Highlighted Aspects From Black Box Fuzzy Modeling For Advanced Control Systems Design
Ginalber Luiz de Oliveira Serra · InTech eBooks · 2012
Will-be-set-by-IN-TECHIn addition, a complete understanding of the physical behavior of a real plant is almost impossible in many practical applications.• Black box modeling.In this case, if such models, from the physical laws, are difficult or even impossible to obtain, is necessary the task of extracting a model from experimental data related to dynamic behavior of the plant.The modeling problem consists in choosing an appropriate structure for the model, so that enough information about the dynamic behavior of the plant can be extracted efficiently from the experimental data.Once the structure was determined, there is the parameters estimation problem so that a quadratic cost function of the approximation error between the outputs of the plant and the model is minimized.This problem is known as systems identification and several techniques have been proposed for linear and nonlinear plant modeling.A limitation of this approach is that the structure and parameters of the obtained models usually do not have physical meaning and they are not associated to physical variables of the plant.• Gray box modeling.In this case some information on the dynamic behavior of the plant is available, but the model structure and parameters must be determined from experimental data.This approach, also known as hybrid modeling, combines the features of the white box and black box approaches.The area of mathematical modeling covers topics from linear regression up to sofisticated concepts related to qualitative information from expert, and great attention have been given to this issue in the academy and industry (Abonyi et al., 2000;Brown & Harris, 1994;Pedrycz & Gomide, 1998;Wang, 1996).A mathematical model can be used for:• Analysis and better understanding of phenomena (models in engineering, economics, biology, sociology, physics and chemistry);• Estimate quantities from indirect measurements, where no sensor is available;• Hypothesis testing (fault diagnostics, medical diagnostics and quality control);• Teaching through simulators for aircraft, plants in the area of nuclear energy and patients in critical conditions of health;• Prediction of behavior (adaptive control of time-varying plants);• Control and regulation around some operating point, optimal control and robust control;• Signal processing (cancellation of noise, filtering and interpolation);Modeling techniques are widely used in the control systems design, and successful applications have appeared over the past two decades.There are cases in which the identification procedure is implemented in real time as part of the controller design.This technique, known as adaptive control, is suitable for nonlinear and/or time varying plants.In adaptive control schemes, the plant model, valid in several operating conditions is identified on-line.The controller is designed in accordance to current identified model, in order to garantee the performance specifications.There is a vast literature on modeling and control design (Åström & Wittenmark, 1995;