不满足匹配条件的非确定性系统的鲁棒滑模控制

针对一类非确定性时变系统实施滑模控制,该系统在状态矩阵和控制输入矩阵中都 包含不满足匹配条件的不确定项.给出了能使系统鲁棒镇定的切换面设计方法和相应的控制 律的形式.同时,也给出了系统渐近稳定的充分条件.设计过程中的代数黎卡提方程和线性矩 阵不等式形式简单,易于求解.仿真结果证明了理论的正确性.     

Quasi sliding mode‐based single input fuzzy self‐tuning decoupled fuzzy PI control for robot manipulators with uncertainty

This paper presents a robust adaptive control strategy for robot manipulators, based on the coupling of the fuzzy logic control with the so‐called sliding mode control (SMC) approach. The motivation for using SMC in robotics mainly relies on its appreciable features. However, the drawbacks of the conventional SMC, such as chattering effect and required a priori knowledge of the bounds of uncertainties can be destructive. In this paper, these problems are suitably circumvented by adopting a reduced rule base single input fuzzy self tuning decoupled fuzzy proportional integral sliding mode control approach. In this new approach a decoupled fuzzy proportional integral control is used and a reduced rule base single input fuzzy self‐tuning controller as a supervisory fuzzy system is added to adaptively tune the output control gain of the decoupled fuzzy proportional integral control. Moreover, it is proved that the fuzzy control surface of the single‐input fuzzy rule base is very close to the input/output relation of a straight line. Therefore, a varying output gain decoupled fuzzy proportional integral sliding mode control approach using an approximate line equation is then proposed. The stability of the system is guaranteed in the sense of the Lyapunov theorem. Simulations using the dynamic model of a 3DOF planar manipulator with uncertainties show the effectiveness of the approach in high speed trajectory tracking problems. The simulation results that are compared with the results of conventional SMC indicate that the control performance of the robot system is satisfactory and the proposed approach can achieve favorable tracking performance, and it is robust with regard to uncertainties and disturbances. Copyright © 2011 John Wiley & Sons, Ltd.     

Event-triggered sliding mode control for a class of nonlinear systems

ABSTRACT

Event-triggering strategy is one of the real-time control implementation techniques which aims at achieving minimum resource utilisation while ensuring the satisfactory performance of the closed-loop system. In this paper, we address the problem of robust stabilisation for a class of nonlinear systems subject to external disturbances using sliding mode control (SMC) by event-triggering scheme. An event-triggering scheme is developed for SMC to ensure the sliding trajectory remains confined in the vicinity of sliding manifold. The event-triggered SMC brings the sliding mode in the system and thus the steady-state trajectories of the system also remain bounded within a predesigned region in the presence of disturbances. The design of event parameters is also given considering the practical constraints on control execution. We show that the next triggering instant is larger than its immediate past triggering instant by a given positive constant. The analysis is also presented with taking delay into account in the control updates. An upper bound for delay is calculated to ensure stability of the system. It is shown that with delay steady-state bound of the system is increased than that of the case without delay. However, the system trajectories remain bounded in the case of delay, so stability is ensured. The performance of this event-triggered SMC is demonstrated through a numerical simulation.     

Fuzzy sliding mode control for a robot manipulator

This work presents the design of a robust control system using a sliding mode controller that incorporates a fuzzy control scheme. The presented control law superposes a sliding mode controller and a fuzzy logic controller. A fuzzy tuning scheme is employed to improve the performance of the control system. The proposed fuzzy sliding mode control (FSMC) scheme utilizes the complementary cooperation of the traditional sliding mode control (SMC) and the fuzzy logic control (FLC). In other words, the proposed control scheme has the advantages which it can guarantee the stability in the sense of Lyapunov function theory and can ameliorate the tracking errors, compared with the FLC and SMC, respectively. Simulation results for the trajectory tracking control of a two-link robot manipulator are presented to show the feasibility and robustness of the proposed control scheme. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

Chaos control and synchronization via a novel chatter free sliding mode control strategy

In this paper, we propose a novel chatter free sliding mode control (SMC) strategy for chaos control and synchronization to the nonlinear uncertain chaotic systems. A new sort of dynamical sliding mode surface with both integral and differential operators is introduced to divert the discontinuous sign function switch term into the first derivative of the control input; hence a chatter free control input is obtained for the chaotic systems with uncertainties. Based on the Lyapunov stability theory and SMC technique, stability analysis is performed and a theorem serving as designing the chatter free sliding mode control input is also proposed. In the simulation part, first, the results regarding chaos control and synchronization are given to show that the proposed strategy can control the states of the uncertain chaotic systems to desired states with fast speed. In order to show the advantage of eliminating chatter in control input of our method, we give the simulation results performed by traditional SMC and the method proposed recently. Simulation results indicate that this novel chatter free sliding mode control strategy is very effective to chaos control and synchronization.     

Anti-synchronization of four-wing chaotic systems via sliding mode control

Sliding mode control is an important method used in nonlinear control systems. In robust control systems, the sliding mode control is often adopted due to its inherent advantages of easy realization, fast response and good transient performance as well as its insensitivity to parameter uncertainties and disturbances. In this paper, we derive new results based on the sliding mode control for the anti-synchronization of identical Qi three-dimensional (3D) four-wing chaotic systems (2008) and identical Liu 3D four-wing chaotic systems (2009). The stability results for the anti-synchronization schemes derived in this paper using sliding mode control (SMC) are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the SMC method is very effective and convenient to achieve global chaos anti-synchronization of the identical Qi four-wing chaotic systems and identical Liu four-wing chaotic systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper.     

Robust sliding mode control using adaptive switching gain for induction motors

A robust sliding mode approach combined with a field oriented control （FOC） for induction motor （IM） speed control is presented. The proposed sliding mode control （SMC） design uses an adaptive switching gain and an integrator. This approach guarantees the same robustness and dynamic performance of traditional SMC algorithms. And at the same time, it attenuates the chattering phenomenon, which is the main drawback in actual implementation of this technique. This approach is insensitive to uncertainties and permits to decrease the requirement for the bound of these uncertainties. The stability and robustness of the closed- loop system are proven analytically using the Lyapunov synthesis approach. The proposed method attenuates the effect of both uncertainties and external disturbances. Experimental results are presented to validate the effectiveness and the good performance of the developed method.     

约束非线性系统的滑模预测控制方法

将预测控制和滑模控制结构起来,提出一种新的非线性模型预测控制方法,通过对系统状态预测得到切换函数预测值,求解约束开环优化求得预测控制律,并将当前时刻的控制作用于对象,下一时刻重复此过程,该方法具有预测控制在线处理约束及滑模控制滑动模态对干扰的不变性的优点,分析了零终端滑模约束模型预测控制的稳定性。     

Augmented Sliding Mode Control for Flexible Link Manipulators

A method of sliding mode control (SMC) is proposed for the control of flexible, nonlinear, and structural systems. The method departs from standard sliding mode control by dispensing with generalized accelerations during the control law design. Global, asymptotic stability of rigid body motion is maintained if knowledge on the bounds of the neglected terms exists. Furthermore, this method provides damping for the measured flexible body modes. This paper investigates an augmented SMC technique for slewing flexible manipulators. A conventional sliding surface uses a first order system including a combination of error and error rate terms. The augmented sliding surface includes an enhanced term that helps to reject flexible degrees-of-freedom. The algorithms are theoretically developed and experimentally tested on a slewing single flexible link robot. The test apparatus is instrumented with a strain gauge at the root and an accelerometer attached at the tip. A DC motor and encoder are used to servo the link from an initial position to a final position. A standard cubic polynomial is employed to generate the reference trajectories. The augmented SMC algorithm showed improved performance by reducing the flexible link tip oscillations.     

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.     

机械手的模糊逆模型鲁棒控制

提出一种基于模糊聚类和滑动模控制的模糊逆模型控制方法,并将其应用于动力学 方程未知的机械手轨迹控制.首先,采用C均值聚类算法构造两关节机械手的高木-关野 (T-S)模糊模型,并由此构造模糊系统的逆模型.然后,在提出的模糊逆模型控制结构中, 离散时间滑动模控制和时延控制(TDC)用于补偿模糊建模误差和外扰动,保证系统的全局 稳定性并改进其动态和稳态性能.系统的稳定性和轨迹误差的收敛性可以通过稳定性定理来 证明.最后,以两关节机械手的轨迹跟随控制为例,揭示了该设计方法的控制性能.     

不确定输入延时网络系统的鲁棒拥塞控制

基于滑模控制（SMC）设计了一种主动队列管理（AQM）算法,该算法可保证具有有界的不确定输入延时网络系统渐进稳定.引入一种状态变换来消除延时的影响,通过Lyapunov稳定性分析,给出了保证系统渐进稳定的最大允许的延时边界.仿真结果表明,该方法可以获得良好的暂态和稳态响应,在网络条件变化的情况下,该算法优于传统的PI控制和滑模控制.     

Second-order Sliding Mode Approaches for the Control of a Class of Underactuated Systems

In this paper, first-order and second-order sliding mode controllers for underactuated manipulators are proposed. Sliding mode control(SMC) is considered as an effective tool in different studies for control systems. However, the associated chattering phenomenon degrades the system performance. To overcome this phenomenon and track a desired trajectory, a twisting, a supertwisting and a modified super-twisting algorithms are presented respectively. The stability analysis is performed using a Lyapunov function for the proposed controllers. Further, the four different controllers are compared with each other. As an illustration, an example of an inverted pendulum is considered. Simulation results are given to demonstrate the effectiveness of the proposed approaches.     

Model-independent position domain sliding mode control for contour tracking of robotic manipulator

In this paper, a new position domain feedback type sliding mode control (PDC-SMC) law is proposed for contour tracking control of multi-DOF (degree of freedom) nonlinear robotic manipulators focusing on the improvement of contour tracking performances. One feature of the proposed control law is its model-independent control scheme that can avoid calculation of the feedforward part in a standard SMC. The new control law takes the advantages of the high contour tracking performance of PD type feedback position domain control (PDC) and the robustness of SMC. Stability analysis is performed using the Lyapunov stability theory, and simulation studies are conducted to verify the effectiveness of the developed PDC-SMC control system. In addition, the effects of control parameters of the SMC on system performances are studied.     

Sliding mode control and active disturbance rejection control to the stabilization of one‐dimensional Schrödinger equation subject to boundary control matched disturbance

In this paper, we are concerned with the boundary stabilization of a one‐dimensional anti‐stable Schrödinger equation subject to boundary control matched disturbance. We apply both the sliding mode control (SMC) and the active disturbance rejection control (ADRC) to deal with the disturbance. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of the solution for the closed‐loop system is proved and the ‘reaching condition’ is obtained. Considering the SMC usually requires the large control gain and may exhibit chattering behavior, we develop the ADRC to attenuate the disturbance for which the derivative is also supposed to be bounded. Compared with the SMC, the advantage of the ADRC is not only using the continuous control but also giving an online estimation of the disturbance. It is shown that the resulting closed‐loop system can reach any arbitrary given vicinity of zero as time goes to infinity and high gain tuning parameter goes to zero. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive sliding mode control for MIMO nonlinear systems based on fuzzy logic scheme

In this study an indirect adaptive sliding mode control (SMC) based on a fuzzy logic scheme is proposed to strengthen the tracking control performance of a general class of multi-input multi-output (MIMO) nonlinear uncertain systems. Combining reaching law approach and fuzzy universal approximation theorem, the proposed design procedure combines the advantages of fuzzy logic control, adaptive control and sliding mode control. The stability of the control systems is proved in the sense of the Lyapunov second stability theorem. Two simulation studies are presented to demonstrate the effectiveness of our new hybrid control algorithm.     

不确定线性2-D 离散系统的鲁棒滑模控制

针对不确定线性离散二维（2-D）系统,研究了其鲁棒稳定性、鲁棒镇定和鲁棒滑模控制问题.基于线性矩阵不等式的方法推导了该系统鲁棒渐近稳定的充分条件,并给出了系统状态反馈镇定器和理想滑动模态存在的充分条件.改进了离散时间滑模控制系统的趋近律方法,使得状态能够到达滑模面上产生理想的滑动模态,并将其推广应用到2-D离散系统中,综合了一类滑模控制器保证闭环系统鲁棒渐近稳定.仿真实例证实了该设计方法的有效性.     

Fractional-order sliding mode control for a novel magneto-electro-elastic microtube robot

In this paper, a tracking controller based on a non-integer sliding surface is proposed for a magneto-electro-elastic (MEE) fluid-conveying microtube robot. The smart/adaptive MEE material enables us to control the robot with no need for external sensors and actuators. The micro-robot lateral motion is modeled by Euler–Bernoulli beam equations. The governing equation of the robot is derived using the constitutive equations of MEE materials and Maxwell's principle followed by Hamilton's variational method. Based on the extracted dynamic model, a novel non-integer order sliding mode controller is introduced to suppress the microtube vibration and to provide robust path following for the robot tip. This control approach is compatible with the parameter-varying nature of the robot dynamics. Theoretical analyses, based on Lyapunov theory, are also conducted to verify the stability of the closed-loop system. Comparative simulations are finally performed to show the efficiency of the proposed system in comparison with the conventional micro tubes made of smart materials and with an integer order sliding mode controller (SMC). The results demonstrate that the proposed robot properly meets the performance requirements in terms of vibration suppression and trajectory tracking, even in the presence of disturbances.     

挠性航天器鲁棒后步滑模姿态跟踪及主动振动控制

针对挠性航天器姿态跟踪及振动抑制问题,提出一种双回路鲁棒控制方法.首先,采用滑模控制与后步法设,计了姿态跟踪控制器,基于Lyapunov方法分析系统的渐近稳定性,并从实际应用角度考虑了反作用飞轮的动态特性;其次,为抑制挠性结构的振动,采用压电智能材料作为敏感器和作动器,设计了应变速率反馈补偿器.仿真结果表明,所提方法在保证完成姿态跟踪任务的同时,能有效抑制挠性附件的振动.     

Boundary stabilization of a cascade of ODE‐wave systems subject to boundary control matched disturbance

In this paper, we are concerned with a cascade of ODE‐wave systems with the control actuator‐matched disturbance at the boundary of the wave equation. We use the sliding mode control (SMC) technique and the active disturbance rejection control method to overcome the disturbance, respectively. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of solution for the closed‐loop via SMC are proved, and the monotonicity of the ‘reaching condition’ is presented without the differentiation of the sliding mode function, for which it may not always exist for the weak solution of the closed‐loop system. Considering that the SMC usually requires the large control gain and may exhibit chattering behavior, we then develop an active disturbance rejection control to attenuate the disturbance. The disturbance is canceled in the feedback loop. The closed‐loop systems with constant high gain and time‐varying high gain are shown respectively to be practically stable and asymptotically stable. Then we continue to consider output feedback stabilization for this coupled ODE‐wave system, and we design a variable structure unknown input‐type state observer that is shown to be exponentially convergent. The disturbance is estimated through the extended state observer and then canceled in the feedback loop by its approximated value. These enable us to design an observer‐based output feedback stabilizing control to this uncertain coupled system. Copyright © 2016 John Wiley & Sons, Ltd.