Model Accuracy for Economic Optimizing Controllers: The Bias Update Case

Abstract

In many advanced control applications the numbers of manipulated and controlled variables are not the same. A combination of steady-state economic optimization and model predictive control has been employed to exploit the optimization opportunities presented by such non-square systems. The economic optimization subsystem uses a process model and is usually coupled with a model updating scheme to compensate for plant/model mismatch. Care must be exercised during the design of such a system to ensure the model-based optimization yields operating conditions which are optimal for the true plant. We present a rigorous criterion for determining under what conditions the model-based optimization embedded within the model predictive controller, using bias update, is capable of finding the plant optimum despite plant/model mismatch. The model accuracy criterion can be applied by solving an appropriate nonlinear programming problem. Further, it is shown that when the embedded model-based optimization problem has linear constraints, the bias update method will ensure convergence to the plant optimum, providing the model accuracy criterion is satisfied and an appropriate filter is included in the feedback path. Discussions are concluded with a demonstration of the methods on a real-time gasoline blending control and optimization problem