Event-Triggered Sliding Mode Control for Trajectory Tracking of Nonlinear Systems

In this paper, an event-triggered sliding mode control approach for trajectory tracking problem of nonlinear input affine system with disturbance has been proposed. A second order robotic manipulator system has been modeled into a general nonlinear input affine system. Initially, the global asymptotic stability is ensured with conventional periodic sampling approach for reference trajectory tracking. Then the proposed approach of event-triggered sliding mode control is discussed which guarantees semi-global uniform ultimate boundedness. The proposed control approach guarantees non-accumulation of control updates ensuring lower bounds on inter-event triggering instants avoiding Zeno behavior in presence of the disturbance. The system shows better performance in terms of reduced control updates, ensures system stability which further guarantees optimization of resource usage and cost. The simulation results are provided for validation of proposed methodology for tracking problem by a robotic manipulator. The number of aperiodic control updates is found to be approximately 44% and 61% in the presence of constant and time-varying disturbances respectively.     

Continuous Finite‐Time Sliding Mode Control for Uncertain Nonlinear Systems with Applications to DC‐DC Buck Converters

This paper investigates the continuous finite‐time control problem of high‐order uncertain nonlinear systems with mismatched disturbances through the terminal sliding mode control method. By constructing a novel dynamic terminal sliding manifold based on the disturbance estimations of high‐order sliding mode observers, a continuous finite‐time terminal sliding mode control method is developed to counteract mismatched disturbances. To avoid discontinuous control action, the switching terms of a dynamic terminal sliding manifold are designed to appear only in the derivative term of the control variable. To validate its effectiveness, the proposed control method is applied to a DC‐DC buck converter system. The experimental results show the proposed method exhibits better control performance than a chattering free controller, such as mismatched disturbances rejection and smaller steady‐state fluctuations.     

挖掘机轨迹跟踪的滑模变结构控制

对液压挖掘机工作装置的轨迹跟踪进行了研究。在分析了液压挖掘机工作装置的动力学方程的基础上,针对其复杂的非线性,提出了一种新的液压挖掘机工作装置轨迹跟踪方法,即应用机器人学理论,建立了三自由度液压挖掘机工作装置的拉格朗日动力学模型,设计了带低通滤波器的滑模控制器,利用低通滤波器的滤除高频信号的功能,消除控制信号的抖动,给出沿规划轨迹工作所需的控制量,并给出了控制系统的设计方法。对三自由度工作装置进行了仿真研究,其结果表明,所设计的控制器对设定轨迹的跟踪具有良好的动态特性,对系统的不确定性具有较强的鲁棒性,在存在模型误差和外部扰动的情况下,该方案既能达到高精度快速跟踪的目的,又能消除滑模控制的抖动问题。     

智能车辆的滑模轨迹跟踪控制

智能车辆是集各种机械装置、传感器、计算机于一体的复杂非线性系统,其轨迹跟踪控制器是研究的关键技术之一。针对高速自主导航智能车辆轨迹跟踪控制器鲁棒性、精确性和实时性的高要求,在智能车辆结构组成与运动模型基础上,设计了一种滑模变结构控制器。通过控制智能车辆的线速度和角速度实现智能车辆对任意路径的跟踪,并用Matlab进行了仿真实验。结果验证了该方法的有效性和可靠性。     

Sum‐of‐Squares‐Based Finite‐Time Adaptive Sliding Mode Control of Uncertain Polynomial Systems With Input Nonlinearities

This paper proposes a novel adaptive sliding mode control (ASMC) for a class of polynomial systems comprising uncertain terms and input nonlinearities. In this approach, a new polynomial sliding surface is proposed and designed based on the sum‐of‐squares (SOS) decomposition. In the proposed method, an adaptive control law is derived such that the finite‐time reachability of the state trajectories in the presence of input nonlinearity and uncertainties is guaranteed. To do this, it is assumed that the uncertain terms are bounded and the input nonlinearities belong to sectors with positive slope parameters. However, the bound of the uncertain terms is unknown and adaptation law is proposed to effectively estimate the uncertainty bounds. Furthermore, based on a novel polynomial Lyapunov function, the finite‐time convergence of the sliding surface to a pre‐chosen small neighborhood of the origin is guaranteed. To eliminate the time derivatives of the polynomial terms in the stability analysis conditions, the SOS variables of the Lyapunov matrix are optimally selected. In order to show the merits and the robust performance of the proposed controller, chaotic Chen system is provided. Numerical simulation results demonstrate chattering reduction in the proposed approach and the high accuracy in estimating the unknown parameters.     

机械臂卷积神经网络滑模轨迹跟踪控制

针对工业技术的发展对于多关节机械臂的精度与快速控制高要求,提出了一种机械臂卷积神经网络滑模轨迹跟踪控制方法。分析机械臂动力学方程,提取其中的不确定部分,针对不确定部分,构建深度卷积神经网络对其进行补偿,将补偿部分引入到滑模控制律中,通过改进后的滑模控制实现对机械臂轨迹跟踪的精确控制,并通过构建Lyapunov函数论证了系统的稳定性。仿真结果显示该方法能够满足轨迹跟踪要求,且减小了抖振现象。通过与其余三种典型控制方法的对比,测试结果表明,该方法加快了轨迹跟踪误差的收敛,且跟踪精度有了明显的提高。     

On Finite‐Time Stabilization of Active Disturbance Rejection Control for Uncertain Nonlinear Systems

This paper designs the active disturbance rejection control (ADRC) to achieve finite‐time stabilization for a class of uncertain nonlinear systems. The proposed control incorporates both an extended state observer (ESO) as well as an adaptive sliding mode controller. The ESO is utilized to estimate the full system states and the total uncertainties, and the adaptive strategy is incorporated to deal with the estimation errors. It is proved that, with the application of the proposed control law, semi‐global finite‐time stabilization can be achieved. Effectiveness of the proposed method is illustrated with a numerical example.     

Straight‐Line Tracking Control of an Agricultural Vehicle with Finite‐Time Control Technique

For the agricultural vehicle straight‐line tracking system, three control algorithms based upon the finite‐time control technique have been proposed to force the vehicle to track a straight line. Without considering the lumped disturbance, a backstepping‐like finite‐time state‐feedback controller is first developed. On this basis, an adaptive state‐feedback controller in conjunction with integral sliding mode is further developed in the presence of the lumped disturbance. Finally, a sliding mode disturbance observer is given to estimate the lumped disturbance, and the composite control scheme is presented. Under the composite controller, the lumped disturbance can be compensated and thus the disturbance rejection property has been significantly improved. Simulation results verify the proposed control algorithms.     

Finite‐Time Optimal Tracking Control for Dynamic Systems on Lie Groups

This paper investigates the problem of finite‐time optimal tracking control for dynamic systems on Lie groups for the situation when the tracking time and/or the cost functions need to be considered. The specific results are illustrated on SE(3) (the specific Euclidean groups of rigid body motions). The tracking time is given according to task requirements in advance. By using Pontryagin's maximum principle (PMP) on Lie groups and the backstepping method, a finite‐time optimal tracking control law is designed to track a desired reference trajectory at the given time. Simultaneously, the corresponding cost functions are guaranteed to be optimal. Compared with existing results of optimal control on Lie groups, it is noteworthy that we consider the finite‐time tracking control for dynamic systems rather than kinematic systems. Furthermore, the obtained optimal control law is described by explicit formulations, which is significant for practical applications.     

广义不确定系统的模糊滑模控制*

研究了广义不确定系统的模糊滑模控制问题。控制结构中采用模糊系统来补偿动态不确定性,利用李亚普诺夫理论,证明了闭环系统的所有状态是全局有界的。     

直线电机轨迹跟踪系统快速终端滑模控制

为提高永磁同步直线电机伺服系统的控制精度和鲁棒性,满足高速度高精度运动控制系统的要求,提出了一种快速终端滑模控制方法并建立了电机系统数学模型.分析和证明该控制算法的稳定性和鲁棒性.与传统的滑模控制方法相比,该算法确保了系统状态在平衡点邻域内具有更快的收敛速度,并最终收敛至平衡点.通过选择控制算法中合适的参数值,系统可达...     

不确定时滞分布参数系统的滑动模控制

本文研究一类不确定时滞分布参数系统的滑动模控制问题，设计了滑动模控制器，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。     

A Novel Sliding Mode Control for a Class of Second‐order Mechanical Systems

This paper considers the tracking control problem of a class of second‐order mechanical systems involving parametric uncertainty and external disturbance by a sliding mode control (SMC) without reaching phase. Specifically, an SMC strategy with modified variable‐gain proportional–integral–derivative (PID)‐type sliding function is proposed, by which the existence of a sliding mode throughout an entire response of the system starting from the initial time instance is ensured. Meanwhile, the introduction of a variable gain in the sliding function design effectively solves the dilemma between quicker response and smaller overshoot. The effectiveness of the proposed strategy is verified by both theoretical analysis and simulation results.     

非线性不确定大系统的分散滑动模控制

本文研究一类非线性不确定大系统的分散滑动模控制问题．首先给出了使滑动模具有良好动态品质的分散切换流形的设计方法；然后给出了一种基于不确定因素已知变化范围的分散滑动模控制器设计方法，该方法只需对各孤立子系统进行降阶滑动模的极点配置及求解降阶Ｌｙａｐｕｎｏｖ矩阵方程即可；最后以一具体例子说明其设计过程。     

Chattering Free Sliding Mode Control for Uncertain Discrete Time‐Delay Singular Systems

The problem of chattering free sliding mode control for a class of uncertain discrete singular systems with state delay is investigated in this paper. As a component of the solution, a new least squares support vector machine (LS‐SVM) reaching law is proposed. In terms of linear matrix inequalities, a delay‐dependent condition for sliding mode dynamics to be regular, causal, and asymptotically stable is established, and the chattering problem that appears in traditional variable structure systems is eliminated. Numerical examples are provided to demonstrate the applicability of the proposed methods.     

Sliding Mode Control for Uncertain Switched Systems with Partial Actuator Faults

This paper considers the sliding mode control for a class of uncertain switched systems with partial actuator faults. By employing a weighted sum of the input matrices, a common integral sliding surface is designed. Moreover, the exponential stability of the sliding mode dynamics is analyzed by adopting the multiple Lyapunov function method and the average dwell time strategy. It is shown that the state trajectory can be driven onto the proposed sliding surface despite the presence of parameter uncertainties, external disturbances, and actuator faults. A numerical example is given to demonstrate the effectiveness of the proposed method.     

具有分布时滞不确定中立型系统的滑模控制

针对一类含有分布时滞和不满足匹配条件的不确定中立型系统,通过利用Lya-punov稳定性理论和线性矩阵不等式(LMI)方法进行了滑模控制研究。首先,选取了依赖于当前状态和状态时滞的滑模面;设计了包含等效控制和非线性切换控制的滑模控制器使得系统满足滑模到达条件,即确保了系统在有限时间内到达滑模面。通过构造适当的Lyapunov函数,利用积分不等式技术,给出了闭环系统渐近稳定的充分条件。该充分条件通过采用虚拟反馈控制思想,结合状态反馈的极点配置方法,转换为线性矩阵不等式的形式,可通过Matlab中的LMI工具箱进行方便的求解。具体算例说明此方法的有效性。     

Adaptive Chattering Free Neural Network Based Sliding Mode Control for Trajectory Tracking of Redundant Parallel Manipulators

In this paper, an adaptive chattering free neural network‐based sliding mode control (ACFN‐SMC) method is proposed for tracking trajectories of redundant parallel manipulators. ACFN‐SMC combines adaptive chattering free radial basis function neural networks (RBFN), sliding mode control with online updating the robust term parameters, and a nonlinear compensation item for reducing tracking errors. The stability of the closed‐loop system with modeling uncertainties, frictional uncertainties, and external disturbances is ensured by using the Lyapunov method. The proposed controller has a simple structure and little computation time while securing dynamic performance with expected quality in tracking trajectories of redundant parallel manipulators. In addition, the ACFN‐SMC strategy does not need to know the upper bound of any uncertainties. From the simulation results, it is evident that the proposed control strategy not only has significantly higher robustness capability for uncertainties but also can achieve better chattering elimination when compared with those using existing intelligent control schemes.     

Uncertain Saturated Discrete‐Time Sliding Mode Control for A Wind Turbine Using A Two‐Mass Model

The aim of this paper is to propose a new design variable speed wind turbine control by discrete‐time sliding mode approach. The control objective is to obtain a maximum extraction of wind energy, while reducing mechanical loads and rotor speed tracking combined with an electromagnetic torque. For this application, we designed a discrete time sliding mode control using the equivalent discrete time reaching law. Furthermore, a systematic and improved design procedure for uncertainties discrete‐time sliding mode control (SMC) with saturation problem is provided in this paper. The saturation constraint is reported on inputs vector. LMI technique and polytopic models are used in the design of the switching surface. To achieve some performance requirements and good robustness, in the sliding mode, the pole clustering method is investigated. Based on the unit vector control approach, a robust control is developed, then, to direct and maintain the system states onto the sliding manifold in finite time. Finally, a systematic design procedure for DSMC required to achieve a given performance level is provided and its effectiveness is varied by applying it to variable speed wind turbine systems.     

移动机器人轨迹跟踪快速终端滑模自抗扰控制

针对移动机器人动力学模型难以精确建立、运动过程中各种干扰对高精度轨迹跟踪造成偏航等问题,构造出一种快速终端滑模自抗扰控制器,实现了高速高精度轨迹跟踪控制目标。首先建立非完整移动机器人的干扰控制模型;然后运用扩张状态观测器实时监测系统未建模动态与各种干扰;同时将扩张状态量和系统反馈量作为快速终端滑模算法的系统变量;最后设计出一种快速终端滑模控制律,代替传统自抗扰算法中的非线性控制律,从而实现位姿的快速精确跟踪。该算法既克服了非线性误差控制律中参数繁杂不易整定的缺陷,又增强了系统鲁棒性和轨迹跟踪的动态品质。对比仿真实验验证了该控制算法的有效性和先进性。