Electronic – Current Amplification

So here is my take, since this application is microcontroller based, couldn't one simply just stop the discharge of the inductor when the current nears zero?

Think about this - the only way to stop the "discharge current" is to prematurely ground the transistor in the boost device to start "charging" current thru the inductor - you have no option - to keep the inductor open circuit is to enter DCM and that is what you are trying to avoid.

The cycle for a boost converter (or flyback converter) can be: -

• Ground the inductor thus current ramps up and inductor stores energy (charge)
• Un-ground the inductor - energy gets released to the output cap and load (discharge)
• If inductor can't sustain current into load via diode you enter DCM and basically the inductor becomes open circuit except for the parasitic capacitance of the MOSFET switcher i.e. you get a damped oscillation until...
• The cycle begins again.

OK, so then what happens (in that cycle) is a tiny little too much energy becomes transferred to the output capacitor and load (during inductor discharge). This causes the output voltage to rise fractionally higher than what it would and, over a period of a few milli seconds, you might exceed the output voltage that is safe for the load. A few seconds later and you have a dead load and a few seconds later you have a dead boost regulator.

OK before you get to this, the control loop would probably have implemented cycle skipping but cycle skipping is noisier than ordinary DCM so why bother?

BTW, going into DCM isn't that bad - the line regulation of the output isn't as good but it's still quite controllable. There isn't much on the web about this but, due to the self-resonance of the inductor and MOSFET drain capacitance, once DCM is entered there is a small oscillating current in the inductor that is asynchronous to the PWM and when the inductor restarts charging it does so at sometimes a slightly positive or negative current. This can cause the noise on a simple controller such as a fixed-on-period controller.

Well thought out and written question.

You are quite correct in your calculations, the 4V Vce is important, it means you need a 16V supply or else your motor will only see 8V and run slow and under power. This lost power will heat up the transistor at 4V x 1.5A = 6W so require a heat sink. The current will likely be a bit lower as the motor is getting less than 12V but not neat 480mA

To get the full current even with the 16V supply the low hfe means that you need to find more gain and this is usually done with a logic buffer to give you the extra drive or an extra transistor to amplify the logic output.

As others have suggested a logic drive MOSFET is a strong contender as long as you are not trying to switch it at high speeds to control the motor speed, this will cause heating in the MOSFET if you do not make use of more elaborate gate drive control.

While starting out in an effort to minimise the risk of having motor voltage reach your controller (and for general galvanic isolation for a lot of reasons) I would recommend a relay as well. The relay you can usually drive with a single transistor and it would be selected to drive the motor with a safe margin.

Remember that your motor starting current may be much higher than the rated running current and if your transistor or relay contact are rated too low you may have regular failures. A 5A rating would be a happy margin.

As mentioned you want a fly-back or free-wheeling diode across the motor (or relay) coil to protect your transistor.

EDIT:
There are also darlington transistors available and these can be used but will have the same high Vce saturation voltage. Your load of 12V and 1.5A is often these days handled with MOSFET or relay when using microcontrollers.

Here is a picture search that may help find ideas. There are lots of alternatives that are worth considering to find what will suit you best.

https://www.google.com/search?q=motor%20+drive+transistor+arduino+schematic+12v+2a+-stepper&tbm=isch