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.