Multiple (local) linear model based process identification and control (Local and global issues)

Fuzzy identification is an effective tool for the approximation of uncertain nonlinear dynamic systems on the basis of measured input-output data. The Takagi-Sugeno (TS) fuzzy model is often used to represent nonlinear dynamic systems, by interpolating between local linear, time-invariant (LTI) ARX models. There are two approaches to extract a linear model from the fuzzy model around a given operating point. The first approach is based on the fact that the TS model interpolates between local linear models. Hence, the extracted linear model is obtained by interpolating the parameters of the local models in the TS model. The second approach extracts the parameters of the linear model by Taylor expansion. The locally interpreted interpolated model is not identical to the model obtained by this Taylor expansion based linearization of the fuzzy model. For the identification of a fuzzy model, also two approaches can be followed. With the global approach the parameters of all rule consequences are estimated within one identification problem, yielding an optimal predictor. The local parameter estimation does not estimate all parameters simultaneously. It rather divides this task into a set of weighted least-squares problems. As it has been shown in this project, only consequent parameters obtained by local estimation (weighted least squares) can be interpreted locally and used as a Linear Parameter Varying (LPV) model in the MPC where the extracted model parameters are interpolated. Parameters obtained by global identification do not lend themselves to the LPV interpretation. Such a model is only applicable where the extracted models are obtained by Taylor-series linearization.

J. Abonyi, T. Chovan, F. Szeifert, Identification of nonlinear systems using gaussian mixture of local models, Hungarian Journal of Industrial Chemistry, 29, 139-134, 2001
J. Abonyi, R. Babuska, L. Nagy, F. Szeifert, Local and global identification for fuzzy model based control, Proceedings of the Intelligent Systems in Control and Measurement Symposium, INTCOM 2000, 111—116, Veszprem, Hungary, 2000
S. Mollov, P. van der Veen, R. Babuska, J. Abonyi, J.A. Roubos, H.B. Verbuggen, Extraction of local linear models from Takagi-Sugeno fuzzy model with application to model-based predictive control, 7th European Conference on Intelligent Techniques and Soft Computing (EUFIT '99) , (CD rom), Aachen, Germany, Sep, 1999
J. Abonyi, R. Babuska, L. Nagy, F. Szeifert, Local and global identification for fuzzy model based control, Proceedings of the Intelligent Systems in Control and Measurement Symposium, INTCOM 2000, 111—116, Veszprem, Hungary, 2000
S. Mollov, P. van der Veen, R. Babuska, J. Abonyi, J.A. Roubos, H.B. Verbuggen, Extraction of local linear models from Takagi-Sugeno fuzzy model with application to model-based predictive control, 7th European Conference on Intelligent Techniques and Soft Computing (EUFIT '99) , (CD rom), Aachen, Germany, Sep, 1999

Fuzzy model identification for model based control, incorporation of prior knowledge

A critical step in the application of model-based control algorithms is the development of a suitable model of the process dynamics. To effectively develop models, one needs to blend information of different nature: experience of operators and designers, measurements and first principle knowledge formulated by mathematical equations. The aim of this project is to design a fuzzy modeling framework that is suitable for the use of this information to generate control-relevant process models.
To incorporate a priori knowledge into data-driven identification of dynamic fuzzy models of the Takagi-Sugeno type a constrained identification algorithm has been developed, where the constrains of the candidate model parameters are based on knowledge about the process stability, minimal or maximal gain, and the settling time. The algorithm has been successfully applied in the on-line adaptation of fuzzy models. It has been shown that fuzzy models built on the basis of data combined with prior knowledge perform better in control than models obtained from
In order to avoid problems arising from the local and global interpretation of Takagi-Sugeno fuzzy models, new fuzzy model structures will be developed. The real-time implementation issues of the algorithms will be studied in laboratory-scaled processes (water-heater, batch reactor, catalytic tube reactor).

J. Abonyi, H. Roubos, R. Babuska, F. Szeifert, Identification of Semi-Mechanistic models with interpretable TS-fuzzy submodels by clustering, OLS and FIS model reduction, Fuzzy modeling and the interpretability-accuracy trade-off. Part I, interpretability issues., Chapter 10., J. Casillas, O. Cordon, F. Herrera, L Magdalena, (Eds.), Studies in Fuzziness and Soft Computing, Physica-Verlag, 2003. pp. 221-248
J. Abonyi, R. Babuska, F. Szeifert, Fuzzy modeling with multidimensional membership functions: Constrained identification and control design, IEEE Systems, Man and Cybernetics, Part B, Oct, 2001
J. Abonyi, A. Bódizs, L. Nagy, F. Szeifert, Hybrid fuzzy convolution model and its application in model predictive control, Chemical Engineering Research and Design, 78(A), 597-604, 2000
J. Abonyi, R. Babuska, H. B. Verbruggen, F. Szeifert, Incorporating prior knowledge in fuzzy model identification, Int. Journal of Systems Science, 31(5), 657-667, 2000
J. Abonyi, J. Madar, F. Szeifert, Combining first principles models and neural networks for generic model control, Soft Computing in Industrial Applications - Recent Advances, Springer Engineering Series, 6th On-Line World Conference on Soft Computing in Industrial Applications (WSC6) (6th : 2001).

Block-oriented fuzzy modelling

The steady-state characteristic of nonlinear control-relevant model has large effect to the control performance. Because of the difficult analysis of the steady-state behavior of dynamic fuzzy models of the Takagi-Sugeno type, block-oriented fuzzy models have been developed. A special modeling approach based on the combination of nonlinear static nonlinearity and gain-independent dynamic model has been studied, and this methodology has been effectively applied to fuzzy modeling and model based control of dynamic systems. By the combination of a fuzzy model that represents the stationer behavior and an a priori knowledge based gain independent impulse response of the system, Hybrid Fuzzy Convolution Model and Wiener Convolution Model have been developed. These models have been applied in Predictor Corrector and Generalized Predictive Controller. The resulted control algorithms have been effectively applied to laboratory scaled processes. In the Fuzzy Hammerstein (FH) model, a static fuzzy model is connected in series with a linear dynamic model. An iterative algorithm has been developed for the identification of a this model, where the static nonlinearly and a unity-gained linear dynamic model are identified simultaneously. The obtained FH model is incorporated in a model-based predictive control scheme. Results show that the proposed FH modeling approach is useful for modular parsimonious fuzzy modeling and fuzzy model-based control of nonlinear systems

.J. Abonyi, R. Babuska, M. Ayala Botto, F. Szeifert, N. Lajos, Identification and control of nonlinear systems using fuzzy Hammerstein models, Industrial and Engineering Chemistry Research, 39, 4302-4314, 2000 
J. Abonyi, A. Bódizs, L. Nagy, F. Szeifert, Hybrid fuzzy convolution model and its application in model predictive control, Chemical Engineering Research and Design, 78(A), 597-604, 2000
J. Abonyi, T. Chován, L. Nagy, F. Szeifert, Hybrid convolution model and its application in predictive pH control, Computers and Chemical Engineering, S221-S224, 1999
J. Abonyi, Á. Bódizs, L. Nagy, F. Szeifert, Predictor corrector controller using Wiener fuzzy convolution model, Hungarian Journal of Industrial Chemistry, 27(3), 227-233, 1999
J. Abonyi, L. Nagy, F. Szeifert, Hybrid fuzzy convolution modelling and identifi cation of chemical process systems, International Journal of Systems Science, 2000, volume 31, number 4, pages 457-466