HAAR WAVELET APPROACH TO OBTAIN DYNAMIC RESPONSE OF LTIV SYSTEM

Abstract

The "Haar wavelet operational matrix" is established and procedure for applying this technique to analyse the dynamic systems is formulated. The main characteristics of this technique is to convert a differential equation into an algebric equation and hence the solution procedure is much simplified. The technique can be interpreted from the incremental and multi resolution viewpoint. An increase of the number of intervals of Haar function enable to approximate the accurate solution and a decrease of the number of interval make the implementation easier. In this dissertation the dynamic response of LTIV system using Haar wavelet method is obtained. Several examples are included for demonstrating the fast, flexible and convenient capabilities of the method. In addition to the comparison is done to compare the fast capabilities of this method over the ODE23 method. ODE23 solves the non stiff differential equation of the from y' = F(t,y) from initial time to final time with initial condition specified. ODE23 is an implemenation of the explicit Runge Kutta (2,3) pair of Bogacki and Shainpine called BS23. The Haar method can be applied to system of any order. Various states of the system are calculated to obtain the dynamic response. The state trajectory of all the states are plotted. The time taken by both methods to solve state equation is also calculated for comparison purpose. Ultimately it was found that Haar wavelet approach is quite suitable for obtaining the dynamic response of the system.