Modeling and Control of Nonlinear Systems Using Wavelet Networks

Abstract

The main objective of this research is to present wavelet networks as a new scheme to model and control nonlinear dynamic systems. The ability to control a system depends on how well it is modeled. Most real-world systems are inherently nonlinear, and conventional PID controllers, having fixed proportional, integral and derivative terms, are not able to deal with time-varying nonlinearities. Such conditions require adaptive controllers that can modify the P, I and D terms to compensate for these nonlinearities. Furthermore, the capability of wavelet networks in the modeling of dynamic nonlinear systems makes them appealing for use in system modeling and control. This research develops an adaptive PID- Dynamic Wavelet Network controller, comprising a digital PID controller and a proposed new wavelet network scheme called the Dynamic Wavelet Network (DWN), in order to model and control nonlinear systems. The learning strategy for the wavelet network and PID controller is developed based on the gradient descent algorithm. The performance of the proposed controller is demonstrated via extensive numerical simulations.