PID tuning - hybrid Skogestad

What could be called a hybrid, or combined, Skogestad method will consist of the following.

1. Find Ti according to Skogestad.

The plant should run at approximately 85% of nominal power on isolated grid. Set it in manual mode and adjust the guide vane until the speed is at or very close to 50 Hz (or 60 Hz as may be the case). The speed in pu should be close to 1.0.

Find the time it takes for the speed to reach 63% of the steady state value for a step in guide vane (injectors in this particular example, since it is a Pelton) of 0.1 pu from the value above. The steady state value after the step is noted as 1,059 pu. 63% of this change becomes a speed of 1.037 pu.

This gives a Ti of 7.1 s.

2. The PID is placed in auto mode on isolated grid and with this Ti = 7.1 s. Now adjust the SP n [pu] down and up again as in the previous trial and error method. Then increase Kp until the overshoot is somewhere between 10 and 25 % depending on how aggressive the PID should be.

In this example a Kp of 3.2 will do fine, but it certainly could be more aggressive.

That's it. The Ti is as good as it gets based on the physics of the plant, and the Kp is as good as one can hope for.

For tuning at idle no load, just set the P Grid [pu] to zero. This is usually done with only one injector.