# System Modelling - Output and State Differential Equation

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Consider the ice-cream manufacture process shown in the attachment. The ice-cream is made up of the following ingredients:

i) Liquid (cream, milk, water etc.) added at a rate r1 [kg/hr] and with a density p1 [kg/1].

... {see attachment for more details}

(a) Find a model for the process with height in the tank and density of manufactured ice-cream as outputs. Be careful of units. Clearly state any futher assumptions you find necessary.

(b) By considering profit as the difference between cost and income, add a state differential equation to your system to give profit an additional output. The liquid ingredients cost C1 [Rand/litre], the sugar costs C5 [Rand/kg] and the air is free (i.e. negligible compression costs etc.). The selling price of ice-cream is S [Rand/litre].

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This solution is provided in 266 words in an attached .doc file. It includes explanation of system modeling, and provides state equations and conservation of law.

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Please check the attached file Q36413.doc.

Answer:

a)

In system modeling, it is nature to use conserved variables as state variables, such as volume, mass, energy, etc. The objective is to construct state differential equations based on these conserved variables to describe the change of states and then utilize state variables to form output variables, which are ...

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