# PID Output

N

#### Nice

As a part of my study project I want to mathematically calculate the output of a Digital PID controller with an input scan time of 2ms. The conditions I intend to set are as follows:

My PV scale is 0 - 100% (Corresponding to 4 - 20mA simulated Process input)

SP is 50%

I'll source exactly 51% current as PV input to the PID. And hold it there. I will connect a mA Meter to the Controller output.

I'll set Kp at 1 and Ti (Integral Time) at 10. I am ignoring Td (Derivative Time Constant) assuming that it will not contribute anything for a constant error.

Given these facts, how to mathematically calculate the output mA begining from time T = 0? Theoretically, at what intervals will the output renew/change and what should be the value of this new/changed mA?

Thank you,
Nice

B

#### Bruce Durdle

You missed an important point - what are the units of integral time? Another important point - is the controller reverse acting or direct acting?

Given that for a gain of 1 the proportional component of the output change will be an exact copy of the input change, you should be able to calculate the proportional effect easily enough.

The integral component of the output will ramp at a rate such that after 1 Integral Action Time the integral contribution to the output equals the proportional term.

Since the scan time is 2 ms, the output will change every 2 ms. The amount of the change depends on the scan time divided by the IAT. For each scan interval the change in output due to integral action is Ts/Ti x error.

That should be enough help...

Bruce