Robust model-reference control for descriptor linear systems subject to parameter uncertainties

Robust model-reference control for descriptor linear systems with structural parameter uncertainties is investigated. A sufficient condition for existing a model-reference zero-error asymptotic tracking controller is given. It is shown that the robust model reference control problem can be decomposed into two subproblems： a robust state feedback stabilization problem for descriptor systems subject to parameter uncertainties and a robust compensation problem. The latter aims to find three coefficient matrices which satisfy four matrix equations and simultaneously minimize the effect of the uncertainties to the tracking error. Based on a complete parametric solution to a class of generalized Sylvester matrix equations, the robust compensation problem is converted into a minimization problem with quadratic cost and linear constraints. A numerical example shows the effect of the proposed approach.

Robust H_∞ Stabilization of Uncertain Linear Time-Delay System with Delayed/Undelayed State Feedback Controllers

This paper focuses on the H∞ controller design for linear systems with time-varying delays and norm-bounded parameter perturbations in the system state and control/disturbance. On the existence of delayed/undelayed full state feedback controllers, we present a sufficient condition and give a design method in the form of Riccati equation. The controller can not only stabilize the time-delay system, but also make the H∞ norm of the closed-loop system be less than a given bound. This result practically generalizes the related results in current literature.

Interval standard neural network models for nonlinear systems

A neural-network-based robust control design is suggested for control of a class of nonlinear systems. The design ap- proach employs a neural network, whose activation functions satisfy the sector conditions, to approximate the nonlinear system. To improve the approximation performance and to account for the parameter perturbations during operation, a novel neural network model termed standard neural network model (SNNM) is proposed. If the uncertainty is bounded, the SNNM is called an interval SNNM (ISNNM). A state-feedback control law is designed for the nonlinear system modelled by an ISNNM such that the closed-loop system is globally, robustly, and asymptotically stable. The control design equations are shown to be a set of linear matrix inequalities (LMIs) that can be easily solved by available convex optimization algorithms. An example is given to illustrate the control design procedure, and the performance of the proposed approach is compared with that of a related method reported in literature.

Simultaneous Stabilization of SISO Plants Using Static Output Feedback

Sufficient and necessary conditions for the simultaneous stability of arbitrary number of SISO plants by a static output feedback controller are proposed in this paper. Both continuous time and discrete time cases are considered. To determine these conditions only requires to check the stability at a finite number of points between consequent critical constants. As a result, not only can the simultaneous stability be ascertained, but also the entire set of the stabilizing output feedback gains can be determined.

Delay-dependent Robust Stabilization and H_∞ Control for Uncertain Stochastic T-S Fuzzy Systems with Discrete Interval and Distributed Time-varying Delays

In this paper, delay-dependent robust stabilization and H∞ control for uncertain stochastic Takagi-Sugeno （T-S） fuzzy systems with discrete interval and distributed time-varying delays are discussed. The purpose of the robust stochastic stabilization problem is to design a memoryless state feedback controller such that the closed-loop system is mean-square asymptotically stable for all admissible uncertainties. In the robust H∞ control problem, in addition to the mean-square asymptotic stability requirement, a prescribed H∞ performance is required to be achieved. Sufficient conditions for the solvability of these problems are proposed in terms of a set of linear matrix inequalities （LMIs） and solving these LMIs, a desired controller can be obtained. Finally, two numerical examples are given to illustrate the effectiveness and less conservativeness of our results over the existing ones.

A Robust Control Strategy to Improve Transient Stability for AC-DC Interconnected Power System with Wind Farms

In view of the variable parameters that affect the transient stability of electromagnetic torque and mechanical torque balance in AC-DC system,and the uncertainty of wind power in large-scale interconnection of wind farm.This paper proposes a linear parameter varying(LPV)robust feedback control method for transient stability of interconnected systems.The proposed LPV robust feedback control method uses the DC channel power control and the mechanical power in the interconnected system as the control target to improve the transient stability of the interconnected system with wind farm channel.Firstly,aiming at the strong nonlinear characteristics of the interconnected system,the power balance and the wind power output uncertainty in the transient process,the transient process is designed as a linear model of variable parameters.Then,the H∞robust output feedback controller is designed according to the LPV model.The transient stability control strategy topology and transfer function of the interconnected system are proposed.Finally,the proposed scheme is verified by an interconnected system formed by four equal-value grids through AC and DC lines in a digital simulation platform.The results show that the LPV robust feedback control model proposed in this paper has better response characteristics and transient stability control effects for interconnected systems with wind power weak sendingend system.

Robust adaptive control for uncertain systems with discrete and distributed delays

In this paper, a robust adaptive control scheme is proposed for the stabilization of uncertain linear systems with discrete and distributed delays and bounded perturbations. The uncertainty is assumed to be an unknown continuous function with norm-bounded restriction. The perturbation is sector-bounded. Combining with the liner matrix inequality method, neural networks and adaptive control, the control scheme ensures the exponential stability of the closed-loop system for any admissible uncertainty.

Delay-dependent robust stability of uncertain networked control systems with multiple state time-delays

In this paper, delay-dependent robust stability for a class of uncertain networked control systems （NCSs） with multiple state time-delays is investigated. Modeling of multi-input and multi-output （MIMO） NCSs with networkinduced delays and uncertainties through new methods are proposed. Some new stability criteria in terms of LMIs are derived by using Lyapunov stability theory combined with linear matrix inequalities （LMIs） techniques. We analyze the delay-dependent asymptotic stability and obtain maximum allowable delay bound （MADB） for the NCSs with the proposed methods. Compared with the reported results, the proposed results obtain a much less conservative MADB which are more general. Numerical example and simulation is used to illustrate the effectiveness of the proposed methods.

Robust H_∞ control for uncertain systems with heterogeneous time-varying delays via static output feedback

This paper is concerned with the problem of robust H∞ control for a novel class of uncertain linear continuous-time systems with heterogeneous time-varying state/input delays and norm-bounded parameter uncertainties. The objective is to design a static output feedback controller such that the closed-loop system is asymptotically stable while satisfying a prescribed H∞ performance level for all admissible uncertainties. By constructing an appropriate Lyapunov-Krasvskii functional, a delay-dependent stability criterion of the closed-loop system is presented with the help of the Jensen integral inequality. From the derived criterion, the solutions to the problem are formulated in terms of linear matrix inequalities and hence are tractable numerically. A simulation example is given to illustrate the effectiveness of the proposed design method,

On absolute stability of Lur'e control systems with multiple non-linearities using linear matrix inequalities

Necessary and suffcient conditions for the existence of a Lyapunov function in the Lur ’ e form to guarantee the absolute stability of Lur’ e control systems with multiple non-linearities are discussed in this paper. It simplifies the existence problem to one of solving a set of linear matrix inequalities (LMIs). If those LMIs are feasible, free parameters in the Lyapunov function, such as the positive definite matrix and the coefficients of the integral terms, are given by the solution of the LMIs. Otherwise, this Lyapunov function does not exist. Some sufficient conditions are also obtained for the robust absolute stability of uncertain systems. A numerical example is provided to demonstrate the effectiveness of the proposed method.

Robust reliable H_∞ control for a class of uncertain time-delay systems

This paper deals with the problem of robust reliable H∞ control for a class of uncertain nonlinear systems with time-varying delays and actuator failures. The uncertainties in the system are norm-bounded and time-varying. Based on Lyapunov methods, a sufficient condition on quadratic stabilization independent of delay is obtained. With the help of LMIs (linear matrix inequalities) approaches, a linear state feedback controller is designed to quadratically stabilize the given systems with a H∞ performance constraint of disturbance attenuation for all admissible uncertainties and all actuator failures occurred within the prespecified subset. A numerical example is given to demonstrate the effect of the proposed design approach.

Robust Suboptimal Guaranteed Cost Control for 2-D Discrete Systems Described by Fornasini-Marchesini First Model

This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New linear matrix inequality (LMI) based characterizations are presented for the existence of static-state feedback guaranteed cost controller which guarantees not only the asymptotic stability of closed loop systems, but also an adequate performance bound over all the admissible parameter uncertainties. Moreover, a convex optimization problem is formulated to select the suboptimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.

Optimal Guaranteed Cost Control via Static Output Feedback for Uncertain Discrete Time Systems

Aim To study the optimal guaranteed cost control problem via static output feedback for uncertain linear discrete time systems with norm bounded parameter uncertainty in both the state and the control input matrices of the state space model. Methods\ An upper bound on a quadratic cost index was found for all admissible parameter uncertainties and minimized by using Lagrange multiplier approach. Results and Conclusion\ Sufficient conditions are given for the existence of a controller guaranteeing the closed loop system quadratic stability and providing an optimized bound. A numerical algorithm for solving the output feedback gain is also presented.

Sliding mode control of uncertain systems with distributed time-delay: parameter-dependent Lyapunov functional approach

The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities （LMIs）, which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme.

A hybrid multi-degree-of-freedom vibration isolation platform for spacecrafts by the linear active disturbance rejection control

The hybrid vibration isolation, which takes advantages of both the passive and active approaches, has been an important solution for space missions. The objective of this paper is to design a vibration isolation platform for payloads on spacecrafts with the robust, wide bandwidth, and multi-degree-of-freedom(MDOF). The proposed solution is based on a parallel mechanism with six voice-coil motors(VCMs) as the actuators. The linear active disturbance resistance control(LADRC) algorithm is used for the active control. Numerical simulation results show that the vibration isolation platform performs effectively over a wide bandwidth, and the resonance introduced by the passive isolation is eliminated. The system robustness to the uncertainties of the structure is also verified by simulation.

内模控制研究的新发展

概述了内模控制(IMC)的研究现状和新发展,详细论述了内模控制特别是非线性系统内模控制研究中的主要方面及其研究成果.首先介绍了内模控制中的各种建模方法,指出它们各自的优缺点,并根据内模控制的发展趋势着重分析了内模控制器的设计及其改进结构,内模控制与其他控制方法的结合方式等几个关键性问题.最后指出了内模控制研究中存在的一些混淆,并探讨了这一研究领域的发展方向.

空空导弹控制系统鲁棒动态逆设计

将导弹动力学分离为快变状态动力学子系统和慢变状态动力学子系统,分别进行非线性动态逆控制设计。应用基于李雅普诺夫稳定性的鲁棒控制方法,设计出期望的慢变动力学和快变动力学,以保证动态逆控制系统对气动系数摄动的鲁棒稳定性。给出了通过构造动态反插值表,由力矩系数指令反解舵偏角指令的反插值方法。动态逆方法所需要的速度指令、滚动角指令及其一、二阶导数通过滤波器得到。对过载回路的稳定性问题和跟踪误差进行了定性分析,给出了过载回路的无静差设计方案,作为对动态逆的补充设计。给出了导弹控制系统六自由度数学仿真结果。

HVDC孤岛运行附加频率鲁棒控制器设计

为提高HVDC孤岛运行时送端系统频率稳定性,提出了一种直流附加频率鲁棒控制器,利用直流功率的快速可控性来稳定系统频率。采用高精度TLS-ESPRIT算法辨识得出系统低阶线性化模型,再采用基于线性矩阵不等式的鲁棒设计方法在兼顾最优性能和鲁棒性能的同时设计了附加频率鲁棒控制器。该附加频率鲁棒控制器控制结构简单、阶数较低,易于实现。在PSCAD/EMTDC中的仿真实验表明,所设计的附加频率鲁棒控制器能显著提高送端系统频率稳定性。并且相比于传统PI控制器,其控制效果更好,对不同运行方式下的不同类型故障都有较强的鲁棒性,即使在联网运行方式下也可继续有效地运行,研究结果可供孤岛运行方式下的实际电力系统应用参考。

电力系统稳定器对电力系统动态稳定的作用及与其他控制方式的比较

给出了电力系统稳定器（ＰＳＳ）在提高电力系统动态稳定作用的仿真研究结果。结果表明，对于单机无穷大母线系统ＰＳＳ可以把动态稳定极限提高到线路极限，对快速励磁系统是如此，对常规励磁系统（Ｔｅ＝０．５ｓ）也是如此。对多区互联复杂电力系统，ＰＳＳ也可以把负阻功率振荡改善为强阻尼功率振荡（阻尼比大于０．１）。文中还给出ＰＩＤ＋ＰＳＳ励磁控制方式和最优励磁控制方式在设计指导思想、控制信号选择、参数选择、适用励磁系统、实际应用中的考虑等方面的比较。文章最后给出了在用作研究非线性Ｈ∞励磁控制和非线性鲁棒控制的两机系统上应用ＰＩＤ＋ＰＳＳ控制方式的仿真结果。结果表明，ＰＩＤ＋ＰＳＳ的控制方式有更好的鲁棒性。

线性最优控制主动悬架系统的鲁棒稳定性研究

本文采用系统性能分析和Monte-Carlo方法,对线性最优控制主动悬架系统作了鲁棒稳定性研究。研究表明,指标的权重系数、状态测量方式、簧上质量和悬架刚度对系统的鲁棒稳定性有重要影响,而作动器和传感器的动态环节则对其影响不大。利用LTR方法,可以对LQG系统进行鲁棒稳定性恢复,同时使系统的性能损失减到最低限度。