分数阶微积分在滑模控制中的应用研究

针对滑模控制所存在的抖振问题以及趋近问题,将分数阶微积分理论与滑模控制策略的优点相互结合,提出一种有效的分数阶趋近律.在控制器的设计过程中,将分数阶微积分引入到滑模控制中提出分数阶趋近律,并运用Lyapunov理论进行证明,从而确保系统的稳定性.将提出的控制方法应用于二关节机械臂上,进行仿真验证.结果表明:所提出的分数...     

非线性积分滑模控制方法

针对一类不确定非线性系统的滑模控制,提出了一类具有"小误差放大,大误差饱和"功能的光滑非线性饱和函数来改进传统的积分滑模控制,以形成非线性积分滑模控制.在保持传统积分滑模控制跟踪精度的同时获得更好的暂态性能.应用Lyapunov稳定性理论和LaSalle不变性原理证明了对最终常值干扰可以完全抑制.考虑控制受限时,所设计...     

精细积分在时滞车辆悬架最优控制中的应用

针对车辆悬架系统中状态和输入存在时滞的最优控制问题,结合科茨求积分和线性插值的精细积分法,将系统的状态方程引入到Hamilton体系下进行研究.依据最优滤波问题和带有时滞的观测器的双重准则,将时滞问题转换成非时滞问题,从而在全状态下对其方程进行精细积分求解.对带有时滞的114车辆悬架模型进行数值仿真,并与经典的数值算法进行比较分析.仿真结果表明,该方法具有很高的计算精确度和稳定性,并为车辆悬架系统的动力学分析提供了新的方法和手段.     

分数阶微积分在数字水印中的应用研究

提出并实现了基于分数阶微积分运算的数字水印系统模型.将分数阶微积分运算阶次v作为水印嵌入与提取的密钥,嵌入的水印能够获得好的不可感知性.在信息提取端,如果不知道确切的分数阶微积分运算阶次,将无法完成水印信息的提取,从而保证了发送者与合法接收者之间通信的有效保密性.利用Matklb进行计算机仿真实验证实了基于分数阶微积分运算的数字水印系统的有效性与可行性.     

基于输出反馈滑模控制的分数阶超混沌系统同步

以具有更大秘钥空间的分数阶超混沌系统为驱动系统和响应系统,利用具有实际应用意义的输出反馈滑模控制实现两个系统的同步.通过对同步误差系统方程进行结构分解,在辅助系统的基础上设计具有输出反馈特性的滑模控制律.在分数阶系统稳定性理论基础上利用MATLAB YALMIP工具箱对滑模参数进行整定,并利用分数阶Lyapunov稳定性定理证明了滑模控制律和自适应滑模控制律的稳定性.最后,数值仿真表明了本文方法的有效性和可行性.     

分数阶微积分在数字水印中的应用研究

提出并实现了基于分数阶微积分运算的数字水印系统模型。将分数阶微积分运算阶次v作为水印嵌入与提取的密钥,嵌入的水印能够获得好的不可感知性。在信息提取端,如果不知道确切的分数阶微积分运算阶次,将无法完成水印信息的提取,从而保证了发送者与合法接收者之间通信的有效保密性。利用Matlab进行计算机仿真实验证实了基于分数阶微积分运算的数字水印系统的有效性与可行性。     

基于Perceptron的非线性滑模控制

利用Ｐｅｒｃｅｐｔｒｏｎ的两类模式分类特性对非线性滑动模式方程的Ｌｙａｐｕｎｏｖ函数进行训练，以求得非线性的切换函数，并进行滑模控制器设计，为非线性滑模控制系统的综合设计提供了一条新的途径，并应用于车削系统中。     

一类非线性不确定系统的高阶积分自适应滑模控制

为有效改善传统积分滑模在一类非线性不确定系统的应用中存在的抖振问题,结合有限时间收敛理论、高阶积分滑模理论和自适应控制理论,提出了一种高阶积分自适应滑模控制方法;该方法通过选取有限时间收敛反馈量和设计高阶积分滑模面,不仅确保了系统状态误差在有限时间内的收敛性,而且还保证了系统具备对不确定性干扰的抑制能力;同时,当系统的不确定项的边界范围无法预先确定时,采用自适应方法对滑模控制的趋近速率进行估计;仿真结果表明所提方法能够有效抑制非线性不确定系统的抖动,并具有较高的控制精度.     

基于RBFNN观测器的车辆非线性悬架预测控制方法

传统车辆非线性悬架预测控制方法存在车身垂直加速度和能量消耗较大、悬架动扰度和车轮动载荷较高问题,悬架控制效果不理想.于是提出基于RBFNN观测器的车辆非线性悬架预测控制方法.构建四分之一非线性悬架模型,通过改进粒子群算法中的数据聚类和参数辨识,构建线性非段仿射(PWA)模型.结合RBFNN观测器和多模型控制理论研究PWA模型的滚动时域优化控制问题,获取最优控制信号,实现车辆非线性悬架预测控制.仿真结果表明,所提方法能够有效降低车身垂直加速度和能量消耗,悬架动扰度和车轮动载荷均较低.     

非匹配不确定MIMO系统的分数阶终端滑模控制

针对一类非匹配不确定多输入多输出(Multi-input multi-output, MIMO)系统提出一种分数阶终端滑模控制(Fractional-order terminal sliding-mode, FOTSM)策略, 使系统输出收敛到零而非其邻域. 该方法解除传统反步法控制律设计中, 虚拟控制增益右伪逆矩阵必须存在的严苛限制; 对系统不确定性的假设不局限于慢时变和H2范数有界型扰动, 分析控制增益存在摄动情况下系统的控制问题. 分数阶终端滑模面及其控制律的设计使得虚拟和实际控制信号连续, 削弱抖振现象, 利用自适应滑模切换增益技术解决由控制增益矩阵摄动引起的代数环问题. 最后, 仿真分析验证所提方法的正确性和优越性.     

A novel continuous fractional sliding mode control

A new fractional-order controller is proposed, whose novelty is twofold: (i) it withstands a class of continuous but not necessarily differentiable disturbances as well as uncertainties and unmodelled dynamics, and (ii) based on a principle of dynamic memory resetting of the differintegral operator, it is enforced an invariant sliding mode in finite time. Both (i) and (ii) account for exponential convergence of tracking errors, where such principle is instrumental to demonstrate the closed-loop stability, robustness and a sustained sliding motion, as well as that high frequencies are filtered out from the control signal. The proposed methodology is illustrated with a representative simulation study.     

Robust H∞ sliding mode control scheme for uncertain fractional stochastic systems: Nonlinear analysis and design

This paper investigates the $H_{\infty }$ sliding mode control (SMC) design for fractional stochastic systems. We study a very general category of stochastic systems that are nonlinear and driven by fractional Brownian motion (fBm). A robust $H_{\infty }$ SMC scheme is presented for a fractional stochastic model with external disturbance, state- and disturbance-dependent noise, and uncertainties, which ensures that the closed-loop system is stochastically stable. We propose a novel sliding surface and then prove its reachability in the state space. Furthermore, the conditions for the stochastic stability of the sliding motion are derived via nonlinear Hamilton–Jacobi (HJ)-type inequalities. In addition, an $H_{\infty }$ SMC method is developed for a special class of fractional stochastic models, and two sets of linear matrix inequality (LMI) conditions are obtained, which are sufficient for stochastic stability. Eventually, the validity of the results is validated via a simulation example.     

分数阶混沌系统的主动滑模同步

结合主动控制和滑模控制原理,提出了一个同步分数阶混沌系统的主动滑模控制方法.该方法首先用分数阶积分对所有维状态分量设计一个滑模面,分数阶混沌系统在该滑模面上稳定.然后采用极点配置的方法获得主动滑模控制器中的增益矩阵.应用Lyapunov稳定性理论、分数阶系统稳定理论对所提的控制器的存在性和稳定性分别进行了分析.对分数阶Lorenz系统进行数值仿真,仿真结果验证了该方法的有效性.     

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).     

Quantized output feedback stabilization of uncertain systems with input nonlinearities via sliding mode control

This paper is concerned with the quantized output feedback stabilization problem for a class of uncertain systems with nonsmooth nonlinearities in the actuator device via sliding mode control schemes. It is assumed that system signals are quantized before being transmitted through communication channels. First, a dynamical compensator is developed to estimate unmeasurable system state. Then a sliding surface, in the augmented space using the system output and the estimated state, is proposed, and an adaptive sliding mode control scheme with a static adjustment law of the quantization parameter is established. It is shown that the proposed quantized feedback control strategy is able to tackle parameter uncertainty, external disturbances, and nonsymmetric input nonlinearity simultaneously and guarantees the reachability of the sliding modes of the uncertain system. Finally, an example is given to verify the validity of the theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Chattering in sliding mode control systems with boundary layer approximation of discontinuous control

It has been a widely accepted notion that approximation of discontinuous control by certain continuous function in a boundary layer results in chattering elimination in sliding mode control systems. It is shown through three different types of analysis that in the presence of parasitic dynamics, this approach to chattering elimination would work only if the slope of the continuous nonlinear function within the boundary layer is low enough, which may result in the deterioration of performance of the system. A few examples are provided. An approach to robust stability of linear systems from the consideration of the saturating control is proposed.     

Adaptive backstepping sliding mode control for feedforward uncertain systems

Output tracking backstepping sliding mode control for feedforward uncertain systems is considered in this article. Feedforward systems are not usually transformable to the parametric semi-strict feedback form, and they may include unmatched uncertainties consisting of disturbances and unmodelled dynamics terms. The backstepping method presented in this article, even without uncertainties differs from that of Ríos-Bolívar and Zinober [Ríos-Bolívar, M. and Zinober, A.S.I. (1999), ‘Dynamical Adaptive Sliding Mode Control of Observable Minimum Phase Uncertain Nonlinear Systems’, in Variable Structure Systems: Variable Structure Systems, Sliding Mode and Nonlinear Control, eds., K.D. Young and Ü. Özgüner. Ozguner, London, Springer-Verlag, pp. 211–236; Ríos-Bolívar, M., and Zinober, A.S.I. (1997a), ‘Dynamical Adaptive Backstepping Control Design via Symbolic Computation’, in Proceedings of the 3rd European Control Conference, Brussels]. In this article, the backstepping is not a dynamical method as in Ríos-Bolívar and Zinober (1997a Ríos-Bolívar, M and Zinober, ASI. 1997a. Dynamical Adaptive Sliding Mode Output Tracking Control of a Class of Nonlinear Systems. International Journal of Robust and Nonlinear Control, 7: 387–405.  [Google Scholar], 1999), since at each step, the control and map input remain intact, and the differentiations of the control are not used. Therefore, the method can be introduced as static backstepping. Two different controllers are designed based upon the backstepping approach with and without sliding mode. The dynamic and static backstepping methods are applied to a gravity-flow/pipeline system to compare two methods.     

Adaptive backstepping sliding mode control with tuning functions for nonlinear uncertain systems

An adaptive backstepping tuning functions sliding mode controller is proposed for a class of strict-feedback nonlinear uncertain systems. In this control design, adaptive backstepping is used to deal with unknown or uncertain parameters and the matching condition restricting the Lyapunov based design. The main drawback of the Lyapunov based adaptive backstepping which is the overparametrisation is eliminated by the tuning functions. The adaptive backstepping tuning functions design is combined with the sliding mode control in order to overcome quickly varying parametric and unstructured uncertainties, and to obtain chattering free control. The proposed controller not only provides robustness property against uncertainty but also copes with the overparametrisation problem. Experimental results of the proposed controller are compared with those of the standard sliding mode controller. The proposed controller exhibits satisfactory transient performance, good estimates of the uncertain parameters, and less chattering.