Profitable and dynamically feasible operating point selection for constrained processes

• Optimal back-off in constrained operation is determined by trading off feasibility vs loss in profit that is quantified by a second order cost function.
• Formulated an optimization problem to simultaneously determine the feasible and profitable operating point and the controller.
• Proposed a novel two stage iterative solution strategy to solve the dynamic back-off problem using semi-definite programming techniques.
• Case studies are presented to demonstrate the significance of the approach.

The operating point of a typical chemical process is determined by solving a non-linear optimization problem where the objective is to minimize an economic cost subject to constraints. Often, some or all of the constraints at the optimal solution are active, i.e., the solution is constrained. Though it is profitable to operate at the constrained optimal point, it might lead to infeasible operation due to uncertainties. Hence, industries try to operate the plant close to the optimal point by “backing-off” to achieve the desired economic benefits. Therefore, the primary focus of this paper is to present an optimization formulation for solving the dynamic back-off problem based on an economic cost function. In this regard, we work within a stochastic framework that ensures feasible dynamic operating region within the prescribed confidence limit. In this work, we aim to reduce the economic loss due to the back-off by simultaneously solving for the operating point and a compatible controller that ensures feasibility. Since the resulting formulation is non-linear and non-convex, we propose a novel two-stage iterative solution procedure such that a convex problem is solved at each step in the iteration. Finally, the proposed approach is demonstrated using case studies.