Adaptive sliding mode control with moving sliding surface

A continuous sliding mode control with moving sliding surface for nonlinear systems of arbitrary order is presented in this paper. The sliding surface is moved repetitively toward the target sliding surface in order to ensure that the system trajectory is close to the actual surface during the whole control process. The parameters of sliding mode control are tuned by a fuzzy logic. The proposed procedure reduces the time when the system operates in the approaching phase during which the control performance is deteriorated since the system is more susceptible to external disturbances and model uncertainties. The effectiveness of the presented approach is demonstrated on a control of a flexible robot manipulator arm.     

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.     

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.     

Application of intelligent sliding mode control with moving sliding surface for overhead cranes

In this paper, neural-based fuzzy logic sliding mode control with moving sliding surface has been designed for supervision of an overhead crane. A mathematical model has been established of the crane, and equations of motion have been obtained. First, the suitable sliding surface coefficient has been determined for the fixed sliding surface in the design of sliding mode control. The sliding surface has been moved by using neural-based fuzzy logic algorithm to eliminate disadvantage of the regular sliding mode control. By application of this control algorithm, the control performance incredibly increased. In the application, during the carriage of the load to a target which was 1 m away by a crane with 3 kg of load and 100 cm of rope length, the parameters of effected controllers were updated and their training was realized. In order to display the insensitiveness of the controller to parametric uncertainty, the value of the load was taken as 8 kg and the length of the rope was taken as 3 m and controls for a different target were realized. MATLAB program was used for numerical solutions, and results were examined graphically. Obtained results displayed the success of the algorithm of neural-based fuzzy logic sliding mode control.     

Design of sliding mode control for a class of uncertain switched systems

This paper considers the problem of sliding mode control for a class of uncertain switched systems with parameter uncertainties and external disturbances. A key feature of the controlled system is that each subsystem is not required to share the same input channel, which was usually assumed in some existing works. By means of a weighted sum of the input matrix, a common sliding surface is designed in this work. It is shown that the reachability of the sliding surface can be ensured by the present sliding mode controller. Moreover, the sliding motion on the specified sliding surface is asymptotically stable under the proposed switching signal dependent on the state and time. Additionally, the above results are further extended to the case that the system states are unavailable. Both the sliding surface and sliding mode controller are designed by utilising state-observer. Finally, numerical simulation examples are given to illustrate the effectiveness of the present method.     

Synthesized sliding mode and time-delay control for a class of uncertain systems

In this note, the sliding mode control (SMC) is incorporated with time-delay control (TDC) during the sliding phase to reduce the switching gain. TDC identifies the unknown system dynamics and disturbance directly for every time-delay. For a system with a lumped perturbation which is relatively slow varying with respect to the sampling interval, a much low switching gain can be used if a reasonably good estimate of the derivative of system state can be obtained using the past information, hence chattering can be reduced or eliminated while retaining the tracking accuracy.     

一类非确定欠驱动系统的串级模糊滑模控制

本文针对一类含有非确定项的欠驱动系统提出了一种串级模糊滑模控制方法.该方法先选取状态变量中两个相关联的系统状态构造第一级滑动平面,然后将第一级滑模函数作为一个广义状态,与剩下系统状态中的一个状态构造第二级滑动平面,直到所有的系统状态都包含在内构造最后一级滑动平面.同时考虑到系统模型中存在的不确定项,利用模糊逻辑的逼近功能进行估计,文中采用Lyapunov方法求取了控制器的控制律以及模糊逼近的有关参数的自适应律.该串级模糊滑模控制器能够保证各级滑动平面的稳定性,并且在仿真实验中得到了验证.     

Multi-input sliding mode control of a class of uncertain nonlinearsystems

An effective way to extend to the multi-input case the variable structure control philosophy is based on a set of m+1 control vectors forming a simplex in R^m and on the corresponding switching of the controlled system from one to another of m+1 different structures. Yet, some problems arise when uncertainties are present in certain matrices characterizing the controlled systems. In this paper, conditions are identified under which, even in the presence of uncertainty, the convergence to the sliding manifold is ensured via the application of a multi-input control strategy still based on a simplex of control vectors     

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．     

一类不确定非线性系统的改进积分型滑模控制

针对一类不确定非线性系统的传统滑模控制,推导了滑模误差和稳态误差的范围．为了减小系统的稳态误差,同时防止积分饱和,设计了一种改进积分型滑模面．在边界层外,通过调节因子对积分项进行削弱,以防止在初始误差较大的条件下积分饱和引起的超调较大和调节时间较长的问题;在边界层内,采用传统积分以减小系统稳态误差．理论分析和仿真研究表明了所提改进积分型滑模控制方法的有效性．     

A frequency-shaping methodology for discrete-time sliding mode control

This paper proposes a frequency shaping methodology for performance enhancement of discrete-time sliding mode control for systems with narrow band disturbances. This approach augments the sliding mode surface as a dynamic feedback system and designs an ‘optimal’ shaping filter in the feedback loop based on H-infinity synthesis, which assures both the stability and the desired frequency-response characteristics of the sliding mode surface. Furthermore, this frequency-shaping technique is advanced to be parameter-dependent to improve the efficiency and flexibility. The methodology enables the design of sliding mode control in frequency domain, which is critically important for high-precision systems that are subjected to high-frequency disturbances. The proposed frequency-shaped sliding mode control is applied onto a hard disk drive in the presence of vibrations with multiple peak frequencies; effective vibration suppression is demonstrated through comprehensive simulation study.     

A class of proportional-integral sliding mode control with application to active suspension system

The purpose of this paper is to present a new robust strategy in controlling the active suspension system. The strategy utilized the proportional-integral sliding mode control scheme. A quarter-car model is used in the study and the performance of the controller is compared to the linear quadratic regulator and with the existing passive suspension system. A simulation study is performed to prove the effectiveness and robustness of the control approach.     

A novel adaptive high-order sliding mode control based on integral sliding mode

This paper presents an adaptive high-order sliding mode control scheme targeting for uncertain minimum phase nonlinear single-input-single-output (SISO) systems, which can be equivalently formulated as the finite-time stabilization of high-order input-output dynamics subject to the uncertainties of parameters such as a chain of integrators. The proposed controller is derived from the concept of integral sliding mode and consists of two parts, one part of which achieves the finite-time stabilization of the high-order input-output dynamics without uncertainties by solving a finite-horizon optimal control problem with a free-final-state. The other part adopts the adaptive sliding mode control technique considering the practical bounded uncertainties, by which a modified switching gain adaptation algorithm is developed so that the on-line switching gain selection can be executed and the upper bounds of the uncertainties are not requisite in advance. As a result, a high-order sliding mode is established, ensuring the sliding variables and its high-order derivatives converge to an arbitrarily small vicinity of the origin in finite time. Therefore, the proposed controller achieves fixed convergence time and further improves strong robustness against bounded uncertainties with lower chattering and the easy implementation. Simulation results are presented in detail to verify the effectiveness and feasibility of the proposed algorithm.     

一类MIMO非线性系统的直接自适应模糊滑模控制

针对一类具有下三角形函数控制增益矩阵的非线性系统, 基于滑模控制原理, 并利用Ⅱ型模糊系统的逼近能力, 提出了一种直接自适应模糊滑模控制器设计的新方案. 通过引入积分型李雅普诺夫函数及逼近误差自适应补偿项, 证明了闭环系统是全局稳定的, 跟踪误差收敛到零. 仿真结果表明了该方法的有效性.     

一类不确定线性切换系统的鲁棒H∞滑模控制

对一类含有非匹配不确定性且有外部干扰的线性切换系统,研究了H∞滑模变结构控制问题.利用LMI技术和单Lyapunov函数方法,设计单H∞滑模面,切换律以及子系统的变结构控制器,确保了切换系统的闭环系统为鲁棒稳定,且具有H∞扰动衰减度γ.系统状态到达滑模面后,该滑模面成为切换系统的全局鲁棒滑模面,可提高系统的暂态性能和鲁棒性.仿真例子说明所提出设计方法的有效性.     

一类不确定非线性系统自适应模糊滑模控制

针对一类带有未知外部扰动的不确定非线性系统,建立自适应模糊滑模控制器。基于Lyapunov稳定性理论,设计系统可调参数的自适应规则,控制器的设计过程中无需知道系统的具体模型及未知非线性函数的先验知识。数值仿真的结果也验证了该方法的有效性。     

New approaching condition for sliding mode control design with Lipschitz switching surface

In this paper, we concern the approaching condition of sliding mode control (SMC) with a Lipschitz switching surface that may be nonsmooth. New criteria on the relation between phase trajectories and an arbitrary Lipschitz continuous surface are examined firstly. Filippov’s differential inclusion is adopted to describe the dynamics of trajectories of the closed-loop system with SMC. Compared with Filippov’s criteria for only smooth surface, new criteria are proposed by utilizing the cone conditions that allow the surface to be nonsmooth. This result also yields a new approaching condition of SMC design. Based on the new approaching condition, we develop the sliding mode controller for a class of nonlinear single-input single-output (SISO) systems, of which the switching surface is designed Lipschitz continuous for the nonsmooth sliding motion. Finally, we provide a numerical example to verify the new design method.     

机器人的低通滤波滑模控制

滑模控制响应快,对系统参数和外部扰动呈不变性,可保证系统的渐进稳定性,但其缺点是控制存在很强的抖动。在一般滑模控制的基础上引入低通滤波器（LPF）,则保证了轨迹跟踪误差的快速收敛,同时使系统具有很强的鲁棒性。通过对两连杆机械手的仿真研究,表明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。     

A decoupled sliding mode control for a continuum arm

The paper treats the control problem of a class of robots constituted by a chain of continuum segments. The technological model basis is a central, long and thin, highly flexible and elastic backbone. The segment control system is a decoupled one. The main parameters of the arm control are determined by the curvature and curvature gradient. The dynamic model is inferred. The primary benefit of the proposed method is that the dynamic equations are represented by a set of ODE’s in time instead of PDE’s in time and space, and the new curvature gradient lumped parameter model is used. A sliding mode control system is used in order to achieve the desired shape of the arm. The stability of the closed-loop control system is proven. Numerical simulations and an experimental platform are also provided to verify the effectiveness of the presented approach.     

A state-dependent boundary layer design for sliding mode control

The use of a boundary layer in sliding-mode control has been a common technique to reduce chattering of the control signal. However, different choices of the boundary layer width lead to conflicting effects: a large/small boundary layer width can more/less effectively alleviate the chattering phenomenon, but leads to less/more accurate control results. This note proposes online adjusting the width of the boundary layer based on the state norm for an uncertain linear system. The proposed state-dependent boundary layer design can effectively eliminate chattering while at the same time ensuring almost perfect control accuracy.