基于异步观测器的离散分段仿射系统控制: LMI方法

基于分段二次Lyapunov函数为离散分段仿射系统提出了一种基于观测器的控制律. 考虑的主要问题是原系统当前所在作用域未知, 且无法根据测量输出推断. 通过将凸多面体作用域用椭球体外逼近, 并将矩阵等式约束用奇异值分解技术予以处理, 所提控制方法能够被转化为线性矩阵不等式(LMI)描述, 比现有的只能转化为双线性矩阵不等式的方法更容易求解. 最后, 将所提方法应用到混沌系统控制.     

一类切换线性奇异系统的H∞控制

研究一类由任意有限多个奇异子系统组成的切换奇异系统的状态反馈和动态输出反馈H∞控制问题.利用共同Lyapunov函数方法和凸组合技术,给出由矩阵不等式表示的控制器存在的充分条件,并设计了相应的子控制器和切换策略.分别采用矩阵变换和消元法,将矩阵不等式分别转化为一组线性矩阵不等式(LMIs).数值算例说明了所提方法的有效性和可行性.     

Markov 系统矩阵未知情况下的控制器设计

针对Markov 系统矩阵参数未知的实际情况, 提出一种基于状态反馈控制与自适应控制相结合的控制方法. 基于线性矩阵不等式技术给出相应控制器参数的求解条件. 与现有大多数自适应控制方法相比, 所提方法不仅使估计误差几乎处处有界, 而且原系统的系统状态几乎处处渐近稳定, 具有较好的收敛特性. 在所得结果的基础上, 进一步讨论了转移速率部分未知时的相关控制问题. 数值算例验证了所提出的设计方法的有效性.

     

一类不确定切换奇异系统的动态输出反馈鲁棒H∞控制

研究一类由任意有限多个不确定子系统组成的切换奇异系统的动态输出反馈鲁棒H∞控制问题. 利用共同 Lyapunov 函数方法和凸组合技术, 给出由矩阵不等式表示的控制器存在的充分条件, 并设计了相应的子控制器和切换策略. 采用消元法, 将该矩阵不等式转化为一组线性矩阵不等式 (LMIs). 最后, 数值实例验证了所提方法的有效性.     

一类切换线性奇异系统的状态反馈H∞控制*

研究了一类由任意多个子系统组成的线性切换奇异系统的状态反馈H∞控制问题。采用共同Lyapunov函数方法和凸组合技术,给出由矩阵不等式表示的使闭环系统渐近稳定且满足H∞性能的控制器存在的充分条件, 并设计了相应的子控制器和切换策略。采用矩阵变换,将矩阵不等式等价转换为一组线性矩阵不等式。数值算例说明了所提方法的有效性和可行性。     

多电机驱动系统的一致性控制

以单摆系统为例,研究一类多电机驱动系统的一致性控制问题.针对一个由6个直流电动机驱动的单摆系统,提出一种基于比例积分观测器的一致性协议控制设计方法.利用H∞技术,所提观测器可以在估计系统状态的同时,得到未知输入和可测噪声的有效估计,在此基础上构建分布式一致性控制协议,并将求解观测器增益矩阵和一致性增益矩阵转化为求解线性矩阵不等式的问题.最后,对某给定参数的多电动机驱动的单摆系统进行Matlab仿真,结果表明所提方法是正确且有效的.     

凸多面体不确定系统的符号稳定性分析

针对一类凸多面体描述的连续线性不确定系统研究其符号稳定性条件,从而从符号稳定的角度探索一种新的不确定系统鲁棒控制器设计方法.在矩阵符号稳定定义和必要条件的基础上,给出了矩阵集合符号稳定的定义和完整同源稳定符号型集合的概念,得到了凸多面体不确定系统符号稳定的充分必要条件.进一步分析了符号稳定凸多面体不确定系统的特征根分布与主对角线元素的关系,提出了基于符号稳定的不确定系统状态反馈镇定控制综合方法.相比于基于Lyapunov稳定性理论的不确定系统鲁棒控制方法,本文所提方法避免了求解线性矩阵不等式,并且更符合工程设计的习惯.通过一类三轴稳定卫星姿态控制问题的算例和仿真验证了所提方法的有效性.     

分数阶时变切换系统有限时间异步控制

针对一类时变切换系统,当考虑子系统具有分数阶（Fractional Order）特性时,提出了一种基于模型依赖平均驻留时间方法的有限时间稳定性条件及异步切换控制策略.借助于Caputo分数阶导数引理和切换Lyapunov函数,利用矩阵不等式技术提出了分数阶时变切换系统有限时间稳定的充分条件.将有限时间稳定的结果进一步推广到有限时间有界的情形,利用平均驻留时间思想提出了分数阶时变切换系统有限时间有界的充分条件,基于该条件设计了系统的异步切换控制器.所给出的设计方法将系统异步切换控制问题转化为矩阵不等式组的求解问题.通过数值仿真验证了所提控制方法的有效性.     

基于α阶逆的大时滞非线性动态矩阵控制

针对一类大时滞非线性系统,提出了基于α阶逆的动态矩阵控制新方法.该方法采用BP神经网络辨识逼近原非线性系统的α阶逆系统,并与原系统串联复合组成伪线性系统;采用基于线性系统的动态矩阵预测控制方法设计系统附加控制器.在系统存在建模误差、存在扰动和模型参数发生较大变化等情况下,采用该控制方法依然具有很好的动、静态性能和很强的鲁棒性.给出了详细的设计原理和步骤,并通过大量的仿真分析与已有的大时滞非线性系统内模控制研究结果进行了比较:内模控制依赖于系统模型,当模型出现严重失配的情况下,系统性能变坏,而采用提出的方法则不依赖系统精确的数学模型,计算量小,简化了非线性系统的设计;研究与仿真结果证明了所提控制方法的有效性.     

具有未知动态的线性系统二人零和博弈问题在线学习方案

针对具有未知动态线性系统的二人零和博弈问题,本文提出了一种新的基于单环迭代方法的在线学习方案.为保证单环迭代方法的收敛性,给出了一种新的分析方法.在系统内部矩阵A,控制输入矩阵B以及干扰输入矩阵D均未知的情况下,通过在线迭代策略,同步得到了博弈代数黎卡提方程的近似解,以及控制和干扰策略.仿真结果表明了所提方法的有效性.     

LPV decoupling for control of multivariable systems

This article investigates methods for decoupling multivariable linear parameter varying (LPV) systems and proposes a new interaction measure for decoupled proportional-integral (PI) feedback control design in LPV systems. The proposed approach seeks to benefit the multivariable control of multi-input multi-output (MIMO) systems with variable operating conditions, variable parameters or nonlinear behaviour. This method can improve the tracking performance and reduce the operating conditions variability of such systems with significant coupling in the system dynamics. We design MIMO decoupling feedback LPV controllers to address loop interaction effects. The proposed method uses a parameter-dependent static inversion or SVD decomposition of the system to minimise the effects of the off-diagonal terms in the MIMO system transfer function matrix. A new parameter-dependent interaction measure is introduced based on the SVD decomposition and static inversion which is subsequently utilised for tuning multi-loop PI controller gains. Numerical examples are presented to illustrate the validity of the proposed LPV decoupling methods, as well as the use of the proposed interaction measures for a decoupled multi-loop PI control design.     

多变量系统多级并失展开方法

研究多变量系统的并失展开方法,给出了判断传递函数矩阵能否并失展开的判据。在此基础上提出多变量系统的多级并失展开设计方法,以克服单级并失展开方法应用的局限性。     

Self-tuning controller design for systems with arbitrary time delays Part 1. Theoretical development

Self-tuning control of multivariable systems with arbitrary time delays has been an active area of research in recent years. The use of an interactor matrix in deriving controllers for such systems has been suggested by various authors. Factorization of the input polynomial matrix has also been proposed for the controller design stage. It is shown in this paper that these two approaches are not, in general, equivalent. A simple and straightforward procedure for the extraction of the input and output time delay matrices is proposed for the input polynomial matrix factorization approach. Conditions for the time delay matrices to exist are also derived for a class of multivariable systems. These conditions provide a theoretical justification for the use of time delay matrices in self-tuning control of such systems.     

设计多变量鲁棒控制系统的正规矩阵方法

本文研究了设计多变量鲁棒控制系统的正规矩阵方法,证明了正规传递函数矩阵是H∞ 范数最优的一个充分条件,从而表明,正规矩阵方法可以达到与H∞方法同样好的鲁棒性.在 此基础上,提出一种正规矩阵参数优化设计方法,该方法既保证了系统的鲁棒性又可兼顾系统 的动静态性能,同时所得到的控制器比较简单.     

Perfect and subperfect regulation in linear multivariable control systems

This paper is concerned with the synthesis of a high-gain feedback control, called perfect regulation (p.r.), for linear multivariable systems with external signals. The existence condition for p.r. is derived, in which the minimum phase property plays an essential role. The use of an observer is discussed for achieving p.r. under restricted state observation. Some asymptotically ideal feedback properties are demonstrated, such as the complete desensitization, the complete servo performance with decoupling and the complete disturbance rejection, which formulate the loop-tightness for multivariable systems. A design method for applying p.r. to non-minimum phase systems, called subperfect regulation (s.p.r.), is proposed based on the factorization of the plant transfer function matrix into the minimum phase part and the totally non-minimum phase part. It is a multivariable extension of a well-known design technique for scalar systems to overcome the difficulty of phase non-minimality. Computational procedures for p.r. and s.p.r. are discussed. An illustrative example is shown.     

多变量系统控制器的参数满意优化设计

为了将满意优化拓展到多变量系统中以解决多变量控制系统线性二次型(LQ)控制器设计中加权系数阵确定难的问题,提出多变量系统满意优化设计方法,通过设计满意度函数,构造出多变量系统的满意优化数学模型,并用改进遗传算法实现二级倒立摆系统LQ控制器满意优化设计.仿真结果显示,系统具有更满意的综合性能指标.证实了该方法的有效性和实用性.本文的研究对多变量系统优化设计具有一定的参考价值.     

A model reference quantitative feedback design theory with application to turbomachinery

A new decentralized robust control design framework, model reference quantitative feedback design (MRQFD), is developed for the design of the MIMO parametric uncertain control systems. An internal model reference loop is proposed to obtain the achievement of generalized diagonal dominance (GDD) and the reduction of uncertainty in the resultant compensated internal loop system. Based on nonnegative matrix theory, a useful design guide is derived to achieve the GDD condition for the internal model reference loop. Then a sensitivity-based quantitative feedback design (QFD) method is developed and used to solve the resulting series of single-loop QFD problems. The MIMO quantitative specifications are guaranteed to be satisfied by the proposed design framework for largely uncertain systems. A successful application to the design of a robust multivariable controller for the Allison PD-514 aircraft turbine engine is presented to demonstrate the effectiveness of the methodology developed here.     

未知多变量非线性系统自适应模糊预测控制

对一类未知多变量非线性系统提出了直接自适应模糊预测控制方法,此方法首先对被控对象提出了线性时变子模型加非线性子模型的预测模型,然后直接用模糊逻辑系统组成的向量来设计预测控制器,并基于时变死区函数对控制器中的未知向量和广义误差估计值中的未知矩阵进行自适应调整．文中证明了此方法可使广义误差向量估计值收敛到原点的一个邻域内．     

A normalizing precompensator for the design of effective and reliable commutative controllers

Sensitivity to parameter perturbation represents the main caution regarding the use of the characteristic locus method on the design of multivariable control systems. The method is not effective when the condition number of the plant eigenvector matrix is high or, equivalently, when the plant transfer matrix differs a great deal from normality. With the view to coping with this problem, it is proposed in this paper a precompensator structure and, in the sequel, two optimization problems are formulated and solved: the first one, for 2 x 2 systems, aims at minimizing the eigenvector matrix condition number; the second one, for the general m x m case, is intended to make the precompensated system as normal as possible by minimizing a defined measure of normality. Once the precompensated system matrix has been made close to a normal one, the characteristic locus method can then be applied effectively, leading to reliable control systems, as far as stability in face of uncertainty is concerned.     

Design of reduced-order state estimators for linear time-varying multivariable systems

The design of reduced-order state estimators for linear time-varying multivariable systems is considered. Employing the concepts of matrix operators and the method of canonical transformations, this paper shows that there exists a reduced-order state estimator for linear time-varying systems that are ‘lexicography-fixedly observable’. In addition, the eigenvalues of the estimator can be arbitrarily assigned. A simple algorithm is proposed for the design of the state estimator.