# Feedback Control Question: Finding compensator numerator (B(s)) and denominator (A(s)) polynomials to satisfy a specific requirement

I wish to find the polynomials B(s) and A(s) in the following compensator equation:

A(s)D(s) + B(s)N(s) = F(s)

Given,

$$N(s) = s - 2$$

$$D(s) = s^2 - 1$$

$$F(s) = s^2 + 3*s + 4$$

Condition

The degree of B(s) should be less than the degree of A(s)

• Are tou certain that its not $A(s)N(s) + B(s)D(s) = F(s)$? Dec 6 '20 at 6:59
• yes I am certain @NMech Dec 6 '20 at 7:40

your question is ill-conditioned: If $$A$$ must have a higher degree than $$B$$, 2 things can happen: $$A$$ is a constant, meaning $$B$$ must be 0: which means you cannot solve the equation as there is no $$s$$ term in $$A(s)(s^2-1)$$. Or $$A$$ is of order one (atleast one $$s$$) and $$B$$ is a constant: Which means the function can not be solved as there will be a $$s^3$$ present on the left hand side.