Let be a process described by the following ODE: =3^2(1+32)+12, (0)=0 Consider that 1 can be used as a control input and the input 2 as a disturbance. Consider that the nominal values of the inputs are: 1_nominal = 6 and 2_nominal= 1.

3. Insert the process into a control system with a PI controller. (i) Draw the schematic of the control system. (ii) Obtain the ODE that describes the control system.

5. Insert each of the linear models in a control system, with a PI controller. (i) Draw the schematic of the control system. (ii) Obtain the ODE, for each linear model, that describes the control system.

For both problems, insert an image where the elaborated control scheme can be easily seen. for both ODEs insert the formula requested.