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FRICTION MODELING AND COMPENSATION IN MOTION CONTROL SYSTEM USING SVR Tijani, I.B., Wahyudi M., and Talib H.H. Presentation @ CSPA 2009 BY Tijani, I.B.

PRESENTATION OVERVIEW INTRODUCTION METHODOLOGY OF SVR OVERVIEW DEVELOPMENT OF SVR-MODEL IMPLEMENTATION FOR COMPESATION RESULTS CONCLUSION REFERENCES

INTRODUCTION Background : The interest in the study of friction in control engineering has been driven by the need for precise motion control in most of the industrial applications such as machine tools, robot systems, semiconductor manufacturing systems and Mechatronic systems. Effects of Friction in motion control system: (Armstrong, 1994) makes the motion of a positioning system slow causes steady state error or limit cycles near the reference position Generally, Friction: is inherently present in all machines/systems incorporating parts with relative motion is characterized with complex nonlinear behaviors: stiction, Stribeck, friction lag, dwell time and d epends on factors such as: Temperature, Contact geometry, Surface materials, Presence and type of lubrication, and Relative motion

INTRODUCTION The need for its compensation and precise modeling : Model-Based Approach, and problem of model selection! System Dynamics: Control Effort:

INTRODUCTION Problem Statement: For Model-based friction, there is not yet a universally accepted model for friction. Hence selection of model thus remains problem-dependent, and selecting appropriate and accurate model from pool of available models (Tustin, Lorentzian,Gaussian,Polynomial,seven parameter, Dahl, Lugre, Luven, GMS, etc) for a particular application is challenging (in terms of time, computational efforts etc) due to complexity of parametric modeling of the friction nonlinearities.

RESEARCH OBJECTIVE/JUSTIFICATION A non-parametric friction model based on Artificial Intelligent using einsensitivity support vector regression ( -SVR) is proposed and developed in this work for the identification and compensation of friction in motion control system. The work has been necessitated by the need for simple and yet efficient model-free representation of friction. the choice of SVR has been motivated by its unique qualities in approximating nonlinear function among AI-paradigms, and Also, SVR has not been extensively explored compared to ANN in friction modeling as indicated in the literatures reviewed.

Plant Modeling Overview Experimental Plant Linear Model Friction Model Linear Model Non-Linear (Friction) + - u w 1/s thetha

Friction Experiment. Experimental Set-up: With MATLAB Xpc-Target Interface Break-away experiment : to yield friction torque @ v=0 Steady state Friction-Velocity experiment: measuring armature current for several steady state velocities in the range and Friction Experiments: for friction-velocity data

THEORY OF SVR Generally, given a set of N input/output data such that and the goal of SVR learning theory is to find a function which minimizes the expected risk: (1) Where is loss function is unknown probability distribution function Since function P is unknown, expression (1) can not be directly computed, hence unlike traditional Empirical risk minimization principle that minimizes only the empirical risk(training error),statistical learning theory seeks to obtain a small risk in terms of both training error and model complexity by minimizing the regularized risk function (structural risk function); (2)

INTRODUCTION CONT.’ Where is the regularization term(or complexity penalizer) used to find the flattest function with sufficient approximation qualities, and is empiric risk defined as: (3) Using e-insensitivity loss function proposed by Vapnik (1995) ,[1]: (4) the goal of the function estimation in -SVR is thus to minimizes; (5)

METHODOLOGY OF SVR Mapping the input space to High dimensional space using the Kernel trick Subject to Formulation of the Constrained Optimization problem in the primal weight space Using

METHODOLOGY OF SVR CONT.’ Formulating the Lagrangian Applying the conditions for optimal solution Solve the Dual Optimization Problem with QP Subject to

DEVELOPMENT OF SVR-FRICTION MODEL MODELING STEPS Kernel Selection Parameters Combinations(rho,C,and e ) Start Computing the Lagrange multipliers,nsv,and bias term Computing the Decision Function(SVR model) Model Validation Model Selection(RMSE,and nsv) END Input Data Partitioning Friction-Velocity Data Pairs

DEVELOPMENT OF SVR-FRICTION MODEL The steps was implemented with MATLAB codes written with reference to the original SVM MATLAB Toolbox codes by Gun[2]. After 50 and 30 parameters combinations for positive and negative directions respectively, the combinations with least RMSE and at the same time smallest number of support vectors (nsv) were selected as reported below: C nsv RMSE Positive 2.5 550 0.0005 16(29%) 0.00047403 Negative 1.5 70000 0.00025 32(58%/) 0.00070062

SVR Friction Model Learning for Negative Motion Positive Negative SVR-FRICTION MODEL RESULTs

SVR MODEL RESULTS CONT.’ Combine SVR-Model with Validation Data Set

IMPLEMENTATION FOR COMPENSATION For MATLAB Real-time implementation of the Developed SVR model, the computed Lagrange multipliers and bias were integrated in an Embedded Matlab function: Input Kernel Computation Output computation Input v Predicted ,f

IMPLEMENTATION FOR COMPENSATION Experimental Set-up For Position Control: Combine SVR-Models

RESULTS: PTP Positioning Control 1 Degree Step Input 0.5 Degree Step Input

RESULTS: PTP Positioning Control Friction Compensators STEP INPUTS Positive Inputs Negative Inputs 0.5-deg. 1-deg. -0.5-deg. -1-deg. ess(%) Tr(sec.) ess(%) Tr(sec.) ess(%) Tr(sec.) ess(%) Tr(sec.) No Compensator 37.6 Inf. 7.6 0.017 44.26 inf. 21 0.017 v -SVR 0.8 0.01 0.4 0.015 0.8 0.013 0.4 0.013 % Reduction in steady state error 97.8 94.7 98.2 98.1

RESULTS: Tracking Positioning Control 0.5 Degree,1Hz Sine Reference Position error comparison

RESULTS: Tracking Positioning Control 1 Degree,1Hz Sine Reference Position error comparison Friction Compensators Root Mean Square Errors (RMSE) 0.5-deg 1-deg. No Compensator 0.0656 0.0874 v -SVR Model 0.0322 0.0530 % reductionin RMSE 50.9 39.35

CONCLUSION SVM based friction model with exponential kernel function was successfully developed and implemented for friction compensation in PTP and Tracking motion control. The results obtained for modeling and compensation show SVR as a viable and efficient technique in representing and compensating frictional effects in motion control system. However, the non-smoothness in the tracking responses especially at low reference input was attributed to the effect of velocity estimation and imperfection of the sensor used in the compensation scheme. This could be improved upon with the use of more efficient position sensor and/or observer based estimation or other more sophisticated velocity estimation scheme.

SELECTED REFRENCES 1. Armstrong-Helouvry B., Control of Machines with Friction, Boston, MA, Kluwer, 1991 2. Armstrong-Helouvry B., Dupont P. and De Wit C., “A survey of models, analysis tools and compensation method for the control of machines with friction”, Automatica, Vol. 30, No. 7 (1994) pp. 1083-1138. 3. V. Vapnik. The Nature of Statistical Learning Theory. Springer, New York, 1995. 4. S. R. Gunn. Support Vector Machines for Classification and Regression. Technical Report, Image Speech and Intelligent Systems Research Group, University of Southampton, 1997.

THANK YOU VERY MUCH “ Had however this friction really existed, in the many centuries that these heavens have revolved they would have been consumed by their own immense speed of everyday…” Leonardo da Vinci (1452-1519) The Notebooks 56 V

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