Feedback linearization controller design for a geared transmission system considering asymmetric backlash and friction

This study is focused on the mathematical modeling, analysis, and controlling of a Geared Transmission System (GTS). Although GTS is used widely in mechanical equipment and mechatronics, the existence of nonlinearities such as backlash and friction made some challenges for its position control. In this paper's proposed method for GTS, the stribeck friction nonlinearity is estimated based on the motor velocity by a linear model. By this approach, the GTS model is reduced to a two-piecewise function. In addition, the asymmetric non-differentiable dead zone is approximated by a differentiable function. Additionally, using the differentiable function for the approximation leads to a reduction in the number of the piecewise function and therefore the number of switching in GTS output. Afterward, a feedback linearization controller is designed for the introduced model, and its stability and tracking of the reference trajectory are investigated. Simulation results indicate the designed controller on the proposed model has a good performance compared to the other models and complete tracking is realized without any steady-state error. Furthermore, due to the structure of the proposed model, position tracking is performed at the lowest time and by the minimum switching number.