(716c) Polynomial Narmax-Based Nonlinear Model Predictive Control of Modular Chemical Systems

Increased interest in both academia and industry in recent years to develop continuous-flow processes for pharmaceutical manufacturing has been motivated by potentially reduced production times, waste material, and product quality variations while simultaneously providing flexibility with regard to demand changes (e.g., see [1,2] and citations therein). Of recent interest is end-to-end synthesis in modular, reconfigurable systems, which employ process intensification and plug-and-play connectivity. The fact that the individual components are limited in number, and can be thoroughly characterized before being combined into an end-to-end system, opens the door for the design of process systems engineering solutions based on first-principles models which involve partial and ordinary differential (algebraic) equations (PDAEs/DAEs).

Spatial discretization methods for the numerical solution of such PDAEs/DAEs result in systems with potentially thousands of states [3]. Such models pose challenges in regard to their incorporation into real-time model-based optimal control due to the computational burden. This high computational cost is avoided in the model predictive control technology widely used in chemical and related industries, which is based on empirical models constructed from linear input-output data. In past work, we have explored ways to expand the applicability of linear input-output models in input-output MPC schemes for the plantwide control including startup of modular chemical systems, including ways to automatically construct linear models from first-principles models while minimizing the effects of uncertainties and nonlinearities on the performance of the closed-loop system (e.g., [3,4] and references cited therein). While these techniques can be effective for many chemical modular systems, the use of linear models can be limiting for processes with strong nonlinearities, especially when the system has a limited number of manipulated variables at the upper level regulatory layer (see [3,4] for discussion of this latter point).

This work explores the formulation of real-time implementable nonlinear model predictive control algorithms for modular chemical systems. The PDAEs/DAEs that arise in modeling modular chemical systems are of too complex to be directly incorporated into real-time nonlinear model predictive control (NMPC), irrespective of whether the optimization is implemented as sequential iterative simulation-optimization or by incorporation of the model equations directly into the optimization as constraints [5,6]. As in industrial model predictive control algorithms, we consider NMPC formulations based on input-output models, so that a real-time implementation would be generally applicable to all modular chemical systems. Given that no experimental data are available when the chemical modular system is first started up, empirical models fit to experimental data are not applicable. Instead, the input-output model should be constructed directly from simulated data generated by first-principles models. Recent literature has typically called these “surrogate models’’ [7] as being distinct from models fit to data, and because surrogate models include both empirical (ignore physics) and the full variation of types of grey box models (a mix of empirical equations and first-principles equations).

Input-output NMPC formulations that incorporate neural network models have been applied in the chemical industry for decades [8]. A drawback of neural network models is that their mathematical structure makes it challenging to derive methods for the nonconservative analysis of stability, performance, and robustness. This talk explores the construction of computationally tractable nonlinear models for on-line optimization and control. We explore the usefulness of nonlinear autoregressive and moving average exogenous input (NARMAX) models, with a focus on polynomial models, which have a mathematical structure that is more amenable to the development of control systems analysis and design algorithms. In particular, advances made in polynomial programming for static systems have been extended to nonlinear dynamical systems to derive nonconservative robust analysis conditions and to formulate NMPC algorithms [9]. While polynomial models have been studied in the literature to some extent, they have been not widely applied in practice due to their tendency to be overparameterized, resulting in identifiability issues and overfitting [10].

In this study, first-principles models for the unit operations in a modular chemical system are used to generate simulation data for use in the model identification, including multiple types of reactor and separation units. Both noise-free and noisy cases are considered, the former for the situation were no experimental data at scale are available and only simulation data are used to construct the polynomial models, and the noisy case for the situation in which sufficient experimental data are available at scale for model construction. Efficient sampling methods are considered to reduce the required amount of data needed to construct a process model sufficiently accurate for incorporation into input-output NMPC algorithms. Then we demonstrate the use of machine learning-based methods for construction of surrogate input-output models with good predictive capabilities when applied for dynamic variations in the process inputs that are very different from that used to generate the simulation data used to construct the polynomial models. The computational times associated with construction and simulation of the polynomial models are low. The methodology is then applied to construct an input-output polynomial model for a chemical modular system, which is described by a system of nonlinear partial differential algebraic equations with thousands of state variables after spatial discretization [3,4]. The model is incorporated into an NMPC algorithm during various plant operating scenarios in which the process exhibits high dynamic nonlinearity.

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