迭代扩张状态观测器及其在迭代学习控制中的应用

针对一类迭代学习控制(ILC)系统的不确定项,根据时域中扩张状态观测器的思想,提出迭代域中线性迭代扩张状态观测器(LIESO),该线性迭代扩张状态观测器可以利用迭代过程的跟踪误差给出迭代学习控制系统的不确定项的显式估计。给出了基于该估计的迭代学习控制算法,并应用类Lyapunov方法证明其收敛性。仿真结果表明,所提出的迭代学习控制算法是有效的,应用迭代扩张状态观测器可以大幅度提高迭代学习效率。     

不确定线性组合大系统的二次稳定性、 联结稳定性H∞小增益定理

本文首先讨论了不确定线性系统ｘ＾．（ｔ）＝｛Ａ＋＾ｋΣｉ＝１ＤｉＦｉ（ｔ）Ｅ｝ｘ（ｔ）的二次稳定性,得到了该系统是二次稳定的充分必要条件。基于本文得到的结论讨论了不确定线性组合大系统的二次稳定性和联结稳定问题,得到了用关于低阶子系统的一组Ｈ∞模描述了大系统稳定性的充分条件。     

基于扩张观测器的非线性不确定系统输出跟踪

针对一类非线性不确定系统，设计出一种高增益扩张观测器，该观测器具有抗干扰性，可用于观测信号的n阶导数．在此基础上设计了一种控制器，使得跟踪误差及其各阶导数在不确定及扰动存在的情况下仍能迅速收敛．仿真结果表明，这种控制方法对于非线性不确定系统具有良好的控制效果．     

基于ESO的无人直升机高精度姿态控制

针对小型无人直升机存在模型参数不确定性、电磁干扰影响的问题,设计了一种基于ESO（扩张状态观测器）的高精度姿态控制方法．直升机姿态通道中的不确定部分及外界复合扰动被视为总扰动,通过ESO进行实时估计,结合状态反馈控制器实现扰动消除．试验结果表明,在0.1 s内姿态角可从0°快速跟踪到5°且无超调．最后将设计的控制器应用于研制的高精度无人驾驶系统,实现系统参数变动等条件下直升机的全自主定点悬停和航迹飞行．     

新型有限时间收敛滑模扩张状态观测器研究

针对一类具有量测噪声的非线性不确定系统,设计了基于新型滑模扩张状态观测器的Terminal滑模控制方案．首先对系统进行两次状态扩张,然后设计一种新型滑模扩张状态观测器,通过采用特殊的滑模面保证观测误差在有限时间内收敛到零．在此基础上,设计Terminal滑模控制器,使系统状态也能在有限时间内收敛到零．严格的理论证明和仿真结果均证明了所设计新型滑模观测器及闭环控制方案的有效性和快速性．     

一类不确定对象的变带宽状态观测器

研究了文献[1]提出的一类不确定对象扩张状态观测器的噪声抑制能力,并在此基础上提出一种利用改变带宽来改善观测器噪声抑制能力的方法,即让观测器的带宽成为信噪比的函数。仿真结果表明,改进后的状态观测器具有较好的噪声抑制能力和动态特性。     

基于代数神经网络的含参多元多项式近似因式分解模型

从首一无平方多项式Ｆ（ｘ,ｙ,ｔ）有根ｘ＝Хｉ（ｙ,ｔ）,ｉ＝１,２,．．．．,ｄｅｇｘ（Ｆ）,其中,Х（ｙ,ｔ）＝Ｃｉ,ｏ（ｔ）＋Ｃｉ,ｌ（ｔ）ｙ＋Ｃｉ,２（ｔ）ｙ＾２＋．．．．．．,入手,设计出一类含参二元多项式求根的神经网络模型和多项式近似因式分解的神经网络模型,为研究基神经网络的学习算法,给出基于代数神经网络的二元多项式的近似因式分解算法,提出一种新的确定误差代价函数的学习方法,相比梯度下     

惯性串联系统的自抗扰控制

针对非线性不确定惯性串联系统的控制问题,提出了惯性串联型扩张状态观测器（Extended state observer,ESO）,使其可直接对惯性串联系统的扩张状态进行估计,同时把被控对象的极点配置到期望位置,在此基础上提出了适合惯性串联系统的自抗扰控制（Active disturbance rejection control,ADRC）方法,该惯性串联型ADRC方法可以充分利用被控对象的已有知识.论文还给出了惯性串联型ADRC和基于扰动观测器（Disturbance observer,DOB）的控制方法之间的联系,指出它们具有相同的三自由度（three-degree of freedom control,3-DOF）控制系统结构和模块功能,都能实现对系统期望模型以外的总扰动进行估计和补偿.仿真结果表明,所提出的方法是有效的,惯性串联型ESO能实现系统总扰动的估计,惯性串联型ADRC能使系统输出能很好地跟踪系统参考输入.     

含死区高阶非线性系统自抗扰动态面控制

针对一类含有未知死区输入的不确定纯反馈非线性系统,为实现精准控制,提出一种新的基于扩张状态观测器的动态面控制算法.用扩张状态观测器代替函数逼近器在线估计高阶系统动态面控制中每一步的不确定函数.结果表明,估计误差显著降低,闭环控制性能得到实质性改善.此外,设计跟踪微分器来消除传统反推方案中计算复杂的问题.通过李雅普诺夫方法分析了具有自适应鲁棒控制器的闭环系统的稳定性.最后,对所提出的自适应鲁棒控制方案进行仿真,取得了满意的结果.     

直流降压变换器的降阶扩张状态观测器与滑模控制设计与实现

本文针对直流降压变换器的负载电阻扰动和输入电压变化等系统不确定因素对输出电压的影响,提出了基于降阶扩张状态观测器的滑模控制方法(SMC+RESO).首先设计降阶扩张状态观测器对系统状态,负载电阻扰动和输入电压变化进行估计,然后基于估计值利用滑模控制技术设计控制器,实现对直流降压变换器系统给定电压跟踪的快速性和准确性.值得注意的是,不同于文[1]所提出的基于扩张状态观测器的滑模控制方法(SMC+ESO),本文所提出的方法采用降阶扩张状态观测器,实现简单,且无需电流传感器,减小了实际应用的成本.利用Lyapunov稳定性定理从理论上证明了所设计的控制器可以保证闭环系统的稳定性.仿真和实验结果表明,与已有的基于扩张状态观测器的滑模控制方法相比,所提出的控制方法更好地改善了系统的跟踪性能和对干扰和不确定性的鲁棒性能,且减少了成本,但是牺牲了系统稳态性能.     

On the convergence of an extended state observer for nonlinear systems with uncertainty

The extended state observer first proposed by Jingqing Han in [J.Q. Han, A class of extended state observers for uncertain systems, Control Decis. 10 (1) (1995) 85-88 (in Chinese)] is the key link toward the active disturbance rejection control that is taking off as a technology after numerous successful applications in engineering. Unfortunately, there is no rigorous proof of convergence to date. In this paper, we attempt to tackle this long unsolved extraordinary problem. The main idea is to transform the error equation of objective system with its extended state observer into a asymptotical stable system with a small disturbance, for which the effect of total disturbance error is eliminated by the high-gain.     

针对一类非线性系统的多变量线性 扩张状态观测器及其收敛性分析

针对一类非线性不确定系统,构造了一种多变量线性扩张状态观测器（Multi-variable linear extended state observer,MVLESO）,用于实时估计非线性系统的不确定动态.采用频域分析方法,剖析了所构造的MVLESO在非线性系统不确定动态估计方面的收敛性,并推导出不确定动态的频域估计误差模型.仿真结果表明,所设计的MVLESO可以较为精准地估计出非线性系统当前的不确定动态,该特性为基于MVLESO鲁棒控制方案的有效实施奠定了基础.     

Output feedback regulation control for a class of cascade nonlinear systems by time‐varying Kalman observer

The global output feedback regulation problem is studied for a class of cascade nonlinear systems. The considered system represents more general classes of nonlinear uncertain systems, including the integral input‐to‐state stable (iISS) unmodeled dynamics, the unknown control direction, the parameter uncertainty, and the external disturbance additively in the input channel. Technically, we explore the changing supply rate technique for the iISS system to deal the iISS unmodeled dynamics and apply the Nussbaum‐type gain into the control design to overcome the unknown control direction. Additionally, a dynamic extended state observer in the form of a time‐varying Kalman observer is novelly constructed to overcome the unmeasured state components in the nonlinear uncertainties. It is shown that the global regulation problem is well addressed by the proposed method, and its efficacy is demonstrated by a fan speed control system.     

Transformation of nonlinear discrete-time system into the extended observer form

The paper addresses the problem of transforming discrete-time single-input single-output nonlinear state equations into the extended observer form, which, besides the input and output, also depends on a finite number of their past values. Necessary and sufficient conditions for the existence of both the extended coordinate and output transformations, solving the problem, are formulated in terms of differential one-forms, associated with the input–output equation, corresponding to the state equations. An algorithm for transformation of state equations into the extended observer form is proposed and illustrated by an example. Moreover, the considered approach is compared with the method of dynamic observer error linearisation, which likewise is intended to enlarge the class of systems transformable into an observer form.     

Extended state observer for uncertain lower triangular nonlinear systems subject to stochastic disturbance

The extended state observer (ESO) is the most important part of an emerging control technology known as active disturbance rejection control to this day, aiming at estimating “total disturbance” from observable measured output. In this paper, we construct a nonlinear ESO for a class of uncertain lower triangular nonlinear systems with stochastic disturbance and show its convergence, where the total disturbance includes internal uncertain nonlinear part and external stochastic disturbance. The numerical experiments are carried out to illustrate effectiveness of the proposed approach.     

Observer‐based adaptive robust control of a class of nonlinear systems with dynamic uncertainties

In this paper, a discontinuous projection‐based adaptive robust control (ARC) scheme is constructed for a class of nonlinear systems in an extended semi‐strict feedback form by incorporating a nonlinear observer and a dynamic normalization signal. The form allows for parametric uncertainties, uncertain nonlinearities, and dynamic uncertainties. The unmeasured states associated with the dynamic uncertainties are assumed to enter the system equations in an affine fashion. A novel nonlinear observer is first constructed to estimate the unmeasured states for a less conservative design. Estimation errors of dynamic uncertainties, as well as other model uncertainties, are dealt with effectively via certain robust feedback control terms for a guaranteed robust performance. In contrast with existing conservative robust adaptive control schemes, the proposed ARC method makes full use of the available structural information on the unmeasured state dynamics and the prior knowledge on the bounds of parameter variations for high performance. The resulting ARC controller achieves a prescribed output tracking transient performance and final tracking accuracy in the sense that the upper bound on the absolute value of the output tracking error over entire time‐history is given and related to certain controller design parameters in a known form. Furthermore, in the absence of uncertain nonlinearities, asymptotic output tracking is also achieved. Copyright © 2001 John Wiley & Sons, Ltd.     

基于观测器的时滞系统鲁棒控制器的设计

研究了一类不确定时滞系统基于观测器的鲁棒镇定问题,系统的不确定性时变未知且范数有界,目的是设计状态观测器和线性无记忆观测状态反馈控制器,使其能够镇定一类状态和控制输入不确定性时滞系统。基于Lyapunov稳定性理论,采用线形矩阵不等式这一有效工具,给出了系统基于观测状态反馈鲁棒镇定的充分条件,并且利用线形矩阵不等式的解构造了使得系统鲁棒稳定的基于观测状态反馈控制器,所得结果与时滞相关,从而相对减弱了控制器设计的保守性。数值算例表明了所提出的设计方法的有效性。