Test Stability using Routh Stability Method

[mym786]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

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

 

[CEL]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

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

i + G(s)H(s) = 0 means:
$$s^3+\alpha s^2 + 1 = 0$$
Since the polynomial is incomplete (there is no term in $$s^1$$) 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 $\alpha$ for which the system can be classified in the critically stable state.