The squareroot locus of a system is sketched below Answer th

The squareroot locus of a system is sketched below. Answer the following questions by referring to this figure. Parameters are identified at one point on the squareroot locus. When the gain is set too this value (4.21), which graph below best illustrates the response to a unit step input? The order of this system is: 1^st order 2^nd order 3^rd order 4^th order 5^th order 6^th order If the gain is increased from the given value (4.21), the system will: Become less stable Respond faster Oscillate faster Increase damping The best operating condition will be obtained when: K_p > 4.21 or K_p

Solution

a) The second graph is the answer. This graph corresponds to a critically damped system where it can´t stop oscillating. You can see that because the closed-loop poles for that value of kp are located in the jw axis.

b) The order of the system is 4th order, because it has 4 open-loop poles.

c) The system will: Become less stable, respond faster AND oscillate faster... All three answers.

d) The best operating condition will be obtained when Kp<4.21

e) The order of the numerator is 2nd order because it has 2 zeros in open loop.