P(s) is a transfer function of a dynamic plant with two stable poles and no zero. The unit-step response of this plant is oscillatory with a damping ratio of 0.4 and damped natural frequency of 4 rad/sec. The unit step response converges to 5.
Determine P(s). Using MATLAB, plot the unit-step response of P(s) versus time.

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)?