Velocity control with disturbance observer for pedal-assisted electric bikes

Abstract

This paper proposes a velocity control approach for light electric bicycles with human power assistance. A disturbance observer mechanism is used to estimate the sum of the human torque and resistance torques. The resulting vehicle velocity control provides better battery energy efficiency by knowledge of the instantaneous human torque assistance and better speed control by knowledge of the instantaneous resistive torque. The disturbance observer is tuned in terms of the DC gain of a low-passed Q-filter for both open-loop and closed-loop schemes. Assuming that the slow varying nature of the disturbance has been properly estimated and compensated, the torque control law is designed via an optimal control approach to achieve multi-objective performances regarding the external disturbance input, control signal magnitude, and velocity tracking error. The three main parameters of the electric bike, including the moment of inertia, the radius of tyre and the vehicle weight are allowed to be variational. Specifically, the deviation of the inertia moment and deviation of the tyre radius are addressed during the controller design in terms of linear matrix inequalities. On the other hand, the effect of vehicle weight deviation on the system behaviour is evaluated when the vehicle is implemented with the constructed control law. Based on the parameters and specifications of the EL-168 electric bike produced by KENTFA Advanced Technology, Taiwan, the design results are verified through time–response simulations.