1. What is an input-output model, and how can you develop it from a state model? When is this possible? 2. Describe a procedure that would allow you to develop the input-output model for an ideal, binary distillation column. 3. Define the concept of degrees of freedom and relate it to the solution of E equations with V variables. 4. How many degrees of freedom do you have in a system composed of P phases with C components? (Recall Gibbs' rule.) 5. How many degrees of freedom do you have in a system composed of P phases with C components if the mass of each phase is given (i.e., M1,M2, ,MP) ? (Recall Duhem's rule.) 6. How does the number of degrees of freedom affect the number and the selection of the control objectives in a chemical process? 7. Why do we claim that d disturbances reduce the number of degrees of freedom by d ? 8. Why can a control system not be designed for an overspecified process? 9. Can you have the desired operation for an underspecified process? If yes, explain why. If no, explain how can you lift the underspecification. 10. Consider a system modeled by the following set of state equations: dtdx1=f1(x1,x2,m1,m2,m3,d1,d2)dtdx2=f2(x1,x3,m1,d2)dtdx3=f3(x1,x2,x3,m2,m3,d1,d2,d3) where x1,x2, and x3 are the state variables, m1,m2, and m3 are the manipulated variables, and d1,d2, and d3 are the external disturbances. (a) How many degrees of freedom does the system possess? (b) How many control objectives can you specify at most? (c) Consider this system at steady state. How many degrees of freedom does it possess