Optimization Algorithms for Integration of Design, Control, and Scheduling for Chemical Processes Subject to Disturbances and Uncertainty

Abstract

Optimization of multiproduct processes is vital for process performance, especially during dynamic transitions between operating points. However, determining the optimal operating conditions can be a challenging problem, since many aspects must be considered, such as design, control, and scheduling. This problem is further complicated by process disturbances and parameter uncertainty, which are typically randomly distributed variables that traditional methods of optimization are not equipped to handle. Multi-scenario approaches that consider every possible realization are also impractical, as they quickly become computationally prohibitive for large-scale applications. Therefore, new methods are emerging for generating robust solutions without adding excessive complexity. This thesis focuses on the development of two of those optimization methods for the integration of design, control, and scheduling for multi-product processes in the presence of disturbances and parameter uncertainty. Firstly, a critical set method is presented, which decomposes the overall problem into flexibility and feasibility analyses. The flexibility problem is solved under a critical (worst-case) set of disturbance and uncertainty realizations, which is faster than considering the entire (non-critical) set. The feasibility problem evaluates the dynamic feasibility of the entire set, and updates the critical set accordingly, adding any realizations that are found to be infeasible. The algorithm terminates when a robust solution is found, which is feasible under all identified scenarios. To account for the importance of grade transitions in multiproduct processes, the proposed framework integrates scheduling into the dynamic model by the use of flexible finite elements. The critical set method is applied to two case studies, a continuous stirred-tank reactor (CSTR) and a plug flow reactor (PFR), both subject to process disturbance and parameter uncertainty. The proposed method is shown to return robust solutions that are of higher quality than the traditional sequential method, which determines the design, control, and scheduling independently. This work also considers the development of a back-off method for integration of design, control, and scheduling for multi-product systems subject to disturbances and parameter uncertainty. The key feature of this method is the consideration of stochastic random variables for the process disturbance and parameter uncertainty, while most works discretize these variables. This method employs Monte Carlo (MC) sampling to generate a large number of random realizations, and simulate the system to determine feasibility. Back-off terms are determined and incorporated into a new flexibility analysis to approximate the effect of stochastic uncertainty and disturbances. The back-off terms are refined through successive iterations, and the algorithm converges, terminating on a solution that is robust to a specified level of process variability. The back-off method is applied to a similar CSTR case study for which optimal design, control, and scheduling decisions are identified, subject to stochastic uncertainty and disturbance. Another scenario is analyzed, where the CSTR is controlled in open-loop, and the control actions are determined directly from the optimization. The back-off method successfully produces solutions in both scenarios, which are robust to specified levels of variability, and consider stochastic representations of process disturbance and parameter uncertainty. The results from the case studies indicate that there are interactions between optimal design, control, scheduling, disturbance, and uncertainty, thus motivating the need for integration of all these aspects using the methods described in this thesis. The solutions provided by the critical set method and the back-off can be compared, since the methods are applied to the same CSTR case study, aside from the differences in disturbance and uncertainty. The back-off method offers a slightly improved solution, though the critical set method demands much less computational time. Therefore, both methods have benefits and limitations, so the optimal method would depend on the available computational time, and the desired quality and robustness of the solution.