Inversion-free feed-forward and feedback control of MSM based actuator with large non-smooth input hysteresis

TL;DR

This work addresses controlling an MSM actuator whose input-output relation is dominated by large, memory-based hysteresis modeled by a Krasnoselskii-Pokrovskii (KP) operator. It develops an inversion-free feedforward compensator based on the internal model principle and couples it with a robust PI feedback in a two-degrees-of-freedom architecture. The analysis shows that, under a positive instantaneous slope, the feedforward can converge toward the inverse of the hysteresis map as the integral gain grows, and experiments demonstrate improved position tracking despite high sensor noise. The study provides practical guidelines for implementing model-based hysteresis compensation in MSM devices and demonstrates superior performance over single-PI or feedforward-only schemes in step and sinusoidal tracking tests.

Abstract

Dynamic systems with a large and non-smooth hysteresis in the feedforward channel challenge the design of feedback control since the instantaneous input gain is varying during the operation, in the worst case between zero and infinity. Magnetic shape memory (MSM) actuators with multi-stable transitions represent such untypical system plant with only the output displacement being measured. This paper provides a case study of designing the feedforward and feedback control system for an MSM-based actuator setup with a fairly high level of the output sensing noise. First, the recently introduced inversion-free feedforward hysteresis compensator is adapted for the Krasnoselskii-Pokrovskii operator model. Then, a robust feedback proportional-integral (PI) loop shaping is performed, while taking into account the lagging behavior of the low-pass filtering and system uncertainties. Experimental results show that the parallel action of feedforward and feedback parts improves the overall performance of position control.

Figures (11)

• Figure 1: Inversion-free feedforward hysteresis control.
• Figure 2: Krasnoselskii-Pokrovskii hysteresis operator.
• Figure 3: Input-output hysteresis by KP model with $N=3$.
• Figure 4: Feedforward compensated hysteresis, (a) hysteresis output versus reference, (b) compensator output.
• Figure 5: MSM actuator system setup: excerpt from CAD drawing (left) and laboratory view (right).