Modeling nonlinear systems using multiple piecewise linear equations

G K K Lowe,M A A Zohdy

doi:10.15388/na.15.4.14317

Abstract

This paper describes a technique for modeling nonlinear systems using multiple piecewise linear equations. The technique provides a means for linearizing the nonlinear system in such a way as to not limit the large signal behavior of the target system. The nonlinearity in the target system must be able to be represented as a piecewise linear function. A simple third order nonlinear system is used to demonstrate the technique. The behavior of the modeled system is compared to the behavior of the nonlinear system.

Highlights

The technique in this paper uses multiple piecewise linear equations to model nonlinear systems. It provides a means for piecewise linearizing the nonlinear system in such a way as to not limit the large signal behavior of the target system
For special classes of nonlinear estimation problems with linear models excited by white Gaussian noise, explicit estimation results may be obtained by using Gaussian probability density functions
A technique was presented for using multiple piecewise linear models on nonlinear systems in order to estimate the internal states

Summary

Introduction

The technique in this paper uses multiple piecewise linear equations to model nonlinear systems. The most basic approach is to linearize the system about an operating point and use standard linear estimation techniques [1] In this case, the first derivative of the nonlinear function, evaluated at a specific operating point, is used to develop a first order set of linear state equations. For special classes of nonlinear estimation problems with linear models excited by white Gaussian noise, explicit estimation results may be obtained by using Gaussian probability density functions These functions are used to predict the most likely values of the state variables based on the current values of the output and the covariance of the state estimation error [4]. The simulation results of the piecewise linear modeled system will be compared to the actual nonlinear system

Piecewise linear modeling

Application to a motor driven pendulum

Conclusions