Bandwidth Based Stability Analysis of Active Disturbance Rejection Control for Nonlinear Uncertain Systems

This paper focuses on the stability analysis of the active disturbance rejection control (ADRC) for a class of uncertain systems. To overcome the difficulty of defining a reasonable Lyapunov function and setting limitations of system parameters, the converse Lyapunov theorem and the disturbance theory are employed. This paper proves that the estimation error of the extended state observer (ESO) and the tracking error of the closed-loop system using ADRC are uniformly ultimately bounded and monotonously diminishing with the increase of their respective bandwidth, so that the stability of the ADRC system could be performed. In order to further illustrate the relationship between the stability range and bandwidths, it analyzes quantitatively the performance of ESO and ADRC based on the root locus and the step response. Finally, an example based on a typical control system is carried out, and simulation results verify the theoretical analysis proved in this paper.     

基于改进粒子群算法的快速反射镜自抗扰控制

为了提高快速反射镜(fast steering mirror, FSM)的跟踪精度和扰动抑制能力, 建立了基于自抗扰控制器(active disturbance rejection control, ADRC)的FSM闭环控制系统, 并对ADRC的参数整定方法进行研究。由于ADRC参数用试凑法整定效率低, 用粒子群优化(particle swarm optimization, PSO)算法整定容易陷入局部最优, 因此提出一种惯性权重基于箕舌线调整的改进PSO(improved PSO, IPSO)算法。通过系统仿真实验, 在考虑卫星平台振动的情况下, 采用基于IPSO、PSO的ADRC和传统比例-积分-微分(proportion integration differentiation,PID)控制器分别控制FSM。结果表明, 在跟踪不同频率的高频正弦信号时, 采用基于IPSO的ADRC控制的FSM跟踪精度相较其他两种控制器控制FSM的跟踪精度均有明显提升。     

量子定位中精跟踪系统状态滤波及控制器设计

量子定位系统中精跟踪系统的跟踪精度是高精度定位的前提。针对卫星平台抖动以及工作环境噪声对量子定位系统跟踪精度的影响,建立了带有卫星平台振动信号模型以及有色噪声信号的精跟踪系统模型;设计了自适应强跟踪卡尔曼滤波器(adaptive strong tracking Kalman filter,ASTKF)算法,对状态扰动和输出噪声进行在线估计;并设计ASTKF对精跟踪系统进行闭环跟踪控制。在系统仿真实验中,对ASTKF进行了数值设计;对带有滤波器和比例积分微分(proportion integration differentiation,PID)控制器的精跟踪系统的控制性能,与仅采用PID控制方法以及采用自抗扰控制方法进行了性能对比实验。结果表明:采用带有所提出的ASTKF的PID控制的跟踪精度相较PID及自抗扰控制精度均有明显提高,可以达到量子定位的精跟踪系统对跟踪精度±2 μrad的要求。     

飞行器不确定系统鲁棒D-稳定控制分配策略

为降低建模误差及外部扰动对飞行器多变量不确定系统的影响,提出了一种闭环系统鲁棒D-稳定的动态混合控制分配策略。飞控系统采用模块化的设计思想,利用线性矩阵不等式方法设计了基于虚拟控制指令的鲁棒D-稳定输出反馈控制律;建立了多目标混合优化控制分配模型,推导并证明了该模型的等价实现形式,用于将虚拟控制指令协调分配到各个操纵面。仿真结果表明,该策略能够综合考虑各操纵面不同的物理约束和控制效能,具有较好的鲁棒性能。     

一类严格反馈时滞系统的自适应输出反馈控制

针对一类单输入单输出的严格反馈时滞系统研究跟踪控制问题。该控制系统包含不确定项、输出约束、未知死区特性和未知时间延迟。首先,设计一个状态观测器来估计无法测量的系统状态;其次,利用径向基函数(radial basis function,RBF)神经网络去逼近未知的系统内部动态;同时,利用障碍李雅普诺夫(Lyapunov)函数确保输出约束及Lyapunov-Krasovskii方法消除时滞项对系统的影响;最后,基于Lyapunov稳定性理论,构造一个鲁棒自适应神经网络输出反馈控制器,并且克服了过参数问题。结果显示,设计的神经网络输出反馈控制器可以保证闭环系统中的所有信号都是半全局最终一致有界的,跟踪误差能收敛到零值小的领域内。文中通过两个例子进一步验证了提出方法的有效性。     

Sampled-Data Semi-Global Robust Output Regulation for a Class of Nonlinear Systems

This paper investigates the semi-global robust output regulation problem for a class of uncertain nonlinear systems via a sampled-data output feedback control law. What makes the results interesting is that the nonlinearities of the proposed system do not have to satisfy linear growth condition and the uncertain parameters of our system are allowed to belong to some arbitrarily large prescribed compact subset. Two cases are considered. The first case is that the exogenous signal is constant. The second case is that the exogenous signal is time-varying and bounded. For the first case,the authors solve the problem exactly in the sense that the tracking error approaches zero asymptotically. For the second case, the authors solve the problem practically in the sense that the steady-state tracking error can be made arbitrarily small. Finally, an example is given to illustrate the effectiveness of our approach.     

Active disturbance rejection control for PMLM servo system in CNC machining

Uncertain friction is a key factor that influences the accuracy of servo system in CNC machine. In this paper, based on the principle of Active Disturbance Rejection Control (ADRC), a control method is proposed, where both the extended state observer (ESO) and the reduced order extended state observer (RESO) are used to estimate and compensate for the disturbance. The authors prove that both approaches ensure high accuracy in theory, and give the criterion for parameters selection. The authors also prove that ADRC with RESO performs better than that with ESO both in disturbance estimation and tracking error. The simulation results on CNC machine show the effectiveness and feasibility of our control approaches.     

Uncoupled PID Control of Coupled Multi-Agent Nonlinear Uncertain systems

In this paper, PID (proportional-integral-derivative) controllers will be designed to solve the tracking problem for a class of coupled multi-agent systems, where each agent is described by a second-order high-dimensional nonlinear uncertain dynamical system, which only has access to its own tracking error information and does not need to communicate with others. This paper will show that a 3-dimensional manifold can be constructed based on the information about the Lipschitz constants of the system nonlinear dynamics, such that whenever the three parameters of each PID controller are chosen from the manifold, the whole multi-agent system can be stabilized globally and the tracking error of each agent approaches to zero asymptotically. For a class of coupled first-order multi-agent nonlinear uncertain systems, a PI controller will be designed to stabilize the whole system.     

飞机全电防滑刹车系统稳定动态面控制

针对机电作动的飞机防滑刹车模型具有的高阶非线性及参数时变特点,提出一种基于障碍Lyapunov函数的动态面控制方法,实现对滑移率的上界约束,保障防滑刹车系统的稳定性。建立飞机刹车动力学模型,与机电作动器的数学模型联立得到整体刹车系统的状态空间模型,并合理简化为严格反馈形式。将刹车系统的控制稳定性问题等效描述为含输出约束的非线性系统镇定问题,设计动态面控制律并通过Lyapunov方法证明滑移率跟踪误差半全局一致最终有界,刹车工作点始终保持在稳定区域内。仿真结果表明,本文所提控制策略具有稳定性优势,且改善了传统控制存在的中低速时滑移率振荡问题,控制效果有显著提升。     

Robust decentralized adaptive output feedback fuzzy controller design and application to AHS

A novel decentralized indirect adaptive output feedback fuzzy controller is developed for a class of large-scale uncertain nonlinear systems using error filtering. By the properly filtering of the observation error dynamics, the strictly positive-real condition is guaranteed to hold such that the proposed output feedback and adaptation mechanisms are practicable in practice owing to the fact that its implementation does not require the observation error vector itself any more, which corrects the impracticable schemes in the previous literature involved. The presented control algorithm can ensure that all the signals of the closed-loop large-scale system keep uniformly ultimately bounded and that the tracking error converges to zero asymptotically. The decentralized output feedback fuzzy controller can be applied to address the longitudinal control problem of a string of vehicles within an automated highway system (AHS) and the effectiveness of the design procedure is supported by simulation results.     

高超声速飞行器新型攻角约束反演控制

针对考虑攻角约束的高超声速飞行器控制问题,提出一种受限指令滤波器与预设性能方法相结合的反演控制方案.首先,从高超声速飞行器运动模型中划分出高度子系统并基于反演控制方法设计控制器.为了解决攻角约束问题,构造受限指令滤波器对攻角虚拟指令限幅并保证指令的可导性.然后,利用预设性能方法预先设定约束范围,保证攻角跟踪误差始终满足...     

考虑姿态禁忌约束的航天器安全姿态跟踪控制

针对航天器姿态跟踪过程中的姿态约束问题,提出了一种基于势函数的安全姿态机动控制算法。与姿态定点机动的姿态约束问题不同,引入误差四元数和误差角速度,建立了航天器姿态跟踪误差模型。采用四元数描述了姿态禁忌区域,并根据禁止姿态最小允许角构造了一种新的规避高斯势函数。利用规避势函数和吸引势函数得到安全姿态机动控制器,对于无扰动和有扰动的情况分别分析了闭环控制系统的Lyapunov稳定性。最后,对于有约束的姿态跟踪情况进行了计算机数值仿真。仿真结果表明,所提出的控制方法既能实现姿态跟踪的目的,又能确保航天器在机动过程中不会进入姿态禁忌区域。     

Adaptive tracking controller using BP neural networks for a class of nonlinear systems

An BP neural-network-based adaptive control (NNAC) design method is described whose aim is to control a class of partially unknown nonlinear systems. Making use of the online identification of BP neural networks, the results of the identification could be used into the parameters of the controller. Not only the strong robustness with respect to uncertain dynamics and nonlinearities can be obtained, but also the output tracking error between the plant output and the desired reference output can asymptotically converge to zero by Lyapunov theory in the process of this design method.And a simulation example is also presented to evaluate the effectiveness of the design.     

基于改进ESO的四旋翼姿态自抗扰控制器设计

针对四旋翼无人机姿态自抗扰控制(active disturbance rejection control, ADRC)系统在姿态角测量反馈信号受传感器噪声污染时, 基于传统非线性非光滑fal函数的扩张状态观测器(extended state observer, ESO)观测精度不足的问题, 构建了一种新型非线性光滑galn函数以重新设计ESO, 并利用Matlab/Simulink仿真软件进行性能验证。仿真结果表明: 与传统fal函数相比, 本文构建的galn函数为光滑且具有更好的收敛性, 更能体现“大误差小增益”的工程思想; 基于galn函数设计的改进型ESO具有更强的误差跟随能力; 采用改进型ESO设计的四旋翼姿态ADRC系统具有更好的跟踪能力和抗干扰能力。     

二阶输出反馈滑模极值搜索控制方法

针对一类单输入单输出(single input single output,SISO)非线性极值系统的控制问题,提出了一种二阶输出反馈滑模极值搜索控制方法。考虑到此系统的状态量不可测,利用斜坡函数作为输出量的参考跟踪信号,以系统的输出跟踪误差及其微分信号构建切换函数,设计出二阶滑模极值搜索控制律。稳定性分析证明了在任意初始条件下,该方法可使系统的输出量全局收敛至其期望极值的任意小邻域内且所有状态量均是一致范数有界。仿真结果验证了该方法的有效性。     

一类不确定非线性系统的自适应模糊控制

对一类不确定非线性系统提出自适应模糊控制方法。此方法用模糊逻辑系统设计自适应模糊监督控制器和自适应模糊控制器,且设计补偿器对逼近误差进行补偿,以此来减少逼近误差对跟踪精度的影响,同时对自适应模糊监督控制器和自适应模糊控制器中的未知参数设计了自适应学习律。证明了该方法不但能保证闭环系统稳定,而且可使跟踪误差收敛到原点的邻域内。仿真结果验证了此方法的有效性。     

Finite-time neural funnel control for motor servo systems with unknown input constraint

In this paper, a finite-time neural funnel control (FTNFC) scheme is proposed for motor servo systems with unknown input constraint. To deal with the non-smooth input saturation constraint problem, a smooth non-affine function of the control input signal is employed to approximate the saturation constraint, which is further transformed into an affine form according to the mean-value theorem. A fast terminal sliding mode manifold is constructed by using a novel funnel error variable to force the tracking error falling into a prescribe boundary within a finite time. Then, a simple sigmoid neural network is utilized to approximate the unknown system nonlinearity including the saturation. Different from the prescribed performance control (PPC), the proposed finite-time neural funnel control avoids using the inverse transformed function in the controller design, and could guarantee the prescribed tracking performance without knowing the saturation bounds in prior. The effectiveness and superior performance of the proposed method are verified by comparative simulation results.     

机械手鲁棒输出跟踪控制与仿真

研究了两自由度机械手终端夹持不定载荷时的输出跟踪问题。应用输入 /输出反馈线性化法和李亚普诺夫方法 ,提出了一种基于不确定项上界的机械手鲁棒输出跟踪控制器设计算法。所述控制器可确保系统输出按指数规律跟踪期望输出 ,同时相应闭环系统的状态一致最终有界。该方法计算简单 ,容易实现。仿真结果证明了其可行性及有效性。     

一类非线性系统的动态面二阶滑模控制

针对一类具有非匹配不确定的严格反馈非线性系统,基于动态面控制和二阶滑模控制设计方法,进行一种新颖的状态反馈控制器设计,实现了不确定系统任意小的跟踪误差。动态面控制类似于反演设计,但其包含一系列低通滤波器;低通滤波器允许控制对象数学模型不可微,这样就避免了反演设计所存在的"膨胀项",减少了计算量,易于实现。同时,由于引入二阶滑模控制,消除了传统滑模控制(一阶滑模控制)存在的抖振现象,既增强了控制系统的鲁棒性,又提高了系统的控制精度。     

二阶动力学系统模型的跟踪设计

考虑了基于分散状态反馈控制律的二阶动力学系统输出渐近跟踪设计,该控制律包括被控对象状态和参考模型状态两部分。给出了问题解的存在条件:两个矩阵方程,其中一个为二阶Sylvester矩阵方程。给出了所有控制器增益阵的完全参数化表达式。归纳出了二阶动力学系统模型参考输出跟踪控制律的设计算法。该算法直接基于原系统的参数矩阵,无须对系统增广或变换,仅涉及自由参数的选取和一些简单的代数运算,便于工程应用。仿真结果说明所给出的算法是有效的。