SECOND‐ORDER NONSINGULAR TERMINAL SLIDING MODE DECOMPOSED CONTROL OF UNCERTAIN MULTIVARIABLE SYSTEMS

This paper proposes a second‐order nonsingular terminal sliding mode decomposed control method for multivariable linear systems with internal parameter uncertainties and external disturbances. First, the systems are converted into the block controllable form, consisting of an input‐output subsystem and a stable internal dynamic subsystem. A special second‐order non‐singular terminal sliding mode is proposed for the input‐output subsystem. The control law is designed to drive the states of the input‐output subsystem to converge to the equilibrium point asymptotically. Then the states of the stable zero‐dynamics of the system converge to the equilibrium point asymptotically. The method proposed in the paper has advantages for higher‐dimensional multivariable systems, in the sense that it simplifies the design and makes it possible to realize a robust decomposed control. Meanwhile, because of the adoption of the second‐order sliding mode, the control signal is continuous. Simulation results are presented to validate the design.     

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.     

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。     

多变量线性模型不确定系统终端滑模分解控制方法

针对线性多变量模型不确定系统系统,提出了一种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,它由值域空间子系统和稳定的零空间子系统组成.提出了特殊的终端滑模超曲面,采用滑模控制策略,使值域空间子系统的状态在有限时间内收敛至平衡点,随后稳定的零空间子系统渐近收敛至平衡点.所提出的方法对于维数较高系统的控制具有较大意义,可简化设计,实现递阶控制.仿真验证了该方法的有效性.     

Adaptive fuzzy terminal sliding mode controller for linear systems with mismatched time-varying uncertainties

A new design approach of an adaptive fuzzy terminal sliding mode controller for linear systems with mismatched time-varying uncertainties is presented in this paper. A fuzzy terminal sliding mode controller is designed to retain the advantages of the terminal sliding mode controller and to reduce the chattering occurred with the terminal sliding mode controller. The sufficient condition is provided for the uncertain system to be invariant on the sliding surface. The parameters of the output fuzzy sets in the fuzzy mechanism are adapted on-line to improve the performance of the fuzzy sliding mode control system. The bounds of the uncertainties are not required to be known in advance for the presented adaptive fuzzy sliding mode controller. The stability of the fuzzy control system is also guaranteed. Moreover, the chattering around the sliding surface in the sliding mode control can be reduced by the proposed design approach. Simulation results are included to illustrate the effectiveness of the proposed adaptive fuzzy terminal sliding mode controller.     

A third-order sliding mode controller for nonlinear multivariable systems

This paper proposes a third-order sliding mode controller for nonlinear multivariable systems with uncertain parameters and subject to external disturbances. The controller achieves fast convergence rate, high tracking accuracy, and a reduced level of chattering. The stability of the controller and its global ultimately uniform convergence is proved by the Lyapunov stability theory. Simulation results on a single inverted pendulum system are given to illustrate the effectiveness of the proposed control scheme by comparing it with methods such as a second-order supertwisting controller, a third-order supertwisting controller, and an integral terminal third-order sliding mode controller.     

非匹配不确定系统的终端滑模分解控制

针对非匹配多变量模型不确定系统,提出了一种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,它由匹配扰动的值域空间子系统和稳定的非匹配扰动的零动态子系统组成.提出了特殊的终端滑模超曲面,采用滑模控制策略,使值域空间子系统的状态在有限时间内收敛至平衡点,随后非匹配扰动的零动态子系统渐近收敛至平衡点附近的邻域内,且建立了该邻域的范围与系统的非匹配不确定性范围之间的数学关系,并用于系统的设计与分析.所提方法对于维数较高的非匹配不确定系统的控制具有较大的意义,可简化设计,实现递阶控制.仿真实     

Fuzzy sliding mode control for an under-actuated system with mismatched uncertainties

This article presents a robust fuzzy sliding mode controller. The methodology of sliding mode control provides an easy way to control under-actuated nonlinear systems with uncertainties. The structure of the sliding surface is designed as follows. First, decouple the entire system into second-order systems so that each subsystem has a separate control target expressed in terms of a sliding surface. Second, from the sliding surface of subsystems, organize the main sliding surface system. Third, generate a control input for the main sliding surface to make whole subsystems move toward their sliding surface. A fuzzy controller is used to obtain a smooth boundary layer to the sliding surface. Finally, the fuzzy sliding mode controller presented is used to control an under-actuated nonlinear system, and confirms the validity of the proposed approach and its robustness to uncertainties.     

一类输入受限的不确定非仿射非线性系统二阶动态terminal 滑模控制

针对一类输入受限的不确定非仿射非线性系统跟踪控制问题, 提出一种二阶动态terminal 滑模控制策略. 在不损失模型精度, 并考虑系统输入饱和受限的前提下, 给出一种适用于全局的不确定非仿射非线性系统近似方法. 提出小波小脑模型干扰观测器设计方法, 实现复合扰动的有效逼近. 构造辅助系统分析输入饱和对跟踪误差的影响. 通过构造基于PI 滑模面的terminal 二阶滑模面, 给出二阶动态terminal 滑模控制器设计过程, 克服了传统滑模的抖振问题. 仿真结果验证了所提出方法的有效性.

     

Robust MIMO water level control in interconnected twin-tanks using second order sliding mode control

A novel second order sliding mode control algorithm is presented for a class of MIMO nonlinear systems in input–output (I–O) form. The algorithm produces a dynamic control and does not require the derivative of the sliding variable, thus eliminating the requirement to design observers or peak detectors. The algorithm has been applied for robust control of liquid level in interconnected twin-tanks. The controller is implemented on a laboratory rig and the results presented validate the proposed theory. The implementation results show robustness to parameter variations such as tank area, the admittance coefficients of various pipes, leakage in the tanks and uncertainty in the pump dynamics. In order to contextualise the results obtained with second-order sliding mode control, the results obtained using a classical PI controller are also presented.     

参数不确定柔性机械手的终端滑模控制

针对参数不确定双臂柔性机械手系统, 提出一种基于遗传算法的终端滑模控制方法, 以实现其末端控制.基于输出重定义方法, 通过输入输出线性化, 将系统分解为输入输出子系统和内部子系统. 设计终端滑模控制策略,使输入输出子系统有限时间内收敛到零, 内部子系统变为零动态子系统; 采用遗传算法优化零动态子系统参数, 使其在平衡点附近渐近稳定. 根据Lyapunov稳定性理论算出末端输出位移的误差范围. 仿真结果证明该方法有效性.     

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.     

Decentralised sliding mode control for nonminimum phase interconnected systems based on a reduced-order compensator

In this paper, a class of interconnected systems with mismatched uncertainties is considered. A sliding surface is proposed in an augmented space formed by the system output and the compensator state variables, and the stability of the corresponding sliding mode is analysed. A robust decentralised reduced-order output feedback sliding mode controller is then designed to drive the system to the composite sliding surface and maintain a sliding motion on it thereafter. The proposed approach allows both the isolated nominal subsystem and the nominal interconnected system to be nonminimum phase. The known interconnections and the bounds on the uncertain interconnections are fully used in the control design to reduce conservatism.     

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.     

基于干扰观测器的一类不确定非线性系统自适应二阶动态terminal滑模控制

针对一类不确定非线性系统的跟踪控制问题,在考虑建模误差、参数不确定和外部干扰情况下,以其拥有良好的跟踪性能以及强鲁棒性为目标,提出基于回归扰动模糊神经网络干扰观测器(recurrent perturbation fuzzy neural networks disturbance observer,RPFNNDO)的鲁棒自适应二阶动态terminal滑模控制策略.将回归网络、模糊神经网络和sine-cosine扰动函数各自优势相结合,给出一种回归扰动模糊神经网络结构,提出RPFNNDO设计方法,保证干扰估计准确性;构造基于带有指数函数滑模面的二阶快速terminal滑模面,给出其控制器设计过程,避免了滑模到达阶段、传统滑模的抖振问题,采用具有指数收敛的鲁棒项抑制干扰估计误差对系统跟踪性能的影响,利用Lyapunov理论证明闭环系统的稳定性;将该方法应用于混沌陀螺系统同步控制仿真实验,结果表明所提方法的有效性.     

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.     

Robust dynamic output feedback second-order sliding mode controller for uncertain systems

This paper addresses the problem of designing a dynamic output feedback sliding mode control algorithm to stabilize a linear MIMO uncertain system having relative degree two. Introducing a suitable dynamic compensator into the sliding variable, the additional degree of freedom can be used to robustly guarantee the closed-loop system stability once the system is in the sliding mode. A modified asymptotically stable second-order sliding mode control is analyzed and the proposed controller can obtain the real second-order sliding mode. Finally, the feasibility of the proposed method is illustrated by a numerical example.     

Adaptive sliding mode trajectory tracking control for wheeled mobile robots

This paper discusses the problem of adaptive sliding mode trajectory tracking control for wheeled mobile robots in the presence of external disturbances and inertia uncertainties. A new fast nonsingular terminal sliding mode surface without any constraint is proposed, which not only avoids singularity, but also retains the advantages of sliding mode control. In order to implement the trajectory tracking mission, the error dynamic system is divided into a second-order subsystem and a third-order one. First, an adaptive fast nonsingular terminal sliding mode control law of the angular velocity is constructed for stabilising the second-order subsystem in finite time. Then, another adaptive fast nonsingular terminal sliding mode control law of the linear velocity is designed to guarantee the stability of the third-order subsystem. Finally, a simulation example is provided to demonstrate the validity of the proposed control scheme.     

Fast terminal sliding‐mode finite‐time tracking control with differential evolution optimization algorithm using integral chain differentiator in uncertain nonlinear systems

This paper presents a fast terminal sliding‐mode tracking control for a class of uncertain nonlinear systems with unknown parameters and system states combined with time‐varying disturbances. Fast terminal sliding‐mode finite‐time tracking systems based on differential evolution algorithms incorporate an integral chain differentiator (ICD) to feedback systems for the estimation of the unknown system states. The differential evolution optimization algorithm using ICD is also applied to a tracking controller, which provides unknown parametric estimation in the limitation of unknown system states for trajectory tracking. The ICD in the tracking systems strengthens the tracking controller robustness for the disturbances by filtering noises. As a powerful finite‐time control effort, the fast terminal sliding‐mode tracking control guarantees that all tracking errors rapidly converge to the origin. The effectiveness of the proposed approach is verified via simulations, and the results exhibit high‐precision output tracking performance in uncertain nonlinear systems.