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.

An array of m-50 thermoelectric modules is installed on the exhaust of a sports car. each module has an effective seebeck coefficient of sp of 0.143 5vk and an internal electrical resistance of r.-4 ? in addition, : (15 points each module is of width w 60mm and contains n=100 pairs of semiconducting pellets. each pellet hasan overall length of 2l-5mm and a cross-sectional area as 1.2 x 10'm and is characterized by a thermal conductivity of kpl2w rnk. the hot side of each module is exposed to exhaust gases at·p650c with hia4ow rrk while the osite side of each module is cooled by pressurized water at surface) and 156 °c (at the cool surface). 11s c with h: -500w/m'k. the modules are wired n series and the load resistance is r d=400ohm .the module surface temperatures, t, and ts are 183 "c (at the hot surface and 156c (at the cool surface) a)-draw a schematic of this scenario and label all parts. a. b. if the induced current, i, is 0.15 amps, what is the total power (pa) for one module? c. what is the total power harvest from the exhaust with all 50 modules?