First I state that connecting the Arduino directly is not a possibility. You will need to use an optoIsolator. Not as complex as you might think.
You will need to do some investigation. Do you have a multimeter?
A lot of controllers say they need a PWM input but often they work with an analog voltage or a simple resistor.
Measure the 0 to 5V input when the motor is fast then slow.
Measure the PWM signal (using the 0 - 5 com) when the motor is fast and slow.
I'm hoping you can find an input where you can simply use a opto (like below) to control the motor from your Arduino. The benefit of the opto is your arduino will be completely isolated from the voltages in the control board. Much much safer.
In the manual for the Minarik controller, as seen in post #20,
"Instead of using a speed adjust potentiometer, the drive may be wired to follow a 0-5 VDC analog input voltage signal that is isolated from earth ground (Figure 7). Connect the signal reference (+) to S2. Connect the signal common (–) to INH2. Make no connection to S3."
So the Arduino PWM would go to pin S2 and the ground would connect to INH2.
NOTE: the manual states it should be isolated from earth ground, so the Arduino's power supply/ PC whatever would need to be isolated.
This is the reason that others have suggested using an opto-isolator between the Arduino and the controller.