A novel dynamic terminal sliding mode control of uncertain nonlinear systems

A new dynamic terminal sliding mode control (DTSMC) technique is proposed for a class of single-input and single-output (SISO) uncertain nonlinear systems. The dynamic terminal sliding mode controller is formulated based on Lyapunov theory such that the existence of the sliding phase of the closed-loop control system can be guaranteed, chattering phenomenon caused by the switching control action can be eliminated, and high precision performance is realized. Moreover, by designing terminal equation, the output tracking error converges to zero in finite time, the reaching phase of DSMC is eliminated and global robustness is obtained. The simulation results for an inverted pendulum are given to demonstrate the properties of the proposed method.     

不确定多变量系统的高阶滑模控制

针对一类系统矩阵和输入矩阵存在不确定性的多变量系统,结合微分估计器技术和极点配置技术,提出一种二阶非奇异终端滑模分解控制方法.所提方法适用于维数较高系统,可简化控制器设计,消除控制信号的高频抖振,实现系统的鲁棒递阶控制.仿真结果验证了所提方法的有效性.     

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.     

不确定非线性系统的自适应反推高阶终端滑模控制

针对一类非匹配不确定非线性系统,提出一种神经网络自适应反推高阶终端滑模控制方案.反推设计的前1步利用神经网络逼近未知非线性函数,结合动态面控制设计虚拟控制律,避免传统反推设计存在的计算复杂性问题,并抑制非匹配不确定性的影响;第步结合非奇异终端滑模设计高阶滑模控制律,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.理论分析证明了闭环系统状态半全局一致终结有界,仿真结果表明了所提出方法的有效性.     

Terminal sliding mode control design for uncertain dynamic systems

A terminal sliding mode control design scheme for uncertain dynamic systems in the pure-feedback form is presented in this paper. This design employs a recursive procedure which utilizes a set of switching manifolds to realize finite time convergence. To avoid a singularity problem, the scheme uses two-phase control: one phase is a preterminal sliding mode control that transfers the trajectory to a specified open region in which the terminal sliding mode control is not singular. Inside the region, the other phase – the terminal sliding mode control takes place bringing the state to the origin in finite time.     

一类非线性不确定系统的非奇异Terminal滑模控制

针对一类二阶非线性系统提出新的Terminal滑模控制面以克服传统的Terminal滑模控制的奇异问题，同时确保系统从任何初始状态能在有限时间内收敛至平衡点．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非奇异Terminal滑模控制（NTSM）控制．最后通过实例比较三种滑模控制方法，仿真结果验证了非奇异Terminal滑模控制能克服传统的Terminal滑模控制的奇异问题，并说明了自适应非奇异Terminal滑模控制的有效性和可行性．     

Non-singular terminal sliding mode control of rigid manipulators

This paper presents a global non-singular terminal sliding mode controller for rigid manipulators. A new terminal sliding mode manifold is first proposed for the second-order system to enable the elimination of the singularity problem associated with conventional terminal sliding mode control. The time taken to reach the equilibrium point from any initial state is guaranteed to be finite time. The proposed terminal sliding mode controller is then applied to the control of n-link rigid manipulators. Simulation results are presented to validate the analysis.     

有限时间快速收敛滑模变结构控制

讨论了一类非线性系统的滑模变结构控制有限时间收敛问题.提出了一种新的收敛滑模超曲面及相应控制方案.研究结果表明,系统状态变量能以较快的收敛速度在有限时间内进入各级滑模超曲面最终到达平衡点,并具有良好的动态性能.最后仿真结果验证了该方案的有效性.     

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.     

Robust sliding mode control of uncertain nonlinear systems

A dynamic sliding mode controller design method is proposed for multiple input-output systems with additive uncertainties. A previous result on the stability of triangular systems is generalised to the case of uniform ultimate boundedness of controlled triangular systems. This is used to prove the stability of the overall closed-loop system. The uncertain system with appropriately chosen sliding mode control is shown to be ultimately bounded if the zero dynamics of the nominal system are uniformly asymptotically (exponentially) stable. The design method is demonstrated with two examples.     

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.     

基于扰动观测器的不确定非线性系统非奇异终端滑模控制

针对一类SISO 非线性不确定系统, 提出一种基于扰动观测器的非奇异终端滑模(NTSM) 控制策略. 在保证控制器非奇异性的情况下, 设计了一种改进的NTSM函数, 理论分析证明了到达滑模面的时间小于传统NTSM控制算法的到达时间. 同时为了消除系统扰动量对控制器抖振的影响, 设计了一种线性扰动观测器以降低滑模切换项的增益, 并采用Sigmoid 函数来替代传统的符号函数. 仿真结果表明了所得结论的正确性和有效性.     

多变量模型不确定系统的二阶滑模分解控制方法

提出一种多变量模型不确定系统的二阶终端滑模分解控制方法。通过状态变换和去耦合处理将系统转换为块能控标准型，它由输入输出子系统和穗定的零动态子系统组成。提出了特殊的二阶终端滑模超曲面和相应的控制策峪，使输入输出子系统状态渐近收敛到平衡点，零动态子系统随后也渐近收敛到平衡点。所提出方法对于控制维教较高的系统具有较大的意义，可简化设计，实现鲁棒分解控制。由于采用了二阶滑模的思想，可有效地消除系统的高频抖振。仿真实例表明了该方法的有效性。     

Terminal sliding mode control of second-order nonlinear uncertain systems

In this paper, a terminal sliding mode control scheme is proposed for second-order nonlinear uncertain systems. 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. In addition, the proposed scheme eliminates the reaching phase problem so that the closed-loop system always shows the invariance property to parameter uncertainties. Copyright © 1999 John Wiley & Sons, Ltd.     

动力定位的分数阶双环自适应终端滑模控制

为了解决具有非线性和环境干扰的船舶动力定位系统的控制问题,本文提出了一种基于分数阶双环自适应快速终端滑模控制算法,证明了闭环系统的稳定性,设计了自适应控制律,计算了滑模的收敛时间。控制系统由外环位置姿态环和内环速度环构成,外环滑模控制实现自动定位于期望位置和姿态,内环滑模控制实现对速度和角速度的定位。通过切换函数的设计,对不确定性和外加干扰具有较强的鲁棒性,避免系统出现抖振现象。对双环滑模控制器进行仿真,计算出动力定位外界环境扰动的变速运动情况下的前进位置、横荡位置、艏向角度、前进速度、横荡速度、艏向角速度、前进控制力、横荡控制力和艏向控制力矩等。对外环控制率增益λ2等参数对控制性能的影响进行了比较分析。结果表明,分数阶双环自适应终端滑模控制动态响应要稍快于传统双环控制,且超调量小,调整时间更短,所设计的控制器对有非线性和环境干扰的船舶动力定位系统都具有较强的鲁棒性。本算法为不确定性系统的变结构控制提供了新的解决方案,扩展了滑模控制算法的应用领域。     

Second-order terminal sliding mode control for hypersonic vehicle in cruising flight with sliding mode disturbance observer

This paper focuses on the design of nonlinear robust controller and disturbance observer for the longitudinal dynamics of a hypersonic vehicle (HSV) in the presence of parameter uncertainties and external disturbances. First, by combining terminal sliding mode control (TSMC) and second-order sliding mode control (SOSMC) approach, the secondorder terminal sliding control (2TSMC) is proposed for the velocity and altitude tracking control of the HSV. The 2TSMC possesses the merits of both TSMC and SOSMC, which can provide fast convergence, continuous control law and hightracking precision. Then, in order to increase the robustness of the control system and improve the control performance, the sliding mode disturbance observer (SMDO) is presented. The closed-loop stability is analyzed using the Lyapunov technique. Finally, simulation results illustrate the effectiveness of the proposed method, as well as the improved overall performance over the conventional sliding mode control (SMC).     

自适应时变Terminal滑模控制研究

针对Terminal滑模控制到达阶段鲁棒性不强的问题,提出了时变Terminal滑模控制方法。分析Terminal滑模面的设计参数对系统性能的影响,提出一种非线性时变Terminal滑模面的设计方法。为了消除多输入多输出(MIMO)非线性系统的不确定,构建动态干扰观测器系统,根据干扰观测误差在线调节参数,从而在线逼近外部干扰,证明了逼近误差一致最终有界。采用倒立摆系统进行仿真验证,提出的自适应时变Terminal滑模控制方法比传统的PID控制镇定时间缩短80%,且无超调。仿真结果表明,所提方法可以用于MIMO非线性系统的控制。     

A robust reinforcement learning using the concept of sliding mode control

In this article, we propose a new control method using reinforcement learning (RL) with the concept of sliding mode control (SMC). Some remarkable characteristics of the SMC method are good robustness and stability for deviations from control conditions. On the other hand, RL may be applicable to complex systems that are difficult to model. However, applying reinforcement learning to a real system has a serious problem, i.e., many trials are required for learning. We intend to develop a new control method with good characteristics for both these methods. To realize it, we employ the actor-critic method, a kind of RL, to unite with the SMC. We are able to verify the effectiveness of the proposed control method through a computer simulation of inverted pendulum control without the use of inverted pendulum dynamics. In particular, it is shown that the proposed method enables the RL to learn in fewer trials than the reinforcement learning method. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

Finite time convergent control using terminal sliding mode

A method for terminal sliding mode control design is discussed. As we know, one of the strong points of terminal sliding mode control is its finite-time convergence to a given equilibrium of the system under consideration, which may be useful in specific applications. The proposed method, different from many existing terminal sliding model control design methods, is studied, and then feedback laws are designed for a class of nonlinear systems, along with illustrative examples.