Prandtl-Ishlinskii磁滞不确定系统自适应补偿与控制

137 浏览量更新于2024-08-26 1 收藏 331KB PDF 举报

"该文研究了具有Prandtl-Ishlinskii磁滞的不确定系统的自适应补偿和控制策略。文章介绍了如何通过采用Prandtl-Ishlinskii模型来描述智能材料执行器的磁滞现象，并利用间接自适应鲁棒控制方法设计控制器。为减少磁滞效应的影响，论文提出了使用最小二乘法进行在线参数估计，以及利用近似模型进行逆补偿的方法。此外，还对反演误差进行了定量分析，并设计了一个鲁棒控制器来应对系统的不确定性与非线性，以确保系统稳定性。仿真结果验证了所提出的自适应鲁棒控制器在输出跟踪性能上的优越性，以及参数估计的准确性。" 在这篇论文中，作者首先关注的是智能材料如电活性聚合物（EAP）等执行器中存在的磁滞现象。磁滞是这些材料在受力或电压作用下表现出的一种历史依赖行为，即其状态不仅取决于当前的输入，还与过去的输入历史有关。Prandtl-Ishlinskii模型被广泛用于模拟这种非线性的磁滞效应，它通过一系列积分器和延时环节来描述磁滞回线。为了减小磁滞对系统性能的影响，文章提出了一个基于最小二乘法的在线参数估计方法。这种方法能够实时更新模型参数，以更准确地捕捉执行器的实际磁滞特性。同时，为了进一步补偿磁滞，他们引入了一个近似的逆模型。这个逆模型通过对估计参数的处理，帮助控制器抵消执行器的磁滞效应。接下来，论文设计了一个鲁棒控制器，该控制器不仅考虑了系统的不确定性，还考虑了系统的非线性特性。这个控制器的设计目标是确保系统的稳定性，即使在存在未知扰动和非线性的情况下，也能保证系统的性能。通过仿真研究，作者展示了所提自适应鲁棒控制器的有效性。仿真结果显示，控制器能够实现良好的输出跟踪性能，这意味着它可以精确地跟随期望的输入信号。此外，参数估计的准确性也得到了验证，这表明控制器能够准确识别和适应执行器的磁滞行为。这篇论文提供了一种处理具有Prandtl-Ishlinskii磁滞的智能材料执行器不确定性的自适应控制方案。这一方法对于提高依赖于这些执行器的系统性能，如机器人、航空航天设备和其他精密工程应用，具有重要的理论和实践意义。

Adaptive Compensation and Control for Uncertain Systems with

Prandtl-Ishlinskii Hysteresis

Jinwen Zheng, Qinglin Wang, Yuan Li

School of Automation, Beijing Institute of Technology, Beijing, 100081

E-mail: zhijinwen@yeah.net, wangql@bit.edu.cn, liyuan@bit.edu.cn

Abstract: The hysteresis for a class of smart-material-based actuators is represented by adopting Prandtl-Ishlinskii

model and a controller was designed based on the indirect adaptive robust control framework. In order to reduce the

hysteresis effect, least squares method for on-line parameter estimation and the associated approximate model for inverse

compensation are employed. And the inversion error is analyzed quantitatively. A robust controller is then designed to

accommodate uncertain and nonlinearities and make the system stable. The simulation shows that the adaptive robust

controller has not only good output tracking performance but also accurate parameter estimates.

Key Words: Adaptive control, identiﬁcation, Prandtl-Ishlinskii model, hysteresis.

1 INTRODUCTION

In recent years, the smart material such as electro-active

polymer (EAP), shape memory alloy (SMA), has got great

development. Many actuators based on smart-material e-

merged [1-3]. However, hysteresis effect exists widely

in the smart-material-based actuator (SMBA) system. It

would lead to poor tracking accuracy or even instability and

self-sustaining oscillation. So the essential control prob-

lem for SMBA is how to deal with the hysteresis nonlin-

earity. The common hysteresis models are Preisach model,

Prandtl-Ishlinskii (P-I) model and Bouc-Wen model. The

general method that deals with the hysteresis method is to

use the inverse hysteresis model for compensation to atten-

uate hysteresis effect. Unfortunately, it is difﬁcult to cal-

culate the inverse model of Preisach model. The existing

adaptive techniques generally require a linear parameteri-

zation of the plant dynamics[4]. Bouc-Wen model does not

have this property, though the inverse model of Bouc-Wen

model can be got analytically [5]. The P-I model has not

only analytical inverse model but also the property of lin-

ear parameterization. So P-I model is widely applied to

represent hysteresis of SMBA.

Reference[6]adopts back-stepping adaptive control

scheme, and references[7-9]use adaptive sliding model

control scheme. These methods belong to direct adaptive

robust control. The advantage of these methods is that it

can make the plants achieve good output tracking perfor-

mance. But it has a poor ability on parameter estimation.

Reference [10]applies off-line parameter estimation and

adopts sliding model control to attenuate the inversion

error. The shortcoming of this control strategy is that the

work of off-line identiﬁcation is tedious and the designer

should design the controller again when the size of actu-

ator changed. Reference[11, 12]research the method of

This work is supported by National Nature Science Foundation under

Grant 61375100 and 61472037.

parameter estimation of hysteresis system, but the control

schemes is not given.

In this paper, we apply the indirect adaptive robust con-

trol (IARC) scheme. This control scheme is widely used in

hydraulic manipulators[13, 14]. In IARC framework, the

design of parameter estimator and the design of controller

are relatively independent. The parameter estimator is al-

ways designed based on least squares method or gradient

method. And a robust controller is used to attenuate the

uncertain of system. The advantage of this method is that

it can enable the plants achieve not only excellent track-

ing performance but also accurate parameter estimates for

secondary application such as fault diagnosis[14]. In this

paper, we use least squares estimator and sliding mode con-

troller.

2 PRANDTL-ISHLINSKII MODEL

Because P-I model[15] is deﬁned based on play operator,

the play operator is introduced ﬁrstly. Let C

[0,t

] denotes

the space of piecewise monotone continuous function on

[0,t

]. For all u(t) ∈ C

[0,t

], there exists a partition of

[0,t

] denoted by 0 = t

< t

< ... < t

= t

such that

u(t) is monotone on each subinterval [t

i+1

]. Then, the

play operator is deﬁned as follows:

⎧



⎨



⎩

[u,

](0)= f

(u(0),

[u,

](t)= f

(u(t), P

[u,

](t

));

< t ≤t

i+1

, 0 ≤ i < N

(u, w)=max(u −r, min(u + r, w)).

(1)

where r > 0 is threshold,

is the initial value, u(t) is the

input of the operator and P

[u,

](t) is the output of the

operator. The simulation experiment shows that the initial

value does not affect the shape of the hysteresis loop. And

if the actuator starts from its de-energized state, the initial

condition can be set to zero [16]. So we assume

= 0 and

let P

[u](t) := P

[u, 0](t) .

1344

978-1-4799-7016-2/15/$31.00

2015 IEEE

下载后可阅读完整内容，剩余5页未读，立即下载

weixin_38742453

粉丝: 15
资源: 945

Prandtl-Ishlinskii磁滞不确定系统自适应补偿与控制

preisach迟滞模型-preisach_model.mdl

Hystersis 模块：Simulink 模块生成迟滞回线-matlab开发

rbf神经网络自适应控制MATLAB仿真的单独代码.rar

Prandtl-Ishlinskii模型下的磁滞线性执行器自适应滑模控制

使用Prandtl-Ishlinskii模型的磁滞线性执行器的自适应滑动模型控制

Prandtl-Ishlinskii回滞模型在连续系统控制中的应用

prandtl-ishlinskii 迟滞模型 matlab代码

我们在整个所需轨迹上开发了迭代学习控制的收敛标准，以获得滞后补偿滞后系统中的前馈输入。 在分析中，利用Prandtl-Ishlinskii模型来捕获

使用扩展的无平行Prandtl–Ishlinskii磁滞补偿器的压电致动微位移台的前馈摩擦级比例积分-导数反馈控制

压电致动微位移台摩擦控制：扩展的无平行Prandtl–Ishlinskii磁滞补偿器

最新资源

我们在整个所需轨迹上开发了迭代学习控制的收敛标准，以获得滞后补偿滞后系统中的前馈输入。在分析中，利用Prandtl-Ishlinskii模型来捕获