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br3ttb / Arduino-PID-AutoTune-Library

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Simulated input equation - Where does it come from? #17

Closed edgsc closed 5 years ago

edgsc commented 6 years ago

Hello, from where does the simulated input equation comes from?

input = (kpmodel / taup) (theta[0]-outputStart) + input(1-1/taup) + ((float)random(-10,10))/100;

What kind of dynamics? How was it linearized?

Thanks!!!

br3ttb commented 6 years ago

By "linearized" I assume you mean "discretized," as the model is already linear.

The model is a standard first order with dead time: taupdydt+y=kpmodeloutput(t-theta)

To discretize, replace dydt with (y- lasty)/deltaT and use algebra to simplify. For the code I assumed deltaT was constant and equal to 1

On Fri, Nov 10, 2017, 1:28 PM edgsc notifications@github.com wrote:

Hello, from where does the simulated input equation comes from?

input = (kpmodel / taup) (theta[0]-outputStart) + input(1-1/taup) + ((float)random(-10,10))/100;

What kind of dynamics? How was it linearized?

Thanks!!!

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