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# mathematical model for a PID controller

## mathematical model for a PID controller

(OP)
Hello,

I'm building a temperature control for a coffee machine and i would like to know if it is possible to make a digital PID or PI controller for it without having the mathematical model of the water boiler.
And if it's not possible, how to get the transfer function of the water boiler.

Replies continue below

### RE: mathematical model for a PID controller

If you don't have first principle model then you can always build input-output model if you want.
Your variable of control is Temperature of Coffee machine and input variable is some heat input to water boiler. If you can give different magnitude inputs and get final steady state temp then you can fit this data to linear model
If you can't do several experiments, then you can give few step input changes (say +/- 5%) and see the dynamics of the system which will give time constant and any lag etc. You can tune your PID controller parameters with this.

best wishes
Prashant

### RE: mathematical model for a PID controller

bubulindo, Isn't a PID controller for Coffee machine a bit of an overkill? Why not just use a Temp. switch. a 5-10 deg. deadband would be more that adequate for this application. It'll certainley be cheaper and more robust. Not too mention, you won't need a qualified instrument tech. to do the constant required calibrations required on a controller.

Hope this helps.
saxon

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