Active disturbance rejection control approach to output‐feedback stabilization of lower triangular nonlinear systems with stochastic uncertainty

In this paper, we apply the active disturbance rejection control approach to output‐feedback stabilization for uncertain lower triangular nonlinear systems with stochastic inverse dynamics and stochastic disturbance. We first design an extended state observer (ESO) to estimate both unmeasured states and stochastic total disturbance that includes unknown system dynamics, unknown stochastic inverse dynamics, external stochastic disturbance, and uncertainty caused by the deviation of control parameter from its nominal value. The stochastic total disturbance is then compensated in the feedback loop. The constant gain and the time‐varying gain are used in ESO design separately. The mean square practical stability for the closed‐loop system with constant gain ESO and the mean square asymptotic stability with time‐varying gain ESO are developed, respectively. Some numerical simulations are presented to demonstrate the effectiveness of the proposed output‐feedback control scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Global disturbance rejection for nonlinear lower triangular systems with iISS inverse dynamics and uncertain exosystem

This paper concerns about the global disturbance rejection problem for uncertain nonlinear lower triangular systems with integral input‐to‐state stable (iISS) inverse dynamics and an uncertain exosystem. The main challenges addressed in this paper include uncertain exosystem, unknown control direction, iISS inverse dynamics, and complex structure of lower triangular systems. Because of the presence of both uncertain exosystem and unknown control direction, simply combining the existing techniques for each of these challenges cannot solve the proposed problem. In fact, to handle the current case, appropriate new update laws for the estimators of the uncertain parameters are required, such that the estimators can be successfully integrated with the internal model principle. Furthermore, the changing supply function technique for iISS systems is utilized to deal with the iISS inverse dynamics. With the proposed controller, the closed‐loop system is globally asymptotically stable, and the disturbance is globally rejected. Two simulation examples are finally presented to show the effectiveness of the proposed control scheme and the practical relevance of our work. Copyright © 2016 John Wiley & Sons, Ltd.     

含有摩擦补偿的全方位移动机器人自抗扰控制

本文针对全方位移动机器人轨迹追踪中的摩擦补偿问题,提出了一种改进的非线性自抗扰控制器.首先建立了含有经典静态摩擦模型的全方位移动机器人动力学模型.其次,基于该模型设计非线性控制器和线性扩张状态观测器并给出了系统的稳定性分析.通过将模型已知项加入线性扩张状态观测器中得到摩擦力的估计值,并将估计值用于非线性控制器中摩擦补偿部分.为减小摩擦力对机器人低速运动轨迹追踪控制的影响,非线性控制器采用变增益控制器进行轨迹追踪控制.最后通过仿真结果验证本文提出控制器的有效性.     

不确定非仿射系统的引入动态逆的自抗扰控制器设计

针对一类不确定非仿射严反馈非线性系统,提出一种引入动态逆的线性自抗扰控制器设计方法.首先,利用微分同胚映射将严反馈非线性系统变换为积分串联型系统,然后针对积分串联型系统设计线性自抗扰控制器.提出的线性自抗扰控制器将闭环系统划分为3个时间尺度,其中线性扩张状态观测器位于最快的时间尺度上,用来估计系统的状态和总和扰动,动态逆位于次快的时间尺度上用以求解非仿射情况下的控制律,系统动态位于最慢的时间尺度上.利用奇异摄动理论分析了闭环系统的稳定性和性能.提出的自抗扰控制设计方法同样适用于控制增益不确定的仿射非线性系统.仿真和实验结果验证了提出的线性自抗扰控制器的可行性.     

航天机电伺服系统的自抗扰控制

航天机电伺服系统作用是接收火箭控制系统的指令信号并带动空气舵或者喷管跟随指令信号运动,其在应用上的主要特点是负载特性变化大.传统的PID算法在航天机电伺服系统上的应用已经比较成熟,但是在空气舵或者喷管本身负载特性发生改变时,传统的PID算法的控制效果会明显下降.因此,本文建立了航天机电伺服系统柔性运动模型,并提出了将自...     

Active disturbance rejection control to MIMO nonlinear systems with stochastic uncertainties: approximate decoupling and output-feedback stabilisation

ABSTRACT

In 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.     

时滞系统的自抗扰控制综述

时滞系统的控制一直是具有挑战性的普遍问题, 而自抗扰控制思想近年来被广泛地应用于时滞系统中. 在简要概述自抗扰控制原理的基础上, 介绍了应用自抗扰控制思想解决时滞系统问题的常用设计方法, 总结了自抗扰控制器的参数整定方法. 最后, 对今后的进一步研究进行了展望.     

具有多层感知器力矩补偿的机器人自抗扰控制

本文针对机器人系统的控制特性,提出了一种基于自抗扰控制(ADRC)的关节控制算法,该算法可以克服传统控制算法中存在的如系统抗干扰能力弱,控制性能受限于建模精度,动态性能与稳态性能难以兼顾,控制律设计较为复杂等问题.针对受控系统特性给出了一套实际控制器的完整设计方法与参数整定方法,并根据控制性能指标设计优化函数完成了最优控制参数的优化,在系统参数辨识的基础上利用多层感知器(MLP)设计了对建模不确定性的补偿网络.数值仿真和实验结果均表明该算法能够实现机器人快速稳定的轨迹跟踪,具有良好的控制精度与很强的抗干扰能力,此外该算法不依赖于精确的系统模型,降低了实际设计和应用的难度,具有很好的工程应用价值.     

事件触发下多智能体系统一致性的干扰主动控制

本文针对带有外部干扰影响的多智能体系统,研究了基于事件触发机制下的多智能体系统Leader-Following一致性的控制问题.采用干扰观测器来估计系统中存在的干扰,并设计了基于事件触发机制的干扰主动控制方案.运用现代控制理论和矩阵论等工具分析了多智能体协同运动算法得到了多智能体系统在分布式事件触发机制下的一致性收敛条件,并且分析了本文设计的分布式事件触发机制的时间间隔存在正的下界.最后通过计算机仿真,验证了本文所提控制算法的有效性.     

Active disturbance rejection control for nonlinear fractional‐order systems

This paper investigates active disturbance rejection control involving the fractional‐order tracking differentiator, the fractional‐order PID controller with compensation and the fractional‐order extended state observer for nonlinear fractional‐order systems. Firstly, the fractional‐order optimal‐time control scheme is studied to propose the fractional‐order tracking differentiator by the Hamilton function and fractional‐order optimal conditions. Secondly, the linear fractional‐order extend state observer is offered to acquire the estimated value of the sum of nonlinear functions and disturbances existing in the investigated nonlinear fractional‐order plant. For the disturbance existing in the feedback output, the effect of the disturbance is discussed to choose a reasonable parameter in fractional‐order extended state observer. Thirdly, by this observed value, the nonlinear fractional‐order plant is converted into a linear fractional‐order plant by adding the compensation in the controller. With the aid of real root boundary, complex root boundary, and imaginary boot boundary, the approximate stabilizing boundary with respect to the integral and differential coefficients is determined for the given proportional coefficient, integral order and differential order. By choosing the suitable parameters, the fractional‐order active disturbance rejection control scheme can deal with the unknown nonlinear functions and disturbances. Finally, the illustrative examples are given to verify the effectiveness of fractional‐order active disturbance rejection control scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

舵鳍联合自抗扰主从控制策略设计

在分析舰船航行中所受干扰特性的基础上,针对目前舵鳍联合控制中存在的问题,以虚拟控制力作为中间变量,设计了主从结构的舵鳍联合控制策略.主控制器采用非线性干扰观测器对环境扰动和模型不确定性进行估计,在此基础上以虚拟控制力作为控制量采用自抗扰结构,对船舶三自由度运动进行联合控制.同时,在主控制器设计中包含了舵/鳍伺服系统的实际约束,保证了从控制器解的可行性.基于遗传算法设计了数值反演从控制器,求取最终的控制量.通过船模试验和仿真对所设计的控制器进行了验证,试验和仿真结果表明所设计的两步主从控制策略具有较好的控制效果.     

Active disturbance rejection based load frequency control and voltage regulation in power systems

An active disturbance rejection controller (ADRC) is developed for load frequency control (LFC) and voltage regulation respectively in a power system. For LFC, the ADRC is constructed on a three area interconnected power system. The control goal is to maintain the frequency at nominal value (60Hz in North America) and keep tie line power flow at scheduled value. For voltage regulation, the ADRC is applied to a static var compensator (SVC) as a supplementary controller. It is utilized to maintain the voltages at nearby buses within the ANSI C84.1 limits (or ±5% tolerance). Particularly, an alternative ADRC with smaller controller gains than classic ADRC is originally designed on the SVC system. From power generation and transmission to its distribution, both voltage and frequency regulating systems are subject to large and small disturbances caused by sudden load changes, transmission faults, and equipment loss/malfunction etc. The simulation results and theoretical analyses demonstrate the effectiveness of the ADRCs in compensating the disturbances and achieving the control goals.     

Active disturbance rejection control: Applications in aerospace

Control of uncertain dynamical systems has been an area of active research for the past several decades and to this end,various robust control approaches have been proposed in the literature. The active disturbance rejection control (ADRC) representsone prominent approach that has been widely studied and applied for designing robust controllers in diverse areas of engineeringapplications. In this work, a brief review of the approach and some of its applications in aerospace are discussed. The resultsshow that the approach possesses immense potential to offer viable solution to reallife aerospace problems.     

On active disturbance rejection control for nonlinear systems with multiple uncertainties and nonlinear measurement

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.     

时延系统的自抗扰动态面控制

本文针对高阶时延系统同时存在系统不确定性和未知输入时延的情况,考虑控制器信号的复杂性问题,在动态面控制方法的基础上,引入自抗扰控制技术设计了自抗扰动态面控制器.利用反步法设计动态面控制信号,采用跟踪微分器对虚拟控制信号滤波,避免了由于对虚拟控制信号重复微分产生的"复杂性爆炸"问题;在控制信号的基础上叠加扰动补偿项,补偿项由扩张状态观测器实时在线估计产生,保证了控制信号的实时性,同时简化了控制器结构以便于实际应用.在闭环系统稳定性判别中运用李雅普诺夫理论做出详细分析.最后,数值仿真结果验证了所提出方法的有效性.     

An approach to improve active disturbance rejection control

ABSTRACT

In order to reduce the error and phase delay of the classical extended state observer (ESO) in estimating the system state and disturbance, in this paper, we combine ESO and tracking differentiator (TD) to construct a tracking differential extended state observer (TDESO). The observation error and observation speed of TDESO are also discussed. Then a nonlinear active disturbance rejection control system improved by TDESO for a linear plant is transformed into a Lurie system. Moreover, the circular criterion is used to analyse the absolute stability of the transformed Lurie system. Finally, TDESO is optimised and an improved linear state error feedback (PLSEF) is proposed to improve the rapidity of the system by using simulation and time domain analysis. And a second-order system is used to illustrate the performance of the proposed scheme. The simulation results show that our algorithm is effective.     

The active disturbance rejection control approach to stabilisation of coupled heat and ODE system subject to boundary control matched disturbance

We consider stabilisation for a linear ordinary differential equation system with input dynamics governed by a heat equation, subject to boundary control matched disturbance. The active disturbance rejection control approach is applied to estimate, in real time, the disturbance with both constant high gain and time-varying high gain. The disturbance is cancelled in the feedback loop. The closed-loop systems with constant high gain and time-varying high gain are shown, respectively, to be practically stable and asymptotically stable.     

永磁同步电机自抗扰反步控制

为实现永磁同步电机的高性能控制,提出一种复合控制策略。在永磁同步电机矢量控制基础上,设计反步控制器用于电流环控制,得到同步旋转坐标系下定子电压,并能保证系统全局稳定。设计结构优化的线性自抗扰控制器用于速度环控制,提高系统抗干扰能力。采用二阶环节平滑速度指令,实现转速无超调。仿真结果表明该控制策略较传统PI控制具有转速适应范围广、无超调、抗扰动性能强等优点。     

自抗扰控制对具边界扰动和区间内反阻尼的波动方程的镇定

本文讨论边界具有外部扰动和区域内具有反阻尼的一维波动方程的的镇定问题. 主要的方法是后退反演变换和自抗扰控制方法. 即通过扩张状态观测器将扰动在线估计并在反馈控制中实时消除. 本文在扩张状态观测器中使用了两种增益调整策略——常数高增益与时变增益. 为避免常数高增益带来的峰值问题, 在控制环节中使用了饱和方法. 时变的增益可以在很大程度上减少扩张状态观测器中由于常数高增益引起的峰值问题同时可以达到完全消除干扰的镇定效果.     

On convergence of active disturbance rejection control for a class of uncertain stochastic nonlinear systems

In this paper, the practical mean-square convergence of active disturbance rejection control for a class of uncertain stochastic nonlinear systems modelled by the Itô-type stochastic differential equations with vast stochastic uncertainties is developed. We first design an extended state observer (ESO) to estimate both the unmeasured states and the stochastic total disturbance which includes unknown internal system dynamics, external stochastic disturbance without known statistical characteristics, unknown stochastic inverse dynamics, and uncertainty caused by the deviation of control parameter from its nominal value. The stochastic total disturbance is then cancelled (compensated) in the feedback loop. An ESO-based output-feedback control is finally designed analogously as for the system without uncertainties. The practical mean-square reference tracking and practical mean-square stability of the resulting closed-loop system are achieved. The numerical experiments are carried out to illustrate the effectiveness of the proposed approach.