Aservomechanism position control has the plant transfer function g(s) = 10/s(s + 1)(s + 10)

you are to design a series compensation transfer function dc(s) in the unity feedback configuration to meet the following closed-loop specifications .

the response to a reference step input is to have no more than 16% overshoot. the response to a reference step input is to have a rise time of no more than 0.4 sec.

the steady -state error to a unit ramp at the reference input must be less than 0.05.

(a) design a lead compensation that will cause the system to meet the dynamic response specifications, ignoring the error requirement

(b) what is the velocity constant kv for your design? does meet the error specification?

(c) design a lag compensation to be used in series with the lead you have designed to cause the system to meet the steady-state error specification.

(d) give the matlab plot of the root locus of your final design.

(e) give the matlab response of your final design to a reference step.