Stability Analysis of Input-Output Linearization Control With LuGre Friction Model Using Lyapunov Exponents

2015 ◽  
Author(s):  
Yun-Hsiang Sun ◽  
Christine Qiong Wu
Keyword(s):  
Control System ◽  
Stability Analysis ◽  
Lyapunov Exponents ◽  
Friction Model ◽  
System Stability ◽  
Control Law ◽  
Input Output ◽  
Lugre Friction Model ◽  
Lugre Friction ◽  
Input Output Linearization

This work performs stability analysis on a control system partially modeled by LuGre friction model. Such a friction model has been proved sufficient to account for many features of friction. However, two parameters in the friction model, σ0 and σ1, are extremely difficult to be identified in real-world applications and the parameter errors (disturbances) coming from the measurements are therefore expected. In this work, we present a systematic methodology to rigorously analyze the effect of the disturbances mentioned above on the control system stability. The obtained analysis result clearly shows the robustness of the selected control law (input-output linearization control law). Lyapunov exponents calculated for two disturbed systems and our stability analysis result are in good agreement. The proposed methodology can be applied to other control laws of interest to examine their robustness.

LuGre Friction Model Based Adaptive Control With Functional Approximation Compensation for a Piezoelectric-Actuating Table

2010 ◽  
Author(s):  
Shiuh-Jer Huang ◽  
Kuan-Lian Her ◽  
Su-Hai Hsiang
Keyword(s):  
System Modeling ◽  
Friction Model ◽  
Hysteretic Behavior ◽  
System Stability ◽  
High Frequency Oscillation ◽  
Control Voltage ◽  
Functional Approximation ◽  
Model Based ◽  
Lugre Friction Model ◽  
Lugre Friction

Since the piezoelectric actuators have the disadvantages of small travel and hysteretic behavior, a long range friction actuating mechanism was designed. The piezoelectric material is used to generate high frequency oscillation for actuating a finger tip which contacted with a slide to induce the back and forth motion. The LuGre friction model is chosen to simulate the dynamics of this friction actuating mechanism. However, this piezoelectric actuating system has obvious nonlinear and time-varying dead-zone offset control voltage due to the static friction and preload. It is difficulty to establish an accurate dynamic model for model-based precision control design. Hence, the functional approximation (FA) scheme is employed to compensate the system modeling error. The Laypunov-like design strategy is adopted to derive the adaptive laws and the system stability criterion. Different trajectories tracking control are planned to investigate the motion control performance and the steady state error of this adaptive controller. The dynamic experimental results of the proposed controller are compared with that of a model-based PID controller.

Modeling and Control Design for a Wheeled Mobile Platform

2013 ◽  
Author(s):  
Byungchan Jung ◽  
Henryk Flashner ◽  
Jill McNitt-Gray
Keyword(s):  
Static Friction ◽  
Friction Model ◽  
Control Law ◽  
Modeling And Control ◽  
Lugre Friction Model ◽  
Backstepping Approach ◽  
Tracking Controllers ◽  
Friction Models ◽  
Lugre Friction ◽  
And Control

A model of a wheeled platform that includes slipping is formulated. Slipping is modeled by adopting the LuGre friction model. This is a dynamic friction model that can reproduce realistic friction phenomena not present in static friction models. Using the backstepping approach, tracking controllers for non-slipping and slipping cases are developed and compared via simulation. The proposed control law is designed to be robust with respect to the change in system parameters such as the platform’s mass and moment inertia. Simulation results show good performance for point stabilization in specific destination postures, as well as for tracking.

LuGre Friction Model Estimation of a Precision Table and Sliding Mode Control Design

2009 ◽  
Vol 147-149 ◽  
pp. 264-271
Author(s):  
Shiuh Jer Huang ◽  
Chun Ming Chiu ◽  
M.C. Huang
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Control Design ◽  
Friction Model ◽  
System Stability ◽  
Adaptive Sliding Mode Control ◽  
Model Based ◽  
Mode Control ◽  
Lugre Friction Model ◽  
Lugre Friction

Piezoelectric friction actuating mechanism is chosen to construct long traveling range sub-micro X-Y positioning table. LuGre friction model is employed to simulate the friction dynamics of this positioning mechanism. The optimization scheme of Matlab toolbox is adopted to search the optimal friction model parameters. However, this piezoelectric actuating system has obvious nonlinear and time-varying dead-zone offset control voltage due to the static friction and preload. The estimated LuGre dynamic model is still not accurate enough for model-based precision control design. Hence, the adaptive sliding mode control (SMC) with robust behavior is employed to design the nonlinear controller for this piezoelectric friction actuating mechanism. The Laypunov-like design strategy is adopted to achieve the system stability criterion. The dynamic experimental results of the proposed nonlinear controllers are compared with that of a model-based PID controller, too.

scholarly journals Asymmetric and chaotic responses of dry friction oscillators with different static and kinetic coefficients of friction

Meccanica ◽  
2021 ◽  
Author(s):  
Gábor Csernák ◽  
Gábor Licskó
Keyword(s):  
Dry Friction ◽  
Continuation Method ◽  
Friction Model ◽  
Lugre Friction Model ◽  
Kinetic Coefficients ◽  
Friction Oscillator ◽  
Lugre Friction ◽  
Friction Parameters ◽  
Two Parameter ◽  
Parameter Bifurcation

AbstractThe responses of a simple harmonically excited dry friction oscillator are analysed in the case when the coefficients of static and kinetic coefficients of friction are different. One- and two-parameter bifurcation curves are determined at suitable parameters by continuation method and the largest Lyapunov exponents of the obtained solutions are estimated. It is shown that chaotic solutions can occur in broad parameter domains—even at realistic friction parameters—that are tightly enclosed by well-defined two-parameter bifurcation curves. The performed analysis also reveals that chaotic trajectories are bifurcating from special asymmetric solutions. To check the robustness of the qualitative results, characteristic bifurcation branches of two slightly modified oscillators are also determined: one with a higher harmonic in the excitation, and another one where Coulomb friction is exchanged by a corresponding LuGre friction model. The qualitative agreement of the diagrams supports the validity of the results.

Wheel independent-drive control based on dynamic tire LuGre friction model

2008 ◽  
Author(s):  
Ruan Jiuhong ◽  
Yang Fuguang ◽  
Qiu Xuyun ◽  
Li Yibin
Keyword(s):  
Friction Model ◽  
Lugre Friction Model ◽  
Drive Control ◽  
Lugre Friction
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