线代数中的核多项式及其在数值计算中的应用(上)

1.引言近年来在线代数计算方法方面有了发展,特别是解线性方程组和计算特征值。由于高速电子计算机的发展,数值计算方法的收敛性和稳定性成了十分重要的问题。因此,一些古典的方法被改进和提炼得更好了,也产生了许多新的计算方法,特别是叠代方法。在计算机上使用叠代方法有一些要求。首先,叠代过程的每一     

《系统建模方法及自适应控制系统的研究》简介

本项研究在系统建模方法和自适应控制方面取得了一些成果,主要有:1.对复合动态系统的输入输出特性作了深入分析,扩展了无源性定理及V.M.Popov的超稳定性判据,使原有结果成为特例。为分析和改进设计递推辨识算法及自适应控制方案提供了理论工具,还可用于设计能保证全局稳定的非线性校正系统、扩展V.M.Popov的绝对稳定性判据等。2.以对反馈系统的无源性分析为理论根据,提出了多步递推参数估计的新算法,可保证有更好的收敛性;提出了一种算法简单但鲁棒性强的自适应控制方案。理论分析和仿真结果表明,在有未建模动     

带控制时滞广义系统的PID型迭代学习算法

研究了一类线性时滞广义系统的迭代学习控制问题.针对广义系统的特点,引入选代学习控制方法,给出了线性时滞广义系统的PID型选代学习算法.结合矩阵广义逆理论,利用λ范数和Bellman引理,并从理论上给出了算法收敛性的完整证明.研究结果表明,只要充分利用广义系统的特点,寻找合适的收敛性分析方法,便可解决控制时滞广义系统的收敛性问题,对时滞广义系统速代学习控制问题的研究具有重要的理论意义与应用价值.     

一类动量交换刚柔耦合系统的自学习组合控制

提出自学习组合控制方法实现对一类动量交换刚柔耦合系统的主动控制. 在推导动力学方程的基础上, 提出组合控制律和在线自学习律并分别证明其稳定性和收敛性. 对刚体旋转和柔性梁振动分别设计 H∞ 控制器和 LQR 调节器, 并馈入角加速度信号构成组合控制系统. 仿真算例表明该方法的有效性.     

奇异摄动系统极限解存在的代数判据

讨论了线性奇异摄动系统广义状态解当ε趋于零时在广义函数空间上的收敛性问题.在已有结论的基础上,得到了奇异摄动系统广义状态解收敛的代数判据,该判据简化了对奇异摄动系统广义状态解收敛性的判别,为系统控制器设计提供了一种代数条件.     

高频角振动测试转台的迭代学习控制

为了提高角振动转台在陀螺高频特性测试时对周期性期望轨迹的跟踪精度,该文在PID型迭代学习控制的基础上,针对转台控制系统的稳定性和迭代学习的收敛性进行解耦设计,得到一种复合迭代学习控制器,并从频域角度给出了其收敛性条件,最后用MatlabSimulink工具箱对该设计进行了仿真研究.仿真结果表明,与常规比例-积分-微分控制相比较,这种设计改善了系统输出跟踪周期性正弦信号输入的精度,提高了系统带宽,并对系统消除周期性干扰有所裨益.结论表明这种复合迭代控制器可以应用于高频角振动转台的控制.     

基于扩张状态观测器的鲁棒迭代学习控制

针对一类包含模型不确定和外界干扰等非重复扰动的线性离散系统,本文通过将迭代学习控制与自抗扰技术相结合,提出一种新的基于扩张观测器的鲁棒迭代学习控制方法.本文以时间轴和迭代轴两个方向同时出发考虑系统的非重复扰动估计和稳定收敛问题.将与时间和迭代轴同时相关的模型不确定及外界干扰等因素归纳为系统总扰动,针对其非重复变化特性给出了扩张观测器的设计,保证在批次内快速、准确地估计系统总扰动;基于上述扰动估计,设计新型的迭代学习控制律,利用线性矩阵不等式方法证明了整个鲁棒迭代学习系统的稳定性和收敛性,并给出合理的控制器参数估计条件.此外,讨论了迭代学习控制中第一批次的控制律设计问题,给出合理的自抗扰控制器设计.最后通过仿真对比实验验证了本文方法的可行性和有效性.     

非线性非仿射离散时间系统的两阶段最优迭代学习控制

针对非仿射非线性离散时间系统, 基于一种新的沿迭代轴的动态线性化技术, 提出了双层最优迭代学习控制算法. 双层意味着分别设计了两个最优学习层, 迭代的改进控制输入序列和学习增益. 其主要特点是控制器的设计和收敛性分析只依赖于动态系统的 I/O 数据. 换句话说, 不需要知道系统的任何其他信息就可以很容易的选取控制器参数. 仿真研究表明了提出的算法沿迭代轴具有几何收敛性, 这一特点在快速路交通迭代学习控制中具有重要的工程意义.     

不确定混沌系统的直接自适应神经网络控制

提出了一种不确定混沌系统动态神经网络直接自适应控制方法.为了确保学习过程收敛性,研究了有效的在线学习算法,证明了闭环系统的稳定性,并针对Lorenz混沌系统进行了计算机仿真研究.     

内模控制框架下时延系统扩张状态观测器参数整定

作为一种有效的控制设计方法, 自抗扰控制研究获得了广泛关注, 然而针对自抗扰控制器的参数整定方法则相对较少. 本文针对一阶惯性加延迟系统, 将线性自抗扰控制转化为内模控制结构, 导出了其中控制器、滤波器、乘性不确定性、互补灵敏度函数的对应表达式, 随后, 利用频域鲁棒稳定性判据, 分析了自抗扰控制器核心—–扩张状态观测器的参数对闭环系统稳定性的影响. 基于该分析, 总结出一阶惯性加延迟系统扩张状态观测器的两条参数整定准则. 数值仿真结果验证了该整定准则的有效性.     

Robot visual servoing with iterative learning control

This paper presents an iterative learning scheme for vision-guided robot trajectory tracking. First, a stability criterion for designing iterative learning controller is proposed. It can be used for a system with initial resetting error. By using the criterion, one can convert the design problem into finding a positive definite discrete matrix kernel and a more general form of learning control can be obtained. Then, a three-dimensional (3D) trajectory tracking system with a single static camera to realize robot movement imitation is presented based on this criterion.     

高相对阶连续时间系统的间接迭代学习控制

本文提出了一类高相对阶线性连续时间系统的间接迭代学习控制算法,该算法相对独立于系统局部控制器,因此可以应用于已有局部反馈控制器的系统.采用具有极点配置的H∞鲁棒控制器作为系统的内环控制,而在外环通过迭代学习控制调整内环系统的指令信号.通过引入拉氏变化,构建了迭代学习系统的2-D Roesser模型,推导了系统渐近收敛条件,并研究了存在有界初始条件偏移和迭代变化外部干扰时算法的鲁棒性能.最后,利用空中加油对接控制的算例进一步验证了算法的有效性.     

A design method for indirect iterative learning control based on two-dimensional generalized predictive control algorithm

Indirect iterative learning control (ILC) facilitates the application of learning-type control strategies to the repetitive/batch/periodic processes with local feedback control already. Based on the two-dimensional generalized predictive control (2D-GPC) algorithm, a new design method is proposed in this paper for an indirect ILC system which consists of a model predictive control (MPC) in the inner loop and a simple ILC in the outer loop. The major advantage of the proposed design method is realizing an integrated optimization for the parameters of existing feedback controller and design of a simple iterative learning controller, and then ensuring the optimal control performance of the whole system in sense of 2D-GPC. From the analysis of the control law, it is found that the proposed indirect ILC law can be directly obtained from a standard GPC law and the stability and convergence of the closed-loop control system can be analyzed by a simple criterion. It is an applicable and effective solution for the application of ILC scheme to the industry processes, which can be seen clearly from the numerical simulations as well as the comparisons with the other solutions.     

A Learning Control for a Class of Linear Time Varying Systems Using Double Differential of Error

In this paper, a new iterative learning control based on the double differential of the error is proposed for the linear time varying system having relative degree greater than one. The convergence criterion of the proposed method is proved. Furthermore, it is shown by simulations that convergence of error can be increased considerably by using our proposed controller as compared to the iterative learning controller using error or single differential of the error for the modification of the control input without increasing the learning gain.     

Robust iterative learning controller design using the performance weighting function of feedback control systems

Iterative learning controllers combined with existing feedback controllers have prominent capability of improving tracking performance in repeated tasks. However, the iterative learning controller has been designed without utilizing effective information such as the performance weighting function to design a feedback controller. In this paper, we deal with a robust iterative learning controller design problem for an uncertain feedback control system using its explicit performance information. We first propose a robust convergence condition in the ?₂-norm sense for an iterative learning control (ILC) scheme. We present a method to design an iterative learning controller using the information on the performance of the existing feedback control system such as performance weighting functions and frequency ranges of desired trajectories. From the obtained results, several design criteria for iterative learning controller are provided. Through analysis on the remaining error, the loop properties before and after learning are compared. We also show that, in the ?₂-norm sense, the remaining error can be less than the initial error under certain conditions. Finally, to show the validity of the proposed method, simulation studies are performed.     

Internal-model-based design of repetitive and iterative learning controllers for linear multivariable systems

Repetitive and iterative learning control are two modern control strategies for tracking systems in which the signals are periodic in nature. This paper discusses repetitive and iterative learning control from an internal model principle point of view. This allows the formulation of existence conditions for multivariable implementations of repetitive and learning control. It is shown that repetitive control can be realized by an implementation of a robust servomechanism controller that uses the appropriate internal model for periodic distrubances. The design of such controllers is discussed. Next it is shown that iterative learning control can be implemented in the format of a disturbance observer/compensator. It is shown that the resulting control structure is dual to the repetitive controller, and that both constitute an implementation of the internal model principle. Consequently, the analysis and design of repetitive and iterative learning control can be generalized to the powerful analysis and design procedure of the internal model framework, allowing to trade-off the convergence speed for periodic-disturbance cancellation versus other control objectives, such as stochastic disturbance suppression.     

新型同步发电机励磁控制器的设计

针对传统的基于迭代学习控制算法的同步发电机励磁控制器存在初始控制信号由经验确定的问题,提出了一种基于即时学习型迭代学习控制算法的同步发电机励磁控制器的设计方案。该方案在迭代学习控制算法中引入即时学习算法,利用即时学习算法计算初始控制信号,有效减少了初始控制信号与理想控制信号之间的误差。仿真结果表明,该励磁控制器收敛速度快,具有更强的维持机端电压的能力。     

一种新型的迭代学习控制器设计研究

针对一般连续系统的迭代学习控制问题进行了讨论,通过对常用的P型迭代学习控制算法的分析,在分析比较P型、PD型迭代学习控制律存在问题的基础上,提出了一种新型的迭代学习控制算法,利用误差信号以及相邻两次误差的差值信号对系统控制律进行逐次修正,既能避免PD型迭代算法由于微分作用而出现的不良影响,又可以充分地利用了系统已保存的有效信息,从而实现良好的跟踪效果以及较快的跟踪收敛速度,最后通过对一非线性连续系统的仿真,结果验证了算法相对于传统P算法的有效性与优越性.     

Robust iterative learning control of single-phase grid-connected inverter

For the single phase inductance-capacitance-inductance (LCL) grid-connected inverter in micro-grid, a kind of robust iterative learning controller is designed. Based on the output power droop characteristics of inverter, the current sharing among the inverters is achieved. Iterative learning strategy is suitable for repeated tracking control and inhibiting periodic disturbance, and is designed using robust performance index, so that it has the ability to overcome the uncertainty of system parameters. Compared with the repetitive control, the robust iterative learning control can get high precision output waveform, and enhance the tracking ability for waveform, and the distortion problem of the output signal can be solved effectively.