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I am making a bot with 4 motors with a stall current rating of 11.7A. I was using 4 separate motor controllers which has a peak current rating of 20A to control each motor. But when I gave power to the motors in my bot, the motor drivers blew off within a second.

Was it due to the starting peak current of the motors? If yes, then how can I reduce the starting current? If no, then what could be other possible problems and their corresponding problems?

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Motors when starting can draw ca. 10x their nominal current. You mentioned that you have a driver attached to the motor. Do you use PWM to control the motor? A soft start when the motor is accelerated in a controlled manner to the required velocity helps limiting this initial large current.

When starting the motor, instead of just setting the required pin to 1, use the PWM function and increase the duty cycle of the PWM slowly (from 0 to 100% min ca. 1-2 seconds). That should reduced the current and make the motor accelerate smoothly to its maximum velocity. You can find a tutorial here, here and here.

As the other answers suggested, adding a capacitor can help, but this is a hardware solution, and I would suggest a software approach. The driver you are using seems to already have capacitors.

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Could be the starting current, try adding an inductance in series with the motor that will limit the rate of the current change. Once the motor starts spinning the current will stabilize. This will however make your motor more inert (respond slower to the change of the supplied voltage).

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DC motor draw more current initially because when motor is in normal speed it creates back emf which reduces drawing current .So initially when DC motor is powered there is no back emf so current drawn is more. Solution a capacitor in parallel to DC motor which will provide more current from its reservoir when motor is initially powered....

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