Batch processes are commonly used for the manufacture of high-value specialty products. As opposed to continuous reactors that are operated around a nominal steady-state, the end-point in a batch reactor is not necessarily an equilibrium/steady-state point, allowing for achieving a wide range of product specifications by changing the initial conditions and input trajectories. This flexibility is particularly important in the polymerization industry as polymerization reactions often require a wide range of operating conditions to yield polymers with a desirable end-use quality, which is the primary control objective. Batch polymerization systems, however, exhibit numerous numerous characteristics, such as nonlinear, time-varying, and coupled dynamics, that complicate the control problem. The biggest challenge in the control problem is that measurements related to the final end-use quality are often unavailable during the batch and only made (off-line) after the batch is complete. Thus, direct control of the end-use qualities is often impractical in practice, and the control objective is pursued indirectly via trajectory tracking methods. In trajectory tracking methods (e.g., see [1–3]), trajectories for a set of measurable secondary variables, which should be related to the end-use properties, are generated off-line (or re-calculated at specific time points during the batch (e.g, see [4,5])) and then subsequently tracked using local proportional-integral-derivative (PID) or predictive controllers. Classical control approaches, such as PID control, are typically inadequate due to the nonlinearities and constraints in the process combined with interactions among the control loops while the benefits from using a predictive controller are dictated by the underlying model's quality.Polymerization models are identified either deterministically from first-principles or empirically from plant/process data. Deterministic polymerization models, however, have limited control applications. For instance, the number of system states is often excessive and/or the differential equations are overly complex (i.e., discontinuities, etc.) for use in any model-based or optimization-based control designs. Moreover, the model’s predictive capabilities are subject to the accuracy of numerous model parameters, many of which may be inaccurate. Furthermore, many of the simplifying assumptions taken during model development are often violated in specific situations in practice. The increased availability of past process data, however, can be exploited to improve the achievable level of accuracy of polymerization models developed using simpler model structures (the empirical models). Identification experiments, such as those in which a pseudo-random binary signal (PRBS) is applied on the process, while suitable for identification at steady states, are often too expensive to justify for polymerization reactors since they result in wasted batches (and therefore wasted monomers and initiators and loss of time). Furthermore, within the range of operating conditions during a polymerization, the process behavior is highly nonlinear and characterized by stages with different dynamics, making conventional system identification approaches, where a single linear model is identified, ill-suited for identifying an accurate dynamic model. The high expenses associated with every batch dictate the need for developing dedicated modeling tools for polymerization processes that minimize wasted batches in the model-development process and yet provide a model that captures the essential nonlinear and complex nature of the process. In our previously completed work , a multi-model approach was developed that exploits the simplicity of local linear models and uses an appropriate weighting scheme to capture the nonlinear nature of the process. However, in , full state measurements were assumed, which permitted identifying local linear state-space models in the form of linear discrete-time systems. In this work, we extend this modeling methodology and demonstrate its efficacy for a batch nylon-6,6 polymerization process where only limited measurements are available. The resulting data-based model is then used to formulate a trajectory tracking predictive controller. Through simulation studies, the modeling approach is shown to capture the major nonlinearities in the nylon-6,6 polymerization process, and closed-loop simulation results demonstrate the effectiveness of the proposed predictive controller and illustrate its advantages over existing trajectory tracking approaches such as conventional proportional-integral (PI) control and latent-variable MPC .
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