Applied Process Control

9Problem Solutions – Optimisation

S_9.1 7.6.5-7.8.3-9.2

1. Bellman's Principle of Optimality

   ‘An optimal policy has the property that whatever the initial state and initial decision are, the remaining decisions must constitute an optimal policy with regard to the state resulting from the first decision’.

2. Evaporator Optimal Solution

   

   The optimal path (not surprisingly) is given by the removal of 1 l per kg of sugar per hour, that is 5 → 4 → 3 → 2 → 1 l kg⁻¹, at a total cost of R4 per kg of sugar in solution →

S_9.2 7.6.5-7.8.3-9.2

LQR

• The LQR uses as an objective function the weighted sum of squares of the future deviations from setpoint ...