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A method of compensating for friction in control systems is presented. The method entails the use of an observer to estimate the friction which is modeled as a constant times the sign of the velocity. The purpose of the observer is to estimate this constant. The observer model is selected to ensure that the error in estimation of the friction constant converges asymptotically to zero. Simulation results verify the theory and show that the method can significantly improve the performance of a control system in which it is used. Although based on the assumption of a constant friction magnitude, the observer displays the ability to 'track' friction whose magnitude depends on velocity.>
Friedland et al. (Wed,) studied this question.