On the identification of linear mechanical systems

Abstract

General purpose controllers or controllers commanding systems which operate at varying conditions need a system identification routine to obtain a model for the response of the system so that it can adapt itself accordingly. Most such mechanical systems are composed of masses moving under the action of position and velocity dependent forces and hence can be modeled by second order linear differential equations. This paper describes how to obtain a simpler mathematical response model in the form of a linear difference equation for a second order linear system. Coefficients of the equation are calculated by using the least squares technique to minimize the error between the discrete position data from the system resulting when actuated by a pseudo-random binary command signal and what the model generates. An analytical solution obtained by the z-transformation of the system transfer function is also presented, to clarify the physical meaning of the coefficients. Experimental and analytical solutions for a variety of systems are presented as application examples.