Uncertain Saturated Discrete‐Time Sliding Mode Control for A Wind Turbine Using A Two‐Mass Model

The aim of this paper is to propose a new design variable speed wind turbine control by discrete‐time sliding mode approach. The control objective is to obtain a maximum extraction of wind energy, while reducing mechanical loads and rotor speed tracking combined with an electromagnetic torque. For this application, we designed a discrete time sliding mode control using the equivalent discrete time reaching law. Furthermore, a systematic and improved design procedure for uncertainties discrete‐time sliding mode control (SMC) with saturation problem is provided in this paper. The saturation constraint is reported on inputs vector. LMI technique and polytopic models are used in the design of the switching surface. To achieve some performance requirements and good robustness, in the sliding mode, the pole clustering method is investigated. Based on the unit vector control approach, a robust control is developed, then, to direct and maintain the system states onto the sliding manifold in finite time. Finally, a systematic design procedure for DSMC required to achieve a given performance level is provided and its effectiveness is varied by applying it to variable speed wind turbine systems.     

LMI-Based Sliding Surface Design for Integral Sliding Mode Control of Mismatched Uncertain Systems

We propose a linear matrix inequality (LMI)-based sliding surface design method for integral sliding-mode control of mismatched uncertain systems. The uncertain system under consideration may have mismatched norm bounded uncertainties in the state matrix as well as the input matrix. We give a sufficient condition for the existence of a sliding surface guaranteeing asymptotic stability of the full order sliding mode dynamics. We also give an LMI characterization of the sliding surface, together with an integral sliding mode control law guaranteeing the existence of a sliding mode from the initial time. Additionally, we give an LMI condition of sliding surfaces guaranteeing the alpha-stability constraint. Finally, we give a simulation result to show the effectiveness of our method     

一类不确定离散Markov 跳变系统滑模状态反馈控制

针对具有不确定的离散Markov跳变系统,研究其滑模状态反馈控制问题.考虑系统的不确定满足匹配条件,以线性矩阵不等式形式给出了离散滑模面存在的充分条件,设计了具有指数趋近律的滑模控制器,保证了系统状态到达滑模面并在滑模带上随机镇定.数值仿真验证了所提出的控制方案的有效性.     

Design of sliding mode controllers with bounded L 2 gain performance: an LMI approach

This paper is devoted to the design of robust controllers for sliding mode control systems. A linear fractional transformation (LFT) framework is adopted to describe the systems subject to model uncertainties and external disturbances. A linear matrix inequality (LMI) technique is then developed into the design of both sliding mode and reaching phase control laws. It is shown that by solving a set of LMIs, the switching surface can be designed such that the dynamics in the sliding mode achieve robust stability and bounded L ₂ gain performance with respect to matched and unmatched uncertainties in the presence of disturbances. Furthermore, a reaching phase control law is presented to eliminate the undesirable chattering effect and maintain the robustness property all the time whether the system evolves into its sliding mode in finite time or not. Finally, an observer based control law is also developed to achieve the robust performance during the reaching phase. The results are illustrated by an example.     

滑模控制一类非线性分布式时滞系统

针对一类状态不可测的非线性不确定分布式时滞系统, 给出了系统滑动模态鲁棒渐近稳定的充分条件. 设计了一类滑模观测器, 同时采用线性矩阵不等式的处理方法给出了该观测器存在的充分条件. 再应用滑模控制的趋近率方法和基于观测器所得到的估计状态, 综合了一类滑模控制器. 该控制器同时保证了估计状态下的滑模面和估计误差状态下的滑模面的渐近可达性.     

带有执行器故障的多水面船固定时间分布式滑模协同控制

针对未知环境干扰、未知执行器故障等多水面船协同控制问题,提出一种带有执行器故障的多水面船固定时间分布式滑模协同控制方法,可保证协同控制系统的全局固定时间的稳定性.首先,设计一种固定时间干扰观测器,用于估计集总扰动(包括未知环境扰动和未知执行器故障);其次,引入固定时间非奇异快速终端滑模面,可有效地消除系统的奇异性,改善系统的抖振;然后,提出一种基于固定时间非奇异快速终端滑模面和固定时间干扰观测器的分布式容错控制器,使得收敛时间上界与系统初始状态无关;最后,通过仿真实验验证所提出控制律的有效性.     

基于主动滑模控制实现一类含有非匹配不确定混沌系统的同步

讨论了一类非匹配不确定混沌系统的同步问题.基于主动控制思想,提出了一种主动滑模控制策略,使得从任意初始条件出发的不确定混沌系统在有限时间内到达滑模面.利用线性矩阵不等式(LMI)技术设计了一个鲁棒稳定的滑模面,以降低非匹配不确定对系统的影响.给出了线性矩阵不等式形式的稳定滑模面存在的充分条件.通过对Rssler系统的同步仿真,验证了该方法的可行性.     

Passivity-based sliding mode control of uncertain singular time-delay systems

In this paper the problem of sliding mode control (SMC) with passivity of a class of uncertain nonlinear singular time-delay systems is studied. An integral-type switching surface function is designed by taking the singular matrix into account, thus the resulting sliding mode dynamics is a full-order uncertain singular time-delay system. By introducing some slack matrices, a delay-dependent sufficient condition is proposed in terms of linear matrix inequality (LMI), which guarantees the sliding mode dynamics to be generalized quadratically stable and robustly passive. The passification solvability condition is then established. Moreover, a SMC law and an adaptive SMC law are synthesized to drive the system trajectories onto the predefined switching surface in a finite time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.     

具有分布时滞不确定中立型系统的滑模控制

针对一类含有分布时滞和不满足匹配条件的不确定中立型系统,通过利用Lya-punov稳定性理论和线性矩阵不等式(LMI)方法进行了滑模控制研究。首先,选取了依赖于当前状态和状态时滞的滑模面;设计了包含等效控制和非线性切换控制的滑模控制器使得系统满足滑模到达条件,即确保了系统在有限时间内到达滑模面。通过构造适当的Lyapunov函数,利用积分不等式技术,给出了闭环系统渐近稳定的充分条件。该充分条件通过采用虚拟反馈控制思想,结合状态反馈的极点配置方法,转换为线性矩阵不等式的形式,可通过Matlab中的LMI工具箱进行方便的求解。具体算例说明此方法的有效性。     

二进制ABR流量控制的离散滑模控制算法

针对ATM网络的拥塞控制问题，考虑网络中的不确定性因素，借助离散滑模控制理论的设计方法。提出一种二进制ABR（可用比特率）流量控制算法．该算法利用线性矩阵不等式设计了一个稳定的滑模面，同时给出了一种能够明显减小滑模面附近抖振的离散趋近律，基于该趋近律的控制律能有效抑制ATM交换机中的队列长度和允许信元速率的振荡．仿真算例证实了所提出算法的有效性．     

Discrete time output feedback sliding mode tracking control for systems with uncertainties

This paper describes a method for designing discrete time static output feedback sliding mode tracking controllers for uncertain systems that are not necessarily minimum phase or of relative degree one. In this work, a procedure for realizing discrete time controllers via a particular set of extended outputs is presented for systems with uncertainties. The conditions for existence of a sliding manifold guaranteeing a stable sliding motion are given. A procedure to synthesize a control law that minimizes the effect of the disturbance on the sliding mode dynamics and the augmented outputs is given. The proposed control law is then applied to a benchmark aircraft problem taken from the literature that represents the lateral dynamics of a F‐14 aircraft under powered approach. Copyright © 2013 John Wiley & Sons, Ltd.     

Dynamic integral sliding mode for MIMO uncertain nonlinear systems

In this paper the authors propose a novel sliding mode control methodology for Multi-Input and Multi-Output (MIMO) uncertain nonlinear systems. The proposed approach synthesizes dynamic sliding mode and integral sliding mode control strategies into dynamic integral sliding mode. The new control laws establish sliding mode without reaching phase with the use of an integral sliding manifold. Consequently, robustness against uncertainties increases from the very beginning of the process. Furthermore, the control laws considerably alleviate chattering along the switching manifold. In addition, the performance of the controller boost up in the presence of uncertainties. A comprehensive comparative analysis carried out with dynamic sliding mode control and integral sliding mode control demonstrates superiority of the newly designed control law. A chatter free regulation control of two uncertain nonlinear systems with improved performance in the presence of uncertainties ensures the robustness of the proposed dynamic integral sliding mode controller.     

基于输出反馈的直升机变结构控制律设计

针对直升机的小扰动模型,设计了静态输出反馈滑模控制器（SOFSMC）。利用参考模型,实现了直升机的相关动态指标。针对滑模面的设计问题,将其等价地转化为一组双线性矩阵不等式（BLMI）,并采用迭代线性矩阵不等式（ILMI）技术来求解。针对控制律的综合问题,给出了一种基于单位向量法的控制律,并通过引入线性反馈来保证系统进入滑动模态后线性控制部分与标称系统的线性控制部分的一致性。仿真结果验证了该方法的有效性。     

一种连续非奇异快速终端滑模控制方法

为解决现有终端滑模控制算法在收敛速度和抖振方面的问题, 提出一种连续非奇异快速终端滑模控制方法. 采用变系数双幂次趋近率和非奇异快速终端滑模面相结合的设计方式, 提高系统状态在趋近和滑动阶段的收敛速度. 通过Lyapunov 稳定性方法证明所提出的控制率可使得状态轨迹在扰动存在的情况下, 在有限时间内快速收敛到一个区域. 与传统方法相比, 所提出的控制率是连续的, 因此抑制了抖振, 拥有更高的控制精度. 将所提出的方法应用于光电稳定平台, 仿真结果验证了算法的有效性.

     

凸胞型不确定系统的变结构控制

讨论了凸胞型不确定系统的变结构控制,利用LMI方法,给出了滑模面存在的充分条件,并且给出了线性滑模面的显式表达式.所设计的变结构控制律不仅能保证系统在有限时间到达滑模面,并且保证受限在滑模面上的降阶等价系统是D_R稳定的.最后,给出一个设计实例来阐明该控制方法的有效性.     

基于LMI的滑模控制在航空发动机中的应用

针对航空发动机运行过程中存在不确定性和稳定性问题,运用状态空间模型理论与线性矩阵不等式LMI相结合的方法设计了控制器,改善了航空发动机的控制性能。以某型涡扇发动机为控制对象,基于LMI对普通终端滑模变结构控制进行了优化设计,在滑模超平面设计中引入了动态补偿器,采用改进的幂次趋近律,对该动态系统进行了性能仿真验证。结果表明,本文提出的方法较之普通终端滑模变结构控制对系统性能有较大改善,不仅使系统主供油量变化率、尾喷口面积变化率等的控制更为平稳,且保证了系统鲁棒性和稳定性。     

Adaptive finite‐time attitude stabilization for rigid spacecraft with actuator faults and saturation constraints

The attitude stabilization problem for rigid spacecraft in the presence of inertial uncertainties, external disturbances, actuator saturations, and actuator faults is addressed in this paper. First, a novel fast terminal sliding mode manifold is designed to avoid the singularity problem while providing high control ability. In addition, fast terminal sliding mode control laws are proposed to make the spacecraft system trajectory fast converge onto the fast terminal sliding mode surface and finally evolve into small region in finite time, which cannot be achieved by the previous literatures. Based on the real sliding mode context, a practical adaptive fast terminal sliding mode control law is presented to guarantee attitude stabilization in finite time. Also, simulation results are presented to illustrate the effectiveness of the control strategies. Copyright © 2015 John Wiley & Sons, Ltd.     

A model-based sliding mode control methodology applied to the HDA-plant

A sliding mode control methodology using output information is demonstrated in application to the HDA-plant, a plant for production of benzene. This process is a highly integrated, non-linear large scale process with non-minimum phase and relative degree zero characteristics. The non-linear control law is designed on the basis of a linear observer-based control system. The non-linear control law uses the states of the linear observer. The performance in the sliding mode is determined by a linear stable sub-manifold of the linear closed loop control system chosen via a robust pole selection scheme. The sliding mode control is optimized to operate in a wide operating region.     

基于半物理仿真的RBF神经网络滑模控制

针对一类不确定时滞系统研究滑模控制的实现问题。对于实际应用对象的时滞特性采取了特殊的线性变换,将原时滞系统转化为无时滞系统。通过设计二次型性能指标计算得到了最优的切换函数,并使用RBF神经网络实现了滑模控制的自适应等效控制,保证了系统能够克服扰动,系统状态在有限时间能够到达滑模面。系统仿真验证了该方法的有效性和稳定性。     

Fixed‐time sliding mode cooperative control for multiagent networks via event‐triggered strategy

In this article, the problem of event‐triggered‐based fixed‐time sliding mode cooperative control is addressed for a class of leader‐follower multiagent networks with bounded perturbation. First, a terminal integral sliding mode manifold with fast convergent speed is designed. Then, a distributed consensus tracking control strategy based on event‐triggered and sliding mode control is developed that guarantees the multiagent networks achieve consensus within a fixed time which is independent of initial states of agents in comparison with the finite‐time convergence. Furthermore, the update frequency of control law can be considerably reduced and Zeno behavior can be removed by utilizing the proposed event‐triggered control algorithm. Simulation examples are used to show the effectiveness of the new control protocol.