How do i use the Nicolas Ziegel approach when the root locus plot of my system never becomes marginally stable , for any gain (unless it is negative).. ??

How do i estimate my ultimate gain value????

  • $\begingroup$ If your system never becomes unstable, what tuning is necessary? In theory you could just use infinite gains. I suspect, though, that your controller is implemented on digital hardware, with a digital clock, in which case there is always a point at which it will become unstable. $\endgroup$ – ryan0270 May 14 '14 at 12:58
  • $\begingroup$ Do you mean the Ziegler-Nichols heuristic PID tuning method? I agree with ryan0270...you're transfer function probably doesn't model the sampling done by a digital system, which is operating in discrete space rather than continuous. As a result, if you simply try to raise your P term in practice I'm sure you'll find the system will start to oscillate eventually. If you have the transfer function, you can model the digital sampling, etc. in Simulink (part of Matlab). $\endgroup$ – Andrew Capodieci May 14 '14 at 13:23
  • $\begingroup$ You are absolutely right about it being a physical system. It's is a DC - motor, in which i read the values using a sample freq. The transfer function is is in S plane, but would it work if i changed it to z-plane, and would the same rules apply here aswell..?? $\endgroup$ – Control May 14 '14 at 14:37
  • $\begingroup$ What connection are you trying to make to the transfer function? Z-N tuning itself is an experimental tuning process meant for systems that you don't know the transfer function for. $\endgroup$ – ryan0270 May 15 '14 at 2:05
  • $\begingroup$ I know the transfer, it has been identified using matlab, but you right about it being in the discrete time domain. So i was wondering if i could use the same method (ziegler nichols method) for a discrete system as i would do in a continuated system? $\endgroup$ – Control May 15 '14 at 7:35

We have two basic Ziegler-Nichols tuning rules: one method is used with the frequency response and one method is characterized by the use of the open-loop step response of the system. You ought to use the latter then, which sticks around the identification of two main parameters $a$ and $\tau$ that are the intercepts of the steepest tangent of the step response with the coordinate axes (see the figure).


Once $a$ and $\tau$ are identified, the method proposes the following heuristic estimates for the PID gains:



  • "Feedback Systems", K. J. Astrom, R. M. Murray.

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