Simple models for integrated optimization and parameter estimation

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Abstract
It is shown in this paper how simple linear steady state models can be constructed for use with a modified two-step algorithm to determine the optimum operating condition of a process. The models are formed in terms of pseudo gain and bias parameters. A number of the bias parameters can be estimated by comparison of the model and process outputs while the remaining model parameters are able to be set with only a minimal amount of prior knowledge of process relations. Besides possible savings in modelling effort, such simple models are computationally more convenient than more complex models for on-line optimization applications. The models exploit the power of the modified two-step procedure to ensure that the optimum operating condition is approached, in spite of model inaccuracies. Two applications are presented to illustrate the performance of the modified two-step algorithm when using a simple linear model. First, a linear process with a quadratic performance index is analysed and it is demonstrated how the correct optimum is achieved. A non-linear dynamic chemical reactor is then examined and a model is constructed which again achieves the correct process optimum.

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