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.     

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.     

拦截高速机动目标的非线性自抗扰制导律

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.     

A composite fractional order active disturbance rejection control method for a class of uncertain systems with multiple disturbances

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.     

Cascade active disturbance rejection control of single-rod electrohydrostatic actuator

Electrohydrostatic actuators (EHAs) are used to replace traditional centralized hydraulic systems to reduce weight and improve efficiency and maintainability. This paper proposes a cascade active disturbance rejection control (C-ADRC) method for single-rod EHAs with parametric uncertainties and severe external disturbances. The studied EHA can be transformed into a cascade connection of a first-order pressure system and a second-order position system. Two linear active disturbance rejection controllers are designed for the inner pressure system and the outer position system to estimate and compensate for various uncertainties in the two loops, respectively. The uniqueness of the C-ADRC is that the two linear active disturbance rejection controllers are designed by making full use of the measurable states and known model information of the EHA system. It is theoretically proved that the closed-loop system is semi-globally uniformly ultimately bounded. Moreover, the proposed controller can theoretically ensure position tracking with desired accuracy as the bandwidth of extended state observers (ESOs) becomes sufficiently high. Simulation and experimental results verify the effectiveness of the proposed method.     

基于滑动窗实时小波降噪的扩张状态观测器及自抗扰控制EI北大核心CSCD

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.     

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.     

On the conditions of exponential stability in active disturbance rejection control based on singular perturbation analysis

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.     

Analytical design of active disturbance rejection control for nonlinear uncertain systems with delay

For first-order nonlinear uncertain systems with delay, the analytical design of active disturbance rejection control (ADRC) with matched time delay is rigorously studied. The conditions of stabilizing the closed-loop system are studied in the form of parameters’ explicit sets such that the tuning laws of ADRC can be directly obtained and intuitively demonstrated in engineering practice. The necessary and sufficient condition of the asymptotical stability for the closed-loop system in the case of linear time-invariant is explicitly given. The condition of stabilizing the closed-loop system with nonlinear uncertain dynamics is quantitatively presented. Moreover, the water tank experiment illustrates the proposed tuning laws.     

线性自抗扰控制的抗饱和补偿措施

控制输入约束是实际工业过程中普遍存在的现象,然而控制器设计中通常都假设执行机构动态是线性的,因此当执行机构存在约束时,执行机构输出信号与控制器输出信号不一致,使系统的动态性能降低,甚至导致系统不稳定.本文针对线性自抗扰控制(linearactive disturbance rejection control,LADRC)执行机构的约束问题,提出两种抗饱和补偿方案,利用LADRC扩张状态观测器估计控制器状态或者控制器输出与执行器输出的误差,从而使LADRC能快速消除饱和.将这两种方法用到含执行机构饱和的一阶惯性加迟延被控对象进行仿真研究,结果表明两种补偿措施下线性自抗扰控制器能得到较好的控制性能.随后本文将LADRC抗饱和思想推广到负荷频率控制系统(load frequency control,LFC)中,仿真表明基于误差补偿的抗饱和方案对于LFC系统更为有效.     

自抗扰控制技术在微机电换能器中的应用

自抗扰技术, 作为一门新兴的鲁棒控制技术, 能够成功补偿微机电制造上的缺陷以及周围环境的扰动, 从而提高微机电传感器和执行器的性能, 增加它们的测量及移动精度. 本文介绍了自抗扰技术在微机电陀螺仪和静电执行器两大微机电换能器上的应用. 通过使用此项控制技术, 微机电陀螺仪可精确测量并输出匀速及时变角速度.此外, 一种模型辅助自抗扰控制器被首次应用到微执行器上. 此模型辅助自抗扰控制器建立在部分模型已知的基础上. 它能够在外干扰存在的情况下, 把静电执行器的位移范围提高到电容间距的99%. 模型辅助自抗扰控制器的抗噪声能力也优于传统的自抗扰控制器. 作者用仿真和实验结果向读者展示了自抗扰技术在微机电领域的鲁棒性, 有效性和实用性.     

航天器姿态输出反馈抗干扰跟踪控制

针对采用四元数描述的航天器姿态运动模型研究输出反馈抗干扰跟踪控制问题.首先在姿态运动模型的基础上,结合四元数的性质设计扩张状态观测器(extended state observer,ESO)来估计角速度和干扰力矩,从理论上保证了ESO中的四元数状态满足范数约束,并证明了观测误差的收敛性;进一步利用互连和阻尼分配无源控制(interconnection and damping assignment passivity-based control,IDA--PBC)理论设计控制律,通过姿态和角速度误差状态变换以及引入误差积分项,使得期望的姿态和角速度误差,以及积分项误差运动方程中均出现阻尼项,提高了系统的抗干扰性能,最后利用Laypunov函数证明了闭环系统一致最终有界稳定.仿真结果验证了所设计ESO和IDA--PBC控制律的有效性.     

桥式起重机定位防摆改进型自抗扰控制

为解决严重外界干扰下桥式起重机长距离运输过程中定位困难、消摆时间长的问题,根据起重机先加速、再匀速、后减速的远程运输特点,利用两段Sigmoid函数,设计了可按需调整各阶段速度且高阶连续的新型跟踪微分器;采用Sigmoid函数构造了增益时变且连续可微的扩张状态观测器,使其具有“大误差小增益,小误差大增益”特性,克服了经典ESO增益在切换点处的突变问题,抑制了观测信号的微分峰值现象,实现了位移和摆角控制回路间的解耦;利用tanh函数改进了误差反馈控制律,避免了大扰动下的控制量饱和问题;综合形成了适用于起重机长距离运输、且能最大程度抑制振动和冲击的改进型自抗扰控制器,并对闭环系统的稳定性进行了严格的理论证明.仿真及实验结果表明,改进型自抗扰控制器在大干扰影响下可全过程平稳且基本无摆地将负载搬运到目标位置.     

有源电力滤波器的自抗扰控制研究

针对采用PI控制器控制有源电力滤波器时存在谐波或基波电流指令而无法实现无静差调节,且数字化后会进一步增大稳态误差,使有源电力滤波器的补偿性能降低的问题,提出一种有源电力滤波器的自抗扰控制策略。该策略利用自抗扰控制器的非线性跟踪-微分器和扩张状态观测器分别处理参考输入和输出,并选择适当的状态误差,实现了对滤波的自动、精确补偿。仿真和实验结果表明,有源电力滤波器采用自抗扰控制策略后具有很强的鲁棒性、稳定性和适应性,控制性能有较大改善。     

Flatness-based active disturbance rejection control for linear systems with unknown time-varying coefficients

A flatness-based active disturbance rejection control approach is proposed to deal with the linear systems with unknown time-varying coefficients and external disturbances. By selecting appropriate nominal values for the parameters of the system, all the deviation between the nominal and actual dynamics of the controlled process, as well as all the external disturbances can be viewed as a total disturbance. Based on the accurately estimated total disturbance with the aid of the proposed extended state observer, a linear proportional derivative feedback control law taking into account the derivatives of the desired output is designed to eliminate the effect of the total disturbance on the system performance. Finally, the load frequency control problem of a single-area power system with non-reheated unit is employed as an illustrative example to demonstrate the effectiveness of the proposed approach.     

实用自抗扰控制在大时滞厚度自动监控系统中的应用

针对热连轧监控AGC(自动厚度控制)大时滞系统具有不确定和干扰因素多等特点, 采用线性降阶模型及参数优化设计, 提出一种实用自抗扰控制(ADRC)控制方案, 以满足简单、实用、好调、节能等工业界的要求. 通过对被控对象和状态观测器的降阶, 使得系统总扰动(内部不确定性、外部扰动) 的实时估计由一个仅为一阶的扩张状态观测器就可实现. 为了把所设计的实用ADRC与常规ADRC、常规Smith预估器和PID控制器进行公平比较, 各控制器的最佳参数均采用变尺度混沌优化方法得到. 仿真结果表明, 两种ADRC的抗扰性和鲁棒性优于常规的Smith预估器和PID控制器. 与常规ADRC相比, 实用ADRC的可调参数大大减少, 能耗指标也明显降低, 为下一步的工程实现提供了途径.     

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.     

自抗扰控制器的发展

以自抗扰控制器的发展为线索, 对其所蕴涵的新思想做一个系统的阐述. 并总结了在自抗扰控制器的研究过程中提出的一些有待解决的新课题.     

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.     

高阶线性自抗扰控制器的性能评估

以二阶系统为研究对象,在线性扩张观测器(LESO)的基础上,给出高增益形式的高阶LESO.基于高阶线性自抗扰控制器(HLADRC)二自由度闭环传递函数和频域特性曲线,证明了其状态估计误差的收敛性以及高阶线性自抗扰控制器的稳定性.同时,系统地分析了输入增益和模型参数不确定性对稳定鲁棒性的影响,推导出满足系统稳定条件的参数??的稳定域以及系统干扰抑制动态特性与带宽的关系.最后,通过与线性自抗扰控制器(LADRC)的对比仿真表明, HLADRC在干扰抑制方面具有很大的优势,而LADRC在稳定鲁棒性和控制品质方面具有更好的效果,从而为工程设计提供了理论依据和实践参考.