Fuzzy Model Based State Estimation and Stability Analysis

• Main Authors: Hung-Shuen Chen, 陳弘順
• Other Authors: Kuang-Yow Lian
• Format: Others
• Language: en_US
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/79353305049420401516

碩士 === 中原大學 === 電機工程研究所 === 90 === Nowadays, T-S fuzzy model is a rapid growing modeling method which originates from Takagi and Sugeno. It is described by fuzzy IF-THEN rules where the consequent parts are local linear models. So it can easily approximate or exact represent a nonlinear system. Once a fuzzy representation of a nonlinear system is described by if-then rules, the control problem becomes to find a local linear or nonlinear compensator to achieve the desired objective. When considering controller and observer design we use the conception of parallel distributed compensation (PDC) to carry out these designs. 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. In this thesis, we will first study the relaxed stability conditions of a nonlinear system. By using the relaxed stability conditions we can get the numerical solution more easier. Furthermore, we know that measuring full states can be difficult and costly because sensors are often subject to noise. An observer is designed to estimate the immeasurable states. Notice that the premise variables in the fuzzy observer are assumed to be measurable in general. However, this assumption of measurable premise variables imposes a strict constraint on the applicability of this design in practical situations. Therefore, we shall give some discussion about the premise variables of the fuzzy observer depend on the estimated state variables. Finally, we discussed the stability of T-S fuzzy model via fuzzy Lyapunov function. It has been paid a lot of attention in recent years due to avoiding conservatism of stability and stabilization problems. Fuzzy Lyapunov function sometimes be called multiple Lyapunov function and it shares the same membership function of plant which is in Takagi-Sugeno fuzzy model. A relaxed condition derived here is represented in terms of LMI and then Matlab's toolbox can be used to get the control gains.