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PID and a Nonlinear process

Industrial PID cannot control nonlinear process properly.

PID controllers are setup by measuring the process gain, process time constant and the dead time.

When these variables are constant over the entire control range, the PID performs well.

When using an fan application both the fan and the airflow are quadratic functions resulting in a third order system. This means process time and gain are dependent on the momentary output of the system.

Below is a graph of the system. We can see that when output is low the PID controller  reacts slowly. In the middle range the PID settings are correct. In the top of the characteristic the process is much faster resulting in overshoot of the process.