摘要：Abstract: The exact backlash model was recently proposed by Nordin, Galic and Gutman. The model is based on the dynamics of an inertia free elastic shaft including internal viscous damping; thus, it is considered as a more realistic model in comparison to the common dead-zone or hysteretic backlash models. To simplify analysis and design of nonlinear control systems, the nonlinear terms are commonly substituted by its Describing Function. In this paper, a sinusoidal-input describing function of the exact backlash model is presented for the first time in analytical form. The presented describing function reveals an additional phase lag at higher frequencies in comparison to the describing function of the common dead-zone backlash model. Thus, the exact backlash model can more appropriately represent the backlash contribution in the frequency domain, e.g. to predict backlash-induced limit cycles. The usefulness of the backlash describing function is shown by comparing its accuracy with other models, and verified by simulations. Describing functions can also be applicable for linear robust control design, where all nonlinearities are substituted by quasi-linear terms with parameter uncertainty. The presented backlash describing function has been integrated into such a control design methodology, and successfully implemented on a real industrial servo system with non-negligible backlash.
