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.     

高动态离心机系统的自抗扰控制设计

针对传统PID在控制高速精密离心机系统时难以满足其高动态过程的要求,对系统目标过渡过程进行安排并设计了自抗扰控制器.所提出的自抗扰控制器包括3个部分:跟踪微分器、扩张状态观测器和误差反馈控制器.由于离心机在启动和制动阶段,系统状态会经历一个快速变化的过程,所以在离心机系统动态变化阶段采用跟踪微分器对目标函数进行过渡过程安排,防止系统出现过大超调;并且设计了扩张状态观测器对系统未知干扰进行估计和补偿;补偿后采用误差反馈控制器实现离心机系统高动态过程的跟踪控制.最后通过对自抗扰控制进行参数整定,使得系统满足所提出的各项性能指标要求.仿真结果验证了相比于传统PID控制,所提出的自抗扰控制器在超调量,调节时间以及稳态控制精度等性能指标上具有优越性.     

Active DIsturbance Rejection Control of Surface Vessels Using Composite Error Updated Extended State Observer

In this paper, a composite‐errors‐based active disturbance rejection control law is proposed for surface vessels with exogeneous disturbances. The low‐frequency disturbances from wind, wave and ocean currents are estimated by a novel composite‐errors‐based extended state observer (ESO). Since the composite errors are composed of trajectory tracking errors and estimation errors, the disturbance rejection control is feedforward‐feedback composite control. The advantages of feedforward control and feedback control are exploited to reject system disturbances. Compared with conventional ESO‐based active disturbance rejection control, smaller estimation errors and smaller tracking errors can be achieved by the proposed disturbance compensation control. The effectiveness and superiority of the designed control law are illustrated by theoretical analysis and simulation results.     

Differential flatness‐based ADRC scheme for underactuated fractional‐order systems

This article mainly studies the fractional‐order active disturbance rejection control (FOADRC) schemes for the underactuated commensurate fractional‐order systems (FOSs). The FOADRC framework for linear FOSs‐based fractional proportion integration differentiation is constructed by using the fractional‐order tracking differentiator and the fractional‐order extended state observer, and the necessary conditions for the system to have stable controllers are provided. The FOADRC scheme for underactuated FOSs based on differential flatness is proposed. For underactuated FOSs, a set of flat output expressions with a fixed format is given under the controllable condition of the system. Moreover, making the flat output as the equivalent of the system output is simple and easy to analyze and calculate. Subsequently, the FOADRC scheme is designed by using the flat output. Finally, the scheme proposed in this article is verified by a simulation example.     

直线型倒立摆的自抗扰控制设计方案

对直线型倒立摆系统,采用自抗扰控制技术来设计控制方案.对于这样的单输入双输出、强非线性、强耦合的不稳定系统,在原自抗扰控制算法的基础上,通过增加一个跟踪微分器和控制律由两个被控量的误差组合构成的方法,突破了原有的自抗扰控制算法只适用于单输入单输出系统的限制,实现了摆的偏角和小台车位移的良好控制效果,数字仿真结果证实了这种方法的有效性.     

Active Disturbance Rejection Control of a Magnetic Suspension System

This paper proposes a novel output feedback control scheme for robust stabilization and tracking tasks in a magnetic suspension system. Active disturbance rejection control, differential flatness and on‐line asymptotic disturbance estimation are properly used for the proposed control synthesis. The controlled system is subjected to a wide spectrum of unknown significant matched and unmatched disturbances due to external forces and voltages, parametric uncertainties, control and state‐dependent perturbations and possibly input unmodeled dynamics. The effectiveness and robustness of the proposed active disturbance control scheme is verified by computer simulations for the robust tracking of a rest‐to‐rest reference position trajectory specified to firstly stabilize the suspended mass at a desired vertical position and next transfer it to another equilibrium position for both continuous and switched control voltage signals.     

复杂条件下倒立摆摆角控制设计与实验研究

首先,研究复杂条件下倒立摆系统的自抗扰摆角控制,将实际系统存在的周期扰动、模型不确定性和间隙迟滞非线性等效成控制系统的输入端扰动．然后,利用扩张状态对输入端扰动进行建模和估计,通过设计扩张状态观测器和状态反馈实现复杂条件下倒立摆系统的摆角控制．最后,针对一类直线倒立摆进行仿真和实验研究．实验结果表明,倒立摆系统的自抗扰摆角控制能够克服三类影响因素对系统性能的影响,并保持良好的控制效果．     

并网逆变器逆系统自学习滑模抗扰控制

针对三相并网逆变器模型的多变量、非线性、强耦合等特点,采用开关函数法建立其开关周期平均模型,在此模型的基础上采用逆系统方法实现反馈线性化和解耦控制,对伪线性系统设计自适应滑模抗扰控制器,使用非线性光滑函数设计扩张状态观测器以实现内部建模误差与外部扰动的扩张状态估计,并将非线性扩张状态观测器和跟踪微分器与自学习滑模控制器结合使用.仿真结果表明,该方法具有响应速度快、控制精度高、抗扰能力强的特性,在并网逆变器中具有较大应用价值.     

航天器姿态自抗扰控制

为抑制航天器自身结构参数变化和内外扰动对姿态控制精度和姿态稳定度的影响, 设计了航天器姿态自抗扰控制器. 自抗扰控制器(ADRC)由跟踪微分器(TD)、扩张状态观测器(ESO)和姿态反馈控制器(AFC)3部分组成.跟踪微分器负责安排姿态指令过渡过程, 并提取其微分信号. 扩张状态观测器(ESO)充分利用姿态敏感器与速率陀螺的量测信息, 可对航天器姿态及内部和外部干扰进行观测. 姿态反馈控制器则在补偿ESO估计的干扰的同时,实现航天器的姿态控制. 与已有研究相比, 扩张状态观测器采用复合量测信息对状态估计进行校正, 性能较好. 而自抗扰控制器只采用一个环路即可实现姿态控制及干扰补偿, 结构简单. 对某航天器姿态控制系统的仿真结果表明,以上自抗扰控制器是可行的.     

A high-performance flight control approach for quadrotors using a modified active disturbance rejection technique

In practice, the parameters of the flight controller of the quadrotors are commonly tuned experimentally with respect to a certain type of reference, such as the step reference and the unit-ramp reference. In this way, the performance of the flight controller might be affected by the variations of the references in real-time flights. Besides, real-time dynamic effects such as measure noises, external disturbances and input delays, which are usually neglected in the reported works, could easily deteriorate the performances of the flight controllers. This work is thereby motivated to develop a high-performance flight control approach utilizing a modified disturbance rejection technique for the quadrotors suffering from input delays and external disturbances. This control approach is developed in a cascaded structure and the attitude angles are chosen as the pseudo control inputs of the translational flight of the quadrotors. To facilitate the development, the dynamic model of the quadrotors is firstly formulated by including the effects of input delays, and the dynamics of the pseudo control variables are identified through real-time experiments. Based on the identified model, the flight control approach is proposed with a modified active disturbance rejection technique, which consists of a time optimal tracking differentiator, an extended state observer/predictor, and a nonlinear proportional–derivative controller. The tracking differentiator is designed to generate smooth transient profiles for the references, and the extended state observer/predictor is implemented for lumped disturbance estimation and state estimation considering the input delays. With the aid of the tracking differentiator and the extended state observer/predictor, the nonlinear proportional–derivative controller can thereby establish a fast tracking control and effectively reject the estimated disturbances. To verify the feasibilities of this development, comparative tests are carried out in both simulations and experiments. The results show that in the presence of small lumped disturbances, such as the measurement zero-drift, the steady-state errors of the proposed control approach for the ramp responses are less than 2 cm, and in the tests of sinusoidal trajectory tracking, the cross-tracking errors are less than 0.04 m. When with large disturbance airflow that is equivalent to strong breeze, the steady-state error achieved by the proposed flight controller is also less than 10 cm. All of these facts demonstrate the effectiveness of this development.     

移动机器人轨迹跟踪快速终端滑模自抗扰控制

针对移动机器人动力学模型难以精确建立、运动过程中各种干扰对高精度轨迹跟踪造成偏航等问题,构造出一种快速终端滑模自抗扰控制器,实现了高速高精度轨迹跟踪控制目标.首先建立非完整移动机器人的干扰控制模型;然后运用扩张状态观测器实时监测系统未建模动态与各种干扰;同时将扩张状态量和系统反馈量作为快速终端滑模算法的系统变量;最后设...     

基于线性自抗扰的开关磁阻电机调速控制研究

开关磁阻电机调速系统是复杂的非线性时变系统,负载扰动大,变量之间耦合严重,针对上述系统的性能特点提出采用线性自抗扰控制策略对系统进行控制的方法。首先为克服负载扰动变化,电机磁链呈非线性以及电流、位置等参数耦合的内外部干扰问题,设计扩张状态观测器对系统内扰和外扰进行准确估计并实时补偿。然后设计PD（比例-微分）控制器抑制系统给定与扩张状态观测器反馈的观测对象状态变量之间的跟踪误差。最后在仿真平台上对设计的控制系统进行试验并与传统PID控制方案进行对比,结果显示,对于给定的阶跃信号线性自抗扰控制器只需0.09s即可达到稳态且无超调,而PID控制器需要3s才能实现稳定跟踪。因此相比于传统PID控制,线性自抗扰控制器拥有更优的动静态性能,并且系统在外部负载扰动和内部模型参数变化的情况下也有良好的控制效果,表现出了很好的鲁棒特性。     

基于定量反馈理论的时滞系统自抗扰控制参数整定

工业过程对象普遍存在时滞、模型参数不确定性和外部扰动多等特点,传统Smith预估控制方法难以设计出满足期望性能的鲁棒控制器.针对模型参数不确定性和外部扰动,本文采用自抗扰控制技术进行估计和补偿.针对系统存在时滞的特点,本文提出改进Smith预估器结构,提升扩张状态观测器对于扰动估计的实时性.在此基础上,本文以一阶时滞系统为例提出了控制器参数整定方法.首先根据最优参数选取准则确定预估器模型,然后在等效模型框架下采用定量反馈理论整定自抗扰控制器参数,确保控制系统达到预期性能指标.在仿真实验中,将所提出方法与几种常见时滞系统控制方法进行比较,通过设定值跟踪、抗扰及蒙特卡罗实验验证了所提出方法具有良好抗扰能力与鲁棒性.     

Anti‐windup design of active disturbance rejection control for sampled systems with input delay

A novel anti‐windup design of active disturbance rejection control (ADRC) is proposed for industrial sampled systems with input delay and saturation. By using a generalized predictor to estimate the delay‐free system output, a modified extended state observer is designed to simultaneously estimate the system state and disturbance, which could become an anti‐windup compensator when the input saturation occurs. Accordingly, a feedback controller is analytically designed for disturbance rejection. By proposing the desired closed‐loop transfer function for the set‐point tracking, a prefilter is designed to tune the tracking performance while guaranteeing no steady‐state output tracking error. A sufficient condition for the closed‐loop system stability is established with proof for practical application subject to the input delay variation. Illustrative examples from the literature are used to demonstrate the effectiveness and merit of the proposed control design.     

基于扩张状态观测器的UCAV自适应滑模控制

针对固定翼UCAV（Unmanned Combat Aerial Vehicle）系统中存在的不确定性和外部扰动，设计了一种基于扩张状态观测器的自适应超扭曲滑模控制器用来抑制系统扰动，从而提高对于UCAV的控制性能。建立固定翼UCAV的六自由度非线性模型，针对姿态控制和速度控制分别设计扩张状态观测器对模型中难以精确测量的状态量和外部扰动进行估计，依据奇异摄动原理分别对姿态和速度设计自适应超扭曲滑模控制器，实现对UCAV的姿态和速度的跟踪控制。采用某型固定翼UCAV非线性模型对所设计的控制器进行仿真验证，并且与传统的自抗扰滑模控制方法进行了对比，仿真结果表明，基于扩张状态观测器的自适应超扭曲滑模控制器具有更小的超调量和稳态误差。     

快速路交通密度的自抗扰控制器设计及不同扰动情况下的性能评价

本文针对快速路主道交通密度的控制问题,提出了一种新的自抗扰匝道调节方法.该方法包括跟踪微分器(TD)、扩展状态观测器(ESO)和非线性输出误差反馈控制律(NLOEF)3个部分.通过微分跟踪环节安排的过渡过程,可有效降低系统的超调;而系统外部不确定性可通过ESO估计,并将估计信息用于NLOEF更新控制信号.本文分别基于宏观MATLAB和微观PARAMICS平台进行了仿真研究,验证了所提出方法抑制不同类型外部扰动的有效性.     

On Finite‐Time Stabilization of Active Disturbance Rejection Control for Uncertain Nonlinear Systems

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.     

Stabilization of a Timoshenko Beam With Disturbance Observer‐Based Time Varying Boundary Controls

This paper is concerned with the boundary feedback stabilization for a Timoshenko beam with external disturbances in the boundary inputs. Based on the idea of active disturbance rejection controls, extended state observers with the time‐varying gains are designed to estimate disturbances and then a control strategy is presented by canceling the disturbances via the feedback channels. The well‐posedness of the resulting closed‐loop system is proved by the dual theory and admissibility theory, and the relationship between the stability and the disturbance is interpreted by Lyapunov's second method. At the end, the numerical experiment illustrate the effectiveness of the proposed control strategy.     

连续搅拌反应釜系统的自抗扰控制

针对连续搅拌反应釜系统(CSTR)大滞后,大惯性以及动态特性随工况不确定性变化的特点,通过设计参数可调的跟踪微分器和扩张状态观测器,改进经典PID算法的固有缺陷,提出不依赖于精确CSTR模型的离散自抗扰控制方案,采用西门子新一代工业可编程控制器-SIMATIC PCS7在多功能过程与控制系统的CSTR实验仿真对象上实现...