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I'm looking for advice or references on how to implement a "type I" compensation network of digitally. An analog example is shown in the following diagram:

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I am familiar with the basics of digital signal processing, and have read about digital integrators. Would it be possible to use something like a first order IIR digital integrator, and just flip the sign of the output depending upon whether the input is above or below VREF? The goal is to drive a PWM output of a microprocessor, so there may be a better way to do this in the digital domain than attempting to copy the analog implementation. Any advice would be appreciated.

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The integrator is unstable, so it will probably just blow up. There's such a thing as a leaky integrator that does an OK job of getting pretty close. Have a look at the algorithm listed here on how you would go about implementing it using code. The math is pretty straightforward.

The differentiator uses b1=1, b2=-1. The integrator is just the inverse, but what you'll find is you need to modify (decrease) the filter coefficient by a subtle amount to make it 'leak'. For the integrator use something like a1=1, a2=-0.99. The closer a2 gets to 1.0 the greater the risk you run on it going unstable. Decreasing a2 to something like -0.95 will result in something that looks less and less like an integrator. Play around with it.

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The leaky integrator suitable for part of your solution. See these links for more information.

Mathematical Proof of Complementary Filter？

How to determine the parameter of a Complementary Filter?

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