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Stability of active disturbance rejection control (ADRC) is analysed in the presence of unknown, nonlinear, and time-varying dynamics. In the framework of singular perturbations, the closed-loop error dynamics are semi-decoupled into a relatively slow subsystem (the feedback loop) and a relatively fast subsystem (the extended state observer), respectively. It is shown, analytically and geometrically, that there exists a unique exponential stable solution if the size of the initial observer error is sufficiently small, i.e. in the same order of the inverse of the observer bandwidth. The process of developing the uniformly asymptotic solution of the system reveals the condition on the stability of the ADRC and the relationship between the rate of change in the total disturbance and the size of the estimation error. The differentiability of the total disturbance is the only assumption made. 相似文献
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Ze-Hao Wu 《International journal of control》2020,93(6):1408-1427
ABSTRACTIn this paper, we apply the active disturbance rejection control, an emerging control technology, to output-feedback stabilisation for a class of uncertain multi-input multi-output nonlinear systems with vast stochastic uncertainties. Two types of extended state observers (ESO) are designed to estimate both unmeasured states and stochastic total disturbance which includes unknown system dynamics, unknown stochastic inverse dynamics, external stochastic disturbance without requiring the statistical characteristics, uncertain nonlinear interactions between subsystems, and uncertainties caused by the deviation of control parameters from their nominal values. The estimations decouple approximately the system after cancelling stochastic total disturbance in the feedback loop. As a result, we are able to design an ESO-based stabilising output-feedback and prove the practical mean square stability for the closed-loop system with constant gain ESO and the asymptotic mean square stability with time-varying gain ESO, respectively. Some numerical simulations are presented to demonstrate the effectiveness of the proposed output-feedback control scheme. 相似文献
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With the rapid deployments of the active disturbance rejection control (ADRC) as a bonafide industrial technology in the background, this paper summarizes some recent results in the analysis of linear ADRC and offers explanations in the frequency response language with which practicing engineers are familiar. Critical to this endeavor is the concept of bandwidth, which has been used in a more general sense. It is this concept that can serve as the link between the otherwise opaque state space formulation of the ADRC and the command design considerations and concerns shared by practicing engineers. The remarkable characteristics of a simple linear ADRC was first shown in the frequency domain, followed by the corresponding analysis in timedomain, where the relationship between the tracking error and the ADRC bandwidth is established. It is shown that such insight is only possible by using the method of solving linear differential equations, instead of the more traditional techniques such as the Lyapunov methods, which tend to be more conservative and difficult to grasp by engineers. The insight obtained from suchanalysis is further demonstrated in the simulation validation. 相似文献
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The existing active disturbance rejection control (ADRC) method may not provide sufficient disturbance rejection to multiple mismatched disturbances for the fractional order systems. In this paper, a composite disturbance rejection approach is developed for a class of fractional order uncertain systems, by synthesizing the fractional order ADRC (FOADRC) approach and a disturbance observer (DO)-based compensation scheme. Taking advantage of more disturbance information and a filter structure, an improved DO is developed to achieve precise estimation of disturbances in the presence of sensor noises. In addition, a state transformation is developed to convert the system into a simple integral chain model with only matched disturbances. Then a composite control law is designed to compensate the disturbances and provide satisfying dynamic performance. The efficiency of the proposed method is demonstrated by a numerical simulation and an actual servo control simulation, as well as the comparison with two kinds of the existing ADRC methods and the commonly used integral sliding mode control (I-SMC) method. 相似文献
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This paper designs the active disturbance rejection control (ADRC) to achieve finite‐time stabilization for a class of uncertain nonlinear systems. The proposed control incorporates both an extended state observer (ESO) as well as an adaptive sliding mode controller. The ESO is utilized to estimate the full system states and the total uncertainties, and the adaptive strategy is incorporated to deal with the estimation errors. It is proved that, with the application of the proposed control law, semi‐global finite‐time stabilization can be achieved. Effectiveness of the proposed method is illustrated with a numerical example. 相似文献
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A generalized extended state observer (GESO) is devised to improve the disturbances rejection performance in a repetitive‐control system (RCS) for a class of single‐input, single‐output nonlinear plants with nonintegral chain form and mismatched disturbances. By appropriately choosing a disturbance compensation gain and incorporating the disturbance estimate into a repetitive control law, a GESO‐based RCS is established. In this system, the repetitive controller ensures tracking of a periodic reference input, and the incorporation of the disturbance compensation into the control input enables attenuating the lumped disturbance from the system output. Stability criteria and design algorithms have been developed for the system. A case study on the speed control of a rotational control system exhibits that the GESO‐based RCS delivers not only a promising disturbance rejection performance but also a superior property of tracking performance. 相似文献
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Zhiqiang Gao 《Asian journal of control》2014,16(6):1612-1622
Piezoelectric beam dynamics are characterized by elastic properties, nonlinearities, uncertainties, and unknown disturbances, thus making vibration suppression a challenging control problem. To meet this challenge, a novel active control method has been designed and rigorously tested on actual hardware without the requirement of extensive modeling. In this unique approach, the piezoelectric beam dynamics, known or unknown, linear or nonlinear, and all external disturbances are treated in their totality as an input disturbance which is subsequently estimated and canceled in real time, reducing the challenging problem to a very manageable one. Simulation and experimental results demonstrate the effectiveness of this practical control method. The frequency domain characteristics of the proposed method are analyzed using Bode and describing function methods. 相似文献
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针对一类包含模型不确定和外界干扰等非重复扰动的线性离散系统,本文通过将迭代学习控制与自抗扰技术相结合,提出一种新的基于扩张观测器的鲁棒迭代学习控制方法.本文以时间轴和迭代轴两个方向同时出发考虑系统的非重复扰动估计和稳定收敛问题.将与时间和迭代轴同时相关的模型不确定及外界干扰等因素归纳为系统总扰动,针对其非重复变化特性给出了扩张观测器的设计,保证在批次内快速、准确地估计系统总扰动;基于上述扰动估计,设计新型的迭代学习控制律,利用线性矩阵不等式方法证明了整个鲁棒迭代学习系统的稳定性和收敛性,并给出合理的控制器参数估计条件.此外,讨论了迭代学习控制中第一批次的控制律设计问题,给出合理的自抗扰控制器设计.最后通过仿真对比实验验证了本文方法的可行性和有效性. 相似文献
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二阶自抗扰控制器的参数简化 总被引：5，自引：0，他引：5
为了克服PID控制器自身具有的缺陷,在PID的基础上提出了自抗扰控制器（ADRC）。该控制器由跟踪微分器、扩张状态观测器和非线性状态误差反馈三部分组成,其控制效果优于经典PID控制器,但是参数众多、调节复杂。通过线性简化和参数整合建立简化的线性自抗扰控制器。MATLAB仿真表明,简化的线性自抗扰控制器参数调节过程大大简化,而控制性能并未受到明显影响。 相似文献
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为实现导弹对目标的高精度拦截, 本文提出了基于加权齐次函数的非线性自抗扰拦截制导设计方法. 首先, 提出了基于加权齐次函数的非线性扩张状态观测器在线估计视线角速率和由目标加速度等内外不确定性因素构成的总扰动. 其次, 设计了基于非线性扩张状态观测器的非线性自抗扰三维制导律对总扰动进行补偿, 该制导律克服了高阶非线性项与强耦合项等不利因素的影响, 提高了拦截制导精度. 本文通过分析误差系统的动力学行为证明了闭环制导系统的稳定性和收敛性. 本文提出的方法在拦截精度等方面优于已有的基于线性扩张状态观测器和基于fal函数的扩张状态观测器的自抗扰制导方法. 仿真结果验证了本文所提出方法的有效性和优越性. 相似文献
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自抗扰控制技术应用已日渐成熟, 但当系统中存在高频非平稳噪声信号时, 线性自抗扰控制(LADRC) 存在难以选取合适的观测器带宽的问题: 当带宽较小时, 线性扩张状态观测器(LESO)难以实现对总扰动的实时观测, 会造成时滞; 当带宽较大时, LESO又会放大噪声对系统的影响, 从而造成总扰动观测失真. 为了解决这一问题, 将小波降噪环节加入LADRC中, 通过设计基于滑动窗实时小波降噪的LESO, 对含噪输出信号进行实时降噪. 使用Simulink搭建系统模型, 分别在输出信号中加入高斯白噪声或谐波等不同类型的高频非平稳噪声进行仿真实验, 并将所提方法与滑动平均法进行对比, 结果验证了所提方法的有效性. 相似文献
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自抗扰控制技术应用已日渐成熟,但当系统中存在高频非平稳噪声信号时,线性自抗扰控制(LADRC)存在难以选取合适的观测器带宽的问题:当带宽较小时,线性扩张状态观测器(LESO)难以实现对总扰动的实时观测,会造成时滞;当带宽较大时,LESO又会放大噪声对系统的影响,从而造成总扰动观测失真.为了解决这一问题,将小波降噪环节加入LADRC中,通过设计基于滑动窗实时小波降噪的LESO,对含噪输出信号进行实时降噪.使用Simulink搭建系统模型,分别在输出信号中加入高斯白噪声或谐波等不同类型的高频非平稳噪声进行仿真实验,并将所提方法与滑动平均法进行对比,结果验证了所提方法的有效性. 相似文献
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The paper proposes a novel control design for nonlinear systems with multiple uncertainties and nonlinear measurement. The output linearization is utilized to handle the nonlinearities in system dynamics and measurement. Firstly, the integrator chain for nonlinear systems with multiple uncertainties is analyzed. Based on the fundamental integrator chain form, the equivalent total effect of multiple uncertainties is summarized as total disturbance. By timely estimating and compensating for the total disturbance, an active disturbance rejection control design to handle both multiple uncertainties and nonlinear measurement is proposed. Moreover, the transient performance of the corresponding closed‐loop system is rigorously studied, which theoretically reveals the high consistence of the tracking performance despite various multiple uncertainties. 相似文献
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This paper deals with the problem of active disturbance rejection control (ADRC) design for a class of uncertain nonlinear systems with sporadic measurements. A novel extended state observer (ESO) is designed in a cascade form consisting of a continuous time estimator, a continuous observation error predictor, and a reset compensator. The proposed ESO estimates not only the system state but also the total uncertainty, which may include the effects of the external perturbation, the parametric uncertainty, and the unknown nonlinear dynamics. Such a reset compensator, whose state is reset to zero whenever a new measurement arrives, is used to calibrate the predictor. Due to the cascade structure, the resulting error dynamics system is presented in a non-hybrid form, and accordingly, analyzed in a general sampled-data system framework. Based on the output of the ESO, a continuous ADRC law is then developed. The convergence of the resulting closed-loop system is proved under given conditions. Two numerical simulations demonstrate the effectiveness of the proposed control method. 相似文献
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三阶扩张状态观测器的优化参数配置方法 总被引：2，自引：0，他引：2
研究三阶非线性扩张状态观测器扰动观测性能的优化问题。首先,采用系数冻结法固定与观测器状态相关的非线性系数,利用线性系统的极点配置方法进行频带拓展;然后,分析配置后的极点随非线性系数的变化规律,在此基础上,提出一种保证扰动观测带宽受系统状态变化影响最小的参数配置方法;最后,通过算例和仿真对比表明了所提出参数配置方法的有效性和优越性。 相似文献
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为了解决传统扩张状态观测器存在对系统状态跟踪速度慢、跟踪精度低的问题,基于滑模控制方法设计一种新型三阶固定时间收敛滑模非线性扩张状态观测器,并对其收敛时间和稳态误差进行分析.首先,提出一种新型固定时间收敛滑模面和滑模趋近律,并借助滑模控制方法设计得到滑模非线性扩张状态观测器;然后,利用Lyapunov函数证明该滑模非线性扩张状态观测器能够实现固定时间收敛,并分析其对系统扰动的估计误差;最后,仿真对比实验表明,与传统扩张状态观测器相比,所提出滑模非线性扩张状态观测器能够实现对系统状态快速且高精度的跟踪、具有显著的性能优势. 相似文献
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针对表面式永磁同步电机( SPMSM) 驱动系统的非线性特点,着眼于调速系统的高性能要求,基于互联和阻尼配置的能量成形方法和端口受控耗散哈密顿( PCHD) 系统原理,研究了SPMSM 系统的统一PCHD 建模和速度控制问题。首先,从能量平衡的观点,建立了逆变器、考虑铁损的SPMSM、机械负载一体的不确定系统统一PCHD 数学模型,然后在此基础上,设计了SPMSM 驱动系统的无源控制器,逆变器非线性扰动由扩张状态观测器进行补偿,最后利用自抗扰控制设计了速度调节器得到q 轴期望的电流,所得控制器更加简单和容易实现。仿真结果表明,所提方法实现了全局稳定性控制、鲁棒性强; 调速系统具有优良的动、静态性能。 相似文献