Complex Performance Controller Design for Linear Stochastic Systems

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Project title

Code/計畫編號

MOST107-2221-E019-051

Translated Name/計畫中文名

針對線性隨機系統設計具複合性能之控制器設計

Project Coordinator/計畫主持人

Cheung-Chieh Ku

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Marine Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=12674183

Year

2018

Start date/計畫起

01-08-2018

Expected Completion/計畫迄

31-07-2019

Bugetid/研究經費

727千元

ResearchField/研究領域

電子電機工程

性能指標是控制領域中一個重要的議題，以往的性能指標大多數都以單一性能指標研究作為控制器設計的目標，對於同時具備兩種性能指標的混和式控制理論也隨著系統的精進與控制的裕度增加而發展，本計畫將以複合性能的研究做為發展主軸進行線性系統的穩定性分析與控制器設計。其中 H2 控制理論可應用於使系統的輸出能量以起始條件為基礎進而達到最小化的動作且保證系統之穩定性，而被動理論則是針對限制外部雜訊對系統的影響，且理論中的能量供應方程式可由設計者自行調配後進行降低外部雜訊對系統的干擾程度，因此被動理論具有較為廣義且彈性的控制器設計方法。另外，由於隨機行為的存在將影響控制器的性能導致系統趨向不穩定之結果，因此對於隨機行為對系統影響的探討與研究也相對顯出其重要性。本計畫將同時探討連續型與離散型隨機系統的穩定性分析與控制器設計之相關議題，並利用里阿伯諾方程式推導充分條件並將其轉換為線性矩陣不等式，根據充分條件提出控制器設計準則。最後我們將以數值模擬驗證所發展理論的有效性與可行性。The performance index is an important issue in control problems. Most the literatures discussing the performance control problems focus on sole performance for presenting the design methods. For two different performance indexes, the mixed performance theory is proposed since sensitivity and controllability of system are increased. Complex performance is the discussion issue in this project for proposing the controller design method. The H2 control scheme is applied to minimize the system energy based on the initial conditions. In order to extend the generality, the passivity theory is introduced in this project to discuss the energy change between system and external disturbance. With setting power supply function well, the passivity theory includes some control schemes, for example: H_inf scheme, positive real theory and so on. Besides, stochastic behaviors, lead instability and affect control performance, are considered in this project. According to the above illustration, the importance of considering stochastic behaviors is increased and emphasized. Thus, mixed H2/passivity performance control of linear stochastic system is discussed and investigated for both continuous case and discrete case. Based on Lyapunov function, the corresponding sufficient conditions are derived into Linear Matrix Inequality (LMI) form for applying convex optimization algorithm. Finally, some numerical simulations are proposed to demonstrate the usefulness and effectiveness of the proposed design method in this project.

Keyword(s)

被動理論
隨機系統
混和性能
H2 控制
線性矩陣不等式
Passivity Theory
Stochastic Systems
Mixed Performance
H2 Control
Linear Matrix Inequality

DSpace CRIS

Complex Performance Controller Design for Linear Stochastic Systems

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