Write the closed-loop transfer function for the system and determine the closed-loop pole locations. Is the closed-loop system stable? (4 pts) b) Determine the damping ratio ζζ and the natural frequency nn of the closed loop system. (2 pts) c) Use inverse Laplace and partial fraction expansion to find the solution yy(tt) to a unit step input in RR? (5 pts) d) Sketch as accurately as possible the time response of the above system to a unit step input in R. Show all relevant time-domain specification calculations used in sketching your response. (

An external consultant recommends that a plant installs a bank of capacitors for power factor correction. this will reduce the peak electrical demand charges by an average of 93 kw every month. the plant current pays $13 per kw in peak demand charges. the capacitor bank will include 223 kw of fixed capacitors, and 183 of variable capacitors. the fixed capacitors cost $59 per kw, and the variable capacitors will cost $65 per kw. the consultant charges 21% of the equipment costs to install the capacitors. because this project will reduce the demand for the electric utility, they are prepared to provide a one-time rebate of $42 per kw of reduced demand. what is the simple payback period for this project (in years)?