具有H-infinity強健性之模糊模式追蹤控制

Fuzzy Model Based Tracking Control with H-infinity Performance

林韋志(Wei-Chi Lin)

指導教授 ： 練光祐

中原大學/工學院/電機工程研究所/碩士(2001年)

https://doi.org/10.6840/cycu200100128

摘要

摘要
T-S 模糊模式化方式(T-S fuzzy model)，是這幾年來被廣泛使用於處理非線性系統的控制方法之一。此方法由Takagi和Sugeno兩位學者在1985年所提出，能將非線性系統以IF-THEN的規則化成許多的一階線性系統來表示，至於在控制器和估測器的設計上是使用所謂平行分布補償(PDC)的概念去設計的，穩定性的分析以及控制增益最後可以使用線性矩陣不等式(LMIs)的方法去求解。追蹤控制問題在實際應用上一直是一個重要的討論方向，諸如機械手臂軌跡追蹤控制、彈道追蹤控制、飛行器姿態追蹤控制等。在本論文我們將以T-S模糊模式化來探討非線性系統的追蹤控制的問題。我們利用非線性 的觀念去設計處理非線性連續時間系統追蹤控制的問題，另外量測所有的狀態是困難且昂貴的工作，再者感測器也常因伴隨著一些雜訊而產出誤差，所以我們也討論觀察器的設計方法藉以估測不可量測得到的狀態。描述系統(descriptor system)與傳統的狀態空間表示式相比，能夠更廣泛的來描述一個系統，在最近幾年此概念也已經延伸到T-S模糊模式系統，當模糊描述系統以T-S模式法來表示，它的好處是會使模糊規則的數目減少，這種可使規則數減少的方法對以LMI為主的控制設計有很大的幫助。
在論文最後我們利用DS1102和SIMULINK的軟體來建構出我們要的實作環境，利用強健追蹤控制器去實現路邊停車控制，而實作的結果也驗證了我們理論推導的可行性。

關鍵字

強健控制 ； 線性矩陣不等式 ； 模糊觀察器 ； 路邊停車 ； 模糊控制 ； 追蹤控制 ； 自走車

並列摘要

abstract
There has recently been a rapid growing interest in using T-S fuzzy model to
approximate nonlinear systems. The T-S fuzzy dynamic model, which originates
from Takagi and Sugeno, is described by fuzzy IF-THEN rules in which the
consequent parts represent local linear models. Once a fuzzy representation
of a nonlinear system is described by if-then rules, the control problem
then becomes to find a local linear/nonlinear compensator to achieve the
desired objective. The controller and observer design of the T-S fuzzy
system is carried out via the so called parallel distributed compensation
(PDC) approach. The stability analysis and controller synthesis are then
systematically formulated into linear matrix inequalities (LMIs). The LMI
problem can be solved very efficiently by convex optimization techniques.
Tracking control design is also an important issue for practical
applications, such as robotic tracking control, missile tracking control,
and attitude tracking control of aircraft. In this thesis, we will study the
tracking control problem of a nonlinear system by the T-S fuzzy model. Based
on the nonlinear $H_infty $ criterion, the controller is designed to cope
with the tracking control problem for a nonlinear continuous-time systems.
Then, we know that measuring full states can be difficult and costly.
Moreover, sensors are often subject to noise. An observer is designed to
estimate the immeasurable states. It has long been known that descriptor
systems have a tighter representations for a wider class of systems in
comparison to traditional state-space representation. Recently this concept
has been extended to T-S fuzzy model systems. On the other hand, if the
fuzzy descriptor system is used, the number fuzzy rules will be decreased.
This rule reduction is an important issue for LMI-based control synthesis
since larger number of LMI rules may lead to infeasible problems. Finally, a
real time control of parallel parking is presented in this thesis. We
utilize the robust tracking controller to realize parallel parking. Based on
the DS1102 and SIMULINK, we can easily use build-up blocks to establish our
experimental environment. Our experimental result verifies the theoretical
derivation in this thesis.

並列關鍵字

T-S fuzzy model ； mobile robots ； Tracking control ； Fuzzy observer ； parallel parking ； H-infinity robust control ； PDC ； LMI ； Model following

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