Question 35.PE.MCQ.8: In the case of a linear constant coefficient second order co......
In the case of a linear constant coefficient second order control system, the system poles will be real and negative for the following condition of damping ratio `ζ ’
(a) ζ > 1 (b) ζ < 0
(c) ζ ≥ 1 (d) ζ = 1
(c) The second-order system is considered by a second-order differential of the form
\frac{d^2 y}{d t^2}+2 \zeta \omega_n \frac{d y}{d t}+\omega_n^2 y=\omega_n^2 x
Such a system has poles at −α ± jω_d, where α =ζω_n and ω_d = ω_n \sqrt{1-\zeta^2}.
For ζ = 0, the poles are at ±jω_n , that is, the poles are imaginary and complex conjugate.
For ζ > 0, but less than 1, the poles complex conjugate and have negative real parts. As ζ becomes smaller, the negative real parts of the complex conjugate poles come closer to the origin. For ζ = 1, the poles are equal, negative and real. The poles are located at−ω_n.
For ζ > 1, the poles are negative and real.
For ζ < 0, the poles lie in the R.H.P. of the s-plane.