自抗扰控制:思想、应用及理论分析

首先从思想方法上剖析利用自抗扰控制思想处理不确定系统控制问题的独特之处,说明在运用自抗扰控制思想处理大范围及复杂结构(非线性、时变、耦合等)不确定系统时,首先需要准确分析系统中影响被控输出的"总扰动".然后,通过几个典型的应用研究实例说明自抗扰控制在处理大范围不确定性以及实现高精度闭环动态性能方面的优良品质.最后,对最新的理论分析结果进行简要综述.     

非线性系统的自抗扰控制引论

系统的不确定和外部干扰是控制理论的主要敌手。最近二十年出现了一个新的对付不确定的控制方法称为自抗扰控制。本文旨在介绍一本这方面的新书:Active Disturbance Rejection Control for Nonlinear Systems:An Introduction,及其相关的背景。该书是一本自抗扰控制数学理论著作。为了引出本书的主要内容,我们扼要介绍了几种其他的对付系统不确定的控制方法,包括鲁棒H∞-控制、滑模控制、自适应控制以及内模原理,说明自抗扰控制的主要思想和与这些方法的异同之处。特别是指出了自适应控制、内模原理的估计和消除策略及其在自抗扰控制中的大规模应用。     

基于自抗扰控制的制导与运动控制一体化设计

针对机动目标的拦截问题,将自抗扰控制的思想用于制导与运动控制一体化设计.其中,基于自抗扰控制的制导律产生在目标机动的情况下使视线角速度快速趋于零所需的制导律;而基于自抗扰控制的运动控制律可以在非线性不确定动态情况下实现所需加速度,从而保证快速有效地完成拦截任务.进一步分析所设计方案对制导与运动控制一体化设计的适用性,并通过计算机仿真验证该方案的有效性.     

智能空间刚架的模糊自抗扰振动抑制研究

智能空间刚架作为太空望远镜支撑架是一种新型智能空间结构.为抑制刚架系统在运动过程中产生的振动,"文章提出了一种基于自抗扰控制的非线性模糊自抗扰控制理论,并设计出模糊自抗扰控制器.首先采用有限元方法计算出空间刚架的质量矩阵、阻尼矩阵和刚度矩阵,进而建立系统模型并设计出自抗扰控制器以实现对系统振动的抑制.基于普通自抗扰控制器,利用模糊推理在线整定控制器中非线性状态误差反馈的参数.该控制器不依赖于被控对象的精确数学模型,具有良好的控制性能,同时参数的在线自整定简化了调参难度.仿真实验验证了所提方法的有效性.     

自抗扰控制处理边界带有干扰的具有尖端质量的Timoshenko梁方程的稳定性

讨论了边界带有不确定扰动的一维Timoshenko梁方程的边界反馈稳定性.运用的方法主要是自抗扰控制,其主要思想是通过构造常数高增益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.最后通过李雅普诺夫方法证明了闭环系统具有实用稳定性.     

《Active Disturbance Rejection Control for Nonlinear Systems:An Introduction(非线性系统的自抗扰控制引论)》

<正>自抗扰控制技术提出二十多年了,在国际国内有很多不同领域的工程应用,可是其理论基础却少有系统的研究。郭宝珠与赵志良的新书《Active Disturbance Rejection Control for Nonlinear Systems; An Introduction(非线性系统的自抗扰控制引论)》是作者们过去多年来关于非线性系统自抗扰控制理论基础的系统性总结,并配有大量的数值模拟。本书详细地引导读者领略自抗扰控制3个主要的部分:跟踪微分器、扩张     

基于模糊自抗扰的塔机消摆控制方法

塔机消摆控制系统是一个非线性、强耦合的复杂系统,传统PID控制效果往往欠佳.对此,建立了一个含阻尼的塔机偏摆系统数学模型,并提出模糊自抗扰控制策略.通过自抗扰控制器对塔机回转与变幅运动进行解耦,模糊算法对自抗扰控制器各参数实施在线调整,并对解耦后的回转、变幅子系统分别进行控制.在仿真实验中,对比其他典型方法,提出的方法摆角消失速度更快,这表明在负载运动过程中,所设计控制器实时性和鲁棒性较好.     

一种具有无扰切换功能的位置型自抗扰控制器数字实现

介绍了一种位置型自抗扰控制器(Active Disturbance Rejection Control,ADRC)的数字实现.根据线性一阶和二阶自抗扰算法的计算原理,提出自抗扰控制器无扰切换的具体逻辑实现方法,使得控制方式转换过程可以平滑进行,避免对系统造成额外干扰.通过C语言的实现形式,测试所提出的数字型自抗扰控制算法基本闭环控制功能,并证明所提出的位置型自抗扰控制器可以实现ADRC/PID/手动模式之间的无扰切换.仿真结果表明了该位置型控制器在过程控制平台中应用的有效性和可实现性.     

一种新型自抗扰控制自适应非线性控制律

针对自抗扰控制(AIDRC)多参数不易整定的问题,提出了一种基于二次函数的非线性PID(NLPID)控制律.该方法用二次函数模拟PID增益参数随误差变化的规律曲线,构造了一个非线性PID神经网络模型,利用最速下降法对各模拟曲线的系数进行在线调整,实现了基于神经网络的自适应自抗扰控制.仿真结果表明,与常规ADRC控制方法相比,文章方法减少了ADRC需调整的参数,并具有较好的控制效果.     

基于ADRC的小型四旋翼姿态控制实现

设计了一个四旋翼飞行系统,提出了一种自抗扰控制方法,解决了该飞行系统的姿态控制问题.将显性互补滤波器与扩张状态观测器相结合,实现了对系统的状态与内外总扰动的实时估计,并在此基础上利用非线性误差反馈控制律对该扰动进行了补偿,消除了内外扰动对系统的影响.最后,分别采用PID与ADRC算法实现四旋翼的姿态控制,对比结果验证了所采用的自抗扰控制方法的有效性和优越性.     

基于预测控制的直接侧向力气动力复合控制方法研究

针对大气层内拦截导弹直接侧向力与气动力复合控制系统设计问题, 首先, 根据发动机的配置建立了复合控制系统模型;其次, 提出了复合控制策略, 包括动态分配算法、直接力控制子系统、气动力控制子系统3部分; 然后, 在考虑两套执行机构动态特性差别的情况下,基于预测控制思想给出了过载误差动态分配算法; 在此基础上, 根据直接侧向力的离散特性, 基于预测控制方法设计了直接力控制规律, 考虑到直接力控制作用对弹体产生的扰动, 基于自抗扰方法设计了气动力子系统; 最后, 通过仿真验证了直接力气动力复合控制策略与方法的有效性.     

Robust Optimal Trajectory Planning for Robots by Stochastic Optimization

In the optimal control of industrial, field or service robots, the standard procedure is to determine first offline a reference trajectory and a feedforward control, based on some selected nominal values of the unknown stochastic model parameters, and to correct then the inevitable and increasing deviation of the state or performance of the robot from the prescribed state or performance of the system by online measurement and control actions. Due to the stochastic variations of the model parameters, increasing measurement and correction actions are needed during the process. By optimal stochastic trajectory planning (OSTP), based on stochastic optimization methods, the available a priori and sample information about the robot and its working environment is incorporated into the control process. Consequently, more robust reference trajectories and feedforward controls are obtained which cause much less online control actions. In order to maintain a high quality of the guiding functions, the reference trajectory and the feedforward control can be updated at some later time points such that additional information about the control process is available. After the presentation of the Adaptive Optimal Stochastic Trajectory Planning (AOSTP) procedure based on stochastic optimization methods, several numerical techniques for the computation of robust reference trajectories and feedforward controls under real-time conditions are presented. Additionally, numerical examples for a Manutec r3 industrial robot are discussed. The first one demonstrates real-time solutions of (OSTP) based on a sensitivity analysis of a before-hand calculated reference trajectory. The second shows the differences between reference trajectories based on deterministic methods and the stochastic methods introduced in this paper. Based on simulations of the robots behavior, the increased robustness of stochastic reference trajectories is demonstrated.     

Numerical solutions for optimal control of monodomain equations

We present the numerical solutions of optimality systems corresponding to optimal control problems governed by the mono-domain equations which are widely used for describing the electrical activity of the cardiac tissue. This mono-domain model is based on a parabolic equation and a system of stiff ordinary differential equations. The space discretization of the state variables and dual variables is done using piecewise linear finite elements and the time discretization is based on linearly implicit Runge-Kutta methods. The main goal of this work is to study the optimal control behavior of the electrical potentials under the influence of extracellular ionic currents as control variables. The numerical results presented are based on first and second order optimization methods. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A time-domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems

We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss–Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.     

Variational integrators for open-loop and closed-loop optimal control of mechanical systems

Mechanical systems have structural properties, e.g. symplecticity, symmetry, and a specific energy behavior, which get lost in standard integration methods. Therefore, symplectic integration methods are used in simulation and control of mechanical systems. This paper combines two methods of the class of structure-preserving control methods, namely a recently developed feedback control method and open loop optimal control based on variational integrator discretization. The combination is applied to the benchmark example of a cart pendulum system. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Superconvergence of splitting positive definite mixed finite element for parabolic optimal control problems

In this paper, we investigate the superconvergence of fully discrete splitting positive definite mixed finite element (MFE) methods for parabolic optimal control problems. For the space discretization, the state and co-state are approximated by the lowest order Raviart–Thomas MFE spaces and the control variable is approximated by piecewise constant functions. The time discretization of the state and co-state are based on finite difference methods. We derive the superconvergence between the projections of exact solutions and numerical solutions or the exact solutions and postprocessing numerical solutions for the control, state and co-state. A numerical example is provided to validate the theoretical results.     

Iterative sliding mode control

Iterative Learning Control (ILC) methods are described and applied ever-increasingly as powerful tools to control dynamics nowadays.

ILC’s methods in most studies are described as based on repetitive process from the beginning to the end of process or as a kind of repetitive control.

Our newly designed controllers based on a particular case of iterative learning control radically differ from conventional methods in attempting to stabilize a class of non linear systems.

In this paper two kinds of ILC method are introduced in two separate sections. In the first, our newly designed method satisfies the condition of a Lyapunov stability theorem in a class of non linear systems in which their structures have the Lipschitz property. In the second, by freezing the time and moving to a new virtual axis, called the index axis, this newly designed method tries to find the best value for control at this time step and can be used in two modes, on-line and off-line.

In both methods, by satisfying the convergence condition of our designed ILC, closed loop stability is obtained automatically.     

Optimal Control in Heterogeneous Domain Decomposition Methods for Advection-Diffusion Equations

New domain decomposition methods (DDM) based on optimal control approach are introduced for the coupling of first and second order equations on overlapping subdomains. Several cost functionals and control functions are proposed. Uniqueness and existence results are proved for the coupled problem, and the convergence of iterative processes is analyzed. The work was supported by the Russian Foundation for Basic Research (04-01-00615) and it was partly carried out while the first author was visiting the IACS at EPFL.     

Optimal Control of the Euler Equations via Relaxation Approaches

We discuss two linear relaxation approaches to the optimal control of nonlinear hyperbolic systems, in particular the control of Euler flows in gas dynamics. The first method is a relaxation system that is due to Jin and Xin [2], the second one is a Lattice-Boltzman approach [3], where we use one spatial dimension and five velocities (D1Q5 model). Both methods are incorporated in an adjoint based steepest-descent algorithm for the optimisation. Convincing numerical results are presented for both methods for an example with discontinuous solutions. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)