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Note I am a beginner :)

I have this 300RPM motor: https://uk.banggood.com/CHIHAI-MOTOR-GM25-370-DC-Gear-Motor-6V-100210300RPM-Encoder-Motor-p-1016183.html?cur_warehouse=CN&ID=519629&rmmds=search

Is the stall current the highest amount of current the motor can draw at one time. If so would I need a motor driver that can supply a continuous current of at least 2.7 amps, to be on the safe side?

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Well, you have an obligation to make sure that the final system does not experience driver failure when the motor is stalled. Motors can stall for a variety of reasons. But there is more than one way to achieve this. Keep in mind, also, that the motor will almost certainly fail if full stall current is allowed to continue for an extended period.

You could have current sensing and limiting in place at all times. Or, since you have an encoder, you can scale the max duty cycle you apply to the motor to avoid full stall current. This is, in effect, current limiting without direct current sensing.

The brute force solution is to put some kind of thermostat inside the motor to protect it from overheating. The driver, then, needs to supply full stall current long enough for the thermostat to trip.

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    \$\begingroup\$ And when the motor fails it burns the insulation off the armature wires and shorts them out, resulting in much higher 'stall' current! Then your controller fails... \$\endgroup\$ Jun 2, 2021 at 7:55
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The answer is yes and no. If you connect the power supply with the motor's nominal voltage at standstill the motor would draw a stall current, this would happen also if the rotor is locked. It may draw this current for a very short period of time, like for startup.

You can supply the motor with a fixed voltage power supply with an additional thermal circuit breaker that will trip in case of excessive current draw. Or you might use a motor driver with the possibility of speed adjustment, ramps, encoder,... the most important feature is the current limit.

Since the motor driver with all these features is expensive is suggest you to use a thermal circuit breaker of rated motor current.

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Is the stall current the highest amount of current the motor can draw at one time.

For a brushed DC motor, the locked rotor current is the greatest amount of current the motor will draw, unless you are trying to reverse direction of rotation.

If so would I need a motor driver that can supply a continuous current of at least 2.7 amps, to be on the safe side?

That depends on the power supply and how it reacts to heavy loads. Some power supplies will "fold back" their output if the output impedance is too low. If you have this kind of power supply and you try to start a motor that draws too much power, it may not start the motor at all.

Other power supplies will go into a constant current mode if they cannot supply the current at their nominal voltage. With this type of supply, the motor may start even if the current supplied by the power supply is only a fraction of the locked rotor current. However, the torque will be less than rated torque, and if the load on the motor is too much, the motor may still not start.

One thing to look out for is that with lower torque, a motor may take longer to get up to operating speed, and thus spend a longer time drawing a higher current. This may, in some cases make the motor hotter than if more current were available initially.

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