Discuss the relative merits of using a proportional plus integral controller over purely proportional control in modifying system performance? [5] A second-order type-0 system with transfer function

G(s)=1/(s+1)(s+5)

is to be compensated using the controller

Gc(s)=1+K/s

under unity feedback. For the overall feedback system:

(i) Derive the system characteristic equation [5]
(ii) Obtain the value of integral gain K for which the system becomes unstable [5]
(iii) Discuss how K can be designed to meet relative stability criteria.

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?