基于状态相关系数系统的非线性控制

针对非线性仿射系统的镇定问题,将待镇定系统表达成相应的状态相关系数系统.在短时段内,可以用一个线性定常系统逼近该状态相关系数系统,将该线性定常系统的镇定控制器用来控制原非线性系统.该设计方法的优点是:设计简单,只用到线性定常系统的控制方法,无需构造复杂的李亚普诺夫函数;扩展容易,可以结合各种线性系统设计方法进行控制器设计.在状态相关系数矩阵满足可换性条件时,可以保证闭环系统的稳定性.对小车倒立摆的仿真结果表明:用该设计方法构造的控制器可以很好地镇定系统.     

一类带有自适应的H∞状态反馈控制

H∞控制做为一种已经相当成熟的理论,已经有了系统的解决方案,从Riccati方法到LMI方法.我们都可以通过Matlab工具箱方便的求得H∞控制器.注意到：这些方法得到的控制器增益都是定常的,这样的控制器虽然在工程实践中易于实现,但是就H∞控制的出发点,即干扰抑制问题本身而言,定常增益的控制器却不是必须的,本文提出了一种在原有的定常控制器基础上加入自适应项的控制器结构,经过理论分析,得出这样的控制器可以使得闭环系统具有更为优越的干扰抑制性能,文中同时给出了一个数值例子来显示该方法的有效性和优越之处.     

具有混合故障模型的时滞系统的可靠控制

针对线性定常时滞系统,基于Lyapunov稳定性理论,讨论考虑执行器具有混合故障的系统存在可靠控制器的充分条件,并结合时滞系统相关处理方法和线性矩阵不等式完成状态反馈可靠控制器的设计.数值仿真验证了本文控制器设计方法的可行性.     

MIMO线性离散系统的最优鲁棒跟踪控制

将MIMO线性离散定常系统在指定信号输入下获取最优时域指标的最优跟踪控制器设计问题归纳为求解一个有限维线性规划问题, 并证明这种最优跟踪控制器也是鲁棒稳定控制器.     

一类时滞分布参数系统滑动模控制器的设计

基于变结构控制理论,提出一种用变结构控制方法来消除参数不确定性对系统性能的影响。首先建立延迟为τ的系统模型,鉴于该系统具有稳定与非稳定因素,我们制定一系列标准,从而写出系统的滑动模运动方程,经过证明,确认系统模型在所给的控制律下能顺利进入滑模区域,且处于该滑动切换面之下时,控制状态是稳定的,因此达到了设计要求。经实验征明,该滑动模控制器具有普遍性。     

一种基于T-S模糊模型的混沌控制方法

用T-S模糊系统来逼近非线性系统,它的IF-THEN规则后件由线性状态空间子系统构成,进而可以应用模糊系统的控制理论求得模糊控制器,用此非线性控制器来控制非线性系统,以求良好的控制效果;将模糊控制技术应用于混沌控制中,可以克服反馈线性化等传统方法对参数完全精确已知的限制;模糊规则后件部分以局部线性方程形式给出的T-S模糊模型可以通过调整相关参数很好地逼近混沌系统,基于该模型采用平行分散补偿技术设计出具有相同规则数目的模糊控制器,控制器所有参数可以通过求解一组线性矩阵不等式一次性得到。仿真结果验证了该方法的有效性。     

基于自适应模糊逻辑系统的预置滑模跟踪控制方法

研究了一类定常线性系统的自适应模糊预置滑模跟踪控制器的设计问题.在系统参数未知的情况下,综合模糊控制和滑模控制策略及自适应方法,得到的控制器能够使得跟踪误差渐近收敛并稳定.仿真研究验证了所提出的控制器综合方法的有效性.     

T-S模糊系统的局部稳定

讨论了T-S模糊系统的局部稳定性及控制器设计问题．给出连续T-S模糊系统局部稳定的定义,利用非二次Lyapunov函数和线性矩阵不等式（LMI）方法得到连续T-S模糊系统局部稳定的充分条件,并给出了基于LMI的局部镇定控制器设计方法．该方法不同于已有的全局稳定控制器设计方法,为判别模糊系统的稳定提供了新的选择．最后通过数值算例演示了控制器的设计方法。并证明了该方法的可行性。     

一维模糊PID控制器的钝性稳定性分析

本文研究新近提出的模糊PID控制器的稳定性问题．由于该模糊PID控制器的模 糊推理部分具有非线性特性，因此本文采用钝性定理来分析它的稳定性．本文给出分析稳定 性的方法，并针对一阶和二阶对象的一般形式，给出了保证系统稳定的参数范围,用仿真验 证了所得结果．高阶对象也可以使用圆判据求取相应结果．     

PI控制中衰减度与H∞指标的相容性

研究n阶线性定常系统在PI控制下衰减度与H∞指标的相容性问题.首先基于D-分割法和边界穿越定理,分别推导了描述PI控制器参数稳定域边界、PI控制器满足期望的衰减度指标的参数边界和期望的H∞指标的参数边界的解析表达式.再应用满意控制思想,对上述期望指标的相容性进行了分析,给出了相容指标较好的取值范围.当上述两类指标相容时,可以迅速得到整个PI控制器相容性解集(满意解集).用一个算例说明了所提出的设计方法的有效性.     

Time-varying feedback laws for decentralized control

Decentralized control schemes are considered for time-invariant, finite dimensional, linear systems with know state equations. It is assumed that the systems are reachable and observable at a fictitious centralized control station, and that there is strong connectivity between the decentralized control stations via the system where necessary. It is shown that whether or not there are decentralized fixed modes in the open-loop system, periodically varying feedback gains at all but one of the control stations permit the remaining control station to observe and control the system given knowledge of the control laws implemented at the other control stations. Certain time-invariant systems which cannot be stabilized by decentralized time-invariant controllers, namely those with unstable decentralized fixed modes, can thus be stabilized by decentralized time-varying controllers.     

Stabilization of decentralized control systems via time-varying controllers

In the design of decentralized control systems it is well known that the existence of unstable fixed modes prevents us from stabilizing it via linear time-invariant local controllers. In this note, we show that such systems might be stabilizable via time-varying controllers. In particular, a design method using sample and hold is proposed.     

Discrete-time control of continuous systems with approximate decentralized fixed modes

In this paper, the discrete-time control of decentralized continuous-time systems, which have approximate decentralized fixed modes, is studied. It is shown that under certain conditions, discrete-time controllers can improve the overall performance of the decentralized control system, when a linear time-invariant continuous-time controller is ineffective. In order to obtain these conditions, a quantitative measure for different types of approximate fixed modes in a decentralized system is given. In this case, it is shown that discrete-time zero-order hold (ZOH) controllers, and in particular, that generalized sampled-data hold functions (GSHF), can significantly improve the overall performance of the resultant closed-loop system. The proposed sampled-data controller is, in fact, a linear time-varying controller for the continuous-time system.     

分散系统经济控制的一种方法

本文讨论用改变分散系统结构,即用交换站间信息的方法来消除分散固定模,对两个控制 站的分散系统给出了最少信息交换通道的个数,同时给出实施的方案.     

Overlapping control systems with optimal information exchange

This paper deals with the stabilizability of interconnected systems via linear time-invariant (LTI) decentralized controllers. Given a controllable and observable system with some distinct decentralized fixed modes (DFMs), it is desired to find a suitable control structure (in terms of information flow) for it. Since a decentralized controller consists of a number of non-interacting local controllers, the objective here is to establish certain interactions between the local controllers in order to eliminate the undesirable DFMs. This objective is achieved by translating the knowledge of the system into some bipartite graphs. Then, the notions of minimal sets and maximal subgraphs are introduced, which lead to a simple combinatorial algorithm for solving the underlying problem. The efficacy of the results obtained is demonstrated by an illustrative example.     

Control of continuous-time LTI systems by means of structurally constrained controllers

This paper deals with the characterization of the fixed modes of multi-channel systems with respect to linear time-invariant (LTI) structurally constrained controllers. Fixed modes can be found numerically for any LTI system with respect to any given control structure, using a random number generator. The existing analytical methods, however, are not capable of characterizing the fixed modes in the most general case of non-strictly proper systems with non-block diagonal (i.e., overlapping) control structure, efficiently. The notion of a decentralized overlapping fixed mode (DOFM) is introduced in this paper to address the above problem in the most general case. To this end, the knowledge of the overlapping control structure is translated into a bipartite graph, whose vertices correspond to the input and output vectors of various control channels. An efficient technique is applied to the obtained graph to identify the DOFMs of the system. It is to be noted that a system is stabilizable via an appropriate LTI decentralized overlapping controller if and only if it does not have any unstable DOFM. Moreover, it is shown how those modes which are not DOFMs can be placed freely in the complex plane using a proper LTI decentralized overlapping controller. The efficacy of this work is demonstrated through an example.     

On the quantitative characterization of approximate decentralized fixed modes using transmission zeros

The spectrum of a linear time-invariant multivariable system, using decentralized linear time-invariant controllers, can only be assigned to a symmetric set of complex numbers that include the decentralized fixed modes (DFM). Hence only systems with stable DFM can be stabilized. Although the concept of DFM characterizes when a decentralized controller can stabilize a system, it gives no indication of howhard it is to effect such a stabilization. A system is considered hard to stabilize if large controller gains are required. Modes that are hard to shift are termedapproximate decentralized fixed modes. In this paper two new assignability measures which quantify the difficulty of shifting a mode are derived. The first is coordinate invariant and is based on the distance between a mode and a set of transmission zeros. The second is coordinate dependent and is based on the minimum singular value of a set of transmission zero matrices. This work has been supported by the Natural Sciences are Engineering Research Council of Canada under Grant No. A4396.     

Fixed zeros of decentralized control systems

Considers the notion of decentralized fixed zeros for linear, time-invariant, finite-dimensional systems. For an N-channel plant that is free of unstable decentralized fixed modes, an unstable decentralized fixed zero of channel i (1⩽i⩽N) is defined as an element of the closed right half-plane, which remains as a blocking zero of that channel under the application of every set of N-1 controllers around the other channels, which make the resulting single-channel system stabilizable and detectable. The paper gives a complete characterization of unstable decentralized fixed zeros in terms of system-invariant zeros     

Optimal stabilization of linear systems via decentralized outputfeedback

Presents an approach to the optimal stabilization of a linear time-invariant system via decentralized control. The class of controllers considered does not restrict the controller to be finite dimensional or time invariant. In fact, the controller structure proposed can be regarded as a form of time varying sampled data control. The main result of the paper presents a scheme for constructing a collection of decentralized controllers which stabilizes the system and is optimal with respect to a quadratic performance index     

An algebraic characterization of quotient decentralized fixed modes

In the control of linear time-invariant (LTI) decentralized systems, a decentralized fixed mode (DFM) is one which is immovable using an LTI decentralized controller. However, some DFMs can be moved using more complicated decentralized controllers; the ones which cannot are labelled quotient DFMs (QDFMs), since they arise from a related quotient system. The classical algorithm used to compute the QDFMs requires two steps: a partitioning of the sub-systems, using graph theory, followed by the application of standard tools from decentralized control. Here the goal is to provide a more direct approach to computing them.