Consider the design of a DERIVATIVE PROPORTIONAL controller WITH FILTER in its standard form, for a plant whose transfer function is P(s)=4/((s+1)(s+4)), =0.8; wn=4; T=0.03.

Solve analytically I) Design and calculation of the analog controller. II) Digitization of the analog controller by Tustin and calculation of the transfer function. III) Inverse sampling to find K, Td and N from the discrete controller.