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首页速率依赖的压电执行器磁滞建模与控制研究
本文主要探讨了压电执行器中与速率相关的磁滞现象的建模与控制。压电材料在电磁能量转换过程中表现出显著的速率依赖性,即其输出位移对输入电压变化率的敏感度。为了准确地理解和管理这种特性,研究者提出了一个基于Prandtl-Ishlinskii模型的速率依赖建模方法。 Prandtl-Ishlinskii模型是一种经典的方法,用于描述材料的非线性行为,特别是磁滞回线中的滞回效应。在这个模型中,动态阈值和权重值的概念被引入,它们分别反映了输入电压速率对磁滞行为的影响程度。动态阈值随速度的变化而调整,而权重值则衡量了不同速率下的响应强度差异。 作者首先构建了该模型,通过将输入电压的速度作为参数,考虑了速率对磁滞曲线的影响。然后,他们通过对比理论预测的输出响应与实际测量的压电执行器在不同输入频率下的实验数据,验证了所提出的速率依赖Prandtl-Ishlinskii模型的有效性。这一步骤对于确保模型的准确性和实用性至关重要,因为它允许研究人员了解模型在实际工作条件下的性能。 进一步,研究者还探讨了一种带有反向馈控制的策略,目的是抵消或减少由于速率依赖性引起的输出误差。这种控制器能够预见并补偿由于输入电压变化率改变导致的磁滞效应,从而提高系统的稳定性和精度。这对于设计高性能的压电驱动系统,特别是在需要快速响应或精密定位的设备中,具有重要的工程应用价值。 这篇研究论文深入剖析了压电执行器中速率依赖磁滞的内在机制,并提出了一种有效的建模和控制策略。这对于优化压电系统的动态性能、提升其在自动化和精密机械领域的应用有着深远的影响。未来的研究可能进一步探索如何优化控制器的设计,以实现更高效、鲁棒的压电执行器系统。
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Modeling and Control of Rate-Dependent Hysteresis in
Piezoelectric Actuators
ZHANG Guilin
1
, ZHANG Chengjin
2
, GU Jason
1,3
1. School of Control Science and Engineering, Shandong University, Jinan 250061, China
E-mail: zhanggueilin0531@163.com
2. School of Mechanical, Electrical and Information Engineering, Shandong University at Weihai, Weihai 264209, China
E-mail: cjzhang@sdu.edu.cn
3. Electrical and Computer Engineering, Dalhousie University, Halifax B3J2X4, Canada
E-mail: jgu@dal.ca
Abstract: Piezoelectric actuators show dependency of the output displacement on the rate of change of the applied input volt-
age. In this paper, a rate-dependent Prandtl-Ishlinskii model is developed to characterize the time-dependent hysteresis in the
piezoelectric actuators. This model employs the dynamic threshold and weighting values formulated on the speed of the input
voltage. The validation of the rate-dependent Prandtl-Ishlinskii model is demonstrated by comparing its out responses with the
measured responses obtained for a piezoelectric actuator under different input frequencies.Finally, a feedforward controller with
an inverse rate-dependent Prandtl-Ishlinskii model is designed to account for the dynamic hysteresis. The results show that the
hysteresis nonlinearities are significantly reduced at both the lower and higher frequencies.
Key Words: Piezoelectric actuator, Rate-dependent hysteresis, Prandtl-Ishlinskii model
1 Introduction
Piezoelectric actuators are widely used in micro-
nanopositioning applications. However, these actuators
generally exhibit strong hysteresis nonlinearity in their
output response [1, 2]. Such nonlinearity often limits system
performance.
Several models have been proposed to describe and com-
pensate for the hysteresis effect in piezoelectric actua-
tors.The most well-known hysteresis model is the Preisach
model. In Preisach model, hysteresis is modeled as a super-
position of all possible Preisach operators, which are param-
eterized by a pair of threshold variables [3, 4]. Two other
popular hysteresis models are Krasnosel”skii-Pokrovskii
(KP) model and Prandtl-Ishlinskii (PI) model, both of them
are derived from the Preisach model. The KP model in-
tegrates a density function and KP operators [5, 6]. The
difference between the Preisach operator and the KP oper-
ator is that the delayed relay elements in the KP operator
have the finite slopes. The PI model employs a combination
of several elementary play operators. which are parameter-
ized by a single threshold variable[7–9]. Mentioned models
above have been widely applied for characterizing the rate-
independent hysteresis nonlinearity. However, experimental
results show that hysteresis effect of piezoelectric actuators
is a rate-dependent phenomenon, which is strongly depend-
ing on the rate of change of the applied input voltage. There-
fore, such models have to be modified for the applications
with high-frequency input voltage.
Research on modeling rate-dependent hysteresis nonlin-
earity in piezoelectric actuators has received attention in re-
cent years [10–16]. Xu and Wong [10] applied the input
value and the input variation rate as the input data of the least
squares supprots vector machines (LV-SVM) model to char-
acterize the rate-dependent hysteresis phenomenon. Wei et
This work is supported by the National Natural Science Foundation of
China (61174044) and the Shandong Province Natural Science Foundation
(ZR2010FM016).
al. [11] proposed a rate-dependent PI model by introducing
a dynamic weighting values. Gu and Zhu [14] used a family
of ellipses function to describe the rate-dependent hystere-
sis effect. Janaideh [15] utilized rate-dependent threshold to
characterize the dynamic hysteresis nonlinearity.
The best way of compensating for hysteresis effect is to
employ a hysteresis inverse to cancel out it. In this pa-
per, we present the inverse rate-dependent PI model and use
this inverse as a feedforward controller to account for the
the rate-dependent hysteresis nonlinearities in a piezoelec-
tric actuator. The main contents of this paper are as follows.
Firstly, the rate-independent play operator together with the
weighting values are modified and applied to derive a rate-
dependent PI model. Secondly, since the inverse of the PI
model is computed analytically, we utilize the inverse rate-
dependent PI model as a feedforward controller to cancel
out the hysteresis effect. Finally, the experimental results
show that the tracking performances are obviously improved
at both the lower and higher frequencies.
1.1 Prandtl-Ishlinskii Model
PI model is a phenomenological method for describing
rate-independent hysteresis effect. This method employs a
combination of several linear play operators P
r
as shown in
Fig. 1. The output of play operator P
r
is given by the fol-
lowing mathematical formula:
P
r
[v](t) = max(v(t) − r, min(v(t)+r, P
r
[v](t − T ))
P
r
[v](0) = max(v(0) − r, min(v(0) + r, y
0
)
(1)
where v(t) denotes the input voltage, P
r
is the output of the
operator, r is the input threshold value and T is the sampling
time, y
0
denotes the initial condition of the operator.
PI model integrates a linearly weighted superposition of
several play operators with different threshold and weight-
ing values. The output of Prandtl-Ishlinskii model can be
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1929
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