A continuous extension of the LuGre friction model with application to the control of a pneumatic servo positioner

Sobczyk, Mario; Perondi, Eduardo André; Cunha, Mauro André Barbosa

doi:10.1109/cdc.2012.6426406

Cited by 6 publications

(7 citation statements)

References 26 publications

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“…We introduce S u = 2 π arctan(K u U[n]) and define it as a smoothness coefficient based on the inverse trigonometric function. In order to obtain a MLM of the continuum type and maintain its own model structure, we introduced (24) to obtain the MLM with reference to [34] and verified its effectiveness in improving the model's stability with simulation experiments. The expressions of MLM in the discrete time domain are as follows:…”

Section: Improvement Of Model Stabilitymentioning

confidence: 99%

Hysteresis modeling and analysis of piezoelectric actuators using a modified LuGre model at different preloads and frequencies

Gan,

Zhang,

et al. 2024

Smart Mater. Struct.

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Despite a large of models proposed to characterize the nonlinear hysteresis of piezoelectric actuators, few of them can show the effects of different preloads on the nonlinear hysteresis. In this paper, a modified LuGre model is presented for piezoelectric actuators under different preloads to accurately characterize its dynamic hysteresis nonlinearity at different frequencies. Based on the classical LuGre model,the presented model introduces infinite impulse response(IIR) filters and smoothness coefficient to simplify it. The parameters of the models were identified by the non linear least squares method. A series of experiments were conducted to verify the validity of the modified LuGre model under different preloads at different frequencies excitation signals.In the constant frequency experiments under different preloads, the modified LuGre model reduces the mean error by 68.1% − 81.9% compared with the classical LuGre model; In the constant preload experiments at different frequencies, the modified LuGre model reduces the mean error by 72.2%−83.0% and 65.9%−83.2% compared with the classical Bouc-Wen model and the classical LuGre model.

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Section: Improvement Of Model Stabilitymentioning

confidence: 99%

Hysteresis modeling and analysis of piezoelectric actuators using a modified LuGre model at different preloads and frequencies

Gan,

Zhang,

et al. 2024

Smart Mater. Struct.

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“…However, this model contains discontinuous terms in its original form, which cannot be resolved for certain classes of systems or controllers that require the time derivative of the estimated friction force. The continuous extension of the LuGre model proposed in solves this problem by introducing continuous and differentiable approximations of the discontinuous terms, such that the passivity and boundedness of the internal states are not affected. This model is represented by the following equations,

\begin{matrix} aligned \\ right ż & left = S_{1} ω - α MathClass-open(ω MathClass-close) S_{2} z, & right \\ right F & left = σ_{o} z + σ_{1} ż + σ_{2} S_{1} ω, \\ right α MathClass-open(ω MathClass-close) & left = \frac{1}{F_{C} + (F_{S} - F_{C}) e^{- {(\frac{ω}{x_{s}})}^{2}}}, \end{matrix}

where z is the friction state, x S is the Stribeck velocity, and F S and F C are the static friction and dynamic friction forces, respectively.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Remark We note that according to LuGre model, the dynamics of z are given by

\begin{matrix} leftalign-star \\ rightalign-odd ż = ω - α MathClass-open(ω MathClass-close) | ω | z . & align-even & rightalign-label \end{matrix}

In , the authors propose first : | ω | = ω × sign ( ω ) ≈ S 0 ( ω ) ω , with S 0 ( ω ) = tanh( k v ω ) and k v > 0. This implies the following dynamics of z

\begin{matrix} leftalign-star \\ rightalign-odd ż = ω - ω \times α MathClass-open(ω MathClass-close) S_{0} MathClass-open(ω MathClass-close) z . & align-even & rightalign-label \end{matrix}

to obtain a nontrivial equilibrium condition

z (t) MathClass-rel= \frac{1}{α (ω) S_{0} (ω)} MathClass-rel\to MathClass-rel\infty MathClass-punc, when ω MathClass-rel\to 0 MathClass-punc.

In order to solve this problem, the following dynamics have been proposed

\begin{matrix} leftalign-star \\ rightalign-odd ż & align-even = S_{1} ω - α MathClass-open(ω MathClass-close) S_{2} z & rightalign-label & align-label \end{matrix}

As in , we propose to introduce the term S 1 in friction force F

\begin{matrix} leftalign-star \\ rightalign-odd F = σ_{o} z + σ_{1} ż + σ_{2} ω & align-even & rightalign-label \end{matrix}

to obtain …”

Section: Problem Formulationmentioning

confidence: 99%

Adaptive backstepping output feedback control of DC motor actuator with friction and load uncertainty compensation

Ahmed

Laghrouche

Harmouche

2014

Intl J Robust & Nonlinear

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SummaryIn this paper, we present an output feedback backstepping controller for mechatronic actuators with dynamic adaptive parameters for friction and load compensation. The targeted application is angular position control of automotive mechatronic valves, which possess nonlinear dynamics due to friction. The proposed controller requires only position measurement. The velocity, current, and friction dynamics are obtained by estimation and observation. The adaptive control law compensates the variations in friction behavior and load torque variation, which are common in real life applications. Lyapunov analysis has been used to show the asymptotic convergence of the closed‐loop system to zero. Simulation and laboratory experimental results illustrate the effectiveness and robustness of the controller. Further experiments on an engine test bench demonstrate the applicability of this controller in commercial engines, as well as its effectiveness as compared with conventional PI controllers.Copyright © 2014 John Wiley & Sons, Ltd.

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“…The modeling of pneumatic servo systems is discussed in many different works [1,2,5]. The model used in this work is developed in detail in [7,8]. Essentially, the system consists of a pressure source, a piston and correspondent load, and a servovalve.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…where M is the mass of the piston-load assembly, y is the acceleration of the piston, f is the friction force, A is the cylinder cross-sectional area, and 1 p and 2 p are the pressures in the two chambers. The friction force is represented by means of a continuous approximation of the LuGre model [8,9], which is largely employed in control applications [2,8,10,11]. The approximation used in this work was developed specifically for systems where the control signal affects the time derivative of the developed mechanical forces, such as hydraulic and pneumatic actuators [1,2,3,5,6,8].…”

Section: Mathematical Modelmentioning

confidence: 99%

Friction-Compensating Feedback Linearization Control Applied to a Pneumatic Servo System

Sobczyk

Suzuki

Sarmanho

et al. 2014

AMR

Self Cite

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This work proposes a feedback linearization control algorithm to be applied to a pneumatic positioning system. Such algorithm aims to compensate the undesirable effects due to the highly nonlinear dynamic behavior of such type of actuator. A mathematical model of the system is presented and the proposed controller is described. Besides, an analysis is provided of the convergence properties of the closed-loop tracking errors of the system when such controller is used. The main features of the proposed controller are illustrated by means of experimental results and respective discussions.

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A continuous extension of the LuGre friction model with application to the control of a pneumatic servo positioner

Cited by 6 publications

References 26 publications

Hysteresis modeling and analysis of piezoelectric actuators using a modified LuGre model at different preloads and frequencies

Hysteresis modeling and analysis of piezoelectric actuators using a modified LuGre model at different preloads and frequencies

Adaptive backstepping output feedback control of DC motor actuator with friction and load uncertainty compensation

Friction-Compensating Feedback Linearization Control Applied to a Pneumatic Servo System

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