Virtual Motor Torque Sensing for Multirotor Propulsion Systems

This letter presents a method to sense motor torque of multirotors in steady state, without additional torque sensors by using the measured input voltage, throttle setting and rotational speed. Torque, rotational speed and current of a brushless direct current (BLDC) motor with electronic speed controller (ESC) are measured on a setup using seven different propeller sizes as torque loads, seven input voltages and 20 throttle settings. The resulting rotational speed, torque and current are measured to create a data set spanning the feasible operating range of this motor with speed controller. A novel model for a BLDC motor with ESC based on only four parameters is proposed and trained on the data of only one propeller as torque load and the data without torque load. This model results in torque errors less than
$\text{0.01 Nm}$
or 4.6% of the data set range for 90% of the data set. For the highest accuracy, the whole data set is re-mapped into a practical 3D lookup table using local fits and results in torque errors less than
$\text{0.005 Nm}$
or 2.3% of the data set range for 90% of the data set. This method can be used for system identification, control design, system monitoring and benchmarking.