基于Delta算子的永磁直线同步电机非脆弱保性能速度控制器设计

利用Delta算子离散化系统采样周期是显式参数的特点,基于Delta算子方法对永磁直线同步电机(PMLSM)不同采样周期下的非脆弱保性能速度控制器的统一化设计问题进行研究.以线性矩阵不等式(LMI)给出该控制器的存在条件.通过对PMLSM闭环系统极点的分析,表明所设计的非脆弱保性能速度控制器不但能保证PMLSM在其对象参数和控制器参数同时发生范数有界摄动时闭环系统仍保持渐近稳定,而且系统的二次型性能指标上界的数学期望值不超过某个给定的上界,而不考虑控制器参数摄动情况所设计的控制器在其参数摄动时闭环系统将无法保持稳定.     

Design of robust non-fragile H-infinity controller based on Delta operator theory

Considering that the controller parameters are of additive norm-bounded uncertainties when realized, a design method of robust non-fragile H-infinity controller for uncertain system based on Delta operator theory is illustrated in this paper. A sufficient and necessary condition of the existence for the controller is given, which is presented in LMI forms. Finally, the designed method is used in the speed control system of permanent magnet linear synchronous motor (PMLSM). With the designed controller, the resulted speed closed-loop system is still stable and has the expected Hinfinity performance even if the sample period is reduced and the parameters of the controller and the controlled object are of variations. The results show that the designed method is effective.     

Design of robust non-fragile H-infinity controller based on Delta operator theory

Considering that the controller parameters are of additive norm-bounded uncertainties when realized, a design method of robust non-fragile H-infinity controller for uncertain systems based on Delta operator theory is illustrated in this paper. A sufficient and necessary condition of the existence for the controller is given, which is presented in LMI forms. Finally, the designed method is used in the speed control system of a permanent magnet linear synchronous motor （PMLSM）. With the designed controller, the resulting speed closed-loop system is still stable and has the expected Hinfinity performance even if the sample period is reduced and the parameters of the controller and the controlled object are varied. The results show that the designed method is effective.     

Robust nonfragile guaranteed cost control for uncertain T-S fuzzy Markov jump systems with mode-dependent average dwell time and input constraint

This paper aims to investigate the problem of robust nonfragile guaranteed cost control for uncertain Takagi-Sugeno fuzzy systems with Markov jump parameters, time-varying delay and input constraint. A nonfragile mode-dependent fuzzy controller with mode-dependent average dwell time (MDADT) is designed with input constraint. A sufficient condition is developed to ensure that the resulting closed-loop system is robust almost surely asymptotically stable with guaranteed cost index not exceeding the specified upper bound. Subsequently, the controller gain and upper bound of the guaranteed cost index can be obtained by solving a set of linear matrix inequalities. Finally, numerical and practical examples are provided to demonstrate the performance of the proposed approach.     

Nonfragile robust exponential stabilization of nonlinear uncertain switched systems with actuator saturation

For nonlinear uncertain switched systems, the problem of how to overcome the controller vulnerability is studied when the actuator saturation is considered. The sufficient condition for guaranteeing nonfragile robust exponential stabilization of the system is derived by using the method of minimum dwell time. Then, a switching law and the nonfragile state feedback controllers are designed such that the closed-loop system can be robustly exponentially stabilized at the origin. Next, when some scalar parameters of the closed-loop system are given, the design issue of the nonfragile state feedback controllers, which aim at enlarging the estimation of domain of attraction for closed-loop system, is transformed into a convex optimization issue with linear matrix inequalities (LMI) constraints. Finally, an example is given to verify the effectiveness of the proposed method.     

Non-fragile robust optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems

This paper is concerned with the problem of non-fragile robust optimal guaranteed cost control for a class of uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model with norm-bounded uncertainties. Our attention is focused on the design of non-fragile state feedback controllers such that the resulting closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible parameter uncertainties and controller gain variations. A sufficient condition for the existence of such controllers is established under the linear matrix inequality framework. Moreover, a convex optimisation problem is proposed to select a non-fragile robust optimal guaranteed cost controller stabilising the 2-D discrete state-delayed system as well as achieving the least guaranteed cost for the resulting closed-loop system. The proposed method is compared with the previously reported criterion. Finally, illustrative examples are given to show the potential of the proposed technique.     

Observer-based H-infinity output feedback control with feedback gain and observer gain variations for Delta operator system

Considering that the controller feedback gain and the observer gain are of additive norm-bounded variations, a design method of observer-based H-infinity output feedback controller for uncertain Delta operator systems is proposed in this paper. A sufficient condition of such controllers is presented in linear matrix inequality （LMI） forms. A numerical example is then given to illustrate the effectiveness of this method, that is, the obtained controller guarantees the closed-loop system asymptotically stable and the expected H-infinity performance even if the controller feedback gain and the observer gain are varied.     

时变时滞复杂动态网络的非脆弱性同步保性能控制

针对一类时变时滞复杂网络系统,提出了一种非脆弱性同步保性能控制方法。在假设非线性向量函数f(x)可微条件下,通过Jacobi矩阵方法进行线性化处理,余项满足匹配条件,设计具有增益摄动的非脆弱性状态反馈控制器,以确保当控制器的参数发生小的摄动时,仍能保证控制器的有效性。通过构造合适的Lyapunov-Krasovskii泛函,采用积分等式、矩阵分析、Schur补定理等方法,在给定的保性能指标的条件下,得到了该系统非脆弱性同步保性能控制存在的充分条件;并证明了该条件等价于一组线性矩阵不等式(LMI)的可行性问题, 给出了LMI约束条件下的凸优解构造方法,求出了闭环时变时滞系统保性能值的最小值。最后,通过数值算例对比验证了设计方法的可行性。     

Energy-Efficient Optimal Guaranteed Cost Intermittent-Switch Control of a Direct Expansion Air Conditioning System

To improve the energy efficiency of a direct expansion air conditioning (DX A/C) system while guaranteeing occupancy comfort, a hierarchical controller for a DX A/C system with uncertain parameters is proposed. The control strategy consists of an open loop optimization controller and a closed-loop guaranteed cost periodically intermittent-switch controller (GCPISC). The error dynamics system of the closed-loop control is modelled based on the GCPISC principle. The difference, compared to the previous DX A/C system control methods, is that the controller designed in this paper performs control at discrete times. For the ease of designing the controller, a series of matrix inequalities are derived to be the sufficient conditions of the lower-layer closed-loop GCPISC controller. In this way, the DX A/C system output is derived to follow the optimal references obtained through the upper-layer open loop controller in exponential time, and the energy efficiency of the system is improved. Moreover, a static optimization problem is addressed for obtaining an optimal GCPISC law to ensure a minimum upper bound on the DX A/C system performance considering energy efficiency and output tracking error. The advantages of the designed hierarchical controller for a DX A/C system with uncertain parameters are demonstrated through some simulation results.      

Non-fragile hybrid guaranteed cost control for a class of uncertain switched linear systems

1 Introduction In recent years, the switched control systems have been attracting considerable attention in the control commu- nity [1～7]. Basically, a switched system belongs to a spe- cial class of hybrid systems, which consist of a family of continuous-time or discrete-time subsystems and a switch- ing law that specifies the switching between them. Such control systems appear in many applications, such as com- municatin networks, switching power converters and many other fields. On the oth…     

不确定时滞系统的指定衰减度保代价可靠控制

针对一类含有时变时滞的不确定参数线性系统,研究了在执行器发生故障情况下系统具有指定衰减度的保代价可靠控制器设计问题。系统中的参数不确定性满足广义匹配条件,时变时滞及其变化率有界,执行器失效采用增益故障模型。系统的性能函数是含有指数项和故障输入项的积分二次型函数。经过适当的状态变换,将原系统的指定衰减度保代价可靠控制问题转化为另一个等价系统的保代价可靠控制问题。根据Lyapunov稳定性理论,得到了系统存在指定衰减度保代价可靠控制器应满足的一个矩阵不等式,进一步将这个矩阵不等式转化为线性矩阵不等式（LMI）,并给出了系统的保代价表达式。利用论文方法设计的指定衰减度保代价可靠控制器能够使得时滞系统对于任意允许的不确定量以及执行器故障都保持鲁棒可靠指数稳定,并且使系统具有保代价的性能指标。     

不确定模糊Delta算子系统的鲁棒H∞控制

研究了一类T-S模糊Delta算子系统的鲁棒H_∞控制问题.首先利用LMI形式给出了模糊Delta算子系统鲁棒镇定的充分条件,然后构造了可使闭环系统鲁棒稳定且对可允许的参数变化满足H_∞性能的状态反馈控制律.本文结果统一了连续与离散模糊系统的鲁棒H_∞镇定设计结论,数值算例说明了方法的可行性.     

Robust non-fragile guaranteed cost control of uncertain large-scale systems with time-delays in subsystem interconnections

In this paper, the robust non-fragile guaranteed cost-control problem is studied for a class of uncertain linear large-scale systems with time-delays in subsystem interconnections and given quadratic cost functions. The uncertainty in the system is assumed to be norm-bounded and time-varying. Also, the state-feedback gains for subsystems of the large-scale system are assumed to have norm-bounded controller gain variations. The problem is to design a state feedback control law such that the closed-loop system is asymptotically stable, and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. A parameterized characterization of the robust non-fragile guaranteed cost controllers is given in terms of the feasible solutions to a certain LMI. A numerical example is given to illustrate the proposed method.     

不确定非线性系统的鲁棒耗散性与保性能控制

考虑了不确定仿射非线性系统的鲁棒耗散性与保性能控制问题,不确定性范数有界,不满足匹配条件.基于HJI不等式,设计了状态反馈控制器.当扰动存在时,控制器能使系统达到耗散,当扰动为零时,所设计的控制器使系统对于给定的性能函数具有上界,最后研究了不确定线性系统的保性能与耗散性控制情形.     

Delay-dependent robust and non-fragile guaranteed cost control for uncertain singular systems with time-varying state and input delays

This paper considers the design problems of a delay-dependent robust and non-fragile guaranteed cost controller for singular systems with parameter uncertainties and time-varying delays in state and control input. The designed controller, under the possibility of feedback gain variations, can guarantee that a closed-loop system is regular, impulse-free, stable, an upper bound of guaranteed cost function, and non-fragility in spite of parameter uncertainties, time-varying delays, and controller fragility. The existence condition of the controller, the controller’s design method, the upper bound of guaranteed cost function, and the measure of non-fragility in the controller are proposed using the linear matrix inequality (LMI) technique. Finally, numerical examples are given to illustrate the effectiveness and less conservatism of the proposed design method. Recommended by Editorial Board member Guang-Hong Yang under the direction of Editor Young Il Lee. Jong-Hae Kim received the B.S., M.S., and Ph.D. degrees in Electronics from Kyungpook National University in 1993, 1995, and 1998, respectively. He was with STRC at Kyungpook National University from Nov. 1998 to Feb. 2002. He has been with Sun Moon University since March, 2002. His research interests focus on robust control, signal processing, and industrial application systems.     

Robust reliable guaranteed cost control of positive interval systems with multiple time delays and actuator failure

This paper addresses the robust reliable guaranteed cost control problem of positive interval systems with multiple time delays and actuator failure for a given quadratic cost function. Through constructing a Lyapunov–Krasovskii functional, a sufficient condition for the existence of robust reliable guaranteed cost controllers is established such that the closed-loop system is positive and asymptotically stable, and the cost function is guaranteed to be no more than a certain upper bound. Based on the linear matrix inequality method, a criterion for the design of robust reliable guaranteed cost controllers is derived which can tolerate all admissible uncertainties as well as actuator failure. Moreover, a convex optimisation problem with linear matrix inequality constraints is formulated to design the optimal robust reliable guaranteed cost controller which minimises the upper bound of the closed-loop system cost. A numerical example is given to show the effectiveness of the proposed methods.     

基于观测器的不确定广义时滞系统保成本控制

讨论了基于观测器的一类不确定广义时滞系统的保成本控制问题,给出了系统保成本控制器的设计方法.控制器的构造使得闭环系统是鲁棒稳定的.利用线性矩阵不等式以及Lyapunov函数方法,给出了鲁棒保成本控制器存在的充分条件以及相应的可保成本指标,并证明了这个条件等价于一组线性矩阵不等式(LM Is)的可解性问题,同时推广了已知的相关结果.最后以算例验证了设计方法的有效性.     

A model-free design of reduced-order controllers and application to a DC servomotor

This paper presents a new model-free technique to design fixed-structure controllers for linear unknown systems. In the current control design approaches, measured data are used to first identify a model of the plant, then a controller is designed based on the identified model. Due to errors associated with the identification process, degradation in the controller performance is expected. Hence, we use the measured data to directly design the controller without the need for model identification. Our objective here is to design measurement-based controllers for stable and unstable systems, even when the closed-loop architecture is unknown. This proposed method can be very useful for many industrial applications. The proposed control methodology is a reference model design approach which aims at finding suitable parameter values of a fixed-order controller so that the closed-loop frequency response matches a desired frequency response. This reference model design problem is formulated as a nonlinear programming problem using the concept of bounded error, which can then be solved to find suitable values of the controller parameters. In addition to the well-known advantages of data-based control methods, the main features of our proposed approach are: (1) the error is guaranteed to be bounded, (2) it enables us to avoid issues related to the use of minimization methods, (3) it can be applied to stable and unstable plants and does not require any knowledge about the closed-loop architecture, and (4) the controller structure can be selected a priori, which means that low-order controllers can be designed. The proposed technique is experimentally validated through a real position control problem of a DC servomotor, where the results demonstrate the efficacy of the proposed method.     

Fuzzy guaranteed cost control for nonlinear systems with time-varying delay

This paper focuses on the problem of guaranteed cost control for Takagi-Sugeno (T-S) fuzzy systems with time-varying delayed state. A linear quadratic cost function is considered as a performance index of the closed-loop fuzzy system. Then, the guaranteed cost control of the closed-loop fuzzy system is discussed, and the sufficient conditions are provided for the construction of a guaranteed cost controller via state feedback and observer-based output feedback. When these conditions, which are given in terms of the feasibility of linear matrix inequalities (LMIs), are satisfied, the designed state feedback controller and observer-based controller gain matrices can be obtained via a convex optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the approaches proposed in this paper.     

一类不确定广义系统的非脆弱保性能控制

研究了一类时变时滞不确定广义系统的非脆弱保性能控制问题。在系统矩阵、滞后状态矩阵、输入矩阵和滞后输入矩阵都具有不确定性时,带有反馈增益扰动的控制器能够保证闭环系统是正则、无脉冲、指数稳定的;且性能函数存在上界。对于出现的两个不确定项乘积的问题,采用两个线性矩阵不等式,两次运用Schur补引理的方法得以解决。控制器的增益可通过求解一系列严格线性矩阵不等式得到。数值仿真实例证明了所提方法的有效性。