Electrical Engineering Stack Exchange is a question and answer site for electronics and electrical engineering professionals, students, and enthusiasts. It only takes a minute to sign up.
Sign up to join this community
I'm trying to understand system stability basics. Let us say I have a system $$ G(s) = \frac{500}{s^2 - 500} $$
Since it has two poles in the right half s-plane, it is unstable.
How can I stabilize it? I have read that a simple pole-zero cancellation would mostly be unreliable.
You can use a Routh–Hurwitz matrix to stabilize the system.
A Routh–Hurwitz matrix is a method for checking wheather or not a system is stable. It can also be used to stabilize the system by giving you a new denominator function for G(s).
According to this method, a system will be stable if the first column of the Routh–Hurwitz matrix contains only positive values.
You can stabilize the system by introducing a gain k and re-calculate the Routh–Hurwitz matrix to determine this k value that makes the system stable. In other words you can stabilize the system by inteoducing feed-back into it to conpensate for the unstable components of G(s).
Check these additional resources if you're still unsure about how to do this:
