Modeling and Identification of Discrete-Time Nonlinear Dynamic Cascade Systems with Input Hysteresis

Jozef Vörös

doi:10.1155/2015/393572

Abstract

A simple approach to modeling and identification of discrete-time nonlinear dynamic systems having an input hysteresis in cascade with a linear dynamic system is presented. A special form of Coleman-Hodgdon model for the hysteresis is considered, which is linear in parameters. For the cascade system parameter estimation, an iterative method with internal variable estimation is proposed. Simulation studies of cascade systems identification using special periodic inputs are included.

Highlights

Hysteresis is a special type of multivalued nondifferentiable nonlinearity and is encountered in a variety of processes where memory effects are involved between the input and output variables
Appropriate hysteresis models may be applied to the formulation of control algorithms
The modeling and identification of systems with hysteresis is of great importance

Summary

Introduction

Hysteresis is a special type of multivalued nondifferentiable nonlinearity and is encountered in a variety of processes where memory effects are involved between the input and output variables. The presence of the hysteretic behavior in sensors and actuators causes a hard nonlinear relationship between inputs and outputs This phenomenon occurs in all the smart material-based actuators such as piezoceramics, magnetostrictive, and shape memory alloys [3,4,5]. A relatively simple differential model of hysteresis, which is appropriate for the representation of rate independent hysteretic systems, is the so-called ColemanHodgdon model studied in [15,16,17] This model is able to capture, in an analytical form, a range of shapes of hysteretic loops, which match the behavior of a wide class of hysteretic systems. A new and simple approach to modeling and identification of discrete-time cascade systems with an input hysteresis followed by a linear dynamic system is presented. To the author’s knowledge, no work dealing with this problem was published up to now

Coleman-Hodgdon Hysteresis Model

Cascade System with Input Hysteresis

Parameter Estimation

Examples

Conclusions