Almost sure stability of second‐order nonlinear stochastic system with Lévy noise via sliding mode control

The almost sure stability of second‐order nonlinear stochastic system with Lévy noise is studied by sliding mode control method. A conventional linear sliding mode surface is first constructed, by employing stochastic analysis technique combined with Lyapunov function method, sufficient conditions are established to ensure the almost sure stability of the system dynamics. Then, a nonsingular terminal sliding mode control technique is used for our system, corresponding controller is designed to guarantee the desired performance. Finally, two examples are given to show the validity of our results.     

A singular system approach to robust sliding mode control for uncertain Markov jump systems

The robust sliding mode control for Markov jump systems with parameter uncertainties and an unknown nonlinear function is discussed. Based on a singular system approach and linear matrix inequality (LMI), a sufficient condition which guarantees the existence of linear switching surface and the stochastic stability of sliding mode dynamics is given. A sliding mode controller is designed such that the closed-loop system is convergent to the switching surface in finite time. A numerical example is given to show the effectiveness of the proposed method.     

SECOND‐ORDER TERMINAL SLIDING MODE CONTROL OF INPUT‐DELAY SYSTEMS

This paper proposes a second‐order terminal sliding mode control for a class of uncertain input‐delay systems. The input‐delay systems are firstly converted into the input‐delay free systems and further converted into the regular forms. A linear sliding mode manifold is predesigned to represent the ideal dynamics of the system. Another terminal sliding mode manifold surface is presented to drive the linear sliding mode to reach zeros in finite time. In order to eliminate the chattering phenomena, a second‐order sliding mode method is utilized to filter the high frequency switching control signal. The uncertainties of the systems are analysed in detail to show the effect to the systems. The simulation results validate the method presented in the paper.     

Discrete Sliding‐Mode Control of Mimo Linear Systems

This paper introduces a discrete sliding‐mode control for linear time‐invariant systems in the presence of matched uncertainties. The switching surface is constructed by applying the pole‐assignment method applying to the overall system, not the system in the sliding mode. Importantly, the control algorithm is derived to handle the rate of convergence to the sliding mode and to prevent the control law from encountering any unreasonably large variations. As for the system stability, it can be found that the system is stabilized and finally restricted to a known region. A numerical example is also included to demonstrate all the features of the developed discrete sliding‐mode control.     

Static output feedback sliding mode control for time‐varying delay systems with time‐delayed nonlinear disturbances

In this paper, a robust stabilization problem for a class of linear time‐varying delay systems with disturbances is studied using sliding mode techniques. Both matched and mismatched disturbances, involving time‐varying delay, are considered. The disturbances are nonlinear and have nonlinear bounds which are employed for the control design. A sliding surface is designed and the stability of the corresponding sliding motion is analysed based on the Razumikhin Theorem. Then a static output feedback sliding mode control with time delay is synthesized to drive the system to the sliding surface in finite time. Conservatism is reduced by using features of sliding mode control and systems structure. Simulation results show the effectiveness of the proposed approach. Copyright © 2009 John Wiley & Sons, Ltd.     

A nonlinear sliding surface to improve performance of a discrete-time input-delay system

A sliding mode controller is proposed for an uncertain input-delay system to enhance performance. A nonlinear sliding surface is proposed to achieve better transient response for general uncertain discrete SISO linear systems with input delay. Both matched and unmatched perturbations are considered and ultimate boundedness of motion is proved. The step tracking problem is analysed. The proposed surface increases the damping ratio of the transformed system (delay free) as the output moves nearer to the setpoint. To simplify the surface design, a linear matrix inequality based tuning procedure is proposed. The control law is designed based on an equivalent control approach which guarantees one step reaching. The scheme is able to achieve low overshoot and low settling time simultaneously which is not possible with a linear sliding surface. Simulation results verify the effectiveness of the proposed nonlinear surface over different linear surfaces.     

直线同步电动机磁悬浮系统的自适应模糊滑模控制

提出一种自适应模糊滑模控制方法用以提高可控励磁直线同步电动机(controllable excitation linear synchronous motor, CELSM)磁悬浮控制系统的性能.根据CELSM的特定结构和运行机理,建立CELSM磁悬浮系统的数学模型,包括励磁回路的电压方程、磁悬浮力方程和运动方程;设计积分滑模面和分段趋近律,系统状态轨迹可以根据距滑模面的距离自动切换趋近速度,以很小的斜率穿越滑模面,减小系统的抖振,推导出相应的滑模控制器;为了克服不确定性扰动对系统的影响,设计自适应律使自适应模糊系统对不确定性扰动进行实时估计,用该估计值进行前馈补偿控制,减小控制律中的切换增益和系统的抖振,进一步推导出自适应模糊滑模控制器;用Matlab对控制系统进行仿真,仿真结果表明,采用自适应模糊滑模控制的CELSM磁悬浮系统的性能得到改善.     

An H∞non‐fragile observer‐based adaptive sliding mode controller design for uncertain fractional‐order nonlinear systems with time delay and input nonlinearity

In this paper the problem of non‐fragile adaptive sliding mode observer design is addressed for a class of nonlinear fractional‐order time‐delay systems with uncertainties, external disturbance, exogenous noise, and input nonlinearity. An H_∞ observer‐based adaptive sliding mode control considering the non‐fragility of the observer is proposed for this system. The sufficient asymptotic stability conditions are derived in the form of linear matrix inequalities. It is proven that the sliding surface is reachable in finite time. An illustrative example is provided which corroborates the effectiveness of the theoretical results.     

GBF-CMAC和滑模控制的柔性结构系统控制

针对一类不确定系统的跟踪控制,设计了一种将GBF-CMAC（cerebellar model articulation controller with Gauss basis function）与滑模控制相结合的控制系统。利用符号距离和分层结构减少了神经网络所需存储器的数量,并提出了一种神经网络参数的自适应学习律。将设计的控制器用于含有不确定性和欠驱动结构的高阶柔性直线结构系统的跟踪控制,并与一般滑模控制和积分滑模控制进行了比较。实验结果表明,所设计的控制器不仅具有较好的鲁棒性,而且改善了滑模控制存在的抖振问题。同时通过调整神经网络的参数对抖振进行控制,实现了抖振和跟踪性能之间的最优选择。     

Reduced‐order design of high‐order sliding mode control system

To design an rth (r>2) order sliding mode control system, a sliding variable and its derivatives of up to (r ? 1) are in general required for the control implementation. This paper proposes a reduced‐order design algorithm using only the sliding variable and its derivatives of up to (r ? 2) as the extension of the second‐order asymptotic sliding mode control. For a linear time‐invariant continuous‐time system with disturbances, it is found that a high‐order sliding mode can be reached locally and asymptotically by a reduced‐order sliding mode control law if the sum of the system poles is less than the sum of the system zeros. The robust stability of the reduced‐order high‐order sliding mode control system, including the convergence to the high‐order sliding mode and the convergence to the origin is proved by two Lyapunov functions. Simulation results show the effectiveness of the proposed control algorithm. Copyright © 2010 John Wiley & Sons, Ltd.     

Observer‐based mode‐independent integral sliding mode controller design for phase‐type semi‐Markov jump singular systems

This paper considers the observer‐based integral sliding mode controller design problem of semi‐Markovian jumping singular systems with time‐varying delays. Firstly, by using a plant transformation and supplementary variable technique in the work of Hou et al, the discussed phase‐type semi‐Markov jump singular system is equivalently transformed into its associated Markov jump singular system. Secondly, an observer‐based sliding mode controller design problem is investigated for the associated singular Markov jump systems. The highlight of this paper is that we construct an observer‐based mode‐independent integral sliding mode surface function, which is different from the mode‐dependant sliding mode surface function in the previous literatures. Based on this, an observer‐based sliding mode controller is designed to guarantee that the associated singular Markov jump system meets the reachable condition. Finally, a practical example is presented to demonstrate the efficiency and effectiveness of our obtained results.     

Novel sliding mode control for multi‐input–multi‐output discrete‐time system with disturbance

This paper investigates sliding mode control for multi‐input–multi‐output discrete‐time system with disturbances. First of all, a novel nonlinear sliding surface, named as hyperbolic hybrid switching sliding surface, is proposed. Two different types of hyperbolic functions are introduced into the proposed sliding surface. Due to the changing of values of the hyperbolic functions, sliding surface switching occurs during the control process, which ensures that both settling time and overshoot can be decreased. The sliding mode controller is obtained based on a novel nonlinear reaching law. The nonlinear reaching law contains several parameters, and by properly designing these parameters, we can decrease the bounds of the sliding variables to small values. The stability analysis of the sliding motion is carried out from singular system viewpoint. Finally, simulation examples and comparison examples are presented to illustrate that the system performance is improved obviously by proposed novel sliding mode control, and the system is robust to the disturbances.     

基于指数保性能的比例-积分-时滞滑模观测器设计

传统状态观测器仅基于当前观测误差重构系统状态,未充分利用系统历史观测数据.针对存在匹配扰动的二阶不确定线性系统,设计一种比例-积分-时滞滑模观测器,实现不确定线性系统状态的鲁棒确切估计.首先,设计带记忆滑模函数,形式为历史观测误差和当前观测误差的线性组合,设计参数包括滑模面增益和人工时滞两部分,将滑模面中的时滞项基于泰勒级数展开,将截断误差表示为积分形式;然后,设计带记忆输出反馈等效控制律,采用时滞依赖型Lyapunov泛函,进行滑模动态指数稳定性分析和观测补偿;接着,将观测器参数设计转化为多目标优化问题,优化目标包括:系统状态衰减率、控制代价、高频噪声不灵敏度,基于粒子群算法,在上述3个优化目标间实现设计参数优化整定,在“快、准、稳”方面进行合理折衷选择;最后,在无源网络系统中,验证所提出滑模观测器的可行性和有效性.     

Chattering‐free adaptive sliding mode control for continuous‐time systems with time‐varying delay and process disturbance

This paper concerns the controller design for continuous‐time linear systems with time‐varying delay and process disturbance. A novel adaptive sliding mode control law is mainly proposed to attract the sliding mode to first‐order sliding surface within a finite time; afterwards, the uniformly ultimately bounded stability of the closed‐loop system on the sliding surface is simultaneously guaranteed. In addition, the chattering phenomena can be conveniently excluded if the disturbance is a low‐intensity process. Once the high‐intensity disturbance is involved, the state variation can be significantly reduced as well. Furthermore, by the technique of a novel exponential free‐matrix technique, the convergence rate of the closed‐loop system can be conveniently preregulated. Numerical example is provided to demonstrate the effectiveness of the proposed method.     

Dynamic output feedback integral sliding mode control design for uncertain systems

This paper addresses the problem of designing a dynamic output feedback sliding mode control algorithm for linear MIMO systems with mismatched parameter uncertainties along with disturbances and matched nonlinear perturbations. Once the system is in the sliding mode, the proposed output‐dependent integral sliding surface can robustly stabilize the closed‐loop system and obtain the desired system performance. Two types of mismatched disturbances are considered and their effects on the sliding mode are explored. By introducing an additional dynamics into the controller design, the developed control law can guarantee that the system globally reaches and is maintained on the sliding surface in finite time. Finally, the feasibility of the proposed method is illustrated by numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

A robust optimal sliding‐mode control approach for magnetic levitation systems

This paper presents a robust optimal sliding‐mode control approach for position tracking of a magnetic levitation system. First, a linear model that represents the nonlinear dynamics of the magnetic levitation system is derived by the feedback linearization technique. Then, the robust optimal sliding‐mode control developed from the linear model is proposed. In the proposed control scheme, the integral sliding‐mode control with robust optimal approach is developed to achieve the features of high performance in position tracking response and robustness to the matched and unmatched uncertainties. Simulation and experimental results from the computer‐controlled magnetic levitation system are illustrated to show the validity of the proposed control approach for practical applications. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Sliding Mode Observer Controller Design for a Two Dimensional Aeroelastic System with Gust Load

The aim of this paper is to develop state estimation and sliding mode control schemes for the vibration suppression of an underactuated wing aeroelastic system in the presence of a gust load disturbance. Ignoring structural elastic deformation and using the concentrated elastic system (spring) to simulate the overall elastic deformation, this aeroelastic model consists of a straight wing and spring system, describing flap and pitch freedoms. The corresponding dynamic motion equation is established using the Lagrange method, and the gust is modeled as a typical “1‐cosine” gust. The aerodynamic lift and moment on the wing are computed by strip theory. The open loop system exhibits the limit cycle oscillations (LCOs) at a certain freestream velocity. The objective is to design a control system for suppressing the LCOs. For the purpose of control, a single trailing‐edge control surface is used. It is assumed that only the pitch angle is measured and the remaining state variables needed for full state feedback are estimated by the designed observer. Then an integral sliding surface is put forward on the estimation space; a new continuous reaching law is proposed to reduce the chattering phenomena. The finite‐time reachability of the predesigned sliding surface is proved and guaranteed by the designed sliding mode control law. The sufficient condition for the asymptotic stability of the closed‐loop system composed of the sliding mode dynamics and the error dynamical system is derived in terms of linear matrix inequality (LMI). The effectiveness of the proposed strategy is finally demonstrated by simulation results.     

Modified Weak‐Pseudo‐Sliding Mode Controller With One Sampling Period Computation Delay

In this paper, a so‐called discrete‐time modified weak‐pseudo‐sliding mode controller with one sampling period computation delay is proposed for the system with system parameter uncertainty. In the meantime, the upper bound of the sampling period is also determined to guarantee the existence of the modified weak‐pseudo‐sliding mode along the prescribed sliding surface in the proposed discrete‐time sliding mode control system.     

线性时滞中立型控制系统的滑动模补偿器方法

利用变结构控制理论，提出了线性不确定系数时滞中立型控制系统的一种新方法－－滑动模补偿器法。即当系统具有不确定系数时，引进一个滑动模补偿器，实现了完全的模型跟踪从而克服了用常规方法确定滑动曲面时所遇到的若干困难，为说明此法的设计技巧，给出了一个数值仿真例子。     

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.