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.     

Observer design for a class of MIMO nonlinear systems

A simple observer is proposed for a large class of MIMO nonlinear systems which includes many physical models. The main characteristic of the proposed observer lies in the easiness of its implementation and calibration. Indeed, the gain of this observer does not necessitate the resolution of any dynamical system and its expression is given. Moreover, its calibration is achieved through the choice of a single parameter. A simulation example is given in order to illustrate the performance of the proposed observer.     

Nonlinear state estimation with robust convergence

The problem of designing a dynamic measurement processor for the on-line estimation of the state of a multi-input multi-output nonlinear plant is addressed. The plant can be either observable or detectable, encompassing a broad range of cases in process systems engineering. On the basis of the structure of a suitable property of robust nonlinear estimability, an estimator is built and its convergence studied, yielding sufficient conditions for robust convergence, a systematic construction, and a tractable gain tuning procedure. The estimability property has a verifiable test, and the execution of the tuning procedure, as well as the interpretation of its convergence features can be achieved within a conventional control framework for linear single-input controllers or single-output filters. The estimation of a continuous polymer reactor is considered as an application example.     

Vehicle state estimation for anti-lock control with nonlinear observer

Vehicle state estimation during anti-lock braking is considered. A novel nonlinear observer based on a vehicle dynamics model and a simplified Pacejka tire model is introduced in order to provide estimates of longitudinal and lateral vehicle velocities and the tire-road friction coefficient for vehicle safety control systems, specifically anti-lock braking control. The approach differs from previous work on vehicle state estimation in two main respects. The first is the introduction of a switched nonlinear observer in order to deal with the fact that in some driving situations the information provided by the sensor is not sufficient to carry out state estimation (i.e., not all states are observable). This is shown through an observability analysis. The second contribution is the introduction of tire-road friction estimation depending on vehicle longitudinal motion. Stability properties of the observer are analyzed using a Lyapunov function based method. Practical applicability of the proposed nonlinear observer is shown by means of experimental results.     

Time-varying increasing-gain observers for nonlinear systems

A full-order state observer for a class of nonlinear continuous-time systems is presented as generalization of the high-gain observer for having a time-varying gain that is let to be small in the first time instants, increases over time up to its maximum, and then is kept constant. The global stability of the resulting estimation error is proved by means of a Lyapunov functional via a change of coordinate. The design of such an observer is obtained by solving a nonlinear programming problem and using series expansions to set the time-varying gain.     

三相电压型PWM整流器的自抗扰控制研究

三相电压型PWM整流器是一个多输入多输出的强非线性结构,并对三相电压型PWM整流器的数学模型和自抗扰控制器进行了原理分析;为了改善整流系统抗扰性及参数摄动等问题,采用一种改进型的非线性自抗扰控制方案,同时给出了离散形式的表达式;然后,重新构造了常规自抗扰控制器中非线性状态误差反馈控制律(NLSEF)和扩张状态观测器(ESO)的非线性函数,以此来克服非线性函数的不平滑性能,从而减小整流系统输出的高频颤振现象;在MATLAB/Simulink环境下进行仿真和搭建了实验样机来验证,改进型自抗扰控制器与常规自抗扰控制器进行对比分析。结果表明了改进型自抗扰控制策略改善了交流侧电压和负载突变敏感的缺点,并降低了交流侧电流总谐波含量,且直流侧电压具有更好的动静态性和鲁棒性。     

Adaptive observers for nonlinearly parameterized class of nonlinear systems

In this paper, one proposes adaptive observers for a class of uniformly observable MIMO nonlinear systems with general nonlinear parameterizations. The state and the unknown parameters of the considered systems are supposed to lie in bounded domains which size can be arbitrarily large and the exponential convergence of the observers is shown to result under a well-defined persistent excitation condition. Moreover, the gain of the observers involves a design function that has to satisfy a simple condition which is given. Different expressions of such a function are proposed and it is shown that adaptive high gain like observers and adaptive sliding mode like observers can be derived by considering particular expressions of the design function. The theory is supported by simulation results related to the estimation of the biomass concentration and the Contois model parameters in a bioreactor.     

An adaptive high-gain observer for nonlinear systems

In this paper the authors provide a solution to the noise sensitivity of high-gain observers. The resulting nonlinear observer possesses simultaneously (1) extended Kalman filter’s good noise filtering properties, and (2) the reactivity of the high-gain extended Kalman filter with respect to large perturbations.The authors introduce innovation as the quantity that drives the gain adaptation. They prove a general convergence result, propose guidelines to practical implementation and show simulation results for an example.     

基于非线性观测器的离散驱动混沌同步

1　引言混沌同步是通过驱动信号的作用使得受迫系统的状态与驱动系统趋于一致.在系统与控制领域有一个相关问题就是通过系统的观测信号来估计该系统的状态,即“观测器”问题.混沌作为一类特殊的非线性动力系统,很自然地可引入观测器理论更系统地进行同步设计,且能用于同步方法所不能实现的某些系统中[1].混沌同步的一个主要应用方面是保密通信,而一般的同步方法均采用时间连续驱动信号,在数字通信占主流的今天,时间离散驱动的同步系统能够提供更高的频谱效率和保密性能[2,3],本文对基于观测器的混沌同步的条件进行分析,并导出了离散驱动时混…     

Nonlinear observer of the thermal loads applied to the helium bath of a cryogenic Joule–Thompson cycle

In this paper, a nonlinear observer of the thermal loads applied to the helium bath of a cryogenic refrigerator is proposed. The thermal loads represent a time-varying thermal disturbance expected to take place in future tokamaks refrigerators such as those used in the cooling systems for the International Thermonuclear Experimental Reactor (ITER) or the Japan Torus-60 Super Advanced (JT-60SA). The proposed observer can serve as a monitoring tool for cryogenic operators and/or in observer-based advanced control strategies. The observer is based on a part of the nonlinear model of the refrigerator. The paper details how the physical model of the Joule–Thompson cycle is obtained and the structure of the observer and validates its performance using experimental data.     

Nonlinear observer design via an extended observer canonical form

Based on the theory of designing unknown input observers, an extended nonlinear observer canonical form is introduced. Observers can easily be constructed for those systems which can be transformed into this canonical form. Necessary and sufficient conditions for the existence of such transformation are derived and furthermore an algorithm for calculating this transformation in given.     

Observer design for systems with multivariable monotone nonlinearities

Globally convergent observers are designed for a class of systems with multivariable nonlinearities. The approach is to represent the observer error system as the feedback interconnection of a linear system and a state-dependent multivariable nonlinearity. We first extend an earlier design (Automatica 37 (12) (2001) 1923) to multivariable nonlinearities, satisfying an analog of the scalar nondecreasing property. Next, we exploit the structure of the nonlinearity to relax the positive real restriction on the linear part of the observer error system. This relaxed design renders the feasibility conditions less restrictive, and widens the applicability of the observer, as illustrated with examples. Finally, output nonlinearities are studied and the design is extended to be adaptive in the presence of unknown parameters.     

Cascade high-gain observers for a class of nonlinear systems with large delayed measurements

This paper proposes a cascade high-gain observer for a class of triangular nonlinear systems with large and diverse time delays at states and output equation. Compared with some existing results in the literature, the main contribution is to consider the simultaneous and diverse delays in both states and output and further, to propose a cascade observer in dealing with arbitrarily large delayed measurements. By choosing a suitable Lyapunov-Krasovskii functional, the sufficient condition is presented that guarantees the exponential convergence of observation error to the origin. Simulation results on a numerical example and a practical case study involving inverted pendulum are finally given to illustrate the effectiveness of the proposed approach.     

Deadbeat观测器的一种新的设计方法及实现

ｄｅａｄｂｅａｔ观测器由于极点在原点而具有系统阵幂零的性质,本文充分利用这一性质,针对离散线性系统,提出了一种新的ｄｅａｄｂｅａｔ观测器设计方法,该方法直接利用的Ｉ／Ｏ数据估计系统内部状态,无需对系统状态有个寝估计,相应的也就可以不受寝估计误差的影响,文中给出了该观测器的具体实现步骤,并通过仿真验证了所提出方法的正确性与有效性。