### Files

### Abstract

J. V. Kadam, W. Marquardt Lehrstuhl für Prozesstechnik, RWTH Aachen University, Turmstr. 46, 52064 Aachen, Germany B. Srinivasan, D. Bonvin Laboratoire d’Automatique, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland Optimization of Transitions in Industrial Polymerization Processes using Solution Models Increasing demand on delivering on-spec product, higher operating costs and diminishing profit margins in the polymerization industry require cost- optimal process operation. This has led to the development of new tools and techniques for the operation of polymerization processes. Besides the added complexity due to market-driven operation, polymerization processes have intrinsic characteristics that cause specific problems in applying advanced optimization and control techniques. Planned or unplanned polymer load and grade changes are typical transitions routinely performed in a polymerization process. In this contribution, transition optimization problems (e.g. minimization of the transition time or the amount of off-spec polymer product) under quality control are considered. We address the challenges faced by any polymerization control strategy, i.e. process uncertainty, which requires on-line updates of any off-line computed solution. Furthermore, it is assumed that measurements of key process variables are available both on- line and at the end of the transition. Two major measurement-based approaches are classified as: 1. Process model approach: Here, measurements are used on-line to correct the current state of the process and re-estimate key model parameters. The inputs are updated subsequently by a repetitive on-line solution of an optimization problem that utilizes a dynamic process model. 2. Solution model approach: Here, measurements are used to directly update the inputs using a parameterized solution model that has been obtained from off-line optimization using a nominal dynamic process model (this is explained later). In the solution model approach considered in this paper (see [1] for more details), the necessary conditions of optimality (NCO) are enforced using a solution model and measurements. Thus, the approach is also labeled NCO tracking [1]. The solution model is obtained by appropriately parameterizing a robust optimal solution of the optimization problem with uncertainty [2]. The solution model is defined in terms of the sequence of input arcs corresponding to constraint-seeking arcs (active path constraints) and sensitivity-seeking arcs. The constrained variables are kept active using simple PID-type controllers. Sensitivity-seeking input arcs minimize the objective function sensitivity. Terminal constraints are handled by updating the corresponding switching times in a run-to-run fashion using the constraint measurements available at the end of the transition. Furthermore, terminal constraints can also be enforced within a single run by proposing a model for predicting the terminal constrained variables or tracking feasible reference trajectories. For the sake of illustration, let us consider the optimal solution shown in Figure 1, where there is the terminal constraint ytf on y. The corresponding solution model includes three arcs: input upper bound arc (left), constraint-seeking arc (middle) and input lower bound arc (right). The input u is kept at its upper bound umax until the constraint y reaches its lower bound ymin that is kept active by manipulating u until the switching time ts is reached. This switching time, which is determined to satisfy the terminal constraint ytf, is adjusted on the basis of a prediction of ytf using a simple empirical. This empirical relationship has to be sufficiently conservative to guarantee end-point feasibility. We assume that this qualitative solution model remains the same in the presence of uncertainty. This might be restrictive in some cases, especially when solving a complex industrial optimization problem with many inputs as well as path and terminal constraints. Techniques to deal with changing sets of active constraints are explained elsewhere (see e.g. [3]). An industrial polymerization process is considered as a case study. The dynamic process model is fairly large with 2500 DAEs. Grade change transition in minimal time is targeted here. The optimization problem has three time-variant inputs and many path and terminal constraints. The optimization problem with nominal model parameters is solved off-line. The resulting solution is subsequently characterized to derive a robust solution model. It is verified that the solution model does not change for the class of uncertainty considered (unknown initial solvent concentration) and the choice of the initial steady state. Furthermore, it is assumed that polymer quality measurements are available on-line. The solution model is quite complex, thus leading to many controllers and switching times for enforcing the terminal constraints. The solution model optimization approach is applied using both within-run and run-to-run and updates for a number of uncertainty realizations. In most of the cases, the transition time is nearly optimal, which is verified by doing re-optimizations. Furthermore, in every realization of the class of uncertainty, all path and terminal constraints can be respected. This approach, in conjunction with techniques for on-line active set change and solution model detection, represents a very efficient and cost-effective operational strategy for general industrial problems. [pic] Keywords: Dynamic optimization, necessary conditions of optimality, optimizing control, constraint tracking, grade change, polymerization. [1] Srinivasan, B., D. Bonvin, E. Visser and S. Palanki (2002): Dynamic optimization of batch processes II: Role of measurements in handling uncertainty, Computers and Chemical Engineering 27, 27-44. [2] Schlegel, M. and W. Marquardt (2004): Direct sequential dynamic optimization with automatic switching structure detection, DYCOPS 2004, Massachusetts. [23 Kadam, J. V. and W. Marquardt (2004): Sensitivity-based solution updates in closed-loop dynamic optimization, DYCOPS 2004, Massachusetts.