Higher order sliding mode control based on integral sliding mode

A higher order sliding mode control scheme for uncertain nonlinear systems is proposed in the present paper. It is shown that the problem is equivalent to the finite time stabilization of higher order input-output dynamics with bounded uncertainties (r∈N). The controller uses integral sliding mode concept and contains two parts. A part achieves finite time stabilization of the higher order input-output dynamics without uncertainties. The other part rejects bounded uncertainties throughout the entire response of the system. As a result, a higher order sliding mode is established. The advantages of the method are that its implementation is easy, the time convergence is chosen in advance and the robustness is ensured. An illustrative example of a car control shows the applicability of the method.     

High‐order sliding mode control design based on adaptive terminal sliding mode

High‐order sliding mode control techniques are proposed for uncertain nonlinear SISO systems with bounded uncertainties based on two different terminal sliding mode approaches. The tracking error of the output converges to zero in finite time by designing a terminal sliding mode controller. In addition, the adaptive control method is employed to identify bounded uncertainties for eliminating the requirement of boundaries needed in the conventional design. The controllers are derived using Lyapunov theory, so the stability of the closed‐loop system is guaranteed. In the first technique, the developed procedure removes the reaching phase of sliding mode and realizes global robustness. The proposed algorithms ensure establishment of high‐order sliding mode. An illustrative example of a car control demonstrates effectiveness of the presented designs. Copyright © 2011 John Wiley & Sons, Ltd.     

Output feedback relay control in the second‐order sliding mode context with application to an electropneumatic system

In this paper, a new second‐order sliding mode output feedback control law is proposed. It amounts to approach the dynamic performance of the twisting algorithm, but the main advantage of this new control method is that it requires only the information of the sliding variable, and not its derivative. A gain adaptation law is also developed for this new control law. Then this control strategy is applied to the position control of an electropneumatic system, and its performance is compared with other two very recent adaptive second‐order sliding mode control laws. Copyright © 2016 John Wiley & Sons, Ltd.     

Force tracking neural block control for an electro‐hydraulic actuator via second‐order sliding mode

This paper presents a novel scheme for identification and control of an electro‐hydraulic system using recurrent neural networks. The proposed neural network has the nonlinear block control form structure. A sliding‐mode control technique is applied then to design a discontinuous controller, which is able to track a force reference trajectory. Due to the presence of an unmodelled dynamics, the standard sliding‐mode controller produces oscillations (or ‘chattering’) in the closed‐loop system. The second‐order sliding mode is used to eliminate the undesired chattering effect. Simulations are presented to illustrate the results. Copyright © 2007 John Wiley & Sons, Ltd.     

Second order sliding mode observers for the ADDSAFE actuator benchmark problem

This paper presents the evaluation process and results associated with two different fault detection and diagnosis (FDD) schemes applied to two different aircraft actuator fault benchmark problems. Although the schemes are different and bespoke for the problem being addressed, both are based on the concept of a second order sliding mode. Furthermore both designs are considered as ‘local’ in the sense that a localized actuator model is used together with local sensor measurements. The schemes do not involve the global aircraft equations of motion, and therefore have low order. The first FDD scheme is associated with the detection of oscillatory failure cases (OFC), while the second scheme is aimed at the detection of actuator jams/runaways. For the OFC benchmark problem, the idea is to estimate the OFC using a mathematical model of the actuator in which the rod speed is estimated using an adaptive second order exact differentiator. For the jam/runaway actuator benchmark problem, a more classical sliding mode observer based FDD scheme is considered in which the fault reconstruction is obtained from the equivalent output error injection signals associated with a second order sliding mode structure. The results presented in this paper summarize the design process from tuning, testing and finally industrial evaluation as part of the ADDSAFE project.     

Discrete second‐order sliding mode control based on optimal sliding function vector for multivariable systems with input–output representation

The technique of linear matrix inequalities is a powerful method for solving optimization problems. In this paper, a sliding function vector was calculated using linear matrix inequalities approach. This technique provided optimal values of the coefficients of the sliding function vector, which led to the reduction of the reachability phase. Then, a discrete second‐order sliding mode control for multivariable systems was developed using this optimal sliding function vector. Two examples were used in order to illustrate the effectiveness of the proposed strategy. Simulation results prove good performances in terms of reduction of the reachability phase. Copyright © 2016 John Wiley & Sons, Ltd.     

The stochastic sliding mode variable structure guidance laws based on optimal control theory

A stochastic sliding-mode variable structure guidance law involving optimal control theory is presented for the missile target intercept model, in which state noise, uncertain system parameters, target movement and measured noise are considered. This guidance law synthesizes the merits of optimal guidance law with line-of-sight rate convergence and sliding-mode guidance law with strong robustness. Through theoretic analysis, it is proved that the sliding mode hyperplane is sub-achievable in the closed loop system. The numerical results show the effectiveness of the proposed control algorithm.     

基于拟连续高阶滑模的高超声速飞行器再入姿态控制

考虑模型参数不确定和外界干扰对再入制导控制性能的影响,基于拟连续高阶滑模控制策略对高超声速飞行器的再入制导控制问题进行了研究.首先,给出再入制导指令的设计过程.其次,基于再入飞行特性对模型进行简化,获得面向控制的姿态模型,在此基础上,通过引入新的控制变量,设计解耦滑模面,实现姿态间的解耦.再次,为了削弱控制抖振,通过引入虚拟控制,对系统进行增广,基于齐次性理论设计拟连续三阶滑模再入姿态控制器,确保系统在有限时间实现对制导指令的稳定跟踪.最后,六自由度再入飞行器的制导控制一体化仿真结果表明,本研究给出的控制策略在不影响系统鲁棒性的同时,能够实现对标称轨迹和再入姿态的综合控制.     

网络拥塞控制的滑模控制策略

针对动态网络的拥塞问题,对TCP网络的动态不确定性进行定量分析,探讨了网络参数的摄动范围,给出TCP网络的不确定线性化系统模型。在此基础上,设计了一种基于滑模控制的主动队列管理算法,并分别在Matlab和NS2两种仿真平台上验证了算法的有效性,实验结果表明队列长度可以很好地稳定在期望值附近。     

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.     

基于自适应模糊滑模控制的分数阶混沌系统的投影同步

基于模糊控制理论和滑模控制理论以及自适应控制理论,研究了一类含有外部扰动的不确定分数阶混沌系统的混合投影同步问题.提出了一种自适应模糊滑模控制的分数阶混沌系统投影同步方法.模糊逻辑系统用来逼近未知的非线性函数和外部扰动,并且对逼近误差采用了自适应控制,同时构造了一种具有较强鲁棒性的分数阶积分滑模面.应用分数阶Barbalat引理设计了自适应模糊滑模控制器和参数自适应律.最后数值仿真结果验证了所提控制方法的有效性.     

A nonlinear sliding mode control design approach based on neural network modelling

A complete nonlinear framework for the modelling and robust control of nonlinear systems is proposed. The use of neural networks for continuous time modelling to obtain a certain nonlinear canonical form is investigated. The model obtained is used with recently proposed dynamic sliding mode controller design methods. The robustness bounds needed for controller design are determined from modelling errors. A modified version of the backpropagation theorem is also introduced. Copyright © 1999 John Wiley & Sons, Ltd.     

Backstepping sliding mode control with functional tuning based on an instantaneous power approach applied to an underwater vehicle

In this paper, we present a modified backstepping sliding mode control to deal with Euler–Lagrange systems. The controller is applied in an underwater vehicle in order to show the effectiveness of the approach proposed. Instantaneous power data provided by the propulsion system are used to tune the controller in order to guarantee robust performance and energy saving. Thanks to the combination of an internal Proportional Integral and Derivative (PID) controller, it is possible implement high gains to deal with the influence of disturbances and uncertainties. A comparative study among this backstepping sliding mode controller and standard sliding mode controls is presented.     

Hybrid‐impulsive second‐order sliding mode control: Lyapunov approach

Dynamic system of relative degree two controlled by discontinuous‐hybrid‐impulsive feedback in the presence of bounded perturbations is considered. The state feedback impulsive‐twisting control exhibits a uniform exact finite time convergence to the second‐order sliding mode with zero convergence time. The output feedback discontinuous control augmented by a simplified hybrid‐impulsive functions provides uniform exact convergence with zero convergence time of the system's states to a real second‐order sliding mode in the presence of bounded perturbations. Only ‘snap’ knowledge of the output derivative, that is, the knowledge of the output derivative in isolated time instants, is required. The output feedback hybrid‐impulsive control with practically implemented impulsive actions asymptotically drives the system's states to the origin. The Lyapunov analysis of the considered hybrid‐impulsive‐discontinuous system proves the system's stability. The efficacy of the proposed control technique is illustrated via computer simulations. Copyright © 2016 John Wiley & Sons, Ltd.     

一类非线性不确定系统高阶滑模自适应控制设计

针对一类非线性不确定系统,提出一种高阶滑模自适应控制算法．为减少系统抖振和不确定边界未知但有界问题,引入可在线调整参数的双极sigmoid函数和控制器增益．利用Lyapunov理论证明系统在有限时间内稳定并具有鲁棒性,且不确定的上界不需要预先确定．仿真结果验证了该方法的有效性．     

‐based optimal sparse sliding mode control for networked control systems

This paper is devoted to the problem of designing a sparsely distributed sliding mode control for networked systems. Indeed, this note uses a distributed sliding mode control framework by exploiting (some of) other subsystems' information to improve the performance of each local controller so that it can widen the applicability region of the given scheme. To do so, different from the traditional schemes in the literature, a novel approach is proposed to design the sliding surface, in which the level of required control effort is taken into account during the sliding surface design based on the control. We then use this novel scheme to provide an innovative less‐complex procedure that explores sparse control networks to satisfy the underlying control objective. Besides, the proposed scheme to design the sliding surface makes it possible to avoid unbounded growth of control effort during the sparsification of the control network structure. Illustrative examples are presented to show the effectiveness of the proposed approach.     

TORA系统基于自调节滑模干扰补偿器的解耦滑模控制

针对欠驱动TORA系统,提出一种基于自调节滑模干扰补偿器的解耦滑模控制方法。所提出的控制方法无需系统不确定性上界的先验信息,对于系统不确定性具有良好的适应性。该控制方法包括设计一种自调节滑模干扰补偿器和一种新型的双幂次趋近律,所设计的自调节滑模干扰补偿器能够利用切换增益自适应算法准确逼近上界未知的系统不确定性,所提出的新型双幂次趋近律能够保证系统状态的快速趋近并抑制控制器的高频抖动。采用Lyapunov稳定性理论证明闭环控制系统的稳定性,并通过数值仿真实验验证所提出的控制方法的有效性。     

MIMO非线性不确定系统二阶滑模控制

提出了一种基于有限状态机切换策略的多输入多输出二阶滑模控制算法。算法保证了传统滑模控制对参数变化和扰动不灵敏的特点,削弱了滑模控制的“抖动”现象。在上界未知的测量噪声和参数变化的情况下,算法通过滑模量及其微分的符号构成控制律,实现了系统的镇定。仿真结果表明算法在噪声环境下能保证系统的稳定性,对参数不确定具有较强的鲁棒性。算法结构简单,便于实现。     

考虑输入饱和的离散最优积分滑模控制

针对含有匹配有界干扰的线性离散系统, 提出一类最优积分滑模控制算法. 在系统开环极点位于单位圆内(上) 的前提下, 考虑输入饱和, 可以实现系统状态的半全局稳定. 该算法是低增益反馈和积分滑模的有益结合, 通过低增益反馈使输入饱和得到满足, 通过滑模控制增强了系统对干扰的鲁棒性; 另外, 该算法可以使特定的性能指标达到最优, 使系统稳态误差达到??(??²) 的量级. 仿真结果验证了所提出算法的有效性.