Design of decentralised adaptive sliding mode controllers for large-scale systems with mismatched perturbations

Based on the Lyapunov stability theorem, a methodology for designing a decentralised adaptive sliding mode control scheme is proposed in this paper. This scheme is implemented for a class of large-scale systems with both matched and mismatched perturbations. The perturbations and the interconnection terms are assumed to be norm bounded under certain mild conditions. The decentralised sliding surfaces with adaptive mechanisms embedded are specially designed for each subsystem, so that when each subsystem enters the sliding mode, the mismatched perturbations and the effects of interconnections can be effectively overcome and achieve asymptotic stability. The decentralised controller with embedded adaptive mechanisms is capable of driving the controlled state trajectories into the designated sliding surface in finite time. This is also achieved without the knowledge of upper bounds of the perturbations except those of the uncertainties in the input channels. A numerical example is included to demonstrate the feasibility of the proposed control scheme.     

Block backstepping control of multi-input nonlinear systems with mismatched perturbations for asymptotic stability

Based on the Lyapunov stability theorem, a methodology of designing the block backstepping controller for a class of multi-input systems with matched and mismatched perturbations is proposed in this article. Some adaptive mechanisms are embedded both in the virtual input controller and in the backstepping controllers so that not only are the mismatched perturbations suppressed, but also part knowledge of the upper bound of perturbation is not required. Finally, an example of stabilising the control-moment-gyro devices is presented to demonstrate the feasibility of the proposed methodology.     

Design of decentralised sliding surfaces for a class of large-scale systems with mismatched perturbations

A novel design methodology of a decentralised sliding surface is proposed in this article for a class of large-scale systems with mismatched perturbations and interconnections. The main idea of this method is that the sliding surface function is obtained through a specially designed state transformation matrix. This transformation matrix, which includes the sliding surface coefficient function, contains adaptive mechanisms with the capability of adapting some unknown constants embedded in the least upper bounds of mismatched perturbations as well as interconnections, so that the perturbations (mismatched and matched) can be effectively overcome and asymptotical stability is guaranteed for each subsystem in the sliding mode. In addition, each decentralised controller also contains adaptive mechanisms to assure that the sliding mode is generated in a finite time without requiring the knowledge of upper bounds of the perturbations and interconnections. A practical example is also demonstrated by simulation for showing the feasibility of the proposed methodology.     

非匹配不确定系统的自适应反步非奇异快速终端滑模控制

针对一类n阶非匹配不确定系统,提出一种自适应反步非奇异快速终端滑模控制方法.控制的前n-1步采用自适应反步控制策略,消除非匹配不确定性的影响;最后一步利用误差的积分构造非奇异快速终端滑模面,设计控制律使系统第n个状态有限时间收敛.该方法对系统中匹配和非匹配不确定项均具有鲁棒性,比自适应反步终端滑模方法具有更快的收敛速度.理论分析证明了闭环系统的稳定性,仿真结果验证了该方法的有效性.     

Adaptive terminal sliding mode control for rigid robotic manipulators

In order to apply the terminal sliding mode control to robot manipulators, prior knowledge of the exact upper bound of parameter uncertainties, and external disturbances is necessary. However, this bound will not be easily determined because of the complexity and unpredictability of the structure of uncertainties in the dynamics of the robot. To resolve this problem in robot control, we propose a new robust adaptive terminal sliding mode control for tracking problems in robotic manipulators. By applying this adaptive controller, prior knowledge is not required because the controller is able to estimate the upper bound of uncertainties and disturbances. Also, the proposed controller can eliminate the chattering effect without losing the robustness property. The stability of the control algorithm can be easily verified by using Lyapunov theory. The proposed controller is tested in simulation on a two-degree-of-freedom robot to prove its effectiveness.     

A multitask sliding mode control for mismatched uncertain large-scale systems

A new sliding mode control (SMC) approach, output variables only, single phase only and chattering phenomenon free, is presented for a class of mismatched uncertain large-scale systems. For a new multitask SMC, it is not required that the system states are available. Moreover, the sliding function in this study just depends on output variables. Using an exponential type sliding surface, the system states are always in the sliding mode at the beginning time t = 0. Using a newly appropriate linear matrix inequality stability conditions by the Lyapunov method are derived such that each subsystem in the new sliding mode is completely invariant to matched uncertainties. As a result, robustness of the mismatched uncertain large-scale systems can be assured throughout an entire response of the system starting from the initial time t = 0. In every subsystem, a scheme of decentralised control using only output states is proposed. In addition, a continuous controller is finally designed for chattering removal. Finally, a numerical example is used to demonstrate the efficacy of the proposed method.     

Adaptive sliding mode control and observation

ABSTRACT

This editorial article gives a short introduction to Special Issue of International Journal of Control on Adaptive Sliding Mode Control and Observation.     

Adaptive sliding mode control of nonlinear robotic systems with time-varying parameters

In this paper an adaptive sliding mode control scheme is presented for nonlinear robotic systems with bounded time-varying parameters. The control scheme developed is very simple and computationally efficient since it does not require a knowledge of either The mathematical model or the parameter values of the robotic dynamics. It is shown that the controller is globally stable in the presence of a class of state-dependent uncertainties and that the size of the tracking error can be made arbitrarily small.     

Buck变换器的改进型互补滑模控制

针对Buck变换器系统中存在匹配和不匹配干扰的问题, 本文提出了一种基于干扰观测器(DOB)的改进型互补滑模控制(CSMC)策略. 首先, 建立存在多重干扰的Buck变换器数学模型, 将模型改写为标准二阶积分型控制对象, 将式中干扰统一为匹配干扰和不匹配干扰. 其次, 设计2个DOB分别估计匹配干扰和不匹配干扰, 实现有限时间内跟踪干扰信号, 以抵消各种不确定性对系统的影响. 然后, 设计互补滑模面, 提出基于等效控制的改进型互补滑模控制律, 保留边界层内鲁棒性的同时, 提升控制器的动态性能, 减小静态误差, 拓宽边界层参数选择范围. 最后, 基于李雅普诺夫理论证明所提出控制器的稳定性. 数字仿真表明, 提出的改进型CSMC控制器结合DOB的总体控制方案能够有效抑制系统匹配和不匹配干扰, 同时获得更快的收敛速度以及更高的跟踪精度.     

牵引车–飞机系统的自适应滑模变结构控制

将自动转向技术应用于牵引车–飞机系统, 并以侧偏位移和相对横摆角作为反馈, 提出一种牵引车四轮主动转向控制策略. 重点考虑牵引车和飞机的侧向和横摆运动, 建立含铰接角在内的牵引车–飞机系统非线性动力学模型. 将牵引车和飞机的轮胎侧偏刚度视为有界的不确定性参数, 将侧向风等因素视为未知的外在扰动, 采用自适应滑模变结构控制方法设计牵引车转向角控制器. 仿真结果表明, 设计出的前、后轮转向控制器能使控制系统同时获得很好的轨迹跟踪性和操纵稳定性, 并且能够有效的克服参数摄动和外界干扰对系统操作性的影响.     

广义双线性系统的二阶终端滑模控制

利用Lyapunov稳定性理论研究了一类广义双线性系统的镇定问题.通过构造特殊的二阶终端滑模超曲面,设计相应的变结构控制器,使闭环系统在有限时间内实现滑动模运动,系统的状态在平衡点渐近稳定.该设计方法能有效削弱系统的高频抖振.仿真结果验证了设计方法的可行性.     

一类非线性系统的Terminal滑模控制

首先结合Terminal滑模控制的基本思想,即突破以往的线性滑动面,将非线性项引入到滑动面设计中,使得系统处于滑动模态阶段时,状态变量能够在"有限时间内"收敛至平衡点,给出了适用于高阶非线性系统的Terminal滑动面设计方法,基于Lyapunov稳定性理论得出了相应的控制器.进一步考虑系统参数摄动和外界扰动等不确定性因素上界的未知性,用Lyapunov稳定性方法给出了一个带有未知性上界参数估计的自适应Terminal滑模控制器.     

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.     

Adaptive backstepping sliding mode control for feedforward uncertain systems

Output tracking backstepping sliding mode control for feedforward uncertain systems is considered in this article. Feedforward systems are not usually transformable to the parametric semi-strict feedback form, and they may include unmatched uncertainties consisting of disturbances and unmodelled dynamics terms. The backstepping method presented in this article, even without uncertainties differs from that of Ríos-Bolívar and Zinober [Ríos-Bolívar, M. and Zinober, A.S.I. (1999), ‘Dynamical Adaptive Sliding Mode Control of Observable Minimum Phase Uncertain Nonlinear Systems’, in Variable Structure Systems: Variable Structure Systems, Sliding Mode and Nonlinear Control, eds., K.D. Young and Ü. Özgüner. Ozguner, London, Springer-Verlag, pp. 211–236; Ríos-Bolívar, M., and Zinober, A.S.I. (1997a), ‘Dynamical Adaptive Backstepping Control Design via Symbolic Computation’, in Proceedings of the 3rd European Control Conference, Brussels]. In this article, the backstepping is not a dynamical method as in Ríos-Bolívar and Zinober (1997a Ríos-Bolívar, M and Zinober, ASI. 1997a. Dynamical Adaptive Sliding Mode Output Tracking Control of a Class of Nonlinear Systems. International Journal of Robust and Nonlinear Control, 7: 387–405.  [Google Scholar], 1999), since at each step, the control and map input remain intact, and the differentiations of the control are not used. Therefore, the method can be introduced as static backstepping. Two different controllers are designed based upon the backstepping approach with and without sliding mode. The dynamic and static backstepping methods are applied to a gravity-flow/pipeline system to compare two methods.     

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。     

Non-linear adaptive sliding mode switching control with average dwell-time

In this article, an adaptive integral sliding mode control scheme is addressed for switched non-linear systems in the presence of model uncertainties and external disturbances. The control law includes two parts: a slide mode controller for the reduced model of the plant and a compensation controller to deal with the non-linear systems with parameter uncertainties. The adaptive updated laws have been derived from the switched multiple Lyapunov function method, also an admissible switching signal with average dwell-time technique is given. The simplicity of the proposed control scheme facilitates its implementation and the overall control scheme guarantees the global asymptotic stability in the Lyapunov sense such that the sliding surface of the control system is well reached. Simulation results are presented to demonstrate the effectiveness and the feasibility of the proposed approach.     

Second‐order sliding mode controller design subject to mismatched unbounded perturbations

The dynamics of the second‐order sliding mode (SOSM) can be obtained by directly taking the second derivative on the sliding variable when it has a relative degree of 2 with respect to the control input. However, there will always appear some state‐dependent certain or uncertain terms in the first derivative of the sliding variable, and the derivative directly imposed on these terms could enlarge the uncertainties in the control channel. One method to reduce the uncertainties in the control channel is to hold this information in the dynamics of the first derivative of the sliding variable, while the original SOSM dynamics could be transformed to be a SOSM system with a mismatched unbounded perturbation. This paper focuses on the controller design problem for SOSM dynamics subject to mismatched unbounded perturbation. By using Lyapunov analysis, a novel backstepping‐like design methodology will be proposed. The rigorous mathematical proof will show that under the derived SOSM controller, the closed‐loop sliding mode dynamics is globally finite‐time stable. Meanwhile, the frequently used constant upper bound assumptions for the standard SOSM system can also be extended to the state‐dependent hypotheses in this paper. An academic example is illustrated to verify the effectiveness of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.     

不确定非线性系统的自适应反演终端滑模控制

针对一类参数严格反馈型不确定非线性系统, 本文提出一种自适应反演终端滑模控制方法. 反演控制的前n-1步结合自适应律估计系统的未知参数, 第n步采用非奇异终端滑模, 使系统最后一个状态有限时间内收敛.利用微分估计器获得误差系统状态的导数, 并设计了高阶滑模控制律, 去除控制抖振, 使系统对于匹配和非匹配不确定性均具有鲁棒性. 同自适应反演线性滑模方法相比, 所提方法提高了系统的收敛速度和稳态跟踪精度, 并且控制信号更加平滑. 仿真结果验证了该方法的有效性.     

基于反演设计的机器人自适应动态滑模控制

针对机器人跟踪控制问题,设计了一种新型的动态滑模控制器,采用反演（backstepping）方法设计一种新的切换函数,将不连续项转移到了控制的一阶导数中,得到了输入的平滑性的动态滑模控制律。该控制律能保证轨迹跟踪误差的快速收敛性和参数不确定的鲁棒性,仿真实例验证了该控制算法的有效性。     

机器人操作器的自适应模糊滑模控制器设计

针对机器人动力学系统提出了一种基于模糊逻辑的自适应模糊滑模控制方案.根据滑模控制原理并利用模糊系统的逼近能力设计控制器,基于李雅谱诺夫方法设计自适应律,证明了闭环模糊控制系统的稳定性和跟踪误差的收敛性.控制结构简单,不需要复杂的运算.该设计方案柔化了控制信号,减轻了一般滑模控制的抖振现象.仿真结果表明了所提控制策略的有效性.