Fuzzy Sliding-Mode Underactuated Control for Autonomous Dynamic Balance of an Electrical Bicycle

The purpose of this paper is to stabilize the running motion of an electrical bicycle. In order to do so, two strategies are employed in this paper. One is to control the bike´s center of gravity (CG), and the other is to control the angle of the bike´s steering handle. As in general, the control of the CG applies a pendulum. An additional factor is the lean angle with respect to the gravitational direction of the bicycle in motion. In this total, the proposed system produces three outputs that will affect the dynamic balance of an electrical bicycle: the bike´s pendulum angle, lean angle, and steering angle. Based on the data of input-output, two scaling factors are first employed to normalize the sliding surface and its derivative. According to the concept of the if-then rule, an appropriate rule table for the ith subsystem is obtained. Then, the output scaling factor based on Lyapunov stability is determined. The purpose of using the proposed fuzzy sliding-mode underactuated control (FSMUAC) is to deal with the huge uncertainties of a bicycle system often caused by different ground conditions and gusts of wind. Finally, the simulations for the electrical bicycle in motion under ordinary PID control, modified proportional-derivative control, and FSMUAC are compared to judge the efficiency of our proposed control method.