Control sets, energy parameter optimization

In developing correlations, one needs to connect energy with product yields and quality. One such example is discussed in detail in Chapter 4. The correlations can be applied for operation optimization. For automatic control, the correlations can be implemented into an APC system, which determines the set points for independent operating parameters. For manual control, operating targets for independent parameters can be obtained based on the correlations. 

A comparative study of the energy requirements and control properties of three thermally coupled distillation schemes and two conventional distillation sequences for the separation of ternary mixtures is presented. The responses to set point changes under closed loop operation with proportional-integral (PI) controllers were obtained. Three composition control loops were used, and for each separation scheme, the parameters of the PI controllers were optimized using the integral of the absolute error criterion. The effects of feed composition and of the ease of separability index were considered. The results indicate that there exist cases in which integrated systems may exhibit better control properties than sequences based on conventional distillation columns. 

Numerical optimization problems arise in many contexts. To predict the geometry of a molecule, we find the conformation of its atoms with the lowest potential energy. In process design x contains parameters such as equipment sizes, flow rates, temperatures, etc., and the cost function is a measure of the economic cost of operating the process. We fit a mathematical model for a system by minimizing the sum of squared differences between the model predictions and experimental data. In optimal control, we choose tiie best set of control inputs to maintain a process at the desired set point. 

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