A hybrid fuzzy decentralized sliding mode under-actuated control for autonomous dynamic balance of a running electrical bicycle including frictional torque and motor dynamics and in the presence of huge uncertainty

Hybrid under-actuated control for the autonomous dynamic balance of a running electrical bicycle including frictional torque and motor dynamics is developed, where includes two control inputs: steering and pendulum voltages, and three system outputs: steering, lean and pendulum angles. Due to the under-actuated feature, two novel reference signals using three system outputs are designed so that the number of control inputs and sliding surfaces is the same. The previous fuzzy decentralized sliding mode under-actuated control (FDSMUC) is first designed. Because the uncertainties of a running electrical 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 the system performance. We call it as “fuzzy decentralized sliding mode adaptive under-actuated control (FDSMAUC).” To avoid the unnecessary transience caused by uncertainties and control signal and to preserve the balance of the bicycle, the combination of FDSMUC and FDSMAUC with a transition (i.e., Hybrid FDSMUC) is designed. Finally, the compared simulations for the suggested control system among the FDSMUC, FDSMAUC and Hybrid FDSMUC validate the efficiency of the proposed method.