I'm commissioning a dissolved oxygen system at a wastewater treatment works, and the PI controller is implemented by a Siemens S7 PLC. So I checked out S7 online and found a Siemens manual at the link below.

file:///C:/Users/35385/Downloads/s71500_pid_control_function_manual_enUS_en-US.pdf

The problem I'm having is with the PI description on page 32 to 33. It shows two graphs.

Then an equation which I believe is for the output y.

I'm assumming that 't = time interval since the step of the control deviation' means the time since the disturbance. Even if it doesn't, as time passes t will increase. This means that the integral term will decrease not increase as time passes and it will just be a proportional controller. Or, am I missing something fundamental.

The controller on site doesn't behave like the above equation. If the error doesn't decrease, the output starts to ramp up, as I would expect an integral to do.

Thanks for any help.