It's the second day at your new job, and your new boss walks up to your new cubicle and says, "I need you to tune the control system for our newest product, the Covidmatic 19TM. Betty designed the system and was supposed to do this, but she just quit and went to work for Google." He then adds, "Oh, in case you didn't know, we have a meeting tomorrow morning with a group of venture capitalists and angel investors, so we really need you to get it working today!"
That's not the only thing you didn't know -- you have absolutely no idea what the Covidmatic 19TM is or what it does.
The boss takes you back to the lab and shows you the Covidmatic 19TM. It has an input knob, an output display, and a PID controller. You notice that the three knobs on the PID controller only allow adjustment for the coefficients for the "standard" PID transfer function -- not the Ziegler-Nichols version. Nothing else about the Covidmatic 19TM looks familiar.
You decide to use the Ziegler-Nichols Maximum Sensitivity method to find "good" initial settings for the controller. You did not know which type (P, PI, or PID) version of the controller to use, so you design all three.
You set the input of the system as well as all the gains on the controller to zero and wait for the system output to go to zero.
Next, you increase the proportional gain in small steps, watching the output and waiting a while between each small change in proportional gain. The output stays at zero until you get to a proportional gain of 9, when the output looks like this:
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