Simultaneous robust normalization and delay‐dependent robust H∞ stabilization for singular time‐delay systems with uncertainties in the derivative matrices

This paper investigates the problem of simultaneous robust normalization and delay‐dependent H_∞ control for a class of singular time‐delay systems with uncertainties. Not only the state and input matrices but also the derivative matrices of the considered systems are assumed to have uncertainties. New sufficient conditions for the existence of a proportional plus derivative state feedback H_∞ controller are derived as LMIs such that the closed‐loop singular system is normal, stable, and guarantee a specific level of performance. Specially, a static state feedback H_∞ controller alone or a state‐derivative feedback H_∞ controller alone can unite to be dealt with by applying our proposed method. Two simulation examples are provided to demonstrate the effectiveness of the proposed approach in this paper. Copyright © 2014 John Wiley & Sons, Ltd.     

鲁棒比例与部分状态导数反馈控制系统设计

基于广义线性系统比例与部分状态导数反馈参数化特征结构配置结果和矩阵对广义特征值灵敏度结果, 得到了关于开环系统矩阵中摄动元素的闭环特征值灵敏度的参数表达式, 并在此基础上提出了广义线性系统比例与部分状态导数反馈最小灵敏度特征值配置的有效算法. 该算法不含有"返回"过程, 允许闭环特征值在希望的区域内方便地参与优化. 一个算例说明了算法的简单性和有效性.     

Decentralised memory static output feedback control for the nonlinear time-delay similar interconnected systems

In this paper, the problem of decentralised memory static output feedback control for a class of nonlinear time-delayed interconnected systems with similar structure is investigated, where both the linear and nonlinear state vectors involve time delay. The contributions of the paper include the following: (1) a new similar structure is presented via memory static output feedback; (2) by exploiting the structure of interconnected systems, the new integral inequalities, constrained Lyapunov equations and LMI method, the decentralised memory static output derivative feedback controllers with similar structure are designed, which is dependent of time delays, to stabilise the interconnected systems uniformly asymptotically; and (3) the stability domain is estimated. The conservatism of the results obtained is reduced by full using the system output information. Finally, the numerical examples are given to demonstrate the effectiveness of the results obtained in this paper.     

Decentralised adaptive output feedback stabilisation for stochastic time-delay systems via LaSalle-Yoshizawa-type theorem

This paper deals with the decentralised output feedback stabilisation problem for a class of large-scale stochastic time-delay nonlinear systems. A general theorem is firstly given to guarantee the global existence and uniqueness of the solution for stochastic time-delay systems. In addition, a stochastic version of the well-known LaSalle-Yoshizawa theorem with time-varying delay is initially proposed for the controller design and stability analysis. Then, for a class of large-scale stochastic systems with time-varying delays, totally decentralised adaptive delay-dependent controllers are designed by using K-filter and backstepping approach. Via LaSalle-Yoshizawa-type theorem and constructing a general Lyapunov function, it is shown that all signals in the closed-loop system are bounded almost surely and the solution is almost surely asymptotically stable. Finally, a simulation example is given to illustrate the effectiveness of the results of this paper.     

Reduced-order observer-based decentralised control of non-linear interconnected systems

The output feedback-based asymptotic stabilisation problem for a class of non-linear interconnected systems is considered, where the non-linear interconnections between subsystems satisfy quadratic constraints. A novel decentralised dynamic output feedback control strategy involving local projection operator-based reduced-order observers is proposed. This decentralised controller is characterised by the separation property. Two easily verifiable conditions that guarantee the asymptotic stability of the closed-loop system driven by the proposed decentralised controller are given. The effectiveness of the developed decentralised control strategy is illustrated with a numerical example and simulations.     

Some investigations on fuzzy P + fuzzy I + fuzzy D controller for non-stationary process

The paper addresses the adaptive behaviour of parallel fuzzy proportional plus fuzzy integral plus fuzzy derivative (FP+FI+FD) controller. The parallel FP+FI+FD controller is actually a non-linear adaptive controller whose gain changes continuously with output of the process under control. Two non-stationary processes, whose characteristics change with time, are considered for simulation study. Simulation is performed using software LabVIEW TM . The set-point tracking response of parallel FP+FI+FD is compared with conventional parallel proportional plus integral plus derivative (PID) controller, tuned with the Ziegler-Nichols (Z-N) tuning technique. Simulation results show that conventional PID controller fails to track the set-point and becomes unstable as the process changes its characteristic with time. But the parallel FP+FI+FD controller shows considerably much better set-point tracking response and does not deviate from steady state. Also, a huge spike is observed in the output of PID controller as the reference set-point and process parameters are changed, while the FP+FI+FD controller gives spike free control signal.     

广义系统输出反馈严格正实控制器设计

研究连续广义系统的正实控制问题。目的是设计静态输出反馈和动态输出反馈严格正实控制器使得闭环系统容许且扩展严格正实。基于广义系统严格正实引理，利用线性矩阵不等式和广义代数Riccati不等式，给出了广义系统静态输出反馈和动态输出反馈严格正实控制器存在的充要条件及设计方法。对动态输出反馈情形，给出了一个数值算例说明控制器设计方法的有效性及可行性。     

Stability Analysis of Parallel Fuzzy P ＋ Fuzzy I ＋ Fuzzy D Control Systems

The study presented in this paper is in continuation with the paper published by the authors on parallel fuzzy proportional plus fuzzy integral plus fuzzy derivative (FP + FI + FD) controller. It addresses the stability analysis of parallel FP + FI + FD controller. The famous"small gain theorem" is used to study the bounded-input and bounded-output (BIBO) stability of the fuzzy controller. Sufficient BIBO-stability conditions are developed for parallel FP + FI + FD controller. FP + FI + FD controller is derived from the conventional parallel proportional plus integral plus derivative (PID) controller. The parallel FP + FI + FD controller is actually a nonlinear controller with variable gains. It shows much better set-point tracking, disturbance rejection and noise suppression for nonlinear processes as compared to conventional PID controller.     

基于输出加微分反馈的广义二阶动力学系统跟踪设计

考虑了基于输出及其微分反馈的广义二阶动力学系统输出渐近跟踪设计．主要给出了如下结果： 广义二阶动力学系统基于输出及其微分反馈的特征结构配置;广义二阶动力学系统基于输出及其微分反馈的 输出渐近跟踪控制律存在的充分条件以及该控制律增益阵的完全参数化表达式．仿真结果说明本文所给出的 算法是有效的．     

Decentralised indirect adaptive output feedback fuzzy H ∞ tracking design for a class of large-scale nonlinear systems

A novel decentralised indirect adaptive output feedback fuzzy controller with a compensation controller and an H _∞ tracking controller is presented for a class of uncertain large-scale nonlinear systems in this article. The compensator adaptively compensates for interconnections between subsystems as well as mismatched errors, while the H _∞ controller suppresses the effect of external disturbances. Based upon the combination of fuzzy inference systems, a state observer, H _∞ tracking technique and the strictly positive real condition, the proposed overall observer-based decentralised algorithm guarantees not only asymptotical tracking of reference trajectories but also an arbitrary small attenuation level of the unmodelled error dynamics including the disturbances on the tracking control. Simulation results substantiate the effectiveness of the proposed scheme.     

Decentralised variable gain robust controller design for a class of large-scale interconnected systems with mismatched uncertainties

In this paper, we propose an LMI-based design method of a decentralised variable gain robust controller for large-scale interconnected systems with mismatched uncertainties. The mismatched uncertainties under consideration are composed of the matched part and the mismatched one, and the proposed decentralised robust controller consists of a state feedback with a fixed gain and one with a variable gain tuned by parameter adjustment laws. Sufficient conditions for the existence of the proposed decentralised variable gain robust controller are given in terms of linear matrix inequalities (LMIs). Finally, a numerical example is illustrated to validate the proposed design procedure.