Applied Process Control

9Problems – Optimisation

P_9.1 7.6.5-7.8.3-9.2

You are attempting to find the optimal evaporation sequence to take a sugar solution from 5 l of water per kg of sugar down to 1 l of water per kg of sugar. (This inverse concentration is used to preserve linearity.) You are planning your evaporation sequence over a period of 4 h, and to simplify the problem, you will only consider integral inverse concentrations at the end of each hour (i.e. 1, 2, 3, 4, 5). To evaporate 1 l of water in 1 h costs R1, but it costs R4 to evaporate 2 kg of water in 1 h, and R9 for 3 kg of water in 1 h and so on. This increasing cost arises from the fact that higher and higher pressure steam must be used.

1. State Bellman's (1957) principle of optimality for this type ...