Consider an open loop process transfer function. GP=(S+1)31 A PID controller with I=1min is to be designed. The PI controller is a special case of the PID controller with D=0. Typically, as D is increased above zero, the derivative action stabilizes the system so that for the same degree of oscillatoriness in the closed loop response, a KC higher than for a PI controller is obtained. If, however, D is increased too much, it destabilizes the closed loop system and the obtained KC for a given degree of oscillatoriness begins to decrease. There thus exists an optimum D that maximizes KC for a given degree of oscillatoriness. a. What is the D that maximizes the PID controller gain for sustained closed loop oscillations. b. Using the value of D above, obtain KC for a dominant closed loop pole = 0.7071. c. Obtain standard Zeigler-Nichols PID settings