Transfer Function Identification for Small DC Gear Motors Using Only Angular Position

This paper describes a method of identifying the transfer function for small DC gear motors such as those used in academic control systems laboratories and for student robotics projects. Many of these motors incorporate a quadrature encoder on the armature shaft and provide ready access to the armature's angular position. The approach that is described in this paper uses only this angular position and the magnitude of the armature voltage to obtain a first-order model for the armature angular velocity in terms of the applied armature voltage. This is accomplished by first identifying and compensating for Coulombic friction using break-away tests. Then, the step response is obtained in response to a Coulombic friction compensated input signal. From both the slope and intercept of the straight line approximation of the steady-state portion of the response curve, which is obtained via least-squares approach, the parameters of the model are calculated. This approach, unlike conventional step response approaches, does not require angular velocity, and therefore no filtered finite-differences or dynamic state-estimation is required, making this method quick, easy to understand, and ideal for obtaining transfer functions for controller design.