Question

(1) When a polynomial for the numerator of a transfer function is represented by the vector [1 3 0j in Matlab, what is the polynomial (in )? Ss35 (2) What is the final value of a response which is given b1612 (o)- (0)-3(0)3 ()undefined (3) Determine the damping ratio of the system described by)235 )1(b) 2.5 (c)5 (d) 10 (e) 25 (f) something else (4) (True or alse) The system with the following characteristic equation is stable. (5) Marginally stable systems are considered (stable, unstable under the BIBO definition of stability 7

Answer 1

When a polynomial for the numerator of a transfer function is represented by [1 3 0] in Matlab, the polynomial (in s) is 1s^2 + 3s + 01 = s^2 + 3s (2) We have to find the value of response which is given by y(s) = 3 (s + 2)/s (s + 1) (s - 2) lim_s rightarrow 0 s y(s) = lim_s rightarrow 0 3 (s + 2)/(s + 1)(s - 2) = 3 middot 2/(1)(2) = -3 \r\n (3) The damping ratio of the system determine by G(s) = 1/s^2 + 10s + 25 = 1/s^2 + 2s 5 +(5)^2 = 1/25 (5)^2/s^2 + 2s 5 + (5)^2 Here steady stale value is 1/25 Damping ration here is 1 (4) The system with following characteristic equation is stable or not s^14 + 8s^13 + 2s^12 + 6s^11 + s^10 + 2s^9 + s^8 3s^7 + 3s^6 + s^5 + 6s^4 4s^3 + 5s^2 + 3s - 1 = 0..