FAQ: If I am controlling a second order delay-less plant, it will never give sustained oscillations with P control. Then how do I find the ultimate gain using the Ziegler Nichols method?
Posted by Karl Astrom 09:21, 31 December 2005 (PST)
There are two Ziegler Nichols (ZN) methods, the step response method and the frequency response method. The ZN step response method characterized the step response by two parameters as shown in Figure 9.14 in the book. The frequency response method is based on an experiment where the system is brought to oscillation under pure proportional control. Since a second order system with no delay will not oscillate, the first method must be used.
Notice that the ZN methods have two drawbacks, they do not use sufficient process information and they give systems with poor robustness and low damping, as discussed in the section titled "Improved Ziegler Nichols Rules". For the step response method, significant improvements are obtained by estimating three parameters.
Alternatively, you can simply fit a second order transfer function based on the frequency and the damping of the step response and then design a PID controller by eigenvalue placement.