(698d) Identification for Control of Batch Processes Using Latent Variable Models

Process system identification has been extensively studied since 1970s. However, most of the results are interpreted in the context of application for continuous processes. As a matter of fact, there are several differences between continuous and batch processes that make the identification problem of these two cases different. Major differences root their origins in the differences between the basic process operations such as time-varying operating conditions and significant nonlinear behaviour in batch processes. There are two major steps in solving a system identification problem. Design of Experiment (DOE) to generate the training dataset, and building a model based on the available dataset.

Design of identification experiments plays an important role in satisfying the identifiability conditions and improving the quality of the identified model. [1-4] discuss the effect of information content of the training dataset on the performance of system identification and find the optimal DOE based on different objective functions and constraints. Of main interest is to solve the identification problem using the dataset collected under feedback conditions due to safety and economic reasons. Necessary and sufficient conditions for identifiability of linear systems operating in closed-loop are derived in [5-8].

Several approaches for process modeling based on the generated training dataset are studied. They can be categorized into two major groups: parametric and nonparametric identification methods [9,10]. Parametric methods include approaches that impose a structure on the process model and include parsimonious number of parameters. On the other hand, nonparametric methods consist of approaches in which no specific model structure is presumed and usually a large number of model parameters are obtained during the identification procedure.

There are few papers discussing the system identification problem in batch processes. Shen et al. [11] try the application of a PID controller on an empirical Linear Time Invariant (LTI) transfer function built for a batch process case study. Nonetheless, this approach does not consider the nonlinearity and time-varying properties, which is very likely to occur in batch processes, in the process model. Ma and Braatz [12] assume the mechanistic model is available, and investigate the effect of parameter uncertainty in the identification DOE and optimal control in batch processes. However, in many practical situations, a reliable mechanistic model is not available. Several studies are performed on the modeling of batch processes using Latent Variable Models (LVMs)[13,14]. Some authors have tried to model the batch processes using Subspace Identification Methods (SIMs) [15,16]. SIMs have received considerable appreciation in the literature, yet the studies on SIMs are mostly confined to developing LTI models which may not be satisfactory for batch process modeling and control. Verhaegen and Yu [17] proposed a new version of SIM for modeling the Linear Time Varying (LTV) processes. However, it conveys extra effort to model the process locally at every sample time, While the approach proposed by Nomikos [13] models the LTV processes with much less effort using LVMs. However, there is no paper discussing the identifiability conditions of batch processes operating in closed-loop and the effect of training data generation step on the model accuracy. In a recent work, Golshan et al.[18] proposed a Model Predictive Control (MPC) approach based on Latent Variable (LV) modeling of batch processes, called LV-MPC. Golshan and MacGregor, [19] investigated the properties of three different modeling approaches that can be used in the course of LV-MPC.

In the current work the system identification issues for batch processes are explored by focusing on the identification for control using LVM approaches. First, the concept of identifiability conditions for batch processes is explored. Second, the necessary and sufficient conditions to satisfy identifiability for batch systems are derived. Furthermore, based on the identifiability conditions, the guidelines for generating the training dataset to be used in the LV modeling of batch processes are proposed for the three modeling approaches presented in [19]. Moreover, the optimal controller tuning to be used to generate the training dataset is proposed. Finally, a comparison of the SIMs and LVMs that reveals the similarities, differences, and connections between these two modeling alternatives is presented and it is shown that the effort included in the SIMs for modeling of LTV systems can be avoided by using LVMs for modeling of LTV systems.

All of the studies are verified by simulations. It is shown that identifiability conditions can be satisfied in many practical situations without the need for external excitations. Furthermore, it is revealed that the controller tuning in the training data generation has an important effect on the quality of the identified model. Finally, it is pointed out that SIMs do not give better model than LVMs in general and the errors embedded in different steps of SIMs can lead them to have less prediction power as compared to LVMs.

References

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[19] M. Golshan and J.F. MacGregor, ?Latent Variable Modeling of Batch Processes for Trajectory Tracking Control,? 9th international Symposium on Dynamics and Control of Process Systems, Leuven, Belgium: 2010.