Neural Network modeling of forward and inverse behavior of rotary MR damper

Magneto-rheological (MR) dampers have received considerable attention within the last decades, mainly because of their design simplicity, low power requirements, large force range and robustness. The most common models to describe the dynamic MR damper behavior are the Bouc-Wen model, the LuGre friction model and the Dahl friction model. However, these mathematical approaches might be complicated due to the high degree of nonlinearity in the system under consideration. From a computational point of view the nonparametric neural network technique is very versatile in connection with most types of nonlinear problems. The present paper concerns the nonparametric neural network modeling of the dynamic behavior of a rotary MR damper. A rotary type MR damper consists of a rotating disk which is enclosed in a metallic housing filled with the MR fluid which is operated in shear mode. The dissipative torque produced is transformed into a translational force through the crank shaft mechanism. A feed-forward back propagation neural network is used to model both the forward and the inverse dynamics of the MR damper. The forward model output is the estimated force and therefore can be used later as observer. The inverse model is needed to solve the force tracking task when the MR damper is used for structural damping. The training and validation data are obtained from tests of the MR damper on a hydraulic test set-up for sinusoidal and triangular displacement at different frequencies and amplitudes and for constant and half-sinusoidal currents. The half-sinusoidal current as input is chosen because the emulation of linear viscous damping results almost in a half-sinusoidal current time history if the current spike during the pre-yield region is neglecting. The forward model is trained with the inputs velocity and current and the force as the goal. The velocity is derived from the measured displacement by numerical differentiation which requires additional low pass filtering besides the nominal filtering of the measured states to remove measurement noise and offsets. The inverse model is trained with the absolute values of velocity and force as input data and the resulting current as the goal. This new approach is chosen because the current is always positive independent of the signs of velocity and force. The validations of both the forward and the inverse models with the proposed neural network approach show acceptably small modeling errors.