Optimal operation with changing control objectives
Abstract
This thesis proposes advances in control structure design, with the goal of solving a steady-state optimization problem through feedback control. When disturbances act upon the system and change the set of constraints that are optimally active, a different control structure becomes necessary to achieve optimal operation. This thesis addresses this challenge by proposing systematic methods for designing control structures that automatically switch control objectives when necessary. One contribution is the proposal of a decentralized control structure for processes with few constraints, where optimal operation is attained with PID controllers and min/max selectors. For processes with several constraints, a region-based MPC is proposed, with different tracking objectives for each set of active constraints, and an active set detection block that switches the control objectives being tracked. Because the ideal controlled variables for the unconstrained degrees of freedom are closely related to the steady-state cost gradient with respect to the inputs, a simple method for cost gradient estimation method is proposed based on known self-optimizing control methods. This estimated cost gradient can be used in a variety of methods for feedback optimizing control. The application of region-based control and primal-dual feedback optimizing control methods is illustrated with some examples. In addition, this thesis presents a problem of optimal inventory management subject to unit bottlenecks, which is inherently a dynamic problem of maximizing production. The bidirectional inventory control structure is extended to deal with minimum flow constraints, resulting in a control structure that is able to satisfy constraints when feasible. Finally, based on the mathematical framework of self-optimizing control, an alternate formulation for existing methods is presented, arriving to an explicit expression for the optimal measurement combination when rejecting disturbances is to be prioritized over measurement error. The obtained expressions are valid regardless of the number of measurements or presence of measurement error.