Minimal modeling methodology to characterize non-linear damping in an electromechanical system

This paper presents a minimal modeling methodology for capturing highly non-linear dynamics in an electromechanical cart system. A theoretical foundation for the method is given including a proof of identifiability and a numerical example to demonstrate the theory. 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 non-linear model reduced the mean absolute prediction error by a factor of three. 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. Computationally, the proposed algorithm is shown to be significantly faster than standard non-linear regression.