Nonlinear order-reduced adaptive controller for a DC motor driven electric cart

The precise control of a voltage-controlled, DC motor driven electric cart would be a 3^rd order task since Classical Mechanics relates the acceleration of the cart to driving torques, while these torques are proportional to the current that cannot be modified abruptly. Abrupt jumps in the control voltage cause abrupt change only in the time-derivative of the motor current. Therefore a 2^nd order controller can only approximate the operation of a 3^rd order one. Modeling imprecisions further complicate the control task. Furthermore, if the cart has two independently driven main wheels and a supporting caster, no exact trajectory tracking can be prescribed simultaneously for the location of the cart in the (x, y) plane and its rotational orientation (θ) since for three prescribed quantities only two control signals are available. For the tracking error of these components, some kinematically formulated compromise must be applied. The aim of the present paper is to show that the simultaneous problems caused by the order reduction, the modeling errors and the necessary kinematic compromises can be elegantly solved by the adaptive controllers designed on the basis of Robust Fixed Point Transformations (RFPT). This statement is substantiated by simulation results.