How to model the motor for this PWM motor driver circuit and is this simulation reliable?

Question

I want to control the speed of this brushed DC motor with PWM control by using a uC board like an Arduino board. So the PWM output is 5V and it can source only upto 20mA so I need to use a transistor buffer. The DC motor specs are given as following:

And below is the driver circuit I plan to use. Before soldering I have some questions not settled, I merged a transistor buffer with this power MOSFET I have at the moment. I only have these transistors at the moment. And I want a non-inverting logic. I mean when PWM is 100% the motor should run at full speed and vica versa. That's why I use two bipolar and drive the load(motor) on the upper side of the MOSFET. PWM frequency can be 500Hz up to 24kHz. Not decided yet.

When I simulate the MOSFET drain voltage, drain current, motor current and the MOSFET power I get the following plots(PWM freq in this case is 500Hz):

1-) If there is not fundamental problem with this driver circuit, how can I model the DC motor? I modeled it as L and R series but the values are based on assumption. Is it correct to estimate motor resistance Rm from the specs as 24/0.3A = 72 Ohm? How about the inductance? Is 1mH realistic?

2-) And from the MOSFET data sheet, upto what max current this MOSFET can handle without a heatsink? I'm asking because I might change the motor voltage or use similar type of motor with more current.

Answer 1

1. For the inductance I cannot think of any other simpler way than measuring it with the help of a signal generator and an oscilloscope as described in this similar question. A more comprehensive DC motor simulation walk-through can be found at this website.

2. First thing, since the supply voltage can reach 24V, you should limit the maximum \$V_{GS}\$ of the MOSFET to below 20V via a zener diode. Add small capacitor close to the motor, in order to reduce the line impedance during start-up. You might also want to add a small series resistor to the MOSFET's gate in order to limit current peaks. From your simulation, there is some ringing during the off-phase of the MOSFET. This comes probably from the resonance of the motor's inductance with the output capacitance of the MOSFET. You can reduce it by adding a snubber (in this case a small cap in parallel to the drain-source ends of the MOSFET, therefore reducing the ringing frequency).

Answer 2

Is it correct to estimate motor resistance Rm from the specs as 24/0.3A = 72 Ohm?

No. When running the motor also acts as a generator whose voltage subtracts from the supply voltage, so the calculated resistance is too high. The actual resistance is much smaller, and only equates to V/I at stall. You can measure the resistance with an ohmmeter across the motor terminals, or pass a known current through it (using eg. a 240Ω resistor in series to get ~100mA at 24V) while preventing it from spinning, and measure the voltage drop across the motor.

Resistance varies depending on where the brushes are on the commutator, so take several readings at different shaft positions and use the highest value.