On identification of nonlinear systems using Volterra kernels expansion on Laguerre and wavelet function

Application of Volterra series to the modeling of static and dynamic nonlinear systems is investigated in this paper and compared to other methods. For nonlinear systems with memory, Volterra series serves as a generalization of convolution integral. To parameterize the Volterra kernels for limited dimension series, different methods are discussed. We use Laguerre functions and wavelet packets as orthonormal basis and we find the poles for the basis through a genetic algorithm search. Our test system is a hydraulic actuator with a highly nonlinear dynamics which is modeled with Volterra series. The results show that dynamic model with wavelet packets give a more accurate model with respect to a static model with an LTI orthonormal function.