一类新的二阶滑模控制方法及其在倒立摆控制中的应用

二阶滑模作为高阶滑模的特殊情形, 不仅具有传统滑模鲁棒性强、对外界干扰不敏感的特点, 而且能够有效地消弱传统一阶滑模中存在的"抖振"现象. 本文设计了一种新的二阶滑模控制算法. 该算法的优点是假设不确定性是由非负函数限制而不是由常数限定. 因此, 该算法在实际应用中具有更广的应用范围. 此外, 算法中的加幂积分技术保证了系统在有限时间内稳定, 而不是传统二阶滑模中普遍存在的有限时间收敛, 并给出了严格的数学证明. 最后, 在倒立摆控制中的应用验证了该算法的有效性.     

飞翼无人机复合连续非奇异终端滑模姿态跟踪容错控制

本文针对受多源干扰和舵面故障影响的飞翼无人机系统姿态跟踪控制问题进行研究, 提出了一种基于高阶滑模观测器的复合连续非奇异终端滑模主动抗干扰容错控制算法, 在实现姿态跟踪误差有限时间收敛的同时, 保证了控制量的连续. 并且针对控制力矩的具体实现问题, 结合飞翼无人机气动舵面冗余特性, 给出了基于加权伪逆算法的舵面分配方案, 该方案在满足舵面约束的情况下, 保证了舵面偏转角度的最优. 仿真结果表明, 所提控制方案显著提升了飞翼无人机姿态跟踪精度和跟踪误差的收敛速度, 并且保证了所有舵面满足偏角约束.     

Derivative and integral terminal sliding mode control for a class of MIMO nonlinear systems

This paper presents derivative and integral terminal sliding mode control (TSMC) for a class of MIMO nonlinear systems in a unified viewpoint. First, integral TSMC is developed for robust output tracking of uncertain relative-degree-one systems by introducing sign and fractional integral terminal sliding modes. Next, by combining derivative and integral terminal sliding modes in a recursive structure, two derivative-integral terminal sliding mode control (DI-TMSC) methods are proposed to achieve exact or approximate finite-time convergence for the output tracking of higher order nonlinear systems. Different from traditional TSMC, this paper accomplishes finite convergence time for more general high-order MIMO systems and avoids the singular problem in the controller design. Furthermore, the control system is forced to start on the terminal sliding hyperplane, so that the reaching time of the sliding modes is eliminated. In other words, the transient response is improved under more relaxed stability conditions. Finally, several numerical simulations and experiments show the expected control performance.     

具有强鲁棒性的滑模变结构控制

针对一类高阶不确定非线性系统,基于指数型快速终端滑模的良好特性,提出了一种新的滑模变结构控制．系统状态变量能以较快的收敛速度在有限时间内到达各级滑模面的邻域,并最终收敛到平衡点附近很小的区域．使用李亚普诺夫稳定性理论证明了系统的渐近稳定性,并推导出各级邻域和系统不确定环节的数学关系．Matlab仿真验证了系统的强鲁棒性．     

统一混沌同步系统的高阶滑模控制研究

研究了一类具有匹配不确定性和外部扰动的统一混沌系统.通过对误差系统进行滑模变结构控制,实现了统一混沌系统的同步,并且利用滑模控制的特点,保证了同步系统的鲁棒性.当使用传统的趋近律方式的控制率时,系统往往会产生高频抖振,控制器在实际应用中得不到良好的效果.针对这一问题,利用高阶滑模的控制率,在保证系统鲁棒性的基础上,有效...     

高阶终端滑模控制在稳定平台中的应用

针对稳定平台伺服系统中干扰对跟踪精度的影响,提出一种高阶终端滑模控制算法.首先,提出一种基于super-twisting算法的高阶滑模干扰观测器的设计方法,实现对系统中干扰的快速估计与实时补偿.其次,提出一种基于Lyapunov函数的高阶终端滑模控制器,由到达条件推导而得,高阶终端滑模控制将不连续的切换项作用于变量的高...     

基于super-twisting算法的多航天器姿态有限时间分布式协同控制

针对受外界干扰和执行器故障影响的多航天器姿态协同控制问题,本文设计了一种基于干扰观测器的分布式协同supper-twisting滑模控制器.首先,将各航天器的外界干扰和执行器故障看作一个集总干扰,设计自适应滑模干扰观测器对其进行估计.其次,将supper-twisting算法和积分滑模面相结合,设计一种基于多航天器姿态...     

基于改进型积分终端滑模控制方法的移动机器人轨迹跟踪设计与实验

为了使移动机器人获得高精度和快速收敛的跟踪性能,设计一种基于积分终端滑模和滑模观测器的轨迹跟踪控制方法.首先,考虑到移动机器人在实际运动过程中会受到地面湿滑、摩擦等原因引起的侧滑扰动的影响,建立其在该扰动影响下的运动学模型;然后,利用该动态模型设计滑模观测器来估计系统受到的扰动;接着,将估计的扰动值前馈至反馈控制器,用来抑制扰动对系统控制性能的影响,从而达到削弱抖振的目的;同时,基于跟踪误差设计积分终端滑模面,并结合滑模面和扰动估计设计新型积分终端滑模控制器;最后,基于Lyapunov稳定性理论对整个闭环系统进行稳定性分析.仿真实验结果表明,所设计的控制器具有更高的跟踪精度和更强的鲁棒性.     

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.     

高阶滑模控制理论综述

滑模控制方法因其结构简单且对系统不确定及外部扰动具有良好的鲁棒性受到人们的广泛关注. 因此, 目前正处于飞速发展阶段. 首先, 本文回顾了滑模控制理论的起源, 简单介绍了传统一阶滑模控制方法的发展; 其次, 列举了几种常用的二阶滑模控制方法, 并介绍了其工作原理; 接着, 总结了高阶滑模控制理论的研究现状, 主要包括齐次性算法和继电–多项式算法的研究成果; 最后, 结合高阶滑模控制方法中需要克服的问题, 讨论了未来可能的研究方向.     

有限时间收敛的Terminal滑模控制设计

讨论了一类SISO非线性系统的滑模变结构控制有限时间收敛问题,提出一种新的Terminal滑动模态及相应控制的设计方法,可用于带有外部扰动的二阶非线性系统。研究结果表明,系统状态在滑模面上能以较快的速度达到平衡点,在滑模面上到达平衡点的时间均是有限的,并且与普通的Terminal滑模相比,在滑模面上能以更短的时间到达平衡点。仿真结果表明了所提方法的有效性。     

一类3阶非线性系统的非奇异终端滑模控制

针对传统非奇异终端滑模控制方法不适用于3阶系统的问题,提出一类具有不确定和外干扰的3阶非线性系统的新型非奇异终端滑模控制方法.该方案首先结合backstepping控制中的动态面方法和传统2阶非奇异终端滑模控制构造非奇异3阶终端滑模面,首次提出采用高阶滑模微分器估计值代替控制器中的负指数项.采用非线性干扰观测器任意精度地估计不确定和干扰,设计控制器中的补偿项.采用终端吸引子函数做趋近律避免抖振的同时能保证有限时间趋近滑模面.基于有限时间稳定李雅普诺夫定理证明了被控状态将在有限时间内收敛到任意小的闭球内.所提出方案快于传统的递阶线性滑模控制和其他非奇异终端滑模控制.仿真中与其他滑模控制方案对比,总误差减小18%以上,超调及收敛时间也显著下降.     

基于扰动观测器的不确定非线性系统非奇异终端滑模控制

针对一类SISO 非线性不确定系统, 提出一种基于扰动观测器的非奇异终端滑模(NTSM) 控制策略. 在保证控制器非奇异性的情况下, 设计了一种改进的NTSM函数, 理论分析证明了到达滑模面的时间小于传统NTSM控制算法的到达时间. 同时为了消除系统扰动量对控制器抖振的影响, 设计了一种线性扰动观测器以降低滑模切换项的增益, 并采用Sigmoid 函数来替代传统的符号函数. 仿真结果表明了所得结论的正确性和有效性.     

非线性不确定系统的非奇异快速终端滑模控制

针对存在非匹配干扰的非线性系统,设计了一种基于干扰观测器和反步法的非奇异快速终端滑模控制.引入非线性干扰观测器估计系统的不确定性,利用反步的思想处理高阶非线性系统,从而可以将非线性干扰观测器估计的干扰值引入反步法的虚拟控制量中,同时设计一种新颖的非奇异快速终端滑模控制律保证系统的收敛速度和精度.利用Lyapunov函数从理论上证明了所设计的控制器可以保证闭环系统的有限时间收敛.最后通过数值仿真验证了所设计的控制方法的有效性.     

A novel fixed-time fractional order nonsingular terminal sliding mode control

In order to reduce the convergence time of permanent magnet linear synchronous motor (PMLSM) and improve the robustness of system, a fixed-time fractional order nonsingular terminal sliding mode control (FTFONTSMC) strategy is designed to realize the rapidity and accuracy of PMLSM position tracking response. Firstly, an improved fixed-time terminal sliding mode (FTTSM) reaching law is proposed to reduce the time of convergence. Secondly, due to the uncertainty of the disturbance in PMLSM system, an exponential convergent disturbance observer (DO) is designed to observe the disturbance. Further, finite time stability of the control system is proved by Lyapunov stability theory. Finally, the above control algorithm is applied to PMLSM, and the proposed control method's effectiveness and superiority are validated by comparing with existing control methods.     

Fast smooth second-order sliding mode control for stochastic systems with enumerable coloured noises

A fast smooth second-order sliding mode control is presented for a class of stochastic systems driven by enumerable Ornstein–Uhlenbeck coloured noises with time-varying coefficients. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the design of the control. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Then the prescribed sliding variable dynamic is presented. The sufficient condition guaranteeing its finite-time convergence is given and proved using stochastic Lyapunov-like techniques. The proposed sliding mode controller is applied to a second-order nonlinear stochastic system. Simulation results are given comparing with smooth second-order sliding mode control to validate the analysis.     

考虑扰动与输入饱和的机械臂连续非奇异快速终端滑模控制

针对机械臂控制过程中由于扰动与输入饱和造成的控制精度低的问题,提出一种连续非奇异快速终端滑模控制算法.首先,针对输入饱和问题,设计饱和补偿系统以消除输入饱和特性;其次,为避免滑模控制的抖振问题,设计二阶模型不确定与扰动估计器(UDE)对扰动项进行估计;同时,为进一步提高控制精度,采用自适应方法对扰动估计误差进行控制;在...     

Second-order sliding mode control with backstepping for aeroelastic systems based on finite-time technique

In this paper, a backstepping second-order sliding mode control scheme (BSOSMC) is proposed for suppressing both flutter and limit cycle oscillation in the aeroelastic system. The proposed control scheme combining the sliding mode control and backstepping technique, which obtain the properties of fast response and improve the control accuracy. To obtain a better disturbance rejection property, we employ compensated control term. The compensated control term provides the complete compensation of the uncertainty and disturbance, and it relax the requirement of the bound of uncertainty and disturbance. The convergence and stability of the proposed control scheme are proved by using Lyapunov’s method. Finally, the simulation results demonstrate the effectiveness of the proposed control scheme.     

Extended observer-based hybrid tracking control strategy for networked system with FDI attacks

This paper studies the speed tracking control of networked control systems (NCSs) with external disturbance and false data injection (FDI) attacks. First, the system model with external disturbances and FDI attacks is built. Then, an extended observer based on discrete time sliding function and neural network (NN) is proposed to observe the extended states and suppress the effect of external disturbance and FDI attacks. Furthermore, a novel hybrid discrete-time sliding mode control (HDSMC) strategy combining discrete time sliding mode control with super-twisting control is designed to perform closed-loop control of the system, in which the exponential term and nonlinear term are constructed to restrain the jitters. The convergence and reachability of the sliding motion are proofed. Finally, the validity and feasibility of the proposed methods are proved by simulations and experiments.     

Robust synchronization of chaotic systems using slidingmode and feedback control

We propose a robust scheme to achieve the synchronization of chaotic systems with modeling mismatches and parametric variations. The proposed algorithm combines high-order sliding mode and feedback control. The sliding mode is used to estimate the synchronization error between the master and the slave as well as its time derivatives, while feedback control is used to drive the slave track the master. The stability of the proposed design is proved theoretically, and its performance is verified by some numerical simulations. Compared with some existing synchronization algorithms, the proposed algorithm shows faster convergence and stronger robustness to system uncertainties.