469338 Subspace Based Quality Control of Variable Duration Batch Processes

Sunday, November 13, 2016: 4:27 PM
Monterey I (Hotel Nikko San Francisco)
Brandon Corbett and Prashant Mhaskar, Chemical Engineering, McMaster University, Hamilton, ON, Canada

Specialty chemical production makes up an important sector of the chemical processing industry. Examples include armaceutical and high quality polymer products. In these processes, economic gains are realized by achieving tightly specified product quality. This and additional factors, such as the ability to produce a wide range of product grades and the high cost of raw materials, favors using batch reactors for these products. While batch reactors provide benefits, they also introduce a variety of difficulties for closed loop control. In this work we address some of those issues and present a novel, data-driven, model predictive control scheme where the objective is explicitly formed to reach product quality. Furthermore, we demonstrate the ability of our method to incorporate time as a decision variable and appropriately implement corrective discrete events such as mid-batch additions.

In a typical batch process, first the reactor is charged with some ingredients then a transforming process is carried out. As the transformation proceeds, the reactor contents transform exposing a wide range of operating states. Since dynamic behavior of chemical systems is dependent on state, these processes are characterized by transient dynamic behavior. Clearly, the traditional control objective of stabilizing operation around a steady-state condition is not meaningful. Instead, the control objective for this class of processes is to reach a desired product quality by the end of the batch. This objective is particularly important to reject feed stock variations that introduce variance which, left uncorrected, would propagate to the product quality. However, direct feedback control on quality is complicated by a number of factors. Foremost of these, is that the desired quality measurements are often not available online. Furthermore, development of reliable first principal models for these processes is often impracticable because of the complex, nonlinear behavior and the wide range of operating conditions. Traditionally then, indirect approaches such as trajectory tracking have been adopted.

Trajectory tracking control for batch processes involves using closed-loop control to track pre-determined trajectories of measurable process variables. These pre-determined trajectories are often taken from historically successful trajectories. Industrially, tracking is usually achieved using PI control (possibly with some gain scheduling to address the nonlinear process dynamics). Additionally, literature contributions have highlighted the improved trajectory tracking using model predictive control [2, 3, 8, 9]. However, even if perfect tracking is achieved, the desired terminal quality may not be met. This is because the predefined trajectories fail to account for disturbances in initial conditions and throughout the batch.

An alternative to trajectory tracking that can be used for direct quality control is inferential control. In these approaches, a data-driven model is built that relates measurable process variables (temperatures, stirrer-torque, etc.) to product quality. To identify this relationship, a database of historical measurement trajectories and the resulting batch qualities is used. The ability of these methods to correctly drive the process to the desired quality naturally depends on two factors: the predictive ability of the identified model, and the validity of the model when applied to new closed loop input policies.

One highly successful inferential modeling and control method has been latent variable control [6, 7, 1, 4]. In these approaches, latent variable PCA or PLS models are identified from historical batch data. Specifically, the historical batch data is unfolded into a regressor matrix where each column (variable) contains a time indexed measurement from a historical batch. Model parameters are then identified to relate this regressor matrix to the available terminal quality measurements. The resulting model can be used in closed loop control by constructing a vector from new time-indexed measurements as the batch progresses, then applying the identified model to make quality predictions for candidate input trajectories. This method has shown success both in simulation studies and in industrial application. However, one significant restriction on these methods is the dependence on time-indexed model parameters. To address this issue, techniques for aligning batches (for instance using monotonically increasing variables) have been investigated. Nonetheless, the ability of these methods to use time as a decision variable to achieve the desired quality is inherently limited.

In recent work, we presented an alternative, state-space motivated, inferential quality control approach. The key idea is to break the problem of quality modeling and prediction into two parts. In the first part, we identify the dynamic (state-space) behavior of the process. This step is motivated by the understanding that the dynamic evolution of the process is fundamentally state-dependent and time independent. Therefore, by capturing a time independent state-space model of the system, we obtain a model that can be applied at any sampling instant without the need for batch alignment. To identify these dynamic models, we adapt the well studied method of subspace identification for use with historical and identification batch data. The second part of the quality modeling problem is making end-of-batch quality predictions. Fundamentally, we understand that the state of a system captures the entire instantaneous condition of the system. This motivates the claim that the terminal state identified in part one can be used to predict the terminal quality. Since the objective is to produce product in a relatively narrow quality range, a linear model is sufficient to relate terminal state and quality. Taken together, these two models, the dynamic state-space model and the quality model, provide a causal way to relate a candidate input trajectory and the resulting quality and can therefore be implemented in a shrinking horizon MPC.

In the current work, we extend these results to explicitly demonstrate the advantage afforded by the time independence of our proposed approach. Significantly, the time-independence of the model permits batch duration to be readily added as a decision variable in the MPC formulation. This is especially advantageous since the duration of a batch is one of the key factors influencing the resulting product quality. Therefore, enabling batch duration to be a manipulated variable substantially improves the ability of the controller to reach the desired quality set-point. [5]

To demonstrate the efficacy of the proposed modeling and control scheme, a simulation study of a batch PMMA polymerization reactor is presented. First a database of historical and identification batches is constructed. To demonstrate the ability of this methodology to account for discrete events, a discrete addition of reactants half way through the reaction is included in the nominal batch recipe. This database is then used to identify a dynamic state-space model and a quality model. Validation results, for batch data excluded from the training data, demonstrate the predictive ability of the combined dynamic and quality models. Finally, the models are implemented in a shrinking horizon MPC. The resulting quality control ability is demonstrated through quality set-point changes and feed stock disturbance rejection.

References
[1] Siam Aumi, Brandon Corbett, Tracy Clarke-Pringle, and Prashant Mhaskar. Data-driven model predictive quality control of batch processes. AIChE Journal, 59(8):2852–2861, Aug 2013.

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

[3] Siam Aumi and Prashant Mhaskar. An adaptive data-based modeling approach for predictive control of batch systems. Chemical Engineering Science, 91:11–21, Mar 22 2013.

[4] Brandon Corbett, Brian Macdonald, and Prashant Mhaskar. Model predictive quality control of polymethyl methacrylate. IEEE Transactions on Control Systems Technology, 23(2):687–692, Mar 2015.

[5] Brandon Corbett and Prashant Mhaskar. Subspace identification for data-driven modeling and quality control of batch processes. AIChE Journal, 62(5):1581–1601, May 2016.

[6] J Flores-Cerrillo and JF MacGregor. Control of batch product quality by trajectory manipulation using latent variable models. Journal Of Process Control, 14(5):539–553, Aug 2004.

[7] J Flores-Cerrillo and JF MacGregor. Iterative learning control for final batch product quality using partial least squares models. Industrial & Engineering Chemistry Research, 44(24):9146–9155, Nov 23 2005.

[8] J Flores-Cerrillo and JF MacGregor. Latent variable mpc for trajectory tracking in batch processes. Journal of Process Control, 15(6):651–663, Sep 2005.

[9] Masoud Golshan, John F. MacGregor, Mark-John Bruwer, and Prashant Mhaskar. Latent variable model predictive control (lv-mpc) for trajectory tracking in batch processes. Journal of Process Control, 20(4):538–550, Apr 2010.


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