多输入多输出线性控制系统的简单极点配置算法

本文给出了对多输入多输出系统进行极点配置的算法。按照本文的结论，任何多输入多输出线性控制系统都可以象单输入单输出线性系统那样进行闭环系统及状态观测器的极点配置。     

线性定常系统的综合性最优控制问题

本文讨论了具有二次型性能指标的线性定常系统的降低性能指标灵敏度、降低轨迹灵敏 度和配置闭环极点的综合性最优控制问题,提出了新的综合性能指标,从而得到了易于计算 的结果;解决了多参数变化时降低轨迹灵敏度的综合性最优控制问题;推导了闭环特征值对 Q阵的梯度阵公式,提出了一种配置互异的全部闭环极点Q阵算法,并给出了算例.     

广义最小方差极点配置自校正PID控制器

此文提出了一种设计广义最小方差极点配置自校正 PID 控制器的新算法,算法性能指标中引入了伺服输入项和控制作用的加权多项式,保证了闭环系统的输出对给定信号的无偏跟踪。闭环极点配置根据二阶系统期望特征多项式进行设计。对系统参数未知采用最小二乘估计。该方法具有设计简单、鲁棒性好、便于工程应用、     

一种具有抑制噪声性质的极点配置自校正控制器

本文提出了一种新的极点配置自校正控制算法。它具有以下三个特点:1)除了配置系统的闭环极点外,还可抑制噪声对系统输出的干扰;2)与其他极点配置自校正控制算法相比,本算法所需的计算量大为减少;3)理论上可得到算法的收敛性结果。该算法已在实际系统中得到了成功的应用。     

干扰解耦和极点配置组合问题的研究*

本文用代数方法研究了干扰解耦和极点配置组合问题,导得了存在一个状态反馈控制器使得干扰—输出完全解耦且同时配置闭环系统全部(或部分)极点的充分条件,给出了实现干扰解耦和极点配置的状态反馈阵的一个检验算法。     

多变量系统鲁棒性复数极点配置的一种新方法*

本文对线性定常多变量系统的鲁棒性极点配置问题,给出了一种算法。这个算法对指定闭环极点中含共轭复极点的情形,用起来十分方便,它把一个带约束优化问题变成了一个无约束优化问题求解,本文末还给出了一个数值例子。     

基于在线优化的线性系统状态反馈鲁棒镇定

建立关于Sylvester方程的鲁棒极点配置梯度流优化算法模型,在线求解相应的二次优化问题,并在线计算状态反馈增益矩阵.使得闭环系统矩阵的伞部特征值位于给定的区域中.对于一切满足条件的扰动,具有最小灵敏度,闭环系统人范围一致渐近稳定.仿真结果验证了该方法适用十非线性系统的鲁棒镇定问题和在线鲁棒极点配置问题.     

闭环连续系统仿真若干问题的分析研究

分析研究了对闭环系统的纯滞后环节如何处理的问题,找到开环系统和闭环系统的理论输出值计算方法,并比较3种Pade近似和全极点近似的精度。将此算法应用到闭环系统中,进一步比较4种近似,以求得闭环系统中误差最小的近似方法。同时提出在计算过程中对纯滞后处理的改进方法,使得误差大大减小,精度提高了一个数量级。研究结果表明,在开环系统和闭环系统,全极点近似由于没有引入零点,使得误差最小;改进方法使误差精度提高了一个数量级。     

具有指定闭环极点的次最优控制系统设计

本文利用多变量系统极点配置的结果,提出了一种具有指定闭环极点,并使二次型指标达到极小的次最优控制系统的设计方法,这种设计方法与标准线性二次型调节器(LQR设计方法的不同之点,就在于设计中引入了闭环极点约束,使闭环系统能具有希望的动态特性,本文还给出了在计算机上易于实现的设计算法和计算过程,以及设计实例。     

多变量自寻优极点配置自校正控制器

本文提出了一种多变量自寻优闭环移动极点极点配置目校正控制算法,其基本策略是:在控制过程中,以多变量广义最小方差为目标自动移动闭环极点,且在控制量允许的范围内,使闭环极点处于理想位置上。理论与仿真表明:本文给出的算法避免了预先确定闭环极点位置所带来的种种不利现象,不仅能实现最优控制,且仍具有极点配置的鲁棒性。     

线性系统的干扰解耦与抑制——基于特征结构配置的设计

本文利用线性系统的输出反馈特征结构配置结果,给出了利用输出反馈实现线性系统的干扰——输出解耦问题的充要条件和求解线性系统干扰抑制问题的一个有效算法,进一步推广了文中的结果。本文给出的方法即可把握闭环系统的特征结构,又可使闭环极点在一定的希望区域内参于优化,从而既较大程度地抑制了干扰的影响,又顾及了系统性能,且还适用于单输入或单输出系统。仿真算例证明了本文方法的有效性。     

Arbitrarily fast and robust tracking by feedback

The output of a singe-input-single-output linear feedback system with more than one pole in excess over the zeros in the loop transmission cannot track arbitrarily fast its input (by the root locus). In this work we extend the linear feedback so that some of the open loop poles may depend on the open loop gain; we call this new class quasi-linear feedback systems. We then derive time domain, pole-zero, and frequency domain conditions which ensure arbitrarily fast and robust tracking by quasi-linear feedback, for an arbitrary number of poles in excess over the zeros. We prove that in a particular case these conditions are equivalent, and that the boundedness in frequency of the closed loop transfer function is no longer necessary for achieving arbitrarily fast tracking. The robustness is to external disturbances and initial conditions, and the open loop has to be minimum phase. Some examples are presented which illustrate these results. They also show that this good performance can be obtained with a reduced control effort, and that quasi-linear feedback can alleviate the limitation on performance of non-minimum phase open loops.     

An augmented system approach to static output‐feedback stabilization with ℋ︁∞ performance for continuous‐time plants

This paper revisits the static output‐feedback stabilization problem of continuous‐time linear systems from a novel perspective. The closed‐loop system is represented in an augmented form, which facilitates the parametrization of the controller matrix. Then, new equivalent characterizations on stability and ??_∞ performance of the closed‐loop system are established in terms of matrix inequalities. On the basis of these characterizations, a necessary and sufficient condition with slack matrices for output‐feedback stabilizability is proposed, and an iteration algorithm is given to solve the condition. An extension to output‐feedback ??_∞ control is provided as well. The effectiveness and merits of the proposed approach are shown through several examples. Copyright © 2008 John Wiley & Sons, Ltd.     

一种新的离散系统最优闭环极点配置方法

分析了LQ逆问题解的存在条件,以便合理选择期望的闭环极点,使之成为一组最优极点．提 出了一种以离散系统LQ逆问题分析为基础的新的最优控制系统设计方法,得到了开环、闭环 特征多项式系数与加权矩阵之间的解析关系,只要给定一组期望闭环极点,即可确定与 之对应的加权矩阵Q和R,从而得到一个具有指定极点的最优控制系统．     

The internal model principle of control theory

The classical regulator problem is posed in the context of linear, time-invariant, finite-dimensional systems with deterministic disturbance and reference signals. Control action is generated by a compensator which is required to provide closed loop stability and output regulation in the face of small variations in certain system parameters. It is shown, using the geometric approach, that such a structurally stable synthesis must utilize feedback of the regulated variable, and incorporate in the feedback path a suitably reduplicated model of the dynamic structure of the disturbance and reference signals. The necessity of this control structure constitutes the Internal Model Principle. It is shown that, in the frequency domain, the purpose of the internal model is to supply closed loop transmission zeros which cancel the unstable poles of the disturbance and reference signals. Finally, the Internal Model Principle is extended to weakly nonlinear systems subjected to step disturbances and reference signals.     

Static Output Feedback Pole Placement via a Trust Region Approach

This technical note presents two closely related algorithms for the problem of pole placement via static output feedback. The algorithms are based on two different trust region methods and utilize the derivatives of the closed loop poles. Extensive numerical experiments show the effectiveness of the algorithms in practice though convergence to a solution is not guaranteed for either algorithm. While desired poles must be distinct, strategies for dealing with repeated poles are also presented.     

Suboptimal mean controllers for bounded and dynamic stochastic distributions

Based on the recently developed algorithms for the modelling and control of bounded dynamic stochastic systems (H. Wang, J. Zhang, Bounded stochastic distributions control for pseudo ARMAX stochastic systems, IEEE Transactions on Automatic control, 486–490), this paper presents the design of a subotpimal nonlinear mean controller for bounded dynamic stochastic systems with guaranteed stability. The B-spline functional expansion based square root model is used to represent the output probability density function of the system. This is then followed by the design of a mean controller of the output distribution of the system using nonlinear output tracking concept. A nonlinear quadratic optimization is performed using the well known Hamilton–Jacobi–Bellman equation. This leads to a controller which consists of a static unit, a state feedback part and an equivalent output feedback loop. In order to achieve high precision for the output tracking, the output feedback gain is determined by a learning process, where the Lyapunov stability analysis is performed to show the asymptotic stability of the closed loop system under some conditions. A simulation example is included to demonstrate the use of the algorithm and encouraging results have been obtained.     

Exponential passivity for output feedback stabilisation of nonlinear uncertain systems

In this article, we address the problem of stabilisation by output feedback for a class of uncertain systems. We consider uncertain systems with a nominal part which is affine in the control and an uncertain part which is norm bounded by a known function. We propose an output feedback such that the closed loop system is globally exponentially stable.     

Nonlinear versus linear control in the direct output feedback stabilization of linear systems

This paper investigates the use of nonlinear direct output feedback in the control of linear time-invariant systems. Inparticular, it is concerned with those nonlinear controllers which result in a closed loop system which is quadratically stable. That is, the closed loop nonlinear system is asymptotically stable and furthermore, a quadratic Lyapunov function can be used to establish this stability. The main result of this paper can be stated roughly as follows: Any linear system which can be made quadratically stable using nonlinear direct output feedback control can also be stabilized using linear direct output feedback control.