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Systematization of Control Theory and Design Methods of Time-Delay Systems

时滞系统控制理论与设计方法的系统化

基本信息

批准号：
63550298
负责人：
WATANABE Keiji
金额：
$ 1.54万
依托单位：
Yamagata University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1988
资助国家：
日本
起止时间：
1988 至 1990
项目状态：
已结题

项目摘要

Finite spectrum assignment method for systems with delays in inputs and/or outputs was presented. Robustness of the control systems with mismatch between nominal values and actual parameters was numerically examined and it was shown that the position of integrator and the structure of observer and the state predictor change the robust stability even though poles of the closed-loop system are equal.Finite spectrum assignment methods for retarded systems with delays in state variables was presented. The characteristic polynomial of the feedback system is given by the form. * sI-A(z)-b(z)f(z) * =s^n+alpha_1(z)S^<n-1>+・・+alpha_n(z)-f(z)M(z)v(s), where z denotes the delay operator. For arbitrary real numbers beta_1, ・・, beta_n, let f(z)=[beta_n-alpha_n(z), ・・, beta_1-alpha_1(z)]M(z)^<-1>, then the characteristic polynomial becomes * sI-A(z)-b(z)f(z) * =s^n+beta_1s^<n-1>+・・+beta_n. To implement the control, an algorithm to transform f(z) into the matrix f(z,s) with polynomials in z and the f … More inite Laplace transforms was presented on the basis of the structure of M(z). Furthermore, a method to transform F(z) into F(z,s) for multi-input case was proposed by using the Smith form.In the design method by transformation the polynomial matrix in z to finite Laplace transform matrix, the calculation is required whenever beta_i are changed. To avoid the computation, a method to find K(z,s) satisfying K(z,s)M(z)v(s)=v(s) was presented in the basis of the equation M(z)v(s)=P(s)v(z) and the structure of M(z). The feedback matrix is given by f(z,s)=[beta_n-alpha_n(z), ・・, beta_1-alpha_1(z)]k(z,s).Finite spectrum assignment of systems with a class of non-commensurate delays was presented. Stabilization of systems with non-commensurate delays was also proposed on the basis of finite spectrum assignment.A solution to finite spectrum assignment problem of neutral systems was presented. In the first step, the neutral system is changed to the quasi-retarded system by using the feedback containing the delayed derivative feedback. In the second step, the finite spectrum assignment method of retarded systems is applied to the quasi-retarded ones.Finite spectrum assignment method was applied to stabilization of the repetitive control systems.Robust adaptive control for systems with mismatch between nominal delay and actual one was presented. Less

提出了具有输入或输出时滞系统的有限频谱分配方法。数值研究了标称值与实际参数不匹配控制系统的鲁棒性，结果表明，即使闭环系统的极点相等，积分器的位置、观测器和状态预测器的结构也会改变系统的鲁棒稳定性。提出了状态变量为时滞的时滞系统的有限频谱分配方法。反馈系统的特征多项式由式给出。*如果在(z) - b (z) f (z) * = s ^ n + alpha_1 (z) s ^ < n - 1 > +・・+ _n (z) - f (z) M (z) v (s),在z表示延迟算子。对于任意实数beta_1，··，beta_n，令f(z)=[beta_n-alpha_n(z)，··，beta_1-alpha_1(z)]M(z)^<-1>，则特征多项式变为* sI-A(z)-b(z)f(z) * =s^n+beta_1s^<n-1>+···+beta_n。为了实现控制，提出了一种将f(z)变换为矩阵f（z,s）的算法，并在M(z)结构的基础上提出了更多的无限拉普拉斯变换。在此基础上，提出了用Smith形式将多输入情况下的F(z)转换为F（z,s）的方法。在将z中的多项式矩阵变换为有限拉普拉斯变换矩阵的设计方法中，每当i改变时都需要进行计算。为了避免计算，在M(z)v(s)=P(s)v(z)的基础上，根据M(z)v(z)的结构，提出了求K（z,s）满足K(z,s)M(z)v(s)=v(s)的方法。反馈矩阵由f(z,s)=[beta_n-alpha_n(z)，··，beta_1-alpha_1(z)]k（z,s）给出。研究一类非相称时滞系统的有限频谱分配问题。在有限频谱分配的基础上，提出了非相称时滞系统的镇定问题。给出了中立型系统有限频谱分配问题的一种解法。第一步，利用包含时滞导数反馈的反馈将中立型系统转变为准滞后系统。第二步，将时滞系统的有限频谱分配方法应用于拟时滞系统。将有限谱分配方法应用于重复控制系统的镇定。针对标称时延与实际时延不匹配的系统，提出了鲁棒自适应控制方法。少