模糊邏輯控制系統之穩定度分析與應用

Abstract

在本篇論文中，我們分析了P與PD型之模糊邏輯控制系統之絕對穩定度，另外也提出了一種基於模糊邏輯控制系統之應用，即只利用傳輸一狀態之數值信號，並利用適應性模糊類神經觀測器 (AFNO)去同步一類的未知混沌系統。關於穩定度分析，包括兩種狀況：確定與非確定性受控體。而穩定度分析包括以下參數：參考輸入、致動增益、區間(Interval )受控體參數。對確定性受控體而言，我們利用Popov或線性化的方法，針對P與PD型之模糊邏輯控制系統，在不同參考輸入信號與致動增益下，作絕對穩定度分析，另外，關於模糊邏輯控制系統在參數空間之穩態誤差也可被分析。針對非確定性受控體，我們利用基於Lur’e系統之參數化強健Popov 準則，來作P型模糊邏輯控制系統之絕對穩定度分析，而關於非確定性受控體之PD型分析，在我們方法中，PD型之模糊邏輯控制器，為一種單一輸入之PD型模糊邏輯控制器，而且此控制器可被轉成一種特殊P型模糊邏輯控制器，而再作進一步分析。與之前研究不同的是，我們利用參數化強健Popov 準則，可針對非零之參考輸入，且非確定性之受控體，作絕對穩定度分析。我們亦利用PSPICE 元件，設計了一個模糊電流控制RC電路，透過數值與PSPICE模擬驗證我們所作分析之結果。另外，在模擬例子中，我們也利用不同平衡點的觀念，解釋模糊邏輯控制系統之震盪機制。最後，我們也比較幾種非確定性系統之絕對穩定度準則，驗證我們的分析的有效性。另一方面，模糊邏輯控制系統也可以被設計用來智慧化同步混沌信號，其應用主要觀念為只藉傳輸一狀態之數值信號，並利用AFNO去同步一類的未知混沌系統，如果此一非線性混沌系統可以藉由微分幾何的方法，被轉換成標準的Lur’e系統，則此方法便可以被應用來作同步。值得一提的是，在這一個方法中，AFNO之適應性模糊類神經(FNN)可以被線上即時調整權重，去對傳送端之非線性項作建模。另外，藉由傳送端傳送一個狀態並利用接收端之觀測器可以對傳送端未知之所有狀態作重建，當所有狀態被觀測到，傳送端與接收端便達到同步。AFNO可以線上適應性估測傳送端之狀態，即使傳送端已經切換到另一個混沌系統，接收端之AFNO還可以與新的混沌系統達到同步。另外一方面，即使存在建模誤差或外加有界干擾，AFNO亦可強健的達到同步。模擬結果驗證ANFO對混沌系統之同步應用是有效的。

This thesis analyzes the absolute stability in P and PD type fuzzy logic control systems with both certain and uncertain linear plants. In addition, the adaptive fuzzy-neural observer (AFNO) is applies to synchronize a class of unknown chaotic systems via scalar transmitting signal only. Stability analysis includes the reference input, actuator gain and interval plant parameters. For certain linear plants, the stability (i.e. the stable equilibriums of error) in P and PD types is analyzed with the Popov or linearization methods under various reference inputs and actuator gains. The steady state errors of fuzzy control systems are also addressed in the parameter plane. The parametric robust Popov criterion for parametric absolute stability based on Lur’e systems is also applied to the stability analysis of P type fuzzy control systems with uncertain plants. The PD type fuzzy logic controller in our approach is a single-input fuzzy logic controller and is transformed into the P type for analysis. In our work, the absolute stability analysis of fuzzy control systems is given with respect to a non-zero reference input and an uncertain linear plant with the parametric robust Popov criterion unlike previous works. Moreover, a fuzzy current controlled RC circuit is designed with PSPICE models. Both numerical and PSPICE simulations are provided to verify the analytical results. Furthermore, the oscillation mechanism in fuzzy control systems is specified with various equilibrium points of view in the simulation example. Eventually, the comparisons are also given to show the effectiveness of the analysis method. On the other hand, the fuzzy control system can be applied to synchronize the chaotic signals in the master end intelligently. With a scalar transmitting signal only, the AFNO is utilized to synchronize a class of unknown chaotic systems. The proposed method can be used for synchronization if nonlinear chaotic systems can be transformed into the canonical form of Lur’e system type by the differential geometric method. In this approach, the adaptive fuzzy-neural network (FNN) in AFNO is adopted on line to model the nonlinear term in the master end. Additionally, the master’s unknown states can be reconstructed from one transmitted state using observer design in the slave end. Synchronization is achieved when all states are observed. The utilized scheme can adaptively estimate the transmitter states on line, even if the transmitter is changed into another chaotic system. On the other hand, the robustness of AFNO can be guaranteed with respect to the modeling error, and external bounded disturbance. Simulation results confirm that the AFNO design is valid for the application of chaos synchronization.