Pei-Zhuang Wang

Fuzzy self-tuning of PID controllers

Abstract This paper presents a novel fuzzy self-tuning PID control scheme for regulating industrial processes. The essential idea of the scheme is to parameterize a Ziegler-Nichols-like tuning formula by a single parameter α, then to use an on-line fuzzy inference mechanism to self-tune the parameter. The fuzzy tuning mechanism, with process output error and error rate as its inputs, adjusts α in such a way that it speeds up the convergence of the process output to a set-point y r , and slows down the divergence trend of the output from y r . A comparative simulation study on various processes, including a second-order process, processes with long dead-time and non-minimum phase processes, shows that the performance of the new scheme improves considerably, in terms of set-point and load disturbance responses, over the PID controllers well-tuned using both the classical Ziegler-Nichols formula and the more recent Refined Ziegler-Nichols formula.

Latticized linear programming and fuzzy relation inequalities

Abstract A logical linear programming problem, the latticized linear programming, is proposed based on fuzzy lattice and fuzzy relation inequalities. The proposed problem is essentially an optimization problem which should be useful under certain logical “if…, then…” situations. To illustrate the proposed approach, numerical examples are solved.

Control of dynamical processes using an on-line rule-adaptive fuzzy control system

Abstract In this paper, we present a detailed discussion on the design of a rule-adaptive fuzzy control system, along with simulation analysis demonstrating its usefulness in controlling plants of various dynamical natures. Conceived first by Wang, and further clarified in [8], the rule-adaptive fuzzy controller considered here generates the fuzzy control signal as a convex combination of the standard fuzzy inputs to the controller, the error and the error rate. Such a combination is automatically adjusted on-line in response to the varying control situations with certain updating scheme. This paper considers two different updating schemes. The first one is based on a fuzzy relationship, and is a revision of the rule presented in [11]. The present paper also proposes the second updating rule that is essentially a nonlinear differential equation. Both of the rules are applied to the simulations of several selected dynamical plants. The simulation results show that the controller is effective in controlling a wide range of dynamical plants. Especially, it shows better performance in controlling the plants found difficult to be controlled by the conventional means. The simulation also shows that the controller can be used to curb the effect of load disturbance in the control process.

The min-max function differentiation and training of fuzzy neural networks

This paper discusses the Delta-rule and training of min-max neural networks by developing a differentiation theory for min-max functions, the functions containing min (wedge) and/or max (V) operations. We first prove that under certain conditions all min-max functions are continuously differentiable almost everywhere in the real number field R and derive the explicit formulas for the differentiation. These results are the basis for developing the Delta-rule for the training of min-max neural networks. The convergence of the new Delta-rule is proved theoretically using the stochastic theory, and is demonstrated with a simulation example.

A factor spaces approach to knowledge representation

Abstract In this paper, a study of knowledge representation is presented based on factor spaces. Examples are presented to show the applications of factor spaces to the concepts of representation and pattern recognition. Some topics as approximate reasoning are studied also.

Pad-analysis of fuzzy control stability

Abstract By means of an index-represented rule mapping, the response g of a fuzzy controller is decomposed into two parts: f , the classical component and g − f , the nonlinear component, called pad. We intend to analyse the pad in order to know what the relation is between fuzzy and classical PID controllers. Fuzzy controllers mentioned here are defuzzified by the typical center of gravity method. In the 1-input case, we get that f − g = 0, which means that the fuzzy controller is exactly the same as the classical P-controller, whenever the rule mapping is simple (Definition 1.2) and the linguistic values are a binary family (Definition 4.1). In the 2-input case of error and error change for simple rule mapping and for simple linguistic values family (4.7), and perfectly for the WXYZ linguistic values family (Definition 6.1), the fuzzy controller can be viewed as a series connection of a classical PD controller and a 1 + pad-element. The describing function of a 1 + pad-element is very simple and fine, and ensures that such fuzzy controller will be stable if the PD controller is. The similar consequences are also obtained for the case of three inputs.

PID self-tuning control using a fuzzy adaptive mechanism

The authors present a novel proportional-integral-derivative (PID) self-tuning control using a fuzzy adaptive mechanism for regulating industrial processes. The essential idea is to parameterize a Ziegler-Nichols-like tuning formula by a single parameter alpha , then to use an online fuzzy inference mechanism to self-tune the parameter. A comparative simulation study on various processes, including processes with long dead-time and non-minimum-phase processes, shows that the performance of the scheme improves considerably, in terms of set-point and bad disturbance responses, over the PID controllers well-tuned using both the classical and the more recent refined Ziegler-Nichols formula.<<ETX>>

Fuzzy inference relation based on the theory of falling shadows

Abstract In this paper, we establish a theoretical approach to define a fuzzy inference relation based on the theory of falling shadows. The main characteristic of our definition of fuzzy inference relation is that it is semantically dependent in the sense that the formula of our definition will vary according to the correlation of the antecedent and the consequence of the given implication. We shall show that the formulae of fuzzy inference relation given by Łukasiewicz, Zadeh and the probability formula are consequences of our definition under three different correlations of the propositions.

Constructive theory for fuzzy systems

Abstract In this paper, a constructive theory is developed to establish the fact that we can build a fuzzy system to approximate any continuous function on a compact set within a prescribed error bound. Based on the theory, an algorithm is described that can actually construct a near minimum fuzzy system for a given function to a desired accuracy.

Set-valued statistics and its application to earthquake engineering

Abstract A new concept in statistics is presented here, called ‘Set-valued Statistics’, where a trial is a crisp or a fuzzy set. Some propositions concerning mathematical properties are given. The falling-shadow theory related to set-valued statistics is briefly discussed. An important application to the prediction of damage caused by earthquakes shows the efficiency of set-valued statistical data processing techniques. Earthquake-generated damage prediction plays an essential role in plan-making as a preparation for seismic disaster and the result of forecasting the number of severely damaged building structures (due to an expected strong motion in an urban area) by using the falling-shadow Bayes principle depicts good future prospects for its application.