Algebraic characterization of fixed modes in decentralized control

Algebraic characterizations are presented for the existence of fixed modes of a linear closed-loop system with decentralized feedback control. The class of controllers for which fixed modes are present is extended beyond that currently known.     

On impulsive modes of linear singular systems subject to decentralized output feedback

Some algebraic properties of linear singular systems at infinity under static decentralized output feedback are studied in this note. New concepts of algebraic multiplicity and geometric multiplicity of the impulsive decentralized fixed modes, and the impulsive decentralized cycle index of the singular system are defined. These concepts indicate how much a singular system can be made close to being impulse-free by decentralized output feedback, and the results are shown to be generic. The geometric multiplicity and the impulsive decentralized cycle index are determined in terms of the system matrices explicitly. The number of impulsive modes that can be eliminated is given in terms of these indexes. The impulsive decentralized cycle index is shown to characterize generic properties on controllability and observability of the closed-loop system through an individual channel (or an external channel). Illustrative examples are provided.     

Algebraic properties of singular systems subject to decentralized output feedback

This paper investigates algebraic properties of decentralized singular systems (DSSs) under local static output feedback. New concepts of the geometric multiplicity (GM) of the finite decentralized fixed mode (DFM), the decentralized output feedback variable polynomial (DVP), and the finite decentralized output feedback cycle index (DCI) of the DSS are defined. The formulas for determining the GM and the DCI are given in terms of the DFM and the system matrices. It is shown that almost any decentralized output feedback can make the zeros of the DVP (i.e., the closed-loop poles that are variable) distinct and away from any given finite set in the complex plane. It is also shown that the finite DFM of the DSS are those uncontrollable and/or observable finite modes of the closed-loop DSS through any single channel. Finally, the minimal number of the inputs and outputs that guarantee the finite modes of the closed-loop DSS controllable and observable is shown to be the finite DCI of the DSS. An illustrative example is provided.     

Computation of the state transition matrix for a class of delay-differential systems†

Control systems can drift into instability or, less catastrophically, exhibit resonance behaviour. One role for adaptive controllers is to learn sufficient information concerning the dominant closed-loop system mode so as to apply effective feedback to dampen these modes. In such situations the adaptive loop augments the fixed controller feedback loop. This paper presents an algorithm for adaptive resonance suppression and provides simulation results to study its behaviour in the presence of high-order unmodelled dynamics. The algorithm appears particularly useful for enhancing existing fixed controller designs.     

The system-matched hold and the intermittent control separation principle

An intermittent controller is a form of hybrid controller which adds a generalised sample and hold mechanism to an underlying continuous-time feedback control system. The sampling may be non-uniform or event driven. One particular form of the hold, termed the system-matched hold (SMH) mimics the behaviour of the closed-loop feedback control signal during the intermittent intervals. It is shown in this article that this choice of hold leads to an intermittent separation principle. In particular, this simple analytical result ensures that when using the SMH, the separation properties of the underlying state-estimate feedback control system carry over to the intermittent control system. This separation principle for the SMH has the important consequence that, unlike the zero-order hold case, the stability of the closed-loop system in the fixed sampling case is not dependent on sample interval. It is therefore suggested that the SMH should replace the conventional zero-order hold in circumstances where the sample interval is unknown, time-varying or determined by events.     

Parametric state-feedback control with model reduction

A parametrization of the class of linear state-feedback controllers that assign a set of desired self-conjugate eigenvalues to the closed-loop system is applied to a method of model reduction. By making the maximum number of the closed-loop modes unobservable, while retaining arbitrary assignment of the remaining modes, a lower-order transfer-function matrix is obtained. The technique may be used to reduce a broad class of multivariable systems to first-order multivariable systems. The main result is a class of mode) reducing fixed-gain state feedback controllers explicitly specified by a set of free parameters which may be chosen to satisfy additional design requirements.     

并联DC-DC变换器系统的固定时间分布式协同控制

针对负载为超级电容的并联DC-DC变换器系统,为了在固定时间内实现电流输出均衡目标,提出固定时间分布式协同控制方法.将耦合子系统之间的通信拓扑,利用无向图进行刻画.借助输入输出反馈线性化技术,将并联DC-DC变换器系统的电流均衡控制设计难题转化为固定时间内一阶多智能体系统的一致性跟踪问题.借助符号函数、拉普拉斯矩阵、牵制增益矩阵,基于最近邻原则,设计参数可调的固定时间电流均衡分布式协同控制律.利用李亚谱诺夫函数严格证明整个闭环系统的稳定性,并推导出收敛时间的上界.所提出的固定时间电流均衡分布式协同控制方法,可以克服有限时间协同控制方法对初始状态依赖性强的缺点,同时改善了系统的收敛性.借助仿真,验证了所提出方法的有效性和可行性.     

On improving the robustness of LQ regulators

Soroka and Shaked have shown that a linear quadratic state feedback regulator may suffer from poor robustness where small changes in the parameters of the system can lead to fast unstable closed-loop modes. It is shown there that the stability properties can be improved if possible nonminimum phase behavior is allowed for in modeling the system prior to the controller design.     

极小极大加系统(F,G,H)的输出反馈镇定

研究了一般化非自治非线性极小极大加系统的输出反馈镇定问题.首先,提出了闭环系统单极大射影系统表达式.其次,研究指出闭环单极大射影子系统存在严格的颜色匹配关系.接着,针对颜色匹配的复杂情况,提出新的着色图构造.以往对闭环单极大射影子系统中出现的新增圈研究,仅涉及含有一条反馈弧的圈,本文指出新增圈中可能包含由多条反馈弧构成的圈.最后,根据新着色图和新增罔特点得到了系统输出反馈镇定的一个充分条件.     

On the robustness of LQ regulators

It is shown that in spite of its large gain and phase margins the linear quadratic state feedback regulator may suffer from poor robustness where small changes in the parameters of the system may lead to fast unstable closed-loop modes.