Can someone explain how can 2nd order transfer function be represented by 1st order transfer function as shown in the equation 16 in the attached picture. I was trying to google it, but I couldn't find a solution. How can inductance be neglected in equations 18 and 19? Is it because the motor is working with no load ? I get why B can be neglected in equation 17 because B is viscous friction coefficient which has a really small value that can be neglected. Thank you in advance!
How can inductance be neglected in equations 18 and 19? Is it because the motor is working with no load ?
It is assumed to be small enough to not matter. Inductance becomes important at 'high' rpm where the LR time constant is a significant proportion of the commutation time. This is often compensated for by advancing the 'timing', either by moving the Hall sensors or subtracting a time off the back-emf zero crossing point in sensorless operation.
When inductance is not taken into account the apparent resistance increases. As the motor is loaded down its speed reduces and the inductance has less effect, then the reduced stator impedance causes current and torque to increase more than expected. Depending on the motor construction (cored/slotted, slotless, ironless) and operating conditions, inductance may cause the calculated values to be off by up to ~20%, particularly with slotted iron cored motors which have relatively high inductance.
The reason inductance can be ignored (i.e set to 0) is that the time constant of the electrical components is much faster than the time constant of the mechanical system. Recall your control systems class and pole placement. The poles of the electrical system (generally) are further left from the real-imaginary axis than the poles of the mechanical system. The poles that are closer to the real-imaginary axis are the dominant system response! This means that electrical dynamics can be ignored with little change to the system response.
See the following response from another question Can't figure out this PMDC motor model