The written part of the transfer function of the PID out and found it to be such
\[{G\text{（}s\text{）}=\frac{{sK\mathop{{}}\nolimits_{{p}}+K\mathop{{}}\nolimits_{{i}}+s\mathop{{}}\nolimits^{{2}}K\mathop{{}}\nolimits_{{d}}}}{{s}}}\]
x=\frac{{-b}\pm\sqrt{b^2-4ac}}{2a}
Molecule can be decomposed into two multiplied by the formula
\[{ \left( s \pm K\mathop{{}}\nolimits_{{1}} \left) \left( s \pm K\mathop{{}}\nolimits_{{2}} \right) \right. \right. }\]
PID control system and a series link, open-loop transfer function is multiplied by two transfer functions. Appropriately adjusting three parameters of PID, dipole cancellation can be achieved. Eliminate the system unstable poles.
Further, the characteristic equation of the system is open-loop transfer function of the molecule plus the denominator.
In other words, adjusting the parameters of the PID three links. I can change the position of the roots of the characteristic equation of the complex plane. Sufficient Conditions system stability is that all roots of the characteristic equation have negative real part. And the three parameters of PID regulator, can change the position of the Roots apparent features.
Then return to the landlord of the problem, obviously, if the characteristic equation of the system is the high-order (higher than second order), and a simple PID has no control over the location of all of the root system may not be able to achieve stable, then the system is clearly You can not be used to control the PID.
There are a lot of people say why PID can get complicated model-free control. . . I guess, probably because of some models of complex systems after local linearization can be achieved dipole cancellation, falling into a low-level system, and I remember talked about the textbooks.
I've just watched a feeling answer to say quite right.
Even in the 21st century today, PID's "highest" theoretical results are limited to a second-order without higher-order response without higher-order terms without delay with no saturation controller system, among other factors, this is not enough. " practical "ah. Control theorists have to work harder ah ......
I suppose I have to do a little impression of the graduation project. . .