COMPUTATIONAL STUDIES IN THE OPTIMIZATION OF SYSTEMS DESCRIBED BY DIFFERENTIAL/ALGEBRAIC EQUATIONS (DYNAMIC MATRIX CONTROL, COLLOCATION)

Modern approaches to process control are model-based, and frequently have problem statements that are optimization problems. In addition, process flowsheeting (large scale process simulation) systems have recently been extended for dynamic simulation. These trends in the computer application areas of chemical engineering have dictated the need for continuing computational studies and generalized optimization methods that are suitable for model forms derived from chemical engineering problems.; A method is presented for the solution of optimization problems subject to differential/algebraic equation constraints. It combines the technologies of successive quadratic programming (SQP) and global spline collocation, and uses piecewise constant functions for the independent variables. The method employs a simultaneous optimization and solution strategy, which has recently been shown to be computationally superior to the sequential optimization and solution strategy.; The SQP algorithm that is used in the method was generalized to solve large scale problems. This was accomplished by use of new Jacobian matrix evaluation technology, sparse linear algebra techniques, and the development of a special quadratic programming algorithm for large scale problems. The method and its underlying mathematical programming components were proven to work by the successful solution of known test problems.; The algorithm was successfully applied to the solution of dynamic optimization problems for a catalytic CSTR in which the ammonia synthesis reaction is taking place. Dynamic Matrix Control (DMC) problem solutions were compared to the conventional optimal control problem solutions with an economic objective functional. The results showed that choosing the time horizons as dictated in DMC yielded final values for the independent variables that end up at their new steady state optimal values corresponding to the currently known or predicted disturbances in every case. It was also shown that the DMC problem can be equivalently expressed as a certain fixed end point problem in a limiting case.; Areas where the method could be beneficially applied are optimal model predictive control, parameter estimation, and process flowsheeting optimization problems involving dynamic and/or distributed models.