Compensation of hysteresis in a shape memory alloy wire system using linear parameter‐varying gain scheduling control

Abstract

Robust tracking control of shape memory alloy (SMA) systems is a challenge because of their highly non-linear response, non-local memory and lack of differentiability. In this work, a linear parameter-varying (LPV) control method is proposed to compensate for the hysteretic behaviour of an SMA actuator. To provide information on the scheduling variable, the Preisach model of hysteresis is utilised. Parameter-dependent controller is updated based on the real-time computation of the instantaneous scheduling variable from the model. An H ∞ controller is also synthesised by representing the hysteresis as a parametric uncertainty. The controllers are implemented on an SMA actuated experimental system. Experimental validation is conducted for various types of reference inputs which can dramatically change the system's response. These reference signals are designed to excite major, minor and frequency dependent hysteresis loops. Trajectory tracking and disturbance rejection results show that the LPV controller has an improved response and the hysteresis is compensated for the full range of the scheduling variable. The tracking performances of both controllers are also compared when the system is under partial and persistent plant disturbances. For these cases, the LPV controller results in a more robust tracking response because of its less conservative structure.

Effect of shape memory alloys partial transformation on the response of morphing structures encompassing shape memory alloy wire actuators

“…Research published by Likhachev (1995), Dutta and Ghorbel (2005), and Feng et al (2011) fall in this category. Adopting the Preisach hysteresis model, Rao et al (2014) developed a thermodynamically consistent model able to predict formation of internal branches, while Kilicarslan et al (2014) scheduled and tested a linear-parameter varying controller in real-time for SMA actuators operating under a range of hysteresis conditions. Prediction of incomplete transformation branches from a phenomenological point-of-view has been considered in the one-dimensional (1-D) model of Bekker and Brinson (1998) that was based on the study of material’s response on the σ − T plane (phase diagram of SMAs).…”

Position control of a shape memory alloy actuator using a four-term bilinear PID controller

“…To switch between the different linear controllers, the gain scheduler monitors one or more observable variables to infer in which operating range is the controlled process. There are some examples of gain scheduling control applied to control the position of SMA actuators, such as the works by Jayender et al [19,20] or Kilicarslan et al [21]. Andrianesis et al [22] implemented a gain-scheduled controller to drive the output of the SMA actuation system of a prosthetic hand.…”

Finite Strain Constitutive Modelling of Shape Memory Alloys Considering Partial Phase Transformation with Transformation-Induced Plasticity

“…1 Schematic example of a PT formation during thermal actuation, determining one closed loop with two reversal points. FR and RF denote the reversal points passing, respectively, from forward to reverse transformation and from reverse to forward include differential equations and Duhem-Madelung type models [15,33,34], Preisach-type models [35][36][37][38][39], purely phenomenological models and state equations based on principles of thermodynamics and/or plasticity [20,[40][41][42][43][44].…”