Fuzzy sliding-mode under-actuated 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 bikepsilas center of gravity (CG), and the other is to control the angle of the bikepsilas steering handle. In addition, the proposed system produces three outputs that will affect the dynamic balance of an electrical bicycle: the bikepsilas pendulum angle, lean angle, and steering angle. Based on the data of input-output, two scaling factors are employed to normalize the sliding surface and its derivative. According to the concept of 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 proposed control method used to generate the handle torque and pendulum torque is called fuzzy sliding-mode under-actuated control (FSMUAC). The purpose of using the FSMUAC is the huge uncertainties of a bicycle system often caused by different ground conditions and gusts of wind; merely ordinary proportional-derivative-integral (PID) control method or other linear control methods usually do not show good robust performance in such situations.