  In order to provide robust, reliable, and accurate position and velocity
control of motor drives, friction compensation has emerged as a key difficulty.
Non-characterised friction could give rise to large position errors and
vibrations which could be intensified by stick-slip motion and limit cycles.
This paper presents an application of two data-driven nonlinear model
identification techniques to discover the governing equations of motor dynamics
that also characterise friction. Namely, the extraction of low-power data from
time-delayed coordinates of motor velocity and sparse regression on nonlinear
terms was applied to data acquired from a Brushless DC (BLDC) motor, to
identify the underlying dynamics. The latter can be considered an extension of
the conventional linear motor model commonly used in many model-based
controllers. The identified nonlinear model was then contrasted with a
nonlinear model that included the LuGre friction model and a linear model
without friction. A nonlinear grey box model estimation method was used to
calculate the optimum friction parameters for the LuGre model. The resulting
nonlinear motor model with friction characteristics was then validated using a
feedback friction compensation algorithm. The novel model showed more than 90%
accuracy in predicting the motor states in all considered input excitation
signals. In addition, the model-based friction compensation scheme showed a
relative increase in performance when compared with a system without friction
compensation.
