A servomechanism position control has the plant transfer function 10 s(s+ 1)(s + 10) G(s) = = You are to design a series compensation transfer function D(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 0.02 (a) Design a lead compensation that will cause the system to meet the dynamic response specifications. (b) If D(s) is proportional control, D(s) = kp, what is the velocity con- stant K? (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.