On Cauchy problem and stability of inversion-free feedforward control of piecewise monotonic Krasnoselskii-Pokrovskii hysteresis

TL;DR

This paper analyzes the existence, uniqueness, and stability of solutions to a differential equation modeling hysteresis in actuated systems, with applications demonstrated on a magnetic shape memory alloy actuator.

Contribution

It provides new theoretical results on the stability and solutions of an inversion-free feedforward control model with hysteresis, supported by numerical examples.

Findings

Proved existence and uniqueness of solutions.

Established global stability of the differential equation.

Validated analysis with numerical simulations on MSMA actuator.

Abstract

We consider the non-homogeneous first-order differential equation with hysteresis described by the Krasnoselskii-Pokrovskii rate-independent hysteresis operator. Existence and uniqueness of solutions as well as the boundedness of solution in response to a bounded input are proved. The global stability of the equation is also investigated. Periodic solutions and their stability are studied in addition. The differential equation under analysis constitutes the so-called inversion-free feedforward control, which was proposed for mitigating arbitrary rate-independent hysteresis effects in the actuated systems. The experimentally identified non-smooth and non-strictly monotonic hysteresis of a magnetic shape memory alloy (MSMA) actuator serves as the case study. The performed analysis is settled in a series of theorems which are illustrated by numerical examples.