Control Systems...

In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of

1. a pair of real roots with opposite sign

2. complex conjugate roots on the imaginary axis

3. a pair of complex conjugate roots with opposite real parts

Which of the following results is/are true regarding the polynomial

s⁴ + 3s³ + 6s² + 12s + 8

Consider the following statement about the system gain k  of a closed loop system G(s)?

a) k = 0 at both pole and zero

b) k = 0 at pole and k = ∞ at zero

c) k = ∞ at pole and k = 0 at zero

d) k = ∞ at pole and k = ∞ at zero

The root locus plot of a system having open loop transfer function will have angle of asymptotes are,

\(G\left( s \right)H\left( s \right) = \frac{{k\left( {s + 10} \right)\left( {s + 70} \right)}}{{{s^3}\left( {s + 100} \right)\left( {s + 200} \right)}}\)

A system has the characteristic equation: s⁴ + Ks³ + 2s² + (K + 1) s + 10 = 0

The following system given by its characteristic equation

A system has the characteristic equation: s⁴ + 25 s³ + 15 s² + 20 s + K = 0