A Modular Direct Description Method With Low Memory Usage and Execution Time for Hysteresis Modeling and Compensation of Piezoelectric Actuators

This paper proposes a modular direct description method based on the relatively weak interdependence among hysteresis properties to establish a hysteresis model that includes the major curves fitter (MaCF) module, the turning points recorder (TPR) module, and the minor curves fitter (MiCF) module. The MaCF module utilizes the Fourier series fitting method to fit the major hysteresis curves, improving model scalability in conjunction with the modular approach. The TPR module is established to manage the turning points. A memory optimization strategy is further proposed to optimize the model in terms of memory consumption and execution time. The MiCF module then employs a two-stage curve fitting strategy to fit the minor hysteresis curves accurately. Finally, three modules are cascaded to construct the hysteresis model. Experiments have been performed to validate the excellent performance of the developed model in terms of model accuracy, memory usage, and execution time. The results indicate that the model only needs 0.28 KB of memory space to achieve accurate prediction and compensation of hysteresis phenomenon, the standardized normalized maximum error (
$NME)$
of hysteresis curve prediction is about 1%, and the
$NME$
value of compensation error is 1.37%. Meanwhile, the average execution time of the model is less than 1
$\mu $
s with a variance of 0.04.
Note to Practitioners
—The presented modular direct description (MDD) method can accurately describe and compensate hysteresis phenomenon. The MDD-based model offers the advantage of small memory consumption, making it suitable for application in memory-constrained scenarios, such as offline deployment of microcontrollers and embedded systems. Meanwhile, the execution time of this model is short and stable, which can be applied in applications requiring a high computational period, such as the precise position control of stick-slip drive motors, the precise speed control of ultrasonic motors, and other scenarios with the presence of high-frequency inputs. The MDD method has the potential to become a general modeling method for solving hysteresis challenges, and can be used by simply modifying the relevant modules according to the hysteresis rules in different domains, such as in the fields of artificial muscles and shape memory alloys.