P Control With I Step

Please can someone explain how a PI controller might work for an FOPDT system if the I correction is only made at the end of each process loop time?

Whenever I try to simulate it, the P and I parts of the calculation are fighting against each other unless both are continuous.
 
Please can someone explain how a PI controller might work for an FOPDT system if the I correction is only made at the end of each process loop time?
What do you mean by the end of each process loop time.

Whenever I try to simulate it, the P and I parts of the calculation are fighting against each other unless both are continuous.
This doesn't make sense.
Below is a link to an example PI control for a heat exchanger. It was a contribution to the www.controlguru.com website way back in 2005. I show how the IMC PI gain are derived. Everything is shown.
Mathcad - FOPDT.pdf
 
Thanks, this is how the manual describes the integral term:
1683498471707.png

Process time is defined in the manual as the time it takes for the measured variable to react to a change in the manipulated variable.

I should say that I'm new to this, but in my understanding this means the proportional control element is already driving the error down at the end of the process time (therefore driving the manipulated variable further away from the setpoint). The integral then steps the manipulated variable closer to the setpoint as the proportional control carries on driving it away. It does eventually tend towards zero error, but it looks really odd, so I must be misunderstanding something fundamental.

I'll try and digest the calcs in the pdf you attached thanks.
 
What you call process times, I call settling time.
It would be nice if you provided a link to the PID manual to reduce the number of questions.
I need units that make sense.

The two gains should be working at the same time like in my PDF. The integral gain will cause the process variable to overshoot when you make step changes to the set point. Much of the overshoot can be avoided if you use the increment or velocity form of a PI controller.

I can see what you are trying to do. You are trying to avoid integrator windup by not enabling it when the error is big.

You have not made it clear what PID controller you are using.
The integral term can be expressed as a gain or a time constant. I have never seen it expressed as just a percentage. It should be a ratio.
It appears your integrator is a gain.
If the integrator is a gain then the output is %control_output/(sum of errors).
If your example is 50% control_output/(sum_of_errors), that is very high.
 
Wallace & Tiernan Instruction Manual V600 Disinfection Controller

Here we go, hope that works as it is too large to attach (6MB). Section 1.2.3 shows the residual control set-up, and section 4.2.1 and 4.2.2 show the P gain, I gain and 'process' time information (happy to use the term settling time, to avoid confusion with other FOPDT terms though).

Here is also a screenshot of the control equation screen in case that helps. The Wq (0.54) part can be ignored, as that is just a correction factor for flowrate, which we can assume remains constant for the purposes of understanding the PI operation.
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