Autonomous dynamic balance of an electrical bicycle using variable structure under-actuated control

In an electric bicycle, two strategies are taken up to stabilize the running motion of a bicycle. One is the control of its center of gravity (CG), and the other is the control of its steering angle of handle. In general, the control of the CG is used a pendulum. In addition, the motion of a bicycle often possesses a lean angle with respect to vertical direction. In this situation, the proposed system contains three outputs: steering angle, lean angle, and pendulum angle, these will affect the dynamic balance of an electrical bicycle. The proposed control generating the handle torque and pendulum toque is called variable structure under-actuated control (VSUAC). The motivation of using the VSUAC is that the system uncertainties of a bicycle are often huge due to different ground conditions and a gust of wind. Merely use an ordinary proportional-derivative-integral (PID) control or other linear controls often can not have good robust performance. Finally, the compared simulations for the electrical bicycle among ordinary PID control, modified proportional-derivative control (MPDC), and VSUAC confirm the usefulness of our proposed control.