proposed controller uses two-phase sliding mode control (SMC) where the 1st phase mainly controls the system in steady states and disturbed states-it is a smoothing phase. The 2nd phase is used mainly in the case of disturbed states. Also, it is an autotuning phase and uses a simple adaptive algorithm to tune the gain of conventional variable structure control (VSC). The modified controller is useful in position control of a permanent magnet synchronous drive.     

Chattering‐free sliding mode control for a class of nonlinear mechanical systems

Second‐order sliding mode control (2‐smc) and dynamic sliding mode control (dsmc) eliminate the disturbing characteristic of chattering in static sliding mode control under the assumption that the derivative of the sliding surface is available or complex inequalities at the acceleration level can be constructed. In this paper, passivity‐based adaptive and non‐adaptive chattering‐free sliding mode controllers are proposed assuming that the upper bound of the norm of the derivative of the sliding surface is available, a weaker and easy to implement assumption in comparison to those of 2‐smc and dsmc. The closed‐loop system accounts explicitly for the invariance condition without reaching phase, and therefore for a desired transient response with global exponential convergence of tracking errors. Preliminary experiments are presented. Copyright © 2001 John Wiley & Sons, Ltd.     

大型空间飞行器的高阶滑模姿态控制律设计

针对大型空间飞行器的大角度姿态控制问题,考虑航天器惯量矩阵中的不确定性和外部扰动力矩,应用高阶滑模控制方法设计了姿态跟踪控制律.采用的二阶滑模控制方法改善了系统针对不确定性及外部扰动的鲁棒性,并减弱了振颤现象.针对所设计的控制器进行了仿真验证,并与一阶滑模控制进行了对比,仿真结果表明了所提出方法的有效性.     

Higher order sliding mode control based on integral sliding mode

A higher order sliding mode control scheme for uncertain nonlinear systems is proposed in the present paper. It is shown that the problem is equivalent to the finite time stabilization of higher order input-output dynamics with bounded uncertainties (r∈N). The controller uses integral sliding mode concept and contains two parts. A part achieves finite time stabilization of the higher order input-output dynamics without uncertainties. The other part rejects bounded uncertainties throughout the entire response of the system. As a result, a higher order sliding mode is established. The advantages of the method are that its implementation is easy, the time convergence is chosen in advance and the robustness is ensured. An illustrative example of a car control shows the applicability of the method.     

基于ESO 的复合滑模面非奇异terminal 滑模控制

针对传统非奇异terminal 滑模控制存在的收敛缓慢和控制输入抖振的问题, 提出采用复合滑模面函数和扩张状态观测器的控制器设计方法. 首先, 结合复合滑模面, 采用分阶段控制律提高系统收敛速度; 然后, 在此基础上使用扩张状态观测器在线估计并补偿系统的不确定量, 以有效削弱系统未建模动力学导致的抖振; 最后, 分别证明了以上两种方法的有限时间收敛特性. 仿真结果验证了所提出方法的有效性, 体现了系统的快速收敛和强鲁棒性等特点.