基于积分反步法的轧机速度系统控制器设计

本文给出了基于积分反步法的控制器设计方法，该方法通过逐步修正算法设计镇定控制器，实现系统的全局调节或跟踪。每一步把状态坐标变换、一个给定的李雅普诺夫函数和虚拟控制联系起来，最终得到一个控制李雅普诺夫函数(clf)。基于上述方法，对直流电机驱动的轧机速度系统进行了反馈控制器设计。仿真研究结果表明，本文所设计的反馈控制器使闭环系统稳定，系统具有良好的跟踪性能。     

反步法在三相电压型脉冲调宽逆变器控制中的应用

针对三相电压型脉冲调宽(pulse-width-modulation,PWM)逆变器这个时变的、多模态的非线性系统,应用开关函数建立了系统数学模型,引入开关周期平均算子将离散的系统化为连续系统,得到具有参数严格反馈形式的二阶非线性多输入多输出系统数学模型.并对此模型应用反向递推方法,通过逐步选择虚拟控制量和构造李雅普诺夫函数,使每个状态分量具有适当的渐近特性,实现整个系统在大扰动下的全局渐近稳定性,进而得到反馈控制律的一般表达式.将三相电压型PWM逆变器系统参数代入后得到其反馈控制规律.最后通过仿真实验验证了该方法的有效性和正确性.     

欠驱动刚体航天器奇异避免的反步姿态控制

为了完成欠驱动刚体航天器(UCRS)姿态系统的稳定控制,使得UCRS全程稳定飞行,本文提出了一种奇异避免的反步控制(SABSC)方法.首先,对于已知的UCRS系统的动力学模型和利用(w, z)参数表述的运动学模型,本文通过构造合适的李雅普诺夫函数,推导得到了两个驱动轴角速度理想的函数表达式,确保了姿态系统参数的一致收敛;其次,在理想姿态角速度的基础上,借助于重构期望的李雅普诺夫函数,设计得到了奇异避免的反步控制器;最终,为了检验本文提出的SABSC的性能,进行了数值仿真实验,实验结果表明本文提出的控制器具有较好的控制性能.     

随机激励下非线性水轮机系统的控制设计

针对一类随机非线性哈密顿系统提出了一种全新的反馈跟踪控制方法.该控制策略可以准确地控制系统输出的概率密度分布特性.闭环系统的稳定性也通过李雅普诺夫函数法得到严格的数学证明.最后,以随机非线性水轮机系统为例,详细演示了控制设计过程及其有效性.仿真结果表明,新的反馈控制策略可以使水轮机系统的输出满足预先指定的平稳概率密度函数.     

基于反步控制的多AUV编队控制方法研究

针对自主水下机器人(AUV)集群编队任务的实际需求,本文提出了一种基于反步控制思想的多AUV编队控制算法.根据多AUV集群系统的平面Leader-Follower编队模型,推导了多AUV编队控制的数学模型和优化目标.对于积分串联型的AUV非线性系统,借鉴反步控制思想设计了一种新型的控制律函数,采用李雅普诺夫理论证明了AUV集群系统编队控制的稳定性.仿真结果表明,采用本文提出的编队控制方法,AUV集群能够较好实现队形保持与队形切换功能,算法收敛,满足实际编队控制的需求.     

不确定非线性切换系统鲁棒容错H∞控制与仿真

为了克服外部扰动与执行器失效对切换系统的不良影响,使系统具有可靠性和抗干扰性,针对一类不确定非线性切换系统,研究了鲁棒容错H∞控制器设计与切换问题.假设系统中存在外部扰动,并且所有的矩阵同时带有未知、时变和范数有界的不确定性.当有执行器失效,并使得每个子系统均不能镇定的情况下,利用线性矩阵不等式技术和多李亚普诺夫函数法设计γ次优鲁棒H∞反馈容错控制器和切换策略,保证切换系统能全局二次稳定并且满足日∞性能指标,对得到的γ次优鲁棒H∞容错控制器进行优化,通过变量替换法获得了γ最优鲁棒H∞容错控制器.仿真结果表明,在执行器正常工作和一些执行器发生失效时,容错控制器和切换策略是有效的.     

倒立摆的自适应积分反步控制策略

针对直线单级倒立摆在模型参数不确定和外部扰动情况下的稳定控制问题,提出一种自适应积分反步控制策略。采用拉格朗日方程建立倒立摆系统的运动学模型,为减少稳态误差,将误差积分项引入反步法,设计了倒立摆的控制器;对含有未知参数的系统非线性状态微分方程,设计适当的Lyapunov函数推导出系统未知参数的自适应更新律,削弱了参数不确定性的影响。将自适应积分反步控制与一般的反步法控制、模糊控制及神经网络控制的仿真结果进行了对比,并在LabVIEW开发环境下进行了实物实验。结果表明,自适应积分反步法可以较为迅速且精确地完成稳定控制,较好地克服系统参数不确定及外部扰动的影响,具有较强的鲁棒性。     

位置和速度受限的微型无人直升机轨迹跟踪控制器

针对微型无人直升机在狭窄空间中的轨迹跟踪问题,设计了一种可以限制直升机位置和速度的跟踪控制器.首先将直升机的模型简化为一个未建模的动态模型.基于简化模型利用受限反步法设计控制器,其中在位置控制回路用障碍李雅普诺夫函数代替传统的纯二次型李雅普诺夫函数,以此来限制直升机的位置和速度;用指令滤波器对反步过程中虚拟控制的导数进行估计,避免了复杂的解析计算.此外,将未建模动态和指令滤波器误差合并成有界扰动项,并设计了自适应算法对扰动的上界进行估计和补偿.稳定性分析证明了直升机的闭环跟踪误差最终一致有界,且位置和速度始终位于预设的限制集合中.仿真结果验证了该控制器的有效性.     

具有对称初始数据的二维反应扩散方程的边界镇定

研究了二维圆盘上具有对称初始数据的反应扩散方程的边界控制. 由于初始条件和边界条件关于圆心旋转对称, 系统可以转化为等价的极坐标系下的一维抛物方程. 此时, 极点的奇异性成为了控制器设计中的难点. 本文设计了一系列方程变换, 消除了核函数方程中极点奇异性的影响, 将其转化为修正的Bessel方程, 求出了显式的核函数表达式和精确的边界反馈控制律, 扩展了偏微分方程的backstepping方法. 系统的收敛速度可通过改变控制器中的一个参数来调节. 然后用Lyapunov函数法证明了闭环系统在H1范数下指数稳定, 表明了系统对初值的连续依赖. 最后用数值仿真验证了方法的有效性.     

改进的Elman模型与递归反传控制神经网络

在Elman网络的基础上提出了两种改进网络:输出-输入反馈Elman网络和输出-隐层反馈Elman网络模型,并以前者作为误差反传的通道,建立了递归反向传播控制神经网络模型.在Lyapunov稳定性意义下分别给出了改进网络的稳定性证明,得到了保证网络稳定收敛的最佳自适应学习速率.分别用Elman网络及其改进网络对超声马达进行了模拟.利用改进的Elman网络模型,除了可以较好地模拟马达速度以外,还得到了一些有意义的结果,据此可以根据现场数据采样的情况,选用不同的网络模型.模拟实验结果表明,递归反向传播控制神经网络对多种形式的超声马达参考速度都有很好的控制效果.     

Robust Backstepping Control of Robotic Systems Using Neural Networks

Neural network (NN) controllers for the robust back stepping control of robotic systems in both continuous and discrete-time are presented. Control action is employed to achieve tracking performance for unknown nonlinear system. Tuning methods are derived for the NN based on delta rule. Novel weight tuning algorithms for the NN are obtained that are similar to -modification in the case of continuous-time adaptive control. Uniform ultimate boundedness of the tracking error and the weight estimates are presented without using the persistency of excitation (PE) condition. Certainty equivalence is not used and regression matrix is not computed. No learning phase is needed for the NN and initialization of the network weights is straightforward. Simulation results justify the theoretical conclusions.     

一类不确定非线性系统的自适应鲁棒控制

针对一类由非线性微分方程描述的不确定单输入单输出(SISO)系统,提出了一种自适应鲁棒控制算法.设计了一动态滤波器并将其与原系统组成扩展系统,由滤波器求得控制律稳定扩展系统.算法绕开辨识模型参数而是直接估计函数值,加快了控制律的求解.设计了状态误差观测器,用观测器的值构造控制律逼近状态反馈时的控制效果.基于Lyapunov 稳定理论分析了扩展系统的渐近稳定性并给出了闭环稳定的充分条件.最后仿真结果验证了算法的有效性和鲁棒性.     

一类不确定离散时间系统的最优鲁棒控制

本文针对一类含有不确定因素的离散单输入系统,采用李雅普诺夫第二种方法设计了一种鲁棒控制器.这个控制器是系统状态的线性函数,并且被证明当矩阵Q给定时,它是最优的.文末给出了仿真例子.     

Recursive Back‐Stepping Design of An Adaptive Fuzzy Controller for Strict Output Feedback Nonlinear Systems

In this paper, a back‐stepping adaptive fuzzy controller is proposed for strict output feedback nonlinear systems. The unknown nonlinearity and external disturbances of such systems are considered. We assume that only the output of the system is available for measurement. As a result, two filters are constructed to estimate the states of strict output feedback systems. Since fuzzy systems can uniformly approximate nonlinear continuous functions to arbitrary accuracy, the adaptive fuzzy control theory combined with a tuning function scheme is developed to derive the control laws of strict output feedback systems that possess unknown functions. Moreover, the H∞ performance condition is introduced to attenuate the effect of the modeling error and external disturbances. Finally, an example is simulated in order to confirm the applicability of the proposed method.     

Neural Network Dynamic Surface Backstepping Control for the Speed and Tension System of Reversible Cold Strip Rolling Mill

To weaken the influences of uncertainties and system coupling items on the coordinated tracking control performance of the speed and tension system of a reversible cold strip rolling mill, a control strategy is proposed based on nonlinear disturbance observers (NDOs), dynamic surface backstepping control, and neural network adaptive approximation. First, the transformation form of the system model is given, and then NDOs are developed to counteract the unmatched uncertainties. Next, controllers for the speed and tension system are presented by combining backstepping with dynamic surface control. Again, the neural network adaptive method is used to approximate the matched uncertainties of the system, and the approximation values are introduced into the designed controllers for compensation. Finally, simulation research is carried out on the speed and tension system of a 1422 mm reversible cold strip rolling mill by using the actual data, and the results show the validity of the proposed control strategy in comparison with the decentralized overlapping control strategy.     

On Assigning the Derivative of a Disturbance Attenuation Control Lyapunov Function

We consider feedback design for nonlinear, multi-input affine control systems with disturbances and present results on assigning, by choice of feedback, a desirable upper bound to a given control Lyapunov function (clf) candidate's derivative along closed-loop trajectories. Specific choices for the upper bound are motivated by ℒ₂ and ℒ_∞ disturbance attenuation problems. The main result leads to corollaries on “backstepping” locally Lipschitz disturbance attenuation control laws that are perhaps implicitly defined through a locally Lipschitz equation. The results emphasize that only rough information about the clf is needed to synthesize a suitable controller. A dynamic control strategy for linear systems with bounded controls is discussed in detail. Date received: March 27, 1998. Date revised: March 11, 1999.     

A Survey on the Control Lyapunov Function and Control Barrier Function for Nonlinear-Affine Control Systems

This survey provides a brief overview on the control Lyapunov function(CLF) and control barrier function(CBF) for general nonlinear-affine control systems.The problem of control is formulated as an optimization problem where the optimal control policy is derived by solving a constrained quadratic programming(QP) problem.The CLF and CBF respectively characterize the stability objective and the safety objective for the nonlinear control systems.These objectives imply important properties including...     

同时镇定一族带有不确定参数的多输入非线性系统

Simultaneous stabilization for a collection of multi-input nonlinear systems with uncertain parameters is dealt with in this paper. A systematic method for obtaining a control Lyapunov function (CLF) is presented by solving the Lyapunov equation. A sufficient condition that a quadratic CLF is a common CLF for these systems is acquired. A continuous state feedback is designed to simultaneously stabilize these systems. Finally, the effectiveness of the proposed scheme is illustrated by a simulation example.     

飞行模拟转台非线性干扰观测器反步滑模控制器设计

本文针对考虑不确定性的飞行模拟转台伺服系统,提出了一种基于非线性干扰观测器的反步全局滑模补偿控制方法。该方法采用反步控制方法设计转速期望虚拟控制,然后利用非线性干扰观测器观测系统不确定干扰,进而对引入非线性干扰观测器的系统设计自适应全局滑模控制器,实现了飞行模拟转台伺服系统期望转角信号的鲁棒跟踪控制,仿真结果表明,该方法控制效果良好,具有很好的工程应用价值。