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.

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.

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.

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

Modeling and Analysis of Spatial Flexible Mechanical Systems With a Spherical Clearance Joint Based on the LuGre Friction Model

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Xiao Tan ◽  
Guoping Chen ◽  
Hanbo Shao
Keyword(s):  
Mechanical Systems ◽  
Beam Element ◽  
Friction Model ◽  
Lugre Friction Model ◽  
Clearance Joint ◽  
Lugre Friction ◽  
Computational Methodology ◽  
Crank Mechanism ◽  
Flexible Components

Abstract A computational methodology for modeling spatial flexible mechanical systems with stick-slip friction in a spherical clearance joint is presented. A modified three-dimensional (3D) absolute nodal coordinate formulation based shear deformable beam element with two nodes is proposed and employed to discretize the flexible components. To avoid locking problems, we employed an enhanced continuum mechanics approach to evaluate the beam element elastic forces. The strain components εyz, εyy, and εzz are approximated using linear interpolation to improve the computational efficiency while the loss of accuracy is acceptable. The contact and friction forces in a spherical clearance joint were evaluated by the hybrid contact and LuGre friction models, respectively. Three numerical examples are presented and discussed. A simple pendulum was utilized to prove the correctness of the modified beam element. A classical slider–crank mechanism was employed to validate the computational methodology. A spatial rigid–flexible slider–crank mechanism with a spherical clearance joint was used to investigate the effect of link flexibility and joint clearance on the dynamic behavior of mechanical systems. Using the LuGre friction model, we reproduced the Stribeck effect as it is expected in real world settings. The components with appropriate stiffness play the role of suspension for spatial mechanical systems with imperfect joints. The vibrations of the flexible components play an active role of intensifying the collision in kinematic joint with clearance.

scholarly journals Study on the Low Velocity Stability of a Prostate Seed Implantation Robot’s Rotatory Joint

Electronics ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 284 ◽  
Author(s):  
Bing Li ◽  
Yongde Zhang ◽  
Lipeng Yuan ◽  
Xiaolin Xi
Keyword(s):  
Prostate Cancer ◽  
Parameter Identification ◽  
Control Method ◽  
Friction Model ◽  
Friction Torque ◽  
Low Velocity ◽  
Seed Implantation ◽  
Compensation Control ◽  
Lugre Friction Model ◽  
Lugre Friction

Prostate cancer has one of the highest incidences of male malignant tumors worldwide. Its treatment involves the robotic implantation of radioactive seeds in the perineum, a safe and effective procedure for early, low-risk prostate cancer. In order to ensure precise positioning, the seed implantation needle is set at low terminal velocity. In this paper, the motion output position instability caused by the friction torque of the robot’s motor and rotating joint during low velocity motion was analyzed and studied. This paper also presents a compensation control method based on the LuGre friction model, which offers piecewise parameter identification with GA-PSO. First, based on an analysis of its structure and working principle, the friction torque model of the robotic system and the torque model of the driving motor are established, and the influence of friction torque on motion stability analyzed. Then, based on experimental data of the relationship between velocity and friction torque for no-friction compensation, the velocity point of the minimum torque of the rotating joint and the critical Stribeck velocity point were used for segmental parameter identification; cubic spline interpolation was used for segmental fitting. Furthermore, on the basis of the LuGre model identification method, parameter identification of the genetic algorithm-particle swarm optimization, and compensation control of the LuGre friction model, a control method is analysed and set forth. Malab2017a/Simulink simulation software was used to simulate and analyze the control method, and verify its feasibility. Finally, the cantilever prostate seed implantation robot system was tested to verify the effectiveness of the segmented identification method and the compensation control strategy. The results reveal that motion output position stability at low velocity meets the requirements of the cantilever prostate seed implantation robot, thus providing a vital reference for further research.

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