Adaptive control system of complex plant on the base of fuzzy dynamic model

ADAPTIVE CONTROL SYSTEM OF COMPLEX PLANT

ON THE BASE OF FUZZY DYNAMIC MODEL

Yuliya M. Drebskaya

Department of Automated Technological Systems

Ufa State Aircraft Technical University

K. Marksa 12, Ufa, 450000, RUSSIA

Tel: (3472) 73-05-26, E-mail: ingo@mail.rb.ru

Abstract — Possible solution of adaptive control problem in conditions of fuzzy information is discussed in this paper. Formal description of plant is based on theory of fuzzy sets and automatic control. Technique is applied for solution of complex plant control problems, such as control of technological process of machining.

1. INTRODUCTION

Technological cutting process is the lowest level in a hierarchical control system of mechanical processing, that defines quality and efficiency of all system and all manufacture. These control systems play the basic role in any manufacture as set production can be received only at presence of the perfect control systems of technological processes.

Technological process of machining as plant is very complicated. Because of a small volume of prior information about internal and external links the mathematical model is inexact. Statistical characteristics of many factors of cutting process float over a wide range. Despite of long researches of the mechanical, thermal, electric phenomena, the chemical processes occuring in a zone of processing, because of their complex combination, mathematical models on the basis of the physical laws explaining these phenomena till now are not received. The models constructed by methods of planning experiments, by experience and intuitions of technologists adequately reflect a subject domain only in a narrow range of technological conditions. Besides feature of knowledge about cutting process is their empirical and heuristic character. The specified circumstances, and also the limited quantity of means of measurement on the process equipment and indirect methods of measurement are the reasons of cutting process models uncertainty. It’s the main problems of creating high effective control system.

One of the most effective ways to control system is to create adaptive control system. But not always adaptive control system can make steady control system. That’s why robust control system progressed intensively.

2. STATEMENT AND SOLUTION OF PROBLEM

For description of random variables and casual processes invariant to their law of distribution, and the quantitative account uncertainty at the description behaviour of cutting process the following mathematical model [3,4]:

State equations:

(1)

Measurement equations:

           (2)

Initial conditions: .

Its feature are fuzzy elements: fuzzy sets and fuzzy functions. Fuzzy sets describe parameters of model, variable a vector of a condition, target coordinates of model, dimension of a vector of a condition, initial conditions, fuzzy functions - the right parts of the differential equations.

Membership functions (MF) of fuzzy sets and fuzzy functions are presented in a parametrical form:

The factor  represents mode of MF, factors  and  set width FP, ,- inclination Membership function to an axis х (contrast). The described factors are defined by methods of identification and recognition of images so MF is interpreted as a degree of affinity elements of some class to each other. Parametrical representation MF allows to receive any form, quantitatively estimate an fuzziness of the information, to raise speed and flexibility of operating by the fuzzy information, processing thus not all elements of fuzzy set, but only five parameters. In turn, the quantitative estimation of aprioristic information fuzziness allows to approach to a choice of a principle and a method of control, and also is a component of criterion of control system quality at formation of operating influence on cutting process.

The solution of the differential equations in conditions of the fuzzy information is carried out on the basis of geometrical interpretation of fuzzy sets, fuzzy and a composite rule of a logic conclusion. Application at calculations of fuzzy sets parameters and fuzzy functions has allowed to replace plural by-element operations on analytical, that has raised speed of calculations at least on 2 orders. And it, in turn, has made model which is applied for estimate fuzziness of variables of a conditions vector during control in real time.