APPLICATION OF GENETIC ALGORITHMS TO SYSTEM IDENTIFICATION Zhang Zibo ,Faze1 Naghdy Department of Electrical and Computer Engineering University of Wollongong Northfields Ave., Wollongong, NSW 2522, Australia fazel@uow.edu.au ABSTRACT: zyxwvutsrqp System idenufication is a pre-requisite to analysis of a dynamic system and design of an appropriate controller for improving its performance. In conventional i d e n ~ c a t i o n methods, a model structure is selected and the parameters of that model are calculated by optimising an objective function. This process usually requires a large set of input/output data from the system whch is not always available. In addition the obtained parameters may be only locally optimal. In zyxwvut thx work genetic algorithms are applied to system identdication. A system is assumed to have an ARMAX model the parameters of whch are obtained using search process of the genetic algorithms. The method developed is presented and results of its application to a number of experimental systems are described. The results obtained are quite encouraging. 1. INTRODUCTION applied to SISO (Single Input Single Output), MJMO System identification is a pre-requisite to (Multiple Input Multiple Output), and non-linear analysis of a dynamic system and design of an systems. The developed algorithm estimates all the appropriate controller for improving its performance. parameters of a system including zeros, poles and time- The more accurate the mathematical model identified delay of the transfer function. for a system, the more effective will be the controller During the course of the paper a brief designed for it. In many identification processes, background on the work will be grven. The genetic however, the obtainable model using available algorithms will be introduced and their relevance to techmques is generally crude and approximate. system idenMication will be discussed. The procedure In conventional identification methods, a used for system identdication is then explained. The model structure is selected and the parameters of that result of the application of the method to a number of model are calculated by optimising an objective experimental systems will be finally reported. function. The methods typically used for optimisation of the objective function are based on gradient descent 2. BACKGROUND techniques. This process usually requires a large set of In spite of their suitability, genetic algorithms input/output zyxwvutsr data from the system which is not always have not been widely applied to system idendication. available. In addition the obtained parameters may be The two references reviewed in th~s paper [I, 21 focus only locally optimal. on SISO systems, though do not address the issues of Genetic Algorithms have been widely used in delay time and model structure. many applications to produce a global optimal solution. In the work carried out by Kristinsson [l] a This approach is a probabilistically guided PRBS (Pseudo Random Binary Signal) is used to optimisation process which simulates the genetic identlfy the poles and zeros of a system. The fitness evolution. The algorithm can not be trapped in a local function chosen is minima as it employs a random mutation procedure. In algorithms are not guided In their search process bY where M is a bias term needed to e n w e a positive local derivatives. Through CoQng the variables, fitness, w is the window size or the number of time populations with stronger fitness are idenMied and steps Over whch the fitness is accumulated and maintained while populations with weaker fitness are zyxwvuts q(t) zyxwvu = y(t) - >(t), The variables y(t) and j(t) are produced from their parents. This search process is the actual input of the output, The iden* global Optimal authors have not addressed how the positive number M parameters of a system. can be selected so that the fitnesses of the individuals In this genetic are to members are significantly different and hence better system identification. A system is assumed to have an are reproduced. The obtained from ARMAX (Auto-Regressive Moving Average) model computer simulation have shown GAI~ are a the parameters of which are obtained using search potential tool for idenMlcation of dynamic process of the genetic algorithms. The method has been zyxwvu w F(f) = CM-(q(t-i))2 contrast to classical optimisation algorithms, genetic zyxwvu 1 =o removed. This process that better Offsprings represent the output of a deterministic system driven by and the and robust and ~ ~ _ ~ ~ ~ _ _ ~ ~ _ _ _ ~