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Discussion Starter #1 (Edited)
I have a dune buggy. Does anything seem dangerously wrong at first glance?
Also, what does a controller do?

I believe I've wired a dune buggy I acquired correctly.
It was started by the previous owner. I attempted to finish using wiring diagrams of the motor manufacturer.











In image 9, I have added cables where the wavy lines connect.

Manufacturer's diagram I i used: <>

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"What does a controller do" is such a fundamental question that it has me very worried about what else you've missed in your project. For your own safety you might want to get some extra help.

To answer the question: you really get two answers. For a DC motor, the controller fundamentally is a current limiting device, which allows you to match the power (voltage times current) of your motor's output to the power you require to achieve a certain speed or acceleration. It's typically a pulse-width modulation device, switching the current to the motor on and off very quickly, with a bunch of other circuitry to keep the electrical noise down and to keep the controller from destroying itself while it is trying to interrupt such huge current flows into an inductive load like a motor. When the controller fails, or is maxed out, the battery is basically directly connected to the motor and the motor will run up in speed until it either blows up, melts, or in the case of a very small motor, until the speed and back EMF of the motor rises high enough to limit the current to something reasonable which also matches the power requirement of the vehicle at that speed. Hence, a very important component in a DC build is a device which can positively interrupt the current flow from the batteries into the controller in the case that the switches (IGBTs typically) melt into a puddle of solid silicon.

For an AC motor, a "controller" is really an inverter. It's a device which takes a DC input and produces a 3 phase sine wave (or close enough) output of a frequency which is varied to produce the desired speed in a synchronous AC motor. Both the voltage and current of the 3 phase output are varied by the inverter in the process, and the current flow can be either positive (out of the battery into the inverter) or negative (out of the motor into the inverter and hence back into the battery). In this case, if the inverter fails, the motor will fail to turn.
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