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????
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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: