You set out to design an automatic shower with a requirement for control of both the flow of water and the temperature. The system specifications are as follows: Data: Delivered flowrate F = 15 L/min of water at 43C by mixing hot water at 70C with cold water at 20C. The system will use regulating control valves to manipulate the flows of both the hot and cold-water streams. Properties of water: Density: Pw = 1000 kg/m3 Specific heat capacity: Cp = 4.18 kJ/(kg C) These parameters remain constant in this case. (i) Develop the relevant process model and determine the steady-state steam flows. (ii) Calculate the respective gain elements for all pairings of controlled and manipulated variables. (iii) Calculate a relative gain array for the system (RGA) and suggest a pairing of controlled and manipulated variables to minimise any interaction. (iv) Neatly sketch your final network labelling all items using conventional control symbols. (v) Could you suggest system modifications to make the pairing of manipulated and controlled variables determined in part (c) more favourable?