Output feedback stabilisation for a cascaded wave PDE-ODE system subject to boundary control matched disturbance

In this paper, we consider output feedback stabilisation for a wave PDE-ODE system with Dirichlet boundary interconnection and external disturbance flowing the control end. We first design a variable structure unknown input type state observer which is shown to be exponentially convergent. Then, we estimate the disturbance in terms of the estimated state, an idea from active disturbance rejection control. These enable us to design an observer-based output feedback stabilising control to this uncertain PDE-ODE system.     

Sliding mode control and active disturbance rejection control to the stabilization of one‐dimensional Schrödinger equation subject to boundary control matched disturbance

In this paper, we are concerned with the boundary stabilization of a one‐dimensional anti‐stable Schrödinger equation subject to boundary control matched disturbance. We apply both the sliding mode control (SMC) and the active disturbance rejection control (ADRC) to deal with the disturbance. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of the solution for the closed‐loop system is proved and the ‘reaching condition’ is obtained. Considering the SMC usually requires the large control gain and may exhibit chattering behavior, we develop the ADRC to attenuate the disturbance for which the derivative is also supposed to be bounded. Compared with the SMC, the advantage of the ADRC is not only using the continuous control but also giving an online estimation of the disturbance. It is shown that the resulting closed‐loop system can reach any arbitrary given vicinity of zero as time goes to infinity and high gain tuning parameter goes to zero. Copyright © 2013 John Wiley & Sons, Ltd.     

Stabilization of ODE with hyperbolic equation actuator subject to boundary control matched disturbance

ABSTRACT

In this paper, we consider stabilisation for a cascade of ODE and first-order hyperbolic equation with external disturbance flowing to the control end. The active disturbance rejection control (ADRC) and sliding mode control (SMC) approaches are adopted in investigation. By ADRC approach, the disturbance is estimated through a disturbance estimator with both time-varying high gain and constant high gain, and the disturbance is canceled online in the feedback loop. It is shown that the resulting closed-loop system with time-varying high gain is asymptotically stable and is practically stable with constant high gain. By SMC approach, the existence and uniqueness of the solution for the closed loop via SMC are proved, and the monotonicity of the ‘reaching condition’ is presented. The resulting closed-loop system is shown to be exponentially stable. The numerical experiments are carried out to illustrate effectiveness of the proposed control law.     

Boundary stabilization of a cascade of ODE‐wave systems subject to boundary control matched disturbance

In this paper, we are concerned with a cascade of ODE‐wave systems with the control actuator‐matched disturbance at the boundary of the wave equation. We use the sliding mode control (SMC) technique and the active disturbance rejection control method to overcome the disturbance, respectively. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of solution for the closed‐loop via SMC are proved, and the monotonicity of the ‘reaching condition’ is presented without the differentiation of the sliding mode function, for which it may not always exist for the weak solution of the closed‐loop system. Considering that the SMC usually requires the large control gain and may exhibit chattering behavior, we then develop an active disturbance rejection control to attenuate the disturbance. The disturbance is canceled 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. Then we continue to consider output feedback stabilization for this coupled ODE‐wave system, and we design a variable structure unknown input‐type state observer that is shown to be exponentially convergent. The disturbance is estimated through the extended state observer and then canceled in the feedback loop by its approximated value. These enable us to design an observer‐based output feedback stabilizing control to this uncertain coupled system. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

滑模控制和自抗扰控制的研究进展

本文概括了滑模控制和自抗扰控制的研究进展,进一步给出了复合控制的思想.滑模控制和自抗扰控制都有它们各自的优点,但是也都有它们各自的局限,例如:滑模控制中的抖振问题和自抗扰控制中的估计能力受限问题.复合控制结合了滑模控制和自抗扰控制的优点,并能提高闭环系统的性能.     

自抗扰控制对边界带有干扰的非线性sine-Gordon方程的镇定

本文讨论边界具有内部不确定和外部扰动的非线性sine-Gordon方程的镇定问题. 为处理sine-Gordon方程中的非线性项, 文章给出一个新的总扰动观测器在线估计未知扰动, 并通过自抗扰控制方法, 设计一个控制器使得在反馈控制中实时补偿(消除)总扰动. 闭环系统被证明适定的并且受控系统是指数稳定而扰动观测器是有界的. 数值模拟说明提出方法的有效性.     

线性自抗扰控制系统的鲁棒稳定性

针对线性自抗扰控制系统,研究了模型参数不确定情况下的鲁棒稳定性问题.首先给出对象为非自治模型时该系统的H∞判据.然后针对线性误差模型的状态矩阵只在某一行存在不确定参数的情况,基于奇异值理论,得到H∞判据的一种新的等价描述,把H∞范数约束转化为对奈奎斯特图的约束.之后为了降低新判据在实际应用中的保守性,对不确定性矩阵的分解方式进行优化.在此基础之上提出了一种新的方法,用于计算时变参数不确定性的最大边界,为线性自抗扰控制器设计提供理论依据.数值实例表明该方法不仅保守性小,而且计算简单.     

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.     

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.     

结晶器多变量耦合系统的自抗扰控制

主要研究新颖实用非线性自抗扰控制算法,在结晶器多变量耦合系统中的应用.自抗扰控制主要特性是实时估计对象模型摄动和外扰的总和作用量,并在控制信号中补偿掉,实现不确定性强非线性对象的实时动态反馈线性化.结合控制对象,建立了结晶器多变量耦合自抗扰控制系统.数值仿真试验表明自抗扰耦合控制的协调性、自适应跟随性和抗干扰性优于传统的PID解耦控制.     

线性自抗扰控制的对偶性分析EI北大核心CSCD

本文对线性自抗扰控制的结构进行了分析,证明了线性自抗扰控制结构实际上是一种基于观测器的比例–积分–微分(PID)结构的对偶.该结构中状态反馈就是常规(高阶)PID控制,而PID控制中输出的积分和各阶导数由一不依赖于模型的扩张观测器获得.这种对偶性表明PID控制和线性自抗扰控制采用了同一个标准系统作为被控对象,但从不同的角度进行处理.理论及仿真表明,线性自抗扰控制是常规PID控制的扩展,克服了常规PID控制受测量噪声影响的问题,为高阶PID的应用提供了实际可行的实现.     

线性自抗扰控制的适用性及整定

线性自抗扰控制将被控对象看成串级积分系统,把其他信息都当成不确定性.这种处理方法简单,但是对什么样的系统有效,目前还没有理论给出确定的答案.本文证明任何带有积分行为的严格正则传递函数都可以由线性自抗扰控制的反馈控制器等价实现,从而表明线性自抗扰控制具有广泛的适用性,即只要其他线性控制方法能够控制的系统,线性自抗扰控制同样可以适用.为简化线性自抗扰控制器参数整定,本文针对工业过程中广泛存在的PID控制器,提出将PID参数转化为二阶自抗扰控制参数的方法.该方法转化的线性自抗扰参数以带宽形式表示,从而保留了传统线性自抗扰简单易调的特性,为线性自抗扰控制在工业过程的应用准备了基础.     

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.     

欠驱动RTAC的滑模自抗扰镇定控制

针对欠驱动RTAC(rotational/translational actuator)的镇定问题,提出了一种滑模自抗扰控制方法,通过对总扰动的观测和补偿降低了未知扰动对RTAC的影响.为克服RTAC的欠驱动特性,所提方法通过将可驱动的摆球角度和无驱动的小车位置两个状态相结合,构建出虚拟被控量作为系统输出,从而使RTA...     

双质量弹簧基准问题自抗扰控制研究

本文研究了自抗扰控制(ADRC)方法在双质量弹簧基准问题的应用.传统的自抗扰控制方法倾向于使用高增益控制来抑制扰动和模型不确定性,但是对于双质量弹簧基准问题,高增益在评分中受到较大惩罚,而且对于模型参数变化没有足够的鲁棒性.为解决这一问题,本文对ADRC设计提出了两种改进方案.首先,为了减小控制信号的幅度,将扩张状态观测器(ESO)的一个极点配置在原点.其次,采用阻尼比来调整带宽.结果表明,所提出的ADRC设计可以很好地解决双质量弹簧基准系统的控制问题.     

压电驱动纳米定位台的线性自抗扰控制

压电驱动的纳米定位系统,磁滞严重降低其定位精度.基于磁滞逆模型的定位控制方法,可提高定位精度.然而,因其对模型依赖大,无法在内、外扰动因素存在时,仍保证良好的定位效果.为此,视磁滞为干扰,设计不基于磁滞及定位系统精确数学模型的自抗扰控制,利用扩张状态观测器主动估计磁滞,并实时补偿之,以保证定位精度.本文分析了扩张状态观测器的收敛性、闭环系统的稳定性;讨论了自抗扰控制参数与纳米定位系统动态响应间的关系;对比了PI控制和自抗扰控制的动态响应、时间与误差绝对值乘积积分、平均绝对误差和均方根误差,数值和实验结果均表明自抗扰控制优于PI控制,证实了自抗扰控制可主动估计磁滞、内部不确定性和外部扰动,在其降低定位精度之前即被补偿、保证良好的定位控制效果.     

Flexible modelling and altitude control for powered parafoil system based on active disturbance rejection control

For the accurate altitude control of the powered parafoil system, a novel modelling method and control methodology are designed in this paper. Firstly, based on computational fluid dynamics, the proposed model can accurately simulate the actual flight state of the powered parafoil system. Then, the double closed-loop controller based on active disturbance rejection control is designed. With this methodology, the precise altitude control can be realised. By analysing the theory of active disturbance rejection control, the proposed control method will be stable and valid. At last, after the detailed verification in the hardware-in-the-loop simulations, the flight experiment is carried out. After the simulation with the proposed model, the adjusted controller parameters can be applied directly in the actual experiment. The results show that the proposed method can provide effective guidance to the flight experiment. It also proves the validity and effectiveness of the proposed modelling and control method.     

电机驱动驻车系统的非线性自抗扰控制

电机是电动汽车的动力源,能快速启动,并通过矢量控制技术精确控制输出转矩.本文针对电动汽车电子驻车系统制动问题,提出了一种采用自抗扰控制技术驱动电机实现驻车制动的有效方法.为此分析了车辆在坡道上的纵向运动学模型,结合电机数学模型和整车模型,设计了电动汽车电子驻车非线性自抗扰控制器,并搭建了闭环仿真模型.仿真结果表明,自抗扰控制系统响应性能明显优于PID控制,最后通过实验,验证所设计的控制方案对驻车过程内外扰动具有较强的鲁棒性,能够实现驻车过程快速有效制动.     

高阶不确定系统的线性串级自抗扰控制

自抗扰控制是我国著名学者韩京清原创的先进控制技术,本文针对自抗扰控制(ADRC)在高阶系统应用中控制器设计和参数整定问题,提出了串级自抗扰控制(CADRC). CADRC把高阶被控对象分解为含确定性部分和含总扰动的低阶部分的串联组合,采用由内环和外环组成的串级控制系统来完成控制.该CADRC方案的内环采用内模控制,外环采用经典ADRC.外环ADRC的被控对象是一个等效的低阶系统,可以采用带宽法进行整定,而内环的内模控制采用高阶低通滤波器进行回路成形设计和参数整定.仿真研究表明,所提出的方法是有效的,具有良好的工程应用前景.