الفهرس 
INTRODUCTIONOnly 14 pages are availabe for public view
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Abstract
Most of the real world dynamical systems are usually nonlinear in their behavior with uncertainties and external disturbances. These problems may affect the control system performance and result in its instability. For these reasons, the classical controllers are not suitable to control such systems. Control of these nonlinear systems has received extensive attention in academic and industry.
Fuzzy logic controller (FLC) is considered a popular intelligent controller in engineering applications. The presence of the system uncertainties increases the merits of the use of the FLC as compared to other controllers. There are exist different uncertainties accompanied with the practical processes. These uncertainties may be classified into stochastic and non-stochastic uncertainties. The uncertainties due to the plant dynamics can be described as non-stochastic uncertainties, and the uncertainties due to random noises in the measured data can be considered as stochastic uncertainties.
In spite of the huge performance improvements of these FLCs compared to their traditional counterparts, it ought to be seen that they are normally not powerful for the situation where the controlled system has stochastic uncertainties. The traditional fuzzy logic system in these controllers uses a deterministic (two-dimensional) fuzzy membership function to represent the input/output variables. Consequently, the FLCs based on traditional fuzzy set barely works in a complex stochastic environment.
On the other hand, the probabilistic theory is a useful tool for handling the stochastic uncertainties. Therefore, the probability theory has been combined in a valuable manner with the fuzzy theory. The fusion of two different features; fuzzy nature and probabilistic analysis, in a distinctive framework leads to a new class of advanced fuzzy logic system for the control problems of industrial processes called probabilistic fuzzy logic system (PFLS). In the light of introducing probabilistic process into an ordinary fuzzy set,
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probabilistic fuzzy set (PFS) is presented in three dimensions including the input variable, fuzzy grade and the associated probability. The additional third dimension enables the PFS to process the stochastic feature and so the ability of the fuzzy controller to overcome the complex uncertainties is enhanced. PFLS expresses a relation between input variables and linguistic terms by employing the 3-dimensional PFS.
This dissertation aims to design advanced fuzzy controller based on PFLS for handling complex uncertainties in nonlinear systems. A probabilistic fuzzy proportional-integral-derivative (PF-PID) controller is developed to overcome various uncertainties in the controlled nonlinear systems. The analytical structure and stability analysis for the proposed PF-PID controller have been derived in this study. The resulting structure is equivalent to nonlinear PID controller and the equivalent gains for the proposed PF-PID controller are a nonlinear function of controller parameters. Moreover, the sufficient stability conditions for the proposed PF-PID controller are obtained.
Then, an adaptive probabilistic fuzzy PID (APF-PID) controller is proposed to improve the performance of PF-PID controller by tuning its parameters on-line. This controller is composed from two parts; the first is the PF-PID controller, which is used as the main controller. The other part is the fuzzy logic system (FLS), which is used as a tuning mechanism.
Then, a probabilistic Takagi–Sugeno–Kang fuzzy PID (PTSKF-PID) controller is developed for controlling nonlinear systems. The proposed PTSKF-PID controller merges the features of the TSK FLS, which possess a superior performance in system size and learning accuracy than the Mamdani-type fuzzy systems and the probabilistic processing method in handling the system uncertainties. The analytical structure and stability analysis for the proposed PTSKF-PID controller have been derived in this study. An adaptive PTSKF-PID (APTSKF-PID) controller is developed and the proposed
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controller stability is achieved by on-line updating the controller’s parameters including the probability parameters based on the Lyapunov theory.
The proposed controllers have been designed for controlling uncertain nonlinear systems including inverted pendulum system to overcome the system uncertainties. The performances of proposed controllers are compared with the performances of their counterparts of type-1 FLCs. Simulation tasks indicate that the efficiency of the proposed controllers have high superiority over the type-1 FLCs for external disturbances, random noise and a large scope of system uncertainties. Thus, the control methodologies proposed in this study can be used to realize a robust advanced fuzzy controller capable of controlling nonlinear dynamical systems that have stochastic and non stochastic uncertainties with acceptable response.