Optimisation Framework Using Hybrid Model

Dynamic Optimisation Framework Using Hybrid Model 

Dynamic sets of process-model mismatches data is generated for a wide range of the optimisation variables (z). These data are then used to train the neural network. The trained network predicts the process-model mismatches for any set of values of z at discrete-time intervals. During the solution of the dynamic optimisation problem, the model has to be integrated many times, each time using a different set of z. The estimated process-model mismatch profiles at discrete-time intervals are then added to the simple dynamic model during the optimisation process. To achieve this, the discrete process-model mismatches are converted to continuous function of time using linear interpolation technique so that they can easily be added to the model (to make the hybrid model) within the optimisation routine. One of the important features of the framework is that it allows the use of discrete process data in a continuous model to predict discrete and/or continuous mismatch profiles. 

The development and training of the neural network estimators for mismatches requires both the state variables (predicted by the model) and the mismatches at discrete points for a wide range of each optimisation variables. The number of sets of state variable and mismatch data for each type of state variable depends on the non-linearity and complexity of the system concerned. 

The state variable profiles of the model are assumed to be continuous and are obtained by integration of the DAEs over the entire length of the time. Also efficient integration methods (as available in the literature) are based on variable step size methods and not on fixed step size method where the step sizes are dynamically adjusted depending on the accuracy of the integration required. Therefore, the discrete values of the state variables are obtained using linear interpolation 

Usually discrete points are of equal length A = ti+, - tt), which usually represents the sampling time of the actual process. Now, if the state variable of the actual process at discrete time f,-, is given by xjj, the discrete mismatch at t will therefore be exdii = x i - xdj. 

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Dynamic Optimisation Framework Using Hybrid Model... 

Mujtaba and Hussain (1998) implemented the general optimisation framework based on the hybrid scheme for a binary batch distillation process. It was shown that the optimal control policy using a detailed process model was very close to that obtained using the hybrid model. 

The present work is based on the use of an optimisation framework dedicated to optimal control of global syntheses (Elgue, 2001). This framework combines an accurate simulation tool with an efficient optimisation method. Because of the step by step structure of global syntheses, the simulation tool is based on a hybrid model. The continuous part represents the hehaviour of batch equipments and the discontinuous one the train of the different steps occurring during the synthesis. 

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