Question
Download Solution PDFThe characteristic equation of a closed loop system is . Then the system is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The standard form of a second-order system’s characteristic equation is:
\( s^2 + 2\zeta\omega_n s + \omega_n^2 = 0 \)
Where:
- \(\zeta\) = Damping ratio
- \(\omega_n\) = Natural frequency
Given: s2 + 2s + 2 = 0
Compare with the standard form: \( s^2 + 2\zeta\omega_n s + \omega_n^2 = 0 \)
So, \(\omega_n = \sqrt{2}, \quad \zeta = \frac{2}{2\sqrt{2}} = \frac{1}{\sqrt{2}} ≈ 0.707\)
Interpretation:
Since \(0<\zeta<1\) ,the system is under-damped.
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