Self tuning has its limits

Regarding Self-Tuning Control (July 2007 by Vance Van Doren). A linear control loop will not develop a limit cycle — its cycle will either decay or expand, depending on whether loop gain is below or above unity, respectively. Limit cycling requires a nonlinear function somewhere in the loop to limit the amplitude of the oscillation, and the waveform is typically non-sinusoidal.
By Control Engineering Staff May 1, 2008

Regarding Self-Tuning Control (July 2007 by Vance Van Doren). A linear control loop will not develop a limit cycle — its cycle will either decay or expand, depending on whether loop gain is below or above unity, respectively. Limit cycling requires a nonlinear function somewhere in the loop to limit the amplitude of the oscillation, and the waveform is typically non-sinusoidal. Changing the tuning of a controller in a limit-cycling loop usually does not eliminate the cycling, but only affects its amplitude and period, rendering self-tuning ineffective. The ineffectiveness of tuning efforts, along with a non-sinusoidal waveform, should direct the user to look for and eliminate the nonlinear element, such as valve deadband.

Greg Shinskey, shinskey@hughes.net

I could quibble over your assertion that self-tuning is ineffective because other phenomena can cause limit cycling, but I believe for different reasons that self-tuners are hard to implement successfully. In general, though, I agree with your observations. Limit cycling can only occur if a limiter of some sort (such as a valve’s maximum and minimum positions) to keep an unstable oscillation constant. Still, the information available from a limit cycle waveform can be used to tune a loop, as Ziegler and Nichols showed in 1942.

Vance VanDoren, controleng@msn.com

Greg responds: I agree that a limit cycle caused by an on-off controller, or by excessive proportional gain, can be used to tune a controller, and some auto-tuners operate this way. But it would not make sense for a self-tuner to wait until the valve cycled between its limits before retuning. And for a velocity-limited valve, the period of that large limit cycle could be much longer than that of a small-amplitude cycle. However, some limit cycles do not drive the controller output to its limits. A very common limit cycle is caused by valve deadband in a PI level-control loop. The manipulated flow cycles in a clipped sine wave, well within the limits of the valve, with amplitude and period varying with the P and I settings. No combination of those settings will eliminate the cycle. A self-tuner will fail in this loop because there is no stable state.

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