Bucek (textbook author) explained how to find system frequency and damping
when the characteristic equation is quadratic. And when it's 3rd order,
as a second-order system with integral control, he factors out a
first-order system, assuming the remainder is zero. Then he wants that
pole on the real axis, and that becomes a design constraint.

But what should I do when my characteristic equation is fourth or fifth order? Just start factoring out first-order terms with no remainder, and put them all on the real axis?

But what should I do when my characteristic equation is fourth or fifth order? Just start factoring out first-order terms with no remainder, and put them all on the real axis?

--

"And don't skimp on the mayonnaise!"

"And don't skimp on the mayonnaise!"