快速高阶滑模微分器

首先利用Terminal吸引子函数代替高阶滑模微分器中的不连续函数,以避免抖振;然后在高阶滑模微分器每一层滑模面中增加快速收敛项,以提高收敛速度,并分别针对不同情况证明了快速高阶滑模微分器的稳定性,给出了估计误差的具体表达式,提出了一种抑噪设计方法;最后比较了快速高阶滑模微分器与标准高阶滑模微分器的收敛时间和误差,总结了快速高阶滑模微分器的一般设计方法,并通过仿真结果表明了所得结论的正确性和有效性.     

非匹配不确定高阶非线性系统递阶Terminal滑模控制

对于高阶非线性系统,首先采用改进的高阶滑模微分器作为间接干扰观测器,获得前n-1个子系统中的非匹配复合干扰的估计值,证明了估计误差可任意小. 为避免代数环,设计了三种方案获得最后一个子系统中非匹配复合干扰的估计值,并证明了估计误差有界. 在此基础上设计递阶Terminal滑模控制器,证明了控制器参数非奇异及结构非奇异,并给出所需条件. 最后,证明了系统稳定,跟踪误差可任意小. 近空间飞行器姿态控制仿真验证了本文结论.     

基于非线性参数的电液伺服系统滑模控制

针对在电液伺服系统跟踪控制中存在非线性不确定参数和外界扰动的问题,提出了一种基于积分微分器的滑模Lyapunov函数的控制方法。首先,在只有位移信号测量输出的情况下,采用高阶积分链式微分器对其速度和加速度信息进行预估。系统存在非线性不确定参数,利用微分器对状态和不确定项的实时估计,设计出积分滑模控制器,实现自适应规律以及对电液伺服系统中不确定扰动的抑制。搭建电液伺服系统AMESim模型并与Matlab构成联合仿真平台,对控制器进行仿真。仿真表明,该控制器具有良好的对非线性不确定参数变化的补偿能力和跟踪性能。     

一类非线性系统的自适应时延观测器设计

利用输出差分及滑模方法研究一类非线性系统的自适应时延状态观测器设计问题. 首先将系统输出的微分及高阶微分用输出和其延迟测量值的差商来表示, 然后在此基础上构造了一种时延状态观测器, 估计误差的影响可由滑模项来消除. 在系统满足线性参数化的条件下给出了一种自适应时延状态观测器设计. 最后给出仿真研究说明设计方法的有效性.     

多输入多输出非线性系统的受限滑模控制

本文针对一类具有执行器和状态约束的多输入多输出非线性系统,研究了基于高阶滑模观测器的滑模控制和稳定性分析问题,通过对该系统进行逆变换并考虑其控制输入系数矩阵的对合跨度分布,我们设计了一类高阶滑模观测器用于实现系统的状态估计,其中,采用鲁棒精确微分器分析了所得误差估计系统的收敛性.然后,利用原系统的部分状态变量设计了二阶...     

二阶动态滑模控制在移动机械臂输出跟踪中的应用

针对移动机械臂的输出跟踪问题,结合高阶滑模控制和动态滑模控制的设计思想为其设计了一种二阶动态滑模控制器.首先给出了包括驱动电机动态特性的移动机械臂的简化动态模型,然后通过微分同胚和输入变换将其分解为四个低阶子系统,并给出了其输出跟踪的二阶动态滑模控制器的设计方法.仿真结果表明,所设计的二阶动态滑模控制器不仅能很好地跟踪给定轨迹,而且能有效地削弱滑模控制系统的抖振.     

Levant微分器参数整定算法及在高空台系统的应用

Levant基于超螺旋算法提出的滑模微分器具有滤波效果好且对特定噪声干扰不敏感等特点. 针对该微分器参数调整问题, 文章利用时间线性变换和坐标变换得到了一种有效的参数整定算法, 该算法可依据给定信号的频率和幅值确定微分器参数. 通过频域和时域对比分析表明, 本文所设计的参数整定算法可在保证跟踪滤波与微分信号提取精度的同时, 便捷地给出Levant微分器的有效参数. 最后, 本文将基于参数整定算法的Levant微分器应用到某航空发动机高空模拟试车台飞行环境模拟控制系统的环境信号处理中, 验证了所提算法的有效性及工程应用价值     

含高阶干扰的非仿射非线性系统自适应跟踪控制

本文考虑了一类带有高阶干扰和未知参数的非仿射非线性系统的自适应跟踪控制问题.为了提高系统的抗干扰性能,首先设计了扩张状态滤波器估计系统受到的高阶干扰,并把干扰估计值引入到控制器中.其次,在每一步递推设计中,为了避免backstepping方法固有的"微分爆炸"问题,引入滑模微分器估计虚拟控制律的微分,进而提出了一种新的自适应控制策略.借助Lyapunov函数理论方法分析了闭环系统的稳定性,即在所提控制策略作用下,可保证闭环系统所有信号是一致最终有界的.最后,利用MATLAB仿真验证了方法的有效性.     

非匹配不确定高阶非线性系统的滑模控制新方法

对具有非匹配不确定的高阶非线性系统,采用改进的高阶滑模微分器获取已知状态的任意阶微分估计值,再以恰当阶次的状态微分估计值之差,得到非匹配不确定项及其微分的估计值,证明了其误差任意小.为避免奇异性和抖振,采用两种方案设计了滑模控制器,并设计鲁棒项提高系统鲁棒性.基于Lyapunov~论证明了系统稳定性.同现有其他方法相比,该方法具有适用范围更广、收敛速度快、控制精度高、运算量小、保守性低等优点.最后仿真证明了本文所有结论.     

不确定非线性系统的自适应反演终端滑模控制

针对一类参数严格反馈型不确定非线性系统, 本文提出一种自适应反演终端滑模控制方法. 反演控制的前n-1步结合自适应律估计系统的未知参数, 第n步采用非奇异终端滑模, 使系统最后一个状态有限时间内收敛.利用微分估计器获得误差系统状态的导数, 并设计了高阶滑模控制律, 去除控制抖振, 使系统对于匹配和非匹配不确定性均具有鲁棒性. 同自适应反演线性滑模方法相比, 所提方法提高了系统的收敛速度和稳态跟踪精度, 并且控制信号更加平滑. 仿真结果验证了该方法的有效性.     

基于改进sigmoid函数的非线性跟踪微分器

本文受神经网络中常用的sigmoid激励函数特性的启发,提出了一种形式简单、调参相对容易的非线性跟踪微分器(STD).首先,在sigmoid函数的基础上引入指数和幅度因子,利用改进后的sigmoid函数构造加速度函数,接着,借助Lyapunov直接法证明了所设计的跟踪微分器的非摄动形式具有全局渐近稳定性,随后利用系统等价性给出了跟踪微分器的具体形式并通过扫频测试分析了其频域特性;最后,与线性微分器(LD)、全程快速跟踪微分器(HSTD)以及改进的跟踪微分器(ITD)、反正切形式的跟踪微分器(ATD)分别进行对比仿真分析.结果表明,基于sigmoid函数设计的跟踪微分器可以兼顾响应的快速性以及平稳性、全程无抖振,对信号的广义导数具有良好的逼近能力和滤波效果.     

基于反双曲正弦函数的跟踪微分器

反双曲正弦函数是光滑连续函数,具有快速并消除速度高频震颤的作用.利用反双曲正弦函数构造加速度函数,设计二阶跟踪微分器,证明了跟踪微分器的收敛性,并分析了跟踪微分器频域特性.仿真实验表明,该跟踪微分器能对输入信号进行低通滤波,且跟踪精度高,响应速度快;同时,它较好地抑制了微分信号的噪声放大效应,可以得到输入函数理想的微分信号.     

Model-free fractional order differentiator based on fractional order Jacobi orthonormal functions

The aim of this paper is to design an algebraic and robust fractional order differentiator to estimate both the Riemann–Liouville and the Caputo fractional derivatives with an arbitrary order of an unknown signal in noisy environment, without knowing the model defining the signal. For this purpose, a new class of fractional order Jacobi orthonormal functions is firstly introduced. Secondly, the truncated fractional order Jacobi orthonormal series expansion is applied to filter the noisy signal, whose fractional derivative is used to estimate the desired one. Thus, the obtained differentiator is exactly given by an integral formula which depends on a set of design parameters. Thirdly, by applying the generalized Taylor's formula, some error analysis is provided. In particular, error bounds are given, which permit to study the design parameters' influence. Fourthly, a digital fractional order differentiator is deduced in discrete noisy case. Finally, by comparing with two existing fractional order differentiators, numerical results are given to illustrate the accuracy and the robustness of the proposed fractional order differentiator.     

Z源逆变器高阶微分反馈控制研究

以航空静止变流器控制为研究对象,针对传统两级逆变结构效率低且系统复杂以及死区效应带来的死区波形畸变问题,引入Z源逆变器设计航空静止变流器。针对Z源逆变器系统高阶且非最小相位造成的控制器设计复杂的问题,引入了一种基于高阶微分器的反馈控制策略,该控制策略利用高阶微分器对系统各阶状态变量进行估计,具有不依赖于精确系统模型的特点。仿真实验表明,将此反馈控制器用于Z源逆变器输出电压控制时能够有效跟踪给定输出电压,系统受到外部扰动时依然能保持良好的静态和动态性能,满足静变流器控制需求。     

Sliding-mode observers for systems with unknown inputs: A high-gain approach

Sliding-mode observers can be constructed for systems with unknown inputs if the so-called observer matching condition is satisfied. However, most systems do not satisfy this condition. To construct sliding-mode observers for systems that do not satisfy the observer matching condition, auxiliary outputs are generated using high-gain approximate differentiators and then employed in the design of sliding-mode observers. The state estimation error of the proposed high-gain approximate differentiator based sliding-mode observer is shown to be uniformly ultimately bounded with respect to a ball whose radius is a function of design parameters. Finally, the unknown input reconstruction using the proposed observer is analyzed and then illustrated with a numerical example.     

Output-feedback control of an underwater vehicle prototype by higher-order sliding modes

This paper describes some experimental results concerning the practical implementation of a recently proposed nonlinear output-feedback control technique based on the higher-order sliding mode approach. The considered technique is applied to the motion control problem for an underwater vehicle prototype that is equipped with a special propulsion system based on hydro-jets with variable-section nozzles. To cope with the heavy uncertainties affecting the prototype dynamics the output-feedback control system has been developed by means of an observer-controller that combines a second-order sliding-mode controller and a second-order sliding-mode differentiator. The reported experiments show that the proposed approach is capable of guaranteeing fast and accurate response under several operating conditions. The control system design procedure, and the main implementation issues, are discussed in detail.     

Adaptive neural network asymptotical tracking control for an uncertain nonlinear system with input quantisation

In this paper, the problem of adaptive neural network asymptotical tracking is investigated for a class of nonlinear system with unknown function, external disturbances and input quantisation. Based on neural network technique, an adaptive asymptotical tracking controller is provided for an uncertain nonlinear system via backstepping method. In order to reduce complexity of the control algorithm in the backstepping design process, a sliding mode differentiator is employed to estimate the virtual control law and only two parameters need to be estimated via adaptive control technique. The stability of the closed-loop system is analysed by using Lyapunov function method and zero-tracking error performance is obtained in the presence of unknown nonlinear function, external disturbances and input quantisation. Finally, an application example is employed to demonstrate the effectiveness of the proposed scheme.     

Two-dimensional fractional-order digital differentiator design by using differential evolution algorithm

Designing a fractional-order digital differentiator often requires considerably complex mathematical operations and numerical approximations. Thus this paper will propose a simple method to achieve the fractional-order digital differentiator design, particularly for two-dimensional fractional-order differentiators. A two-dimensional finite impulse response (FIR) digital filter structure is utilized and designed so that its corresponding magnitude response can satisfy that of a desired fractional-order differentiator of two variables. The algorithm used to design such two-dimensional digital differentiator is the differential evolution (DE), which is one of evolutionary computations and has excellent searching capacity. The efficiency of the proposed scheme can be confirmed by some illustrative examples.