Test Stability using Routh Stability Method

mym786

1. The problem statement, all variables and given/known data

For a control system that has G(s)H(s) = [itex]\frac{1}{s^{2}*(s+\alpha)}[/itex]


2. Relevant equations

1 + G(s)H(s) = 0

3. The attempt at a solution

Exam question i messed up . I really need to know the answer.

CEL

i + G(s)H(s) = 0 means:
[tex]s^3+\alpha s^2 + 1 = 0[/tex]
Since the polynomial is incomplete (there is no term in [tex]s^1[/tex]) there is at least one root in the RHP and the system is unstable. No need to use Routh algorithm.

mym786

I forgot one more thing. It also says find the value of [itex]\alpha[/itex] for which the system can be classified in the critically stable state.