PID control with electronic differential for two brushless DC motors

Abstract

This document presents an angular velocity PID tuning for a control system with electronic differential for two brushless electric motors with permanent magnets in the wheel axles in Lizard vehicle. The main objective is to allow the vehicle to make a smooth curve, since it has no mechanical differential due to independent motors at each wheel. Three tunings were performed, two of them based on the open-loop response curve in s, by Ziegler-Nichols and Cohen-Coon, and a third trial and error tuning. The three tunings are compared for a step input, a sinusoidal input and a ramp-type input. A very similar response is observed between the Ziegler-Nichols tuning method and the Cohen-Coon one, being slightly faster the Cohen-Coon response for step and sinusoidal inputs, but slightly slower for a ramp-type input. However, both types of tunings had high overdamping for a step response. The trial and error tuning was slower than the others but presented a balanced answer, due to lesser overdamping. Manual tuning achieved better results; having the mathematical model of the system and the simulation software allow us to optimize the results of tunings like the Ziegler-Nichols and the Cohen-Coon ones