(363ad) Adaptive Economic Model Predictive Control for Batch Processes: Application to Rotational Molding Process

The present work addresses the problem of handling process non-linearity in batch process operation and control via a reidentification based subspace identification approach deployed within a Model Predictive Control (MPC) framework. In contrast to existing re-identification algorithms for continuous and batch processes, where all the recent and past experimental data is chosen to reidentify the model, the proposed approach is designed to use the most appropriate subset of the data. In particular, the data for re-identification is determined by first determining the equivalent of the locator from the training data set, and only using the portion of training batches from the locator to batch termination. The idea is to try and build the model using data pertaining to the state space region that the system is presently passing through. The proposed approach is implemented on a rotational molding lab scale setup along with an existing model monitoring technique deployed within the MPC which detects the model mismatch and triggers the re-identification algorithm. The results first utilize validation data sets to demonstrate the improved model resulting from the proposed re-identification approach followed by closed-loop experimental results demonstrating improved performance.

Batch processes are commonly found in many domains including mechanical, biochemical, agriculture and pharmaceutical industries due to the requirement of producing high-value products. Since the productions amount is small in batch process, it is important to maintain consistency in obtaining products with excellent quality and this can be only achieved by deploying a suitable control strategy. Rotational molding, or simply rotomolding, is one such batch process, used in industries for fabricating hollow plastics. Oftentimes, rotomolding is applied in producing large scale products like dinghies, water tanks and some automobile parts. Production of these items can be made profitable by using optimal control to significantly reduce the waste costs and in order to develop such a strategy one must focus on the modelling aspect associated with the same, especially for this process in which the quality variables which have to be tracked are not measurable and thus not available during the process.

Developing a first principles model based on physical that capture the process evolution can be one of the approaches for obtaining a high-fidelity model which can then be incorporated within an appropriately designed model predictive control (MPC) routine to obtain desired product qualities. However, coming up with an appropriate set of differential equations describing the heat transfer, particle dynamics and polymer rheology for the rotomolding process is itself a laborious task and may result in a highly complex model with lot of parameters. What makes this problem almost intractable is the need to develop a model that not only is able to model and predict properties such as the melt temperature, but the important quality attributes such as surface roughness and impact strength.

An alternative yet preferred data-driven modelling technique for this focused work on rotomolding is subspace identification where one builds a model with a certain structure, namely a linear time invariant (LTI) model, based on experimental batch data. The key is that by including previous experiments with varying product quality results, the model captures the dynamics of the system well enough so that it enhances the performance of the predictive controller and aids the economics of the operation. Data-driven model designs for continuous processes have been adapted for batch processes, with a batch modeling and control approach based on subspace identification, recently demonstrated. The proposed approach permits batches of variable duration to be used to build the model without the need for any batch alignment.

Although, even once a satisfactory LTI model is built, there is no guarantee that it will continue to perform well during a new experiment. This is due to many process factors like disturbances, non-linearity and/or existence of multiple phases in the system. One way to tackle this to use a non-linear model inside the predictive controller. However, this would make the problem complex and the computations slower for the controller to give control actions in time. The other way is to allow for the model to adapt according to the ongoing process conditions. Motivated by the above considerations, a new algorithm for online model re-identification in the context of batch processes is proposed, where a 'locator' is used to decide the portions of batch data best suited for training the model in terms of predictability.

An LTI state space model is identified initially before the start of an experiment. A few more steps and modifications are introduced when the above discussed subspace identification routine is triggered by a monitoring algorithm during an ongoing run. One has to recognise that re-identification in the context of batch processes is slightly different from that in continuous processes. Traditionally, in continuous processes where the historical data collected from the same sequence usually operated across a process mean, re-identification is done using the most recent data to account for most recent process behaviour. However, due to the batch nature, with a specified start and end points for the process, the algorithm can be re-designed to include only the 'future' data from all the past experimental batches for coming up with a state space model. The emphasis on 'future' data is made to realise that the primary goal of any modelling technique in the context of predictive controller is to come up with a model that can accurately predict the future. It doesn't really matter how well it predicts the completed portions of the batch since the process won't visit back the finished phases.

The results of the proposed approach in a closed-loop experimental setup demonstrate the algorithm’s success in achieving improved prediction and control performance.