(748b) Accommodating Missing, Non-Uniformly Sampled and Delayed Measurements for Modeling and Control of Variable Duration Batch Processes in a Subspace Identification Framework

Batch processes are an indispensable part of chemical manufacturing industry used for manufacturing of specialty chemical products such as polymers, pharmaceuticals etc. Further, large chemical plants in nominal continuous operation exhibit batch behavior during plant startups and shutdown phase. Acquisition of measurements from operation of batch processes is an important part of process control where important processes variables are sampled and stored in a database for process modeling and monitoring / control. Often some measurements may be corrupted, for instance, due to sensor faults leading to missing values in the database. Further, it is always not possible to measure all the variables at the same sampling time. For instance, measurement of certain variables may depend on offline analysis which may not arrive at a fixed time interval leading to delayed and non-uniform measurements. Therefore, a batch process modeling and control approach is required which can explicitly handle such cases.

A variety of approaches for development of data-driven models have been proposed in the literature. One excellent approach is partial least squares (PLS), which models the process in a projected latent space [3]. These models are essentially time-varying linear models, linearized around mean past trajectories, and therefore require the batches to be of same length, or to recognize an appropriate alignment variable. To account for these limitations, a multi-model approach was proposed in [2]. These models were based on the 'current measurements' of the process instead of the 'time'. These developments were followed by contributions in integration of these data-driven models with the advanced control formulations [1-2]. More recently a subspace identification based batch control approach was proposed in [4] where a LTI state-space model of the batch process is estimated. The subspace identification approach in [4] differed from conventional subspace identification approach for continuous process [5] in Hankel matrices construction to utilize data from multiple batches. A direct consequence of this approach is that it does not require alignment of different batch lengths. This approach will be referred to as batch subspace identification in this work.

The existing formulations of batch subspace identification method have dealt generally with all process variables being measured at a fixed rate [4,6,7]. Recently, [8] discussed the formulation for a multi rate process, to handle the case where some of the measurements are available at different rate than others. However, these results do not explicitly consider missing and delayed measurements in the batch subspace identification formulation. Further, the formulation of batch subspace identification requires generalization for the case of non-uniformly sampled measurements, that is, the rate at which variables are measured is not same during the entire batch duration.

Motivated by these considerations, this work presents a subspace identification based state-space modeling and control approach for batch process with missing, non-uniformly sampled and delayed measurements. The key idea is to adapt batch subspace identification using the error minimization principles of classical system identification through an iterative algorithm to explicitly handle missing and non-uniformly sampled measurements. The efficacy of the proposed modeling approach is demonstrated using a simulated batch process. The historical batch database is first modeled using the proposed approach. The identified model is then validated on new batches to demonstrate its predictive quality. Finally, the identified model is deployed in an MPC to demonstrate its control ability.

[1] S. Aumi, P. Mhaskar, Integrating Data-Based Modeling and Nonlinear Control Tools For Batch Process Control, AIChE Journal 58 (2012) 2105-2119.

[2] S. Aumi, B. Corbett, P. Mhaskar, and T. Clarke-Pringle. Data-based modeling and control of nylon-6, 6 batch polymerization. Control Systems Technology, IEEE Transactions on, 21(1):94-106, Jan 2013.

[3] J. Flores-Cerrillo, J. F. MacGregor, Control of particle size distributions in emulsion semibatch polymerization using mid-course correction policies, Industrial and Engineering Chemistry Research 41 (7) (2002) 1805-1814.

[4] B. Corbett, P. Mhaskar, Subspace identification for data-driven modelling and quality control of batch processes, AIChE Journal 62 (2016) 1581-1601.

[5] L. Ljung, System Identification: Theory for the User, Pearson Education, 1998.

[6] Abhinav Garg, P. Mhaskar (2017), Subspace Identification Based Modeling and Control of Batch Particulate Processes, Industrial and Engineering Chemistry Research, 56 (26) 7491-7502.

[7] 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.

[8] Rashid, M. M., Mhaskar, P., & Swartz, C. L. (2017). Handling multi‐rate and missing data in variable duration economic model predictive control of batch processes, AIChE Journal 63(7), 2705-2718.