Identification of nonlinear mechatronic servo system having backlash

This paper describes a new method of identification of nonlinear mechatronic servo system having small backlash element by use of M-sequence correlation method. In this method, we can obtain Volterra kernels of up to 3rd order of the nonlinear system. Strictly speaking, a multi-valued nonlinear system such as backlash element can not be expressed by Volterra kernel representation mathematically. But in practice, we encounter many cases where we have to control such a nonlinear system. In those cases, we need some mathematical expression for the nonlinear system. Here we dare to suppose that backlash nonlinear system can be approximated by Volterra kernel representation. And we would like to see what the approximation is. Simulations and actual experiments are carried out on a nonlinear system consisting of linear part plus backlash element in mechatronic servo system. And Volterra kernels are measured. The outputs calculated from the observed Volterra kernels are in good agreement with the actual outputs, and we can say that when the width of backlash is small, the nonlinear system can be approximated by a Volterra kernel representation.