Consider the following data for the design of a PI controller in its parallel form by pole placement system, G(s)=1/(2s+1); =0.8; wn=1.5 rad/s, T=0.25 [s]. Analytically develop the following items: 1) Design of the analog controller and calculation of its values. 2) Digitization, transfer function, parameterization and calculation of its discrete controller values by the Tustin method. 3) Digitization of the plant by ZOH, 4) Direct Digital Design, design matrix and values. 5) Inverse sampling of the controller, determine the value of Ki and Kc of the controller designed in (4)