Operator‐Based Robust Right Coprime Factorization and a Nonlinear Control Scheme for Nonlinear Plant with Unknown Perturbations

This paper is concerned with operator‐based robust right coprime factorization for nonlinear plants with unknown perturbations. Firstly, the right factorization for by nonlinear plant with unknown perturbations is realized using isomorphism and some sufficient conditions are proposed to guarantee the robust stability of the obtained nonlinear feedback control system as well as the plant output asymptotically tracking to the reference input. Secondly, a quantitative control scheme is designed to satisfy the sufficient conditions. Finally, the effectiveness of the proposal is demonstrated by the simulation results.     

Robust Control for Uncertain Nonlinear Feedback Systems Using Operator-based Right Coprime Factorization

The robust control issue for uncertain nonlinear system is discussed by using the method of right coprime factorization. As it is difficult to obtain the inverse of the right factor due to the high nonlinearity, the proving of the Bezout identity becomes troublesome. Therefore, two sufficient conditions are derived to manage this problem with the nonlinear feedback system as well as that with the uncertain nonlinear feedback system under the definition of Lipschitz norm. A simulation of temperature control is given to demonstrate the validity of the proposed method.      

Operator-Based Robust Nonlinear Control for SISO and MIMO Nonlinear Systems With PI Hysteresis

In this paper, operator based robust nonlinear control for single-input single-output (SISO) and multi-input multi-output (MIMO) nonlinear uncertain systems preceded by generalized Prandtl-Ishlinskii (PI) hysteresis is considered respectively. In detail, by using operator based robust right coprime factorization approach, the control system design structures including feedforward and feedback controllers for both SISO and MIMO nonlinear uncertain systems are given, respectively. In which, the controller design includes the information of PI hysteresis and its inverse, and some sufficient conditions for the controllers in both SISO and MIMO systems should be satisfied are also derived respectively. Based on the proposed conditions, influence from hysteresis is rejected, the systems are robustly stable and output tracking performance can be realized. Finally, the effectiveness of the proposed method is confirmed by numerical simulations.      

Operator-Based Robust Nonlinear Free Vibration Control of a Flexible Plate With Unknown Input Nonlinearity

In this paper,a robust nonlinear free vibration control design using an operator based robust right coprime factorization approach is considered for a flexible plate with unknown input nonlinearity.With considering the effect of unknown input nonlinearity from the piezoelectric actuator,operator based controllers are designed to guarantee the robust stability of the nonlinear free vibration control system.Simultaneously,for ensuring the desired tracking performance and reducing the effect of unknown input nonlinearity,operator based tracking compensator and estimation structure are given,respectively.Finally,both simulation and experimental results are shown to verify the effectiveness of the proposed control scheme.     

基于演算子理论的IPMC人工肌肉精确位置控制

IPMC(Ionic Polymer Metal Composite)人工肌肉是一种离子交换聚合金属材料,由于具有在低电压作用下可以产生较大弯曲的特性,已经被作为分布式传感器和执行器广泛应用于各种仿生机器人构建中。为了在各种仿生机器人中应用IPMC人工肌肉,期望的位置或偏移量必须能够精确地控制。针对这个问题,通过应用鲁棒右互质分解方法,本文设计一种基于演算子理论的IPMC人工肌肉精确位置控制系统,该系统不仅保证了鲁棒稳定性,而且能够实现精确的位置跟踪。最后,通过仿真和实验结果,系统的有效性进一步得到验证。     

具有非线性扰动和混合时滞的中立型系统的时滞依赖鲁棒稳定性

This paper concerns the delay-dependent robust stability problem of uncertain neutral systems with mixed neutral and discrete delays. Nonlinear time-varying parameter perturbations are considered. Based on the newly established integral inequalities, the neutral-delay-dependent and discrete-delay-dependent stability criterion is derived without using a fixed model transformation. The condition is presented in terms of linear matrix inequality and can be easily solved by existing convex optimization techniques. A numerical example is given to demonstrate the less conservatism of the proposed results.     

非线性参数扰动多重时滞系统的鲁棒稳定性分析与变结构控制

研究一类非线性参数扰动满足范数有界条件的多重时滞系统,利用Ｌｙａｐｕｎｏｖ函数方法,获得了一个新的鲁棒稳定性充分条件,并应用变结构控制实现了该类非线性参数扰动多重时滞系统的鲁棒镇定。     

具有非线性扰动和混合时滞的中立型系统的时滞依赖鲁棒稳定性

This paper concerns the delay-dependent robust stability problem of uncertain neutral systems with mixed neu- tral and discrete delays.Nonlinear time-varying parameter per- turbations are considered.Based on the newly established in- tegral inequalities,the neutral-delay-dependent and discrete- delay-dependent stability criterion is derived without using a fixed model transformation.The condition is presented in terms of linear matrix inequality and can be easily solved by existing convex optimization techniques.A numerical example is given to demonstrate the less conservatism of the proposed results.     

基于鲁棒右互质分解的直流伺服系统精确跟踪控制

对含有不确定性的直流伺服控制系统,通过应用鲁棒右互质分解方法,设计了一种基于鲁棒右互质分解的精确跟踪控制系统;通常情况下,直流伺服系统中存在诸如非线性特性及参数辨识引起的模型误差和外界扰动,在设计的控制系统中,未知模型误差和外界扰动对系统性能的影响都被看作直流伺服系统的不确定性;在考虑到这些不确定性情况下,设计了一种基于鲁棒右互质分解理论的精确跟踪控制;首先在考虑未知的不确定模型影响系统性能指标的情况下,设计了一种基于演算子理论的反馈控制结构,此结构可以消除不确定模型的影响,在此基础上,设计了基于鲁棒右互质分解的鲁棒精确跟踪控制系统,得出精确跟踪条件;仿真结果表明使用提出的方法可以有效地消除不确定性,使得伺服系统具有很强的鲁棒性和精确跟踪能力。     

具有非线性扰动多时滞系统鲁棒稳定性分析与分散鲁棒控制

研究一类非线性参数扰动满足范数有界条件时多重时滞系统的鲁棒稳定性及其分散鲁棒控制。首先利用Lyapunov函数方法分析系统的鲁棒稳定性,获得一种新的稳定性条件,然后利用标量Lyapunov方程方法讨论系统指数稳定的条件,通过对系统采取分散反馈控制,进一步得到系统可鲁棒镇定和可指数镇定的条件。     

非线性系统的有界增益分解

本文对一类典型结构的反馈控制系统，讨论了对象的有界增益稳定的右互质分解和闭环系统有界增益稳定性的关系，对存在有界增益右互质分解的系统，给出了一种镇定方案。并且研究了这种的鲁棒性。     

一类新非线性控制方法:基于演算子理论的控制方法综述

以基于演算子理论的鲁棒右互质分解 (Operator-based robust right coprime factorization, RRCF) 为基础, 提出了一种较新的非线性鲁棒控制方法.本文将简述此方法的概念、 基本理论及其应用. 具体地说, 本文首先介绍此方法的起源与基本概念; 然后,讨论此方法在系统的鲁棒稳定性、 输出跟踪与故障检测方面的设计等问题;最后,介绍此方法的实际应用从而进一步证明其有效性.     

一类多变量非线性动态系统的模糊自适应控制

对一类非线性多变量未知动态系统，提出了一种模糊处在适应控制策略。证明了该控制算法能保证闭环系统稳定，跟踪误差收敛。     

Robust control for nonlinear systems with unknown perturbations using simplified robust right coprime factorisation

This article is concerned with operator-based robust control for nonlinear feedback system with unknown perturbations with simplified robust right coprime factorisation method. By the designed simplified robust controllers, the Bezout identity for the nominal nonlinear system and the perturbed nonlinear system are guaranteed to be simply satisfied, which means that not only the nonlinear system with nominal plant but also that with perturbed plant can be stabilised. Moreover, the plant output can be guaranteed to asymptotically track the reference output. The effectiveness of the proposed design scheme is verified by the simulation results.     

非线性系统的反馈镇定和右互质分解

本文在一种很广泛的框架中讨论因果的非线性输入-输出算子的右互质分解问题,给出了在不同稳定性定义下的反馈镇定和存在右互质分解之间的关系.     

线性离散系统的鲁棒约束方差控制--含结构参数扰动的情形

研究一粪性能鲁棒控制器的设计问题,即针对含结构参数扰动的线性离散随机系统,设计反馈控制器,使闭环系统不仅渐近稳定,而且其每个状态分量的稳态方差不大于各自预先给定的上界.基于一个修正的代数Riccati方程,给出了上述性能鲁棒控制器的存在条件及解析表达式,并举出相应的数值例子,以说明本文设计方法的简单性与直接性.     

基于演算子理论的液位控制系统应用研究

为了模拟工业锅炉液位过程控制,以水箱过程控制实验装置为基础进行了液位控制的实验研究。首先提出了基于演算子理论的右互质分解方法实现非线性控制系统的设计;接着以PCL-812PG数据采集卡为基础进行了数据采集与驱动设计;然后利用设计好的控制器在Visual C++开发环境下对该液位系统进行了实验研究;实验中液位设定值为300mm,结果显示液位控制系统上升时间小于260s,系统超调低于5%,满足要求的性能指标;实验结果表明了控制系统设计的有效性。     

非线性系统鲁棒控制器设计的研究*

本文首先指出「１」中证明不足，进一步在补充假设下，对一类含非匹配不确定项的系统设计出新的鲁棒控制器，仿真结果表明，此控制器有保证闭环系统具有理想品质。     

非线性系统的鲁棒采样最优控制

采样系统控制作为一种数字控制的直接设计方法,近年来引起了广泛的重视,另一方面系统的时域约束在工业控制中是不可避免的。利用实用稳定性理论,研究了具有输出约束的一类非线性系统的鲁棒采样最优控制问题,结果表示为一些矩阵不等式,最后给了出了一个迭代算法。     

控制方向未知的时变非线性系统鲁棒控制

针对一类具有未知时变控制方向、不确定时变参数以及未知时变有界干扰的严反馈非线性系统,给出一种带有死区修正算法的鲁棒控制方法.在控制系数符号未知的情况下,通过在反步法中引入Nussbaum增益和死区修正技术,得到一种修正的鲁棒反步设计方法.该方法不需要未知时变控制系数的上下界先验知识以及不确定参数和外界干扰的上界信息.算法保证了闭环系统所有信号的有界性,同时使得跟踪误差收敛于零的任意小邻域内.