Theoretical and Numerical Study on Sampled-Data Control of Parabolic Distributed Parameter Systems

抛物型分布参数系统采样数据控制的理论与数值研究

• 批准号: 16540111
• 负责人: SANO Hideki
• 金额: $ 1.09万
• 依托单位: Kagoshima University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540111/
• 关键词: parabolic system; unbounded output operator; sampled-data H∞ control; finite-dimensional controller; residual mode filter; hyperbolic system; exponential stability; observability, reachability; 並流型熱交換器; 境界フィードバック; 強連続半群; スペクトル; 可観測性; 可到達性; 非

This research is concerned with sampled-data H_∞ control of parabolic systems with unbounded output operators. Especially, the output operator is assumed to be (-L)^γ-bounded, where 0<γ<1/2. For example, diffusion systems with boundary control can be formulated as parabolic systems with output operators of such a type. For the parabolic system with an ideal sampler and a zero-order hold, the aim is to construct a finite-dimensional discrete-time stabilizing controller that makes the L^2 -induced norm of the feedback sampled-data system less than a given positive number. For that purpose, the infinite-dimensional continuous-time system is formulated as an infinite-dimensional discrete-time system by using a lifting technique and a variable transformation. Based on a reduced-order model with a finite-dimensional state space for the infinite-dimensional discrete-time system, a finite-dimensional controller containing a residual mode filter is designed to provide the desirable performance.Moreover, systems whose axial dispersion coefficients are sufficiently small and can be neglected are treated as control objects. A parallel-flow heat exchanger with boundary inputs is described by two parabolic equations when the axial dispersion is taken into consideration. On the other hand, the parabolic equations become hyperbolic equations in the case where the axial dispersion can be neglected. In this research, the stability analysis is carried out, for the closed-loop system which consists of the hyperbolic system and an output feedback law. In addition, the dynamical analysis such as observability and reachability is performed for the hyperbolic system.

这项研究涉及具有无界输出算子的抛物线系统的采样数据 H_∞ 控制，特别是，输出算子被假设为 (-L)^γ 有界，其中 0<γ<1/2。具有边界控制的系统可以表示为具有此类输出算子的抛物线系统 对于具有理想采样器和零阶保持的抛物线系统，目的是构造一个有限维离散时间稳定控制器。反馈采样数据系统的 L^2 诱导范数小于给定的正数为此，通过使用提升技术和 a 技术将无限维连续时间系统表示为无限维离散时间系统。基于无限维离散时间系统的有限维状态空间降阶模型，设计了包含残差模式滤波器的有限维控制器，以提供理想的性能。色散系数足够小，可以忽略不计当考虑轴向色散时，具有边界输入的平行流换热器可以用两个抛物线方程来描述；而当轴向色散可以被考虑时，抛物线方程就变成了双曲方程。本研究对双曲系统和输出反馈律组成的闭环系统进行了稳定性分析，并对双曲系统进行了可观性、可达性等动力学分析。系统。

项目成果

Observability and reachability for parallel-flow heat exchanger equations

• DOI: 10.1093/imamci/dnl016
• 发表时间: 2007-03
• 期刊: IMA J. Math. Control. Inf.
• 作者: H. Sano

非有界出力作用素をもつ線形放物型システムのサンプル値H∞制御

具有无界输出算子的线性抛物线系统的样本值H∞控制

• 发表时间: 2004
• 期刊: 計測自動制御学会論文集 Vol.40, No.9
• 作者: H.Sano;N.Kunimatsu;佐野 英樹
• 通讯作者: 佐野 英樹

境界フィードバックを伴う並流型熱交換方程式の指数安定性について

边界反馈平行流换热方程的指数稳定性

• 发表时间: 2005
• 期刊: システム制御情報学会論文誌 Vol.18, No.6
• 作者: K.Ohkitani;P.Constantin;佐野 英樹
• 通讯作者: 佐野 英樹

On exponential stability of parallel-flow heat exchanger equations with boundary feedback

边界反馈并流换热器方程的指数稳定性

• 发表时间: 2005
• 期刊: Transactions of the Institute of Systems, Control and Information Engineers (in Japanese) Vol.18, No.6
• 作者: H.Sano;N.Kunimatsu
• 通讯作者: N.Kunimatsu

Sampled-data H∞ control of linear parabolic systems with unbounded output operators

具有无界输出算子的线性抛物线系统的采样数据 H∞ 控制

• 发表时间: 2004
• 期刊: SICE Transactions (in Japanese) Vol.40, No.9
• 作者: H.Sano;N.Kunimatsu;佐野 英樹;H.Sano
• 通讯作者: H.Sano