## 283446 Multi-Tiered Dynamic Optimization of Partial Shutdowns with Constrained Ukf-Based State and Parameter Estimation

Thursday, November 1, 2012: 10:15 AM
323 (Convention Center )
Zhiwen Chong and Christopher L. E. Swartz, Chemical Engineering, McMaster University, Hamilton, ON, Canada

Process units are shut down from time to time either for maintenance or due to equipment failure. Shutdowns in intermediate units constitute a disruption in the processing chain, which can adversely affect the plant's ability to continue operation.  They frequently also have a negative effect on the operating economics of a plant due to the attendant loss of production capacity.

Our research focuses on the development of systematic strategies and formulations for the optimal operation of plants under partial shutdown conditions.  A partial shutdown is a type of circumscribed plant unit shutdown that permits the rest of the plant to continue operating to some degree. The goal of a partial shutdown strategy is to manipulate the available degrees-of-freedom in a plant, during and after a shutdown, such that production is restored in a cost optimal fashion while meeting all safety and operational constraints.  This can be accomplished through adjustments of production rates, recycles and buffer levels.

In order to compute these adjustments, we solve a differential-algebraic equation (DAE) based dynamic optimization problem containing a model of the plant. The DAE system is discretized using orthogonal collocation on finite elements, which results in a large-scale optimization problem.  An economics-based nonlinear model predictive control (MPC) control structure was used to mitigate effects of model uncertainty and disturbances.  Within this broad framework, we adopt a multi-tiered dynamic optimization approach that allows us to prioritize multiple competing objectives (economics, product quality, move suppression, etc.) and specify the trade-offs from one tier to the next. In this approach, separate optimization problems are solved sequentially, with the preceding tiers providing information to the latter tiers.  The optimal value of the objective function in a current tier is enforced as a constraint in the subsequent tier.  An attractive feature of the multi-tiered optimization approach is that unlike a weighted-penalty approach, it permits one to specify, for example, the exact amount of the economics one is willing to sacrifice (in dollar terms) in order to obtain say, smoother input trajectories.  In contrast, the specification of weights in a weighted penalty approach may lead to unpredictable trade-offs in the final solution.

A further aspect of this work is the investigation of the use of nonlinear state and parameter estimation algorithms to moderate the adverse effects of plant-model mismatch.  The estimation algorithms are based on novel configurations of the constrained Unscented Kalman Filter (UKF), a nonlinear derivative-free observer that received considerable attention in recent years.  The UKF was used to perform state and parameter estimation of large-scale DAE models.  Constraints on the state and parameter estimates are enforced through a simple projection method that is based on solving a quadratic program (QP).  States, parameters, as well as disturbance biases are estimated using this scheme.

Plant-model mismatch can often render terminal/restoration constraints infeasible. To address this, we propose a dynamic feasibility tier (in our multi-tiered optimization problem) that ensures that terminal constraints and parameter estimates from a one-step estimator are feasible throughout the model prediction horizon in the control optimization problem.   This represents a practical method for ensuring the feasibility of terminal constraints and parameter values obtained from a state/parameter estimator whose prediction horizon is shorter than that of the control optimization problem.

The strategies in this work are illustrated through simulation case studies based on Kraft pulp mill.  Conclusions are drawn and avenues for further work are identified.