Non linear electromechanical cart characterization using minimal modeling approach

This paper presents a minimal modelling methodology for capturing highly non-linear dynamics in an electromechanical cart system. The second order differential equation model describing the cart system is reformulated in terms of integrals to enable a fast method for identification of both constant and time varying parameters. The model is identified based on a single experimental proportional step response and is validated on a proportional-derivative (PD) controlled step input for a range of gains. Two models with constant damping and time varying non-linear damping were considered. The fitting accuracy for each model was tested on three separate data sets corresponding to three proportional gains. The three data sets gave similar non-linear damping models and in all cases the non-linear model gave smaller fitting errors than the linear model. For the PD control responses, the constant damping model gave a higher average percentage prediction errors than the non-linear model. The non-linear model also provided significantly better PD control design. These results demonstrate the ability of the proposed method to accurately capture significant non-linearities in the data.