Based on previous studies, two strategies, the controls of the center of gravity (CG) and the angle of steering handle, are employed to stabilize the bicycle in motion. In general, a pendulum is applied to adjust the CG of the bicycle. An additional factor is the inclination with respect to gravitational direction of the bicycle in motion (i.e., lean angle). As a whole, the system produces three outputs that will affect the dynamic balance of the electric bicycle: the angles of the pendulum, the lean, and the steering. The proposed control method used to generate the handle and pendulum torques is named variable structure under-actuated control (VSUAC), possessing the number of control inputs smaller than the system output. The purpose of using the VSUAC is the huge uncertainties of a bicycle system, often encountered with irregularities in ground conditions and gusts of wind. Merely using the ordinary proportional-derivative-integral (PID) control or other linear control methods usually do not show good robust performance when the aforementioned conditions are present. Finally, the simulations of the electrical bicycle in motion using ordinary PID control, modified proportional-derivative control (MPDC), and VSUAC are compared to judge the effectiveness and efficiency of the proposed control.
