How to design a PID controller for this application?

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The project involves designing a PID controller using a microcontroller to manage speed control. The desired speed will be compared to the actual speed to generate an error signal. The PID controller will process this error signal through integration, differentiation, and multiplication to achieve the desired output. A pulse width modulation factor will be calculated to determine the duration for which the device should run to adjust the speed until the next sample. Researching PID algorithms is recommended for further understanding and implementation.
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I just took over a project for a person that left the company. The project was supposed to be fully documented, but the documentation seems to have come up missing.
The application involves using a microcontroller as a PID controller.
I will have a desired speed, and the actual speed.
I will get an error signal by subtracting the actual speed from the desired speed.
One of my colleagues says that the PID controller will just integrate, differentiate, and multiply the error signal and I should get what I want.
I want to get a pulse width modulation factor so I will know how long I should run the device to lower my speed until the next sample.
 
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It might be a good idea to read up on PID algorithms. You might just answer your own question.
 
http://en.wikipedia.org/wiki/PID_controller" should give you about all you need.

Regards
 
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