On Real-Time Optimization using Extremum Seeking Control and Economic Model Predictive Control : With Applications to Bioreactors and Paper Machines

Sammanfattning: Process optimization is used to improve the utility and the economic performance of industrial processes, and is as such central in most automation strategies. In this thesis, two feedback-based methods for online process optimization are considered: Extremum seeking control (ESC), a classic model-free method used for steady-state optimization which dates back to the early 1900's, and economic model predictive control (EMPC), a more recent method which utilizes a model to dynamically optimize the closed-loop process economics in real time.Part I of the thesis concerns ESC. Due to a well known result by Krsti\'c and Wang, it is known that the classic ESC-loop will possess a stable stationary solution in a neighborhood of the optimum when applied to dynamic plants. However, existence and stability of an optimal solution alone are not sufficient to guarantee that the ESC-loop will converge to the optimum; uniqueness also has to be considered. In this thesis, it is shown that the near-optimal solution is not necessarily unique, not even in cases where the objective, i.e., the steady-state input-output map, is convex. The stationary solutions to the loop are shown to be characterized by a condition on the local plant phase-lag, and for a biochemical reactor it is found that this condition can be satisfied not only locally at the optimum but also at arbitrary points away from the optimum. Bifurcation theory is used to show that the observed solution multiplicity may be explained by existence of fold bifurcation points, and conditions for existence of such points are given.The phase-lag condition for stationarity combined with the result by Krsti\'c and Wang suggest that the process phase-lag is connected to steady-state optimality. In this thesis, it is shown that the steady-state optimum corresponds to a bifurcation of the plant zero dynamics which is reflected in large local phase-lag variations. This explains why the classical ESC method will have a near-optimal stationary solution when applied to dynamic plants, and it also shows that a steady-state optimum may be located using only phase information. Finally, we introduce greedy ESC which is applicable to plants where the dynamics may be separated into different time-scales. By optimizing only the fast plant-dynamics, significant performance improvements may be achieved.Part II of this thesis concerns EMPC.The method is first evaluated for optimization of a paper-making process by means of simulations. These reveal several important properties of EMPC, e.g., that EMPC in the presence of excessive degrees of freedom automatically selects the inputs which are currently most efficient, and that EMPC effectively plans ahead which leads to significantly improved performance during grade changes. However, it is also observed that EMPC often operates with constraints active since economic objectives frequently are monotone, and this may lead to issues with robustness. To avoid active constraints, constraint margins are introduced to force the closed-loop to operate in the interior of the feasible set. The margins affect the economic performance significantly and the optimal choice is dependent on the uncertainty present in the problem. To avoid modeling of the uncertainty, it is suggested that the margins are adapted based on feedback from the realized closed-loop economic performance.