A fuzzy decentralized sliding-mode robust adaptive under-actuated control for autonomous dynamic balance of an electrical bicycle

Based on the previous studies, the dynamic balance of an electrical bicycle includes two control inputs: steering and pendulum torques, and three system outputs: steering, lean and pendulum angles. Two novel reference signals are first designed so that the uncontrolled mode is simultaneously included into these two control modes. Two scaling factors for each subsystem are first employed to normalize the sliding surface and its derivative. The so-called fuzzy decentralized sliding-mode under-actuated control (FDSMUC) is first designed. Because the uncertainties of a bicycle system, caused by different ground conditions, gusts of wind, and interactions among subsystems, are often huge, an extra compensation of learning uncertainty is plunged into FDSMUC to enhance system performance. We call it as ldquofuzzy decentralized sliding-mode adaptive under-actuated controlrdquo (FDSMAUC). To avoid the unnecessary transient response and then destroy the balance of the bicycle, the combination of FDSMUC and FDSMAUC with a transition (i.e., fuzzy decentralized sliding-mode robust adaptive under-actuated control, FDSMRAUC) is designed. Finally, the compared simulations for an electrical bicycle among the FDSMUC, FDSMAUC and FDSMRAUC validate the efficiency of the proposed method.