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"On-Line PI Controller Tuning Using Closed-Loop Setpoint Responses for Stable and Integrating Processes", M. Shamsuzzoha, S. Skogestad, I.J. Halvorsen. Presented at IFAC conference on dynamics and control of process systems processes (DYCOPS), Belgium, July 2010

You probably already know about my SIMC PI tunings rules from JPC in 2003:
    (1) kc = (1/k) (tau1/(tauc+theta)),
    (2) tauI=min[tau1,4(tauc+theta)],
See  http://www.nt.ntnu.no/users/skoge/publications/2003/tuningPID/

These rules are claimed to be "probably the best simple PI tuning rules in the world" but they require that you first obtain a first-order model (k, tau1, theta).

Now, we have come up with a method which is based on the same rules but which is simpler to use because it requires only one setpoint experiment (it uses P-control - a bit similar to Ziegler-Nichols (ZN) - but is much quicker than ZN because one does not need to crank up the gain to get persistent oscillations). This is "probably the fastest simple PI tuning approach in the world."

From the setpoint response (using P-controller with gain kc0 and setpoint change ys) you read off:

	overshoot = (ymax-y(infinity))/y(infinity) (try to get overshoot about 0.3)
        tp = time to reach peak (overshoot)
        relative steady-state change: b = y(infinity)/ys
       
and the tunings are (for "fast robust control" corresponding to tauc=theta in SIMC set F=1, but use F>1 to detune):

 (1) kc = kc0 * A / F
 (2) tauI = min (0.86A*tp *b/(1-b), 2.44*tp*F)
 where A = 1.152*overshoot^2 - 1.607*overshoot + 1.0  (A=0.62 for overshot=0.3)

We would be VERY happy of you could report back to us any real-life experiences with the method (good or bad).

Best regards, Sigurd