(629b) Model Predictive Control of a Rotational Molding Process

Rotational Molding, also known as rotomolding or rotational casting, is a batch process used for the processing of plastics through distinct heating and cooling phases [11]. In this process a mold filled with a powdered charge is slowly rotated in a heated oven, resulting in the softened material being dispersed and sticking to the walls of the mold. In order to maintain an even wall thickness, the mold is continuously rotated at all times both during the heating and cooling phase. One of the control challenges is to obtain consistent high-quality products from one batch to another while avoiding unfinished parts with incomplete curing or degradation due to prolonged overheating.

Traditional approach for control of rotational molding processes has been to use an open loop, recipe-based policy. In this approach, a predefined input trajectory is applied to each batch [1]. The approach assumes that the desired product quality can be obtained by repeating historically successful input profiles. Although these approaches are easy to implement and do not require a model for the process, they are incapable of rejecting disturbances that affect the process. This has motivated the use of feedback control strategies.

A classical closed loop control approach that could be used in the rotomolding process is trajectory tracking. In this approach, a predefined set-point trajectory for a measured process variable, such as internal mold air temperature, is tracked. PI controllers are often used for implementing trajectory tracking control. The challenge with trajectory tracking approach is that even with perfect tracking, it may not result in desired quality, as the relationship between the measured/tracked variable and final quality may change significantly with changes in the process conditions across batches.

These challenges are addressed by control strategies that are cognizant of the causal relationship, not only between the manipulated and the (online) measured variables, but also between the manipulated and the final quality variables. A popular model-based control approach, model predictive control (MPC), has increasingly been studied for the control of batch processes [2-5]. The reasons for the popularity of these control schemes are twofold: first, the feedback controller can counter the model uncertainties that are associated with model simplifications and measurement errors; the other being their ability to handle the ever-present input/output constraints. In implementing these formulations, where possible, good first principles models are preferred due to the ability to predict process behavior beyond the data set used and estimate model parameters. However, first principles models are difficult to develop, as it is often impractical to estimate the parameters through experiments, particularly because of the associated cost. Furthermore, these first principles models pose computational challenges for direct use in predictive control formulation, for instance, in case of distributed parameter systems such as batch particulate processes.

These issues have motivated the use of simpler, often linear, models derived from past batch data. A variety of approaches for the development of data-driven models have been proposed. One excellent approach is partial least squares (PLS), which models the process in a projected latent space [6]. These models are essentially time-varying linear models, linearized around mean past trajectories, and therefore require the batches to be the same length, or to recognize an appropriate alignment variable. To account for these limitations, a multi-model approach was proposed in [5]. The multiple models were based on the 'current measurements' of the process instead of the 'time'. These developments were followed by contributions in the area of integration of these data-driven models with the advanced control formulations [4-5]. More recently, a subspace identification based batch control approach was proposed in [7] where a LTI state-space model of the batch process is estimated. Subspace identification methods, in general, are a class of model identification methods that is non-iterative in nature and models a process as a state-space linear time invariant system, identifying the system matrices along with the order of the system. One of the major advantages with this approach is that it facilitates the accommodation of variable duration batches without the need for alignment of batch lengths as demonstrated through different applications in [7-10].

Motivated by these considerations, this work presents a subspace identification based state-space modeling and control approach for rotational molding process to achieve desired quality specifications. Contributions from this developed system represent the progression of this industry towards advanced manufacturing practices, with improved reliability between batches.

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[9] Abhinav Garg, Brandon Corbett, Prashant Mhaskar, Gangshi Hu, Jesus Flores-Cerrillo (2017), High Fidelity Model Development and Subspace Identification of a Hydrogen Plant Startup Dynamics, Computers and Chemical Engineering, 106 183-190.

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[11] Felipe P.C. Gomes, Abhinav Garg, P. Mhaskar and Michael R. Thompson, Quality monitoring of rotational molded parts using a nondestructive technique, ANTEC (2018), Accepted.