准确运用"伯德图中奈奎斯特稳定判据"

1　文[1]的表达式不具代表性当υ≤3时,至少对下述四类系统不适用:1)如G(s)H(s)=S 1S2,(S 1)(S 2)S3,……;2)如G(s)H(s)=1-T2S1 T1S(T1>T2>0);2TS1-TS,KS(1-TS),……,(K,T>0);3)如G(s)H(s)=2TS-1,2S 1S(TS-1),……,(T>0);4)如G(s)H(s)=K-TSTS(T≠0,K≠0,-1),……;…….当?..     

Stability of polynomials with conic uncertainty

In this paper we describe a conic approach to the stability theory of uncertain polynomials. We present necessary and sufficient conditions for a conic setp ₀+K of polynomials to be Hurwitz stable (K is a convex cone of polynomials of degree n and degp ₀=n). As analytical tools we derive an edge theorem and Rantzer-type conditions for marginal stability (semistability). The results are applied to prove an extremal-ray result for conic sets whose cone of directions is given by an interval polynomial.The second author would like to thank the Deutsche Forschungsgemeinschaft (DFG) for its support during the writing of this paper.     

A Kharitonov-like theorem for interval polynomial matrices

As an extension of Kharitonov's theorem, robust stability of interval polynomial matrices is studied. Here a polynomial matrix is said to be stable if its determinant has all roots with negative real parts. The present paper shows that the robust stability of interval polynomial matrices is equivalent to that of the subclasses where each row (column) has only one element that involves Kharitonov edge polynomials and all the other elements take on one of the four Kharitonov vertex polynomials.     

ISE tuning rule revisited

The integral square error (ISE) method is applied to approximate the internal model control (IMC) system by the PID control system. Simulations show that the proposed method to design PID controllers can relieve some disadvantages of the original ISE method and IMC-based PID controller design methods.     

Quantification of model uncertainty from data

Identification of linear models in view of robust control design requires the identification of a control-relevant nominal model, and a quantification of model uncertainty. In this paper a procedure is presented to quantify the model uncertainty of any prespecified nominal model, from a sequence of measurement data of input and output signals from a plant. By employing a nonparametric empirical transfer function estimate (ETFE), we are able to split the model uncertainty into three parts: the inherent uncertainty in the data due to data imperfections, the unmodelled dynamics in the nominal model, and the uncertainty due to interpolation. A frequency-dependent hard error bound is constructed, and results are given for tightening the bound through appropriate input design.     

线性状态空间模型的稳定鲁棒性改善

本文讨论线性定常系统的稳定鲁棒性问题。文中给出了线性定常系统的稳定鲁棒性范围的新改善界限。在结构扰动情况下,本文给出的稳定鲁棒性界限比引文[1]中的相应结果更好。用数值计算方法容易得到这一动扰界限。文中给出的两个例子证实了本文结果的优点。     

线性状态空间模型的稳定鲁棒性改善

本文讨论线性定常系统的稳定鲁棒性问题。文中给出了线性定常系统的稳定鲁棒性范围的新改善界限。在结构扰动情况下，本文给出的稳定鲁棒性界限比引文[1]中的相应结果更好。用数值计算方法容易得到这一动扰界限。文中给出的两个例子证实了本文结果的优点。     

MATLAB环境下频率响应曲线的绘制方法

本文给出了MATLAB环境下线性系统的Bode图、Nyquist图、Nichols图的绘制方法,为线性控制系统的频域分析提供了一种简单有效的途径。     

感应加热过程调频锁相-移相调功复合控制

串联谐振感应加热过程包括调频锁相和移相调功两个控制环节,二者具有较强的非线性和耦合性;在分析逆变频率、输出功率同锁相角、移相角关系的基础上,提出了基于频率分离原理的调频锁相-移相调功复合控制方案,将锁相-调功过程分解为快-慢子系统,并对两个过程分别设计了具有鲁棒稳定性的锁相控制器和移相控制器,解决了感应加热电源的调频锁相-移相调功环节的协调控制问题;将调频锁相-移相调功复合控制方案应用于额定功率20kW,输出电流40A的超音频串联谐振感应电源中,验证了该控制方案在确保逆变过程开关器件安全可靠的同时,提高了功率输出的效率;在保证了调功灵活性的同时,又实现了电源的阻抗自匹配。     

线性自抗扰控制系统的鲁棒稳定性

针对线性自抗扰控制系统,研究了模型参数不确定情况下的鲁棒稳定性问题.首先给出对象为非自治模型时该系统的H∞判据.然后针对线性误差模型的状态矩阵只在某一行存在不确定参数的情况,基于奇异值理论,得到H∞判据的一种新的等价描述,把H∞范数约束转化为对奈奎斯特图的约束.之后为了降低新判据在实际应用中的保守性,对不确定性矩阵的分解方式进行优化.在此基础之上提出了一种新的方法,用于计算时变参数不确定性的最大边界,为线性自抗扰控制器设计提供理论依据.数值实例表明该方法不仅保守性小,而且计算简单.     

A study of disturbance observers with unknown relative degree of the plant

Robust stability of the disturbance observer (DOB) control system is studied when the relative degree of the plant is not the same as that of the nominal model. The study reveals that the closed-loop system can easily become unstable with sufficiently fast Q-filter when the relative degree of the plant is not known. In a few cases of unknown relative degree, however, robust stability can be obtained, and we present a design guideline of the nominal model, as well as the Q-filter, for that purpose. Moreover, a universal design of DOB is given for a plant whose relative degree is uncertain but less than or equal to four.     

Separator-type robust stability theorem of sampled-data systems allowing noncausal LPTV scaling

This paper derives a necessary and sufficient condition for robust stability of sampled-data systems, which is stated by using the notion of separators that are dealt with in an operator-theoretic framework. Such operator-theoretic treatment of separators provides a new perspective, which we call noncausal linear periodically time varying scaling and leads to reducing conservativeness in robust stability analysis. A numerical example is given to demonstrate the results.     

Analytical and graphical design of lead–lag compensators

In this article an approach based on inversion formulae is used for the design of lead–lag compensators which satisfy frequency domain specifications on phase margin, gain margin and phase (or gain) crossover frequency. An analytical and graphical procedure for the compensator design on the Nyquist and Nichols planes is presented with some numerical examples.     

基于Matlab的绝缘材料电气性能测试系统设计

针对传统的绝缘性能测试仪存在功能单一和无法兼容频域介电响应等新方法的问题,通过选用常见设备,设计了一套基于Matlab绝缘材料电气性能测试系统。该系统利用前置滤波器消除了频率响应函数对系统输出的不利影响,使系统不仅拥有常规的直流跟工频检测功能,也具备在50Hz-1kHz频率范围内进行电压试验的能力,测试时的最高电压能够达到10kV。通过测量试验中流过介质的漏电流,该系统适用于对被测物的绝缘性能进行综合的评估。试验结果表明该系统达到了设计指标,并且能够满足日常工作中的测试需要     

A Brouwer domain invariance approach to boundary behavior of Nyquist maps for uncertain systems

The boundary preserving properties of a fixed frequency Nyquist mapping from a compact, convex region of uncertainty inR ^" onto the Horowitz template are investigated via a topological approach. In the casen=2, the boundary preserving properties of the Nyquist mapping and its inverse are shown to be corollaries of the Brouwer domain invariance and the Carathéodory conformal invariance of the boundary. The casen>2 is derived from the casen=2 by taking many two-dimensional slices through the domain. Finally, the edge test results are examined in the light of the Brouwer domain invariance. The second author was supported by NSF Grant ECS-95-10656.     

On sufficient conditions for the stability of interval matrices

We investigate the Hurwitz and Schur stability of interval matrices using Lyapunov's second method and interval analysis techniques. Previous results require a check of the definiteness of 2^{n(n − 1)/2} concerns of a certain interval matrix. The present results require a check of the definiteness of only 2^{n − 1} corners.     

线性多变量反馈系统频域法CAD软件包

MSFDCADP是一个在个人计算机上用编译BASIC语言建立的、以多变量系统现代频域法为基础的CAD软件包。它包括正、逆Nyquist阵列法设计,并矢展开法设计,数据处理模块和系统仿真模块。本文介绍了MSFDCADP的设计原则、层次结构和功能,并给出了所用的一些核心算法。最后用两个设计实例说明了MSFDCADP应用的有效性。     

基于向量分析的频域稳定性判据及其应用

稳定性是控制系统性能分析的首要问题,频域稳定性判据以其方便直观的特性获得了广泛应用。本文基于特征矢量分析,利用系统极点分布与特征多项式相频特性幅角增量的关系,推导了一种关系直接、概念清楚的频域稳定性判据表达形式,改善了目前采用复变函数幅角映射理论论述Nyquist判据时不够直观易懂的不足。针对判据应用中出现的开环幅相频率图的画法和稳定性判断方法进行了论述,化繁为简,并给出了实例互为印证。