CSPA 2008 Presentation

[object Object],[object Object],[object Object],[object Object],[object Object]

PRESENTATION OVERVIEW ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

INTRODUCTION ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

INTRODUCTION ,[object Object],[object Object],System Dynamics: Control Effort:

INTRODUCTION ,[object Object],[object Object],[object Object],[object Object]

RESEARCH OBJECTIVE/JUSTIFICATION ,[object Object],[object Object],[object Object],[object Object]

Plant Modeling Overview ,[object Object],[object Object],[object Object],Linear Model Non-Linear (Friction) + - u w 1/s thetha

Friction Experiment. ,[object Object],[object Object],[object Object],[object Object]

THEORY OF SVR ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

INTRODUCTION CONT.’ ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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 ,[object Object],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 ,[object Object],[object Object],C nsv RMSE Positive 2.5 550 0.0005 16(29%) 0.00047403 Negative 1.5 70000 0.00025 32(58%/) 0.00070062

[object Object],[object Object],SVR-FRICTION MODEL RESULTs

SVR MODEL RESULTS CONT.’ ,[object Object]

IMPLEMENTATION FOR COMPENSATION ,[object Object],[object Object],[object Object],[object Object],Input v Predicted ,f

IMPLEMENTATION FOR COMPENSATION ,[object Object],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 ,[object Object],[object Object],[object Object]

SELECTED REFRENCES ,[object Object],[object Object],[object Object],[object Object]

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

CSPA 2008 Presentation

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