g-Liang Chen

Design and analysis of a fuzzy logic controller

The fuzzy logic controller (FLC) presented by Siler and Ying (1989) is discussed here and is proved to be equivalent to a non-fuzzy, nonlinear, proportional-integral (PI) controller. Some characteristic properties of this fuzzy logic controller are then investigated. The achievable performance of such a specific fuzzy controller is examined and found to be not necessarily better than that of the conventional, linear, non-fuzzy PI controller. Various extended designs of the basic FLC, including the FLC with dual control laws and the three-piece FLC, are then presented to enhance control performance. These extensions can provide servo-control performance. These extensions can provide servo-control performance superior to that of the basic FLC design, as illustrated by simulation results. Finally a highly nonlinear neutralization process is advanced to demonstrate the applicability of the various FLCs to industrial process control.

Theoretical analysis of crisp-type fuzzy logic controllers using various t-norm sum-gravity inference methods

The input-output parametric relationship of a class of crisp-type fuzzy logic controllers (FLCs) using various t-norm sum-gravity inference methods is studied. Four most important t-norms are used to calculate the matching level of each control rule and the explicit mathematical forms of reasoning surfaces obtained by using these four t-norms are addressed. Reasoning surfaces of these crisp-type FLCs are proved to be composed of a two-dimensional multilevel relay no matter which t-norm is used and a local position-dependent nonlinear compensator with output pattern influenced by the t-norms is selected. By analyzing the intrinsic operation of the four t-norms, the authors find that both standard intersection and algebraic product are suitable operators to perform the inference of the FLC. However, bounded difference and drastic intersection are disqualified because they cannot satisfy some important criteria. A measure of relative degree-of-nonlinearity is defined to examine the output figures of these crisp-type FLCs. The ultimate behavior of these crisp-type FLCs as the number of linguistic terms approaches infinity is also explored. The local stability criteria for the proportional-integral (PI)-type fuzzy control systems and the natural global stability characteristic for the proportional-derivative (PD)-type fuzzy control systems are also examined.

Theorectical analysis of a fuzzy-logic controller with unequally spaced triangular membership functions

Abstract The mathematical analysis concerning the explicit input/output relation of the fuzzy logic controller (FLC) is addressed in this article. Under the assumption of simple rule mapping and the use of arbitrarily located triangular fuzzy partitions as the membership functions, the inferred output of the FLC can be decomposed into two terms: the global multilevel relay and the local nonlinear compensator. The ultimate control behavior of this FLC and the equivalence to nonlinear proportional-integral (PI) controller, as the number of linguistic terms are approaching to infinity, are also investigated. The local stability criteria for PI-type FLCs are derived and the global stability properties for PD-type FLCs are established. This analysis is a generalization to previous related research works where the FLC is characterized by equally spaced triangular fuzzy partitions on the universal sets.

Numerical solution of dynamic optimization problems with flexible inequality constraints by iterative dynamic programming

A solution strategy for optimizing the dynamic systems with flexible inequality constraints is proposed. To apply fuzzy inference in solution, the flexible portion in the problem is treated as fuzzy constraints. After functional values are bounded in a region, the objective function of this problem can also be fuzzified easily. When the problem is formulated as a fuzzy dynamic optimization problem, the iterative dynamic programming integrated with fuzzy inference is adopted to find the solution. Two examples are employed, demonstrating the facility of the proposed algorithm.

Recursive parameter estimation of transfer function matrix models via Simpson's integrating rules

Recursive formulae for repeated integration of a continuous-time function with uniformly sampled data using Simpsons 1/3 and 3/8 integrating rules are derived. Combined with the recursive algorithm of the least-squares solution, a method for recursive parameter estimation of transfer function matrix models in multiple-input-multiple-output systems is proposed. It is demonstrated that the use of the popular integrating rules for parameter estimation can be as effective as sophisticated methods that use orthogonal functions and the associated operational properties reported in the literature. The proposed algorithm is suitable for on-line applications and computer programming. Three numerical examples are included to illustrate the applicability of the proposed method.

Self-organizing neural control system design for dynamic processes

Abstract This paper discusses the achievable nominal performance of a well-parametrized neural feedback control system, and proposes an efficient training method for parametrizing such a controller. A self-organizing neural control (SONC) system is presented in which a layered feedforward neural network is adopted as the controller structure in order to apply directly existing back-propagated learning techniques. A self-organizing methodology is introduced to provide the training set for adjusting parameters of the neural controller. One important feature of the proposed adaptive mechanism is that, though it should lack extensive knowledge of the process dynamics at the outset of controller design, it will still be able to achieve its desired results by employing the subjective experience of control specialists as its training aids. Tuning variables of the SONC system are reviewed through exploring their effects on five typical transfer functions. The applicability of the SONC system is also demonstrated ...

An LMI approach to H ∞ fuzzy-output feedback control for nonlinear systems

An LMI approach for designing an H/sup /spl infin// fuzzy controller for nonlinear dynamic systems is presented. The entire operating range for a nonlinear system is partitioned into several regimes. A local linear model with parameter uncertainties is identified for each region. These local models are integrated as the norm-bounded Tagaki-Sugeno (T-S) fuzzy model. The output feedback H/sup /spl infin// fuzzy controller design procedures are then investigated based on the T-S fuzzy model, therein the standard H/sup /spl infin// design problem is formulated as Linear Matrix Inequalities (LMIs). The necessary and sufficient conditions for the existence of an H/sup /spl infin// controller is derived. One numerical example is supplied, demonstrating the effectiveness of the proposed design procedures.

Expert system for real-time control of an ironmaking reactor

A real-time expert system is developed to support efficient operation and management of the No. 2 ironmaking reactor (blast furnace) in the China Steel Corporation. The expert system integrates the deep theoretical knowledge represented in reactor models with the practical experience of sophisticated field engineers. Fuzzy logic reasoning is applied in the expert system to deal with inherent indeterminacy of the operators‘ in-field knowledge of furnace heat levels. This expert system is divided into ‘information’ and ‘reasoning’ sub-systems. The information sub-system receives operational data from the process computer and executes the model calculations relevant to ironmaking. The sensory data and computation results of various models are then displayed on the operators terminal by way of attractive diagrams and tables to help field engineers to comprehend the furnace conditions as an integrated whole. The treated data afforded by the information sub-system are then periodically extracted by a reasoning...

Augmented hybrid method for continuous process identification from sampled data with coloured noise

The identification of a linear continuous-time model for a multivariable dynamic system from sampled input-output observations is considered. An augmented hybrid parametric method is proposed to overcome the interference of the coloured output noise in the sampled output. The parameters of the continuous-time process model are estimated from an augmented input-output realization which utilizes the dynamic information of the discrete-time noise model. Numerical examples are presented to illustrate how to obtain an adequate dynamic process model, considering the coloured output noise, by using a discrete-time noise model.

Identification of MIMO continuous-time models by indirect methods

The problem of using indirect methods to identify a linear MIMO continuous-time model from sampled input–output records of a multivariable process is discussed. In the indirect identification methods, a discrete-time model is first found by any existing standard methods; next a continuous-time model as an equivalent to the discrete-time one is determined. Three algorithms, each employing state-conversion, moment-matching and frequency-response matching methods, are proposed to carry out the second step of the indirect identification methods. Numerical examples are included to illustrate the applicability of the proposed methods.