Fuzzy Model Identification for Control

2000

In order to solve the problem of model based control arising from the process model has to be obtained by using small amount and different type of available information, a fuzzy modeling framework has been developed for the utilization of a priori knowledge. The proposed modeling approach transforms the different types of information into the structure of the model (fuzzy rule base), constraints defined on the parameters and variables, dynamic local model or data, and steady-state data or model. This modeling step is followed by an optimization procedure based on these transformed information. The paper describes one element of this framework that was developed to use prior knowledge in constrained adaptation of the rule consequences of Takagi-Sugeno fuzzy models. Experimental results have been obtained for a laboratory setup consisting of two cascaded tanks. It has been shown that by using constrained adaptation, good control performance can be achieved for a nonlinear, time-varying process. 1

There are two approaches to extract a linear model from a Takagi-Sugeno fuzzy model for model based control. The first local approach obtains the linear model by interpolating the parameters of the local models in the TS model, while the second one is based on linearization by Taylor expansion. The locally interpreted interpolated model is not identical to the model obtained by the linearization of the fuzzy model. The paper analyzes the origin of this difference with regard to the applied identification method and the application of the resulted model in model predictive control. In order to keep the analysis simple and transparent, a fuzzy model of a Hammerstein system is studied.

Chemical Engineering Research & Design; vol. 77, num. 4, pp. 281-290, 1999

This study presents an adaptation method for Sugeno fuzzy inference systems that maintain the readability and interpretability of the fuzzy model during and after the learning process. This approach can be used for the modelling of dynamical systems and for building adaptive model-based control algorithms for chemical processes. The gradient-descent based learning algorithm can be used on-line to form an adaptive fuzzy controller—this ability allows these controllers to be used in applications where the knowledge to control the process does not exist or the process is subject to changes in its dynamic characteristics. The proposed approach was applied in an internal model (IMC) fuzzy control structure based on the inversion of the fuzzy model. The adaptive fuzzy controller was applied in the control of a non-linear plant and is shown to be capable of providing good overall system performance.

Mathematical and Computer Modelling, 1991

2007 IEEE International Fuzzy Systems Conference, 2007

In this paper, a nonlinear fuzzy identification approach based on Genetic Algorithm (GA) and Takagi-Sugeno (TS) fuzzy system is presented for fuzzy modeling of a multi-input, multioutput (MIMO) dynamical system. In this approach, GA is used for tuning the parameters of the membership functions of the antecedent parts of IF-THEN rules and Recursive Least-Squares (RLS) algorithm is employed for parameter estimation of the consequent linear sub-model parts of the TS fuzzy rules. The presented method is implemented on a simulated nonlinear MIMO distillation column. The results show that the presented method gives a more accurate model in comparison with the conventional TS fuzzy identification approach.

1996

The past few years have witnessed a rapid growth in the use of fuzzy logic controllers for the control of processes which are complex and ill-defined. These control systems, inspired by the approximate reasoning capabilities of humans under conditions of uncertainty and imprecision, consist of linguistic 'if-then' rules which depend on fuzzy set theory for representation and evaluation using computers. Even though the fuzzy rules can be built from purely heuristic knowledge such as a human operator's control strategy, a number of difficulties face the designer of such systems. For any reasonably complex chemical process, the number of rules required to ensure adequate control in all operating regions may be extremely large. Eliciting all of these rules and ensuring their consistency and completeness can be a daunting task. An alternative to modelling the operator's response is to model the process and then to incorporate the process model into some sort of model-base...

2003

Fuzzy systems are often used to model the behavior of nonlinear dynamical systems in process control industries because the model is linguistic in nature, uses a natural-language rule set, and because they can be included in control laws that meet the design goals. However, because the rigorous study of fuzzy logic is relatively recent, there is a shortage of well-defined and understood mechanisms for the design of a fuzzy system. One of the greatest challenges in fuzzy modeling is to determine a suitable structure, parameters, and rules that minimize an appropriately chosen error between the fuzzy system, a mathematical model, and the target system. Numerous methods for establishing a suitable fuzzy system have been proposed, however, none are able to demonstrate the existence of a structure, parameters, or rule base that will minimize the error between the fuzzy and the target system. The piecewise linear approximator (PLA) is a mathematical construct that can be used to approximate an input-output data set with a series of connected line segments. The number of segments in the PLA is generally selected by the designer to meet a given error criteria. Increasing the number of segments will generally improve the approximation. If the location of the breakpoints between segments is known, it is a straightforward process to select the PLA parameters to minimize the error. However, if the location of the breakpoints is not known, a mechanism is required to determine their locations. While algorithms exist that will determine the location of the breakpoints, they do not minimize the error between data and the model. This work will develop theory that shows that an optimal solution to this nonlinear optimization problem exists and demonstrates how it can be applied to fuzzy modeling. This work also demonstrates that a fuzzy system restricted to a particular class of input membership functions, output membership functions, conjunction operator, and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

1999

This paper presents an algorithm for incorporating of a priori knowledge into data-driven identification for dynamic fuzzy models of the Takagi-Sugeno type. Knowledge about the modeled process such as its stability, minimal or maximal static gain, or the settling time of its step response can be translated into inequality constraints on the consequent parameters. By using input-output data, optimal parameter values are then found by means of quadratic programming. The proposed approach was successfully applied to the identification of a laboratory liquid level process.

Stochastic Control, 2010

1999

Abstract Traditional (non-fuzzy) control methodology deals with situations when we know exactly how the system behaves and how it will react to different controls, and we want to choose an appropriate control strategy. This methodology enables us to transform the description of the plant's (system's) behavior into an appropriate control strategy. In many practical situations, we do not have the exact knowledge of the system's behavior, but we have expert-supplied fuzzy rules which describe this behavior.