This problem assumes our standard unity (H(s) = 1) negative feedback closed-loop control system. The given open-loop transfer function is 2 ( ) ( 2) G s s s   . Using denominator parameter matching, design a PD (proportional-derivative) controller ( ) G s K Ks C PD   to achieve a closed-loop overdamped second-order response with 1s  2 and 2 s  4 . What is the resulting numerical closed-loop transfer function T(s)? For a unit step input R(s) and assuming 1.0 is the desired steady-state output value, determine the closed-loop correction factor, if one is required. Determine the pre-filter transfer function ( ) G s P , if one is required. Given a unit step input R(s), sketch the open-loop and input-corrected, pre-filtered closed-loop output responses, assuming zero initial conditions for both cases.

A3-mm-thick panel of aluminum alloy (k 177 w/m-k, c 875 j/kg-k and ? = 2770 kg/m) is finished on both sides with an epoxy coating that must be cured at or above t,-150°c for at least 5 min. the production line for the curing operation involves two steps: (1) heating in a large oven with air at ts,0-175°c and a convection coefficient of h, 40 w/m2. k, and (2) cooling in a large chamber with air at 25°c and a con- vection coefficient of he 10 w/m2.k. the heating portion of the process is conducted over a time interval te which exceeds the ime required to reach 150°c by 5 min (h = r + 300 s). the coating has an emissivity of ? = 0.8, and the temperatures of the oven and chamber walls are 175 and 25°c, respectively. if the panel is placed in the oven at an initial temperature of 25°c and removed from the chamber at a safe-to-touch tempera ture of 37°c, what is the total elapsed time for the two-step curing operation?