机器人鲁棒控制器参数演化设计

论文将讨论具有控制输入幅值限制的机器人轨迹跟踪控制问题。将利用基于信号补偿的鲁棒控制方法设计机器人的子关节系统控制器。该控制器由标称控制器和鲁棒补偿器组成。标称控制器对于一标称受控对象实现所希望的轨迹跟踪特性,鲁棒补偿器则用于减小实际受控对象和标称受控对象之间的差异对跟踪特性的影响。当输入存在饱和约束的情况下,对鲁棒补偿器进行了修改,并且基于演化寻优的方法求取鲁棒补偿器参数。     

一类不确定性系统的鲁棒正实性分析与综合

考虑一类具有多项式型不确定性系统的鲁棒正实性分析和综合问题。这类不确定模型是区间摄动和范数有界摄动系统的自然推广。给出了一个系统具有鲁棒扩展严格正实性 (ESPR)的充分条件 ,利用该条件可估计出使系统保持 ESPR的最大参数摄动范围。在 ESPR分析的基础上 ,进一步给出了ESPR控制器的存在条件和控制器的构造方法。通过凸优化算法 ,得到了所提出方法意义下具有最大摄动界的 ESPR控制器设计方法。     

复合摄动系统的H∞ 鲁棒性能设计

本文对具有实参数摄动和未建模动态不确定性的复合摄动问题的鲁棒性能设计进行了深入研究，首次提出利用H∞控制理论中的混合灵敏度方法处理某些复合摄动问题的鲁棒性能设计．其思路是：首先将复合摄动问题的鲁棒性能设计转化为参数不确定性系统的鲁棒性能设计问题；然后将这种参数不确定性问题变换成标准H∞控制问题结构；最后利用“DGKF”或状态反馈的方法获得问题的解．     

基于鲁棒可靠性的不确定时滞系统最优H∞控制器设计

用区间变量描述控制系统参数的不确定性,提出了不确定时滞系统鲁棒H_∞控制的鲁棒可靠性方法,基于鲁棒可靠性的不确定时滞系统最优状态反馈H_∞控制器设计方法,将系统的最优控制器设计归结为基于线性矩阵不等式(LMI)的优化问题．所设计的控制器可以在满足对所有不确定性鲁棒可靠的前提条件下,具有最优的H_∞鲁棒性能,并能在控制系统的设计中综合考虑控制性能、控制代价和鲁棒可靠性．数值算例说明了所提方法的有效性和可行性．     

不确定多时滞系统非脆弱鲁棒保代价控制

针对一类含有多时滞的不确定线性系统，在控制器增益存在乘性和加性两种摄动形式时分别设计了非脆弱具有鲁棒性能的保代价控制器．利用构造的Lyapunov函数和线性矩阵不等式，证明并给出了非脆弱鲁棒保代价状态反馈控制问题有解的充分条件，仅通过求解相应的线性矩阵不等式就可得到非脆弱鲁棒保代价控制器．所设计的控制器不仅使闭环系统具有鲁棒性，能满足所给的的鲁棒保代价性能指标，而且当控制器增益参数变化时，系统性能指标同样能够满足要求．该系统对环境参数的变化具有更好的适应能力。     

具动态不确定性系统的观测器－控制器设计的鲁棒性

研究存在动态不确定性的线性化系统的龙伯格观测器一控制器设计的鲁棒稳定性问题，并给出了易于通过系统参数摄动界来验证鲁棒稳定的充分条件．     

基于LMI的高超鲁棒控制及仿真

研究了高超声速飞行器鲁棒飞行控制器设计以及飞行控制系统的仿真验证问题,通过选择适当的加权函数矩阵,确定广义受控对象.线性矩阵不等式(LMI)技术是控制领域中研究问题的有效工具,控制器的分析与综合等问题可转化为LMI问题的求解,采用基于线性矩阵不等式的H∞控制器设计方法,设计了鲁棒控制器.仿真结果表明所设计的飞行控制系统具有鲁棒性,能有效地抗飞行过程中存在各种各样的干扰及摄动,很好地满足了飞行控制系统性能指标.     

互质因子摄动下的最优鲁棒稳态跟踪控制器设计

研究了存在未知外部干扰时的互质因子摄动系统的鲁棒稳态追踪问题.利用Youla参数化方法，提出了一个最坏情况稳态绝对误差的精确计算公式.该公式使得最优稳态跟踪控制器设计问题等价于保证系统鲁棒稳定时e1的最优鲁棒控制器设计问题.     

带有丢包的网络化控制系统非脆弱鲁棒H￥控制

针对带有丢包的Lipschitz非线性NCS中控制器参数存在摄动的问题,设计了一种加性非脆弱状态反馈H￥控制器。利用Lyapunov稳定性理论和线性矩阵不等式方法,将具有控制器参数不确定的非脆弱鲁棒 H￥控制器设计问题,转化为具有线性矩阵不等式约束和线性目标函数的凸优化问题求解,给出了丢包情况下的非脆弱鲁棒 H￥控制器存在的充分条件。所设计的控制器在容许的参数摄动和丢包概率下,不仅能保证闭环NCS的稳定性和性能要求,而且是非脆弱的。数值仿真验证了方法的有效性。     

离散区间系统鲁棒容错控制器的设计

讨论了离散线性系统的鲁棒容错控制问题.针对离散线性系统,当系统矩阵和控制矩阵存在参数区间摄动时,通过Lyapunov稳定性理论分析了系统同时存在传感器失效情况下的鲁棒稳定问题,给出了系统鲁棒稳定的一个充分条件,并在此基础上给出离散区间系统鲁棒容错控制器的设计方法.最后用数值算例解释了该算法的有效性.     

A nonparametric approach to design robust controllers for uncertain systems: Application to an air flow heating system

This paper presents an approach to design robust fixed structure controllers for uncertain systems using a finite set of measurements in the frequency domain. In traditional control system design, usually, based on measurements, a model of the plant, which is only an approximation of the physical system, is first built, and then control approaches are used to design a controller based on the identified model. Errors associated with the identification process as well as the inevitable uncertainties associated with plant parameter variations, external disturbances, measurement noise, etc. are expected to all contribute to the degradation of the performance of such a scheme. In this paper, we propose a nonparametric method that uses frequency-domain data to directly design a robust controller, for a class of uncertainties, without the need for model identification. The proposed technique, which is based on interval analysis, allows us to take into account the plant uncertainties during the controller synthesis itself. The technique relies on computing the controller parameters for which the set of all possible frequency responses of the closed-loop system are included in the envelope of a desired frequency response. Such an inclusion problem can be solved using interval techniques. The main advantages of the proposed approach are: (1) the control design does not require any mathematical model, (2) the controller is robust with respect to plant uncertainties, and (3) the controller structure can be chosen a priori, which allows us to select low-order controllers. To illustrate the proposed method and demonstrate its efficacy, an application to an air flow heating system is presented.     

区间系数不确定性系统的鲁棒控制器设计

本文提出了一种方法用于设计区间系数不确定性系统的鲁棒镇定控制器，所考虑的区间系数可以是时变的，控制器的设计仅依赖于区间系数的上下界，而设计步骤具有迭代特征。虽然所提到的控制器是线性和确定性的，但能够承受所有容允不确定性。所提出的方法通过一个电力系统负荷频率控制例子加以说明。     

Robust control of systems with fuzzy representation of uncertainties

In this paper, an approach is proposed to design robust controllers for uncertain systems with the linguistic uncertainties represented by fuzzy sets. With a provided technique, the fuzzy sets are best approximated by intervals (crisp sets). Then the Kharitonovs theorem is applied to construct a robust PID controller for the uncertain plant with time-invariant uncertainties represented by interval models. Also, for the uncertain system with linguistic values of the time-varying uncertainties best approximated by intervals (which are bounded), a robust sliding mode controller is developed to stabilize the uncertain system if the sliding coefficient conditions are satisfied. Moreover, the best approximation intervals are shown to be more related to the possibility distribution of the elements in the universes of discourse of fuzzy sets than the type of membership functions used for fuzzy sets. Examples and simulation results are included to indicate the design approach and the effectiveness of the proposed robust controller.This work is partly supported by the the R.O.C. National Science Council through Grant NSC 90-2213-E-197-002.     

Robust reliability method for non-fragile guaranteed cost control of parametric uncertain systems

The problem of non-fragile guaranteed cost control of uncertain systems is studied from a new point of view of reliability against uncertainties. An efficient robust reliability method for the analysis and design of non-fragile guaranteed cost controller of parametric uncertain systems is presented systematically. By the method, a robust reliability measure of an uncertain control system satisfying required robust performance can be obtained, and the robustness bounds of uncertain parameters such that the control cost of a system is guaranteed can be provided. The optimal non-fragile guaranteed cost controller obtained in the paper may possess optimal guaranteed cost performance satisfying the precondition that the system is robustly reliable with respect to uncertainties occurring in both the controlled plant and controller gain. The presented formulations are in the framework of linear matrix inequality and thus can be carried out conveniently. The presented method provides an essential basis for the tradeoff between reliability and control cost in controller design of uncertain systems. Two numerical examples are provided to demonstrate the efficiency and feasibility of the presented method. It is shown that the coordination and simultaneous realization of the system performance, control cost, and robust reliability in control design of uncertain systems are significant.     

Robust output tracking control of SISO plants with multiple operating points and with parametric and unstructured uncertainties

The robust output tracking control problem is considered for single-input single-output plants with multiple operating points and with both parametric and unstructured uncertainties (i.e. interval parameter uncertainties and norm-bounded unmodelled dynamics). The parametric uncertainties can involve parameter perturbations as well as degree variations. The plant with uncertainties is assumed to be of minimum phase, but is not required to have a fixed number of unstable poles. A new method is presented by which a linear time-invariant robust controller is designed in two steps: first, a nominal controller is designed to get exact output tracking for the nominal plant; then, a robust compensator is added to achieve robust properties. It is shown that robust stability, robust static state property, robust transient property and robust tracking property can be achieved simultaneously. A computationally tractable design procedure is presented. A salient feature of our results, shown in the present paper, is that we can tell the users how to tune on-line the parameters of the controller with the proposed structure.     

Robust Control System Design for an Uncertain Nonlinear System Using Minimax LQG Design Method

A systematic approach to design a nonlinear controller using minimax linear quadratic Gaussian regulator (LQG) control is proposed for a class of multi‐input multi‐output nonlinear uncertain systems. In this approach, a robust feedback linearization method and a notion of uncertain diffeomorphism are used to obtain an uncertain linearized model for the corresponding uncertain nonlinear system. A robust minimax LQG controller is then proposed for reference command tracking and stabilization of the nonlinear system in the presence of uncertain parameters. The uncertainties are assumed to satisfy a certain integral quadratic constraint condition. In this method, conventional feedback linearization is used to cancel nominal nonlinear terms and the uncertain nonlinear terms are linearized in a robust way. To demonstrate the effectiveness of the proposed approach, a minimax LQG‐based robust controller is designed for a nonlinear uncertain model of an air‐breathing hypersonic flight vehicle (AHFV) with flexibility and input coupling. Here, the problem of constructing a guaranteed cost controller which minimizes a guaranteed cost bound has been considered and the tracking of velocity and altitude is achieved under inertial and aerodynamic uncertainties.     

NETWORK‐INDUCED DELAY‐DEPENDENT H∞ CONTROLLER DESIGN FOR A CLASS OF NETWORKED CONTROL SYSTEMS

This paper is concerned with the problem of robust H_∞ controller design for a class of uncertain networked control systems (NCSs). The network‐induced delay is of an interval‐like time‐varying type integer, which means that both lower and upper bounds for such a kind of delay are available. The parameter uncertainties are assumed to be normbounded and possibly time‐varying. Based on Lyapunov‐Krasovskii functional approach, a robust H_∞ controller for uncertain NCSs is designed by using a sum inequality which is first introduced and plays an important role in deriving the controller. A delay‐dependent condition for the existence of a state feedback controller, which ensures internal asymptotic stability and a prescribed H_∞ performance level of the closed‐loop system for all admissible uncertainties, is proposed in terms of a nonlinear matrix inequality which can be solved by a linearization algorithm, and no parameters need to be adjusted. A numerical example about a balancing problem of an inverted pendulum on a cart is given to show the effectiveness of the proposed design method.     

分数阶区间系统的鲁棒稳定性分析

由于实际的物理系统常会存在各种不确定结构,这些不确定结构给系统的稳定性分析带来了困难和一定的影响,因此对这类带有不确定结构的分数阶系统控制问题的研究,具有广泛的实际应用意义。本文主要针对带有区间不确定性的分数阶控制系统,分析了该系统的鲁棒稳定性问题,首先将区间矩阵用分式线性变换(LFT)表示,然后基于分析得出了此类系统鲁棒稳定的充分必要条件。并给出两个数值算例阐释该方法,仿真结果表明了该方法的有效性。     

Stabilization of perturbed system via IMC: An application to load frequency control

This paper proposes a robust controller for a parametric uncertain system of order three. The scheme conceptualizes the approach of selecting the worst-case plant and then the controller is designed using the internal model control principle which constitutes the reduced model of worst-case plant. The beauty of the proposed approach is that even though the plant is uncertain, the complete robust stability analysis and controller design is carried out by a single linear model. As an illustrative example, a load frequency control (LFC) problem is considered for single- and multi-area power systems in presence of unexpected disturbances, parametric uncertainties and physical constraints. The proposed controller is also applied to the network topology similar to standard IEEE 39 bus system (New England 10 machine test system) to validate the more realistic LFC application. Simulation studies show that the proposed controller brings robust and fast disturbance rejection attributes.