Development of the rate-dependent Prandtl–Ishlinskii model for smart actuators

Abstract

A generalized Prandtl-Ishlinskii model is proposed for characterizing the rate-dependent hysteresis behavior of smart actuators. A rate-dependent play operator is formulated and integrated to the Prandtl-Ishlinskii model together with a dynamic density function to predict hysteresis properties as a function of the rate of change of the input. Relaxation functions are further proposed to relax the congruency in the output of the Prandtl-Ishlinskii model. The fundamental properties of the proposed rate-dependent operator are systematically provided, which conform with important effects of the time rate of input on the hysteresis output established from the reported experimental data. Additional laboratory experiments were performed to characterize the rate-dependent hysteresis behavior of a PZT actuator under excitation in the 1-500 Hz frequency range. The measured data were used to demonstrate the validity of the proposed generalized model. The comparisons suggest that the proposed rate-dependent operator and density functions allow for prediction of the rate-dependent hysteresis under dynamically varying inputs. From the simulation results attained under varied dynamic inputs, it is shown that the proposed model can predict both major and minor hysteresis loops, and that the hysteresis increases significantly with increasing frequency.

A precise positioning actuator based on feedback-controlled magnetic shape memory alloys

“…[9][10][11] are some recent examples of piezo-devices for position and vibration control). Essentially, there exist three main approaches to cope with hysteresis: (1) open-loop compensation, where a mathematical model of the hysteresis, such as the widely used Preisach [12,13], or Prandtl-Ishlinskii [14][15][16] models, is defined and its inverse is used in a feed-forward compensation, (2) closed-loop control, where a feedback controller, ranging from standard PIDs [17] to more evolved adaptive or robust schemes [18][19][20][21], is used to achieve control objectives while mitigating the effects of the hysteresis without explicit model-based compensation, and (3) hybrid strategies, where a hysteresis compensator is adopted together with a feedback controller to combine the advantages of both schemes. For instance, an effective hybrid strategy has been successfully documented in [22], where a feedback loop containing a hysteresis compensator in feedforward and a PID controller is analyzed and discussed.…”

Position control of shape memory alloy actuator based on the generalized Prandtl–Ishlinskii inverse model

“…The main contribution of this work is to experimentally demonstrate the feasibility of position control of a SMA-actuated large deformation flexible beam by compensation of the generalized Prandtl-Ishlinskii inverse model. It is shown in the current research by experimental data that the generalized Prandtl-Ishlinskii hysteresis model developed by Al Janaideh et al in [4,52,57] has powerful ability to model hysteresis of SMA actuator and the result of the new submitted paper [3] also shows that among the phenomenological hysteresis models like Preisach model and Krasnoselskii-Pokrovskii model, the Generalized Prandtl-Ishlinskii model leads to more accurate results in prediction the behavior of SMA actuators. In addition, since the problem of tracking minor hysteresis loops due to high nonlinear behavior of system in these areas was not investigated in many papers, this issue has been addressed and considered in this paper.…”

Open loop control of piezoelectric tube transducer

“…The hysteresis positioning error is typically about 10-25% of the full measurement range, and has been reported to increase up to 35% when the rate of the input signal increases [12,13]. Additionally, it is rate dependent, which means that the loop's shape will broaden when the input signal rate increases [14,15]. The hysteresis behavior causes significant positioning inaccuracy of the system in open-loop control.…”