The root locus of an open loop transfer function is shown be

The root locus of an open loop transfer function is shown below. Referring to this graph, answer the following questions by checking the best response: What is the order of the transfer function denominator? What is the order of the transfer function numerator? When the proportional gain is zero, the damping ratio, zeta, is zero is approximately, Letters A thru F identify points on the root locus. The point where the proportional gain is zero is identified by letter: Letters A thru E identify on the root locus. The point where the proportional gain is infinite is: Letters A thru E identify points on the root locus. The system exhibits oscillatory response when the root locus is between: (Check all that apply) Letters A thru E identify points on the root locus. The system damping, zeta, is about 10%: Letters A thru E identify points on the root locus. The time constant is about 0.5:

Solution

(a) the plot shows three poles with solid circles therefore order of the characteristic equation is three and hence denominator order is three..

(b)

the plot shows three zeros with light circles therefore order of the numerator equation is three .