Electronic – Vary the integration factor of a opamp integrator

Since there is no resistor in series with the - input, you really are using the opamp as a comparator and the feedback resistor can be removed. Your circuit is a inverting comparator, BUT, its threshold level is 0 V since that's what you are feeding into the + input.

There are several things you need to do to fix this circuit:

1. Set the threshold voltage about halfway between the high and low voltage of the digital signal. Assuming the digital signal goes between power and ground of something like a 3.3 V or 5 V supply, all you need is a resistor divider. Connect around 10 kΩ between the digital supply and the + input, and another 10 kΩ between the + input and ground. This will float the + input at half the supply voltage, which we are assuming is the middle of the digital signal voltage range.

2. Make sure the opamp is properly powered. If you want the output to swing ±15 V, then the supply needs to be at least ±15 V. Most opamps that can take such a large supply range can't swing their outputs all the way to the supply rails. This headroom can be almost 3 V in some cases. Check the datasheet. The TL081 you show is known for having a rather large headroom.

   However, don't just blindly connect ±18 V or whatever power to the opamp. Check the datasheet to make sure you don't exceed the maximum supply voltage the opamp can tolerate. If your opamp can't handle enough to guarantee ±15 V out, then you either have to live with a smaller output voltage range or get a different opamp.

3. Lose R1. It does nothing useful. It could even hurt the digital output when swinging well past the digital supply range.

I take it the resistor values (especially R5/R6? 200 ohms is an awfully heavy load on an op-amp) and maybe the op-amp number are just for illustration.

The 'P' gain is 0.1

The output slews at a rate of Vfb/(100K * 470nF) volts/second for the integral gain so the I time constant is 47ms.

There is no 'D' term.

The diodes and R5/R6 are to clamp the output asymmetrically (mainly to prevent integral windup). Presumably the output 0-100% requires an asymmetric swing like 0.5 to -7.5V or something like that. It's important in analog circuits to prevent integration from continuing once the output is saturated. It's infinitely more important in firmware implementations since there's almost no limit to how high the integration term could get (especially if you're using floating point). It's also important to limit it or at least initialize it. The controller might otherwise take longer than the age of the universe to recover if the integral term got set to something weird, which many customers might find unacceptable.