(99d) Case Studies on the Combined Identification and Offset-Free Control of Chemical Processes

Model predictive control (MPC) is widely used in the chemical process industries as an advanced feedback control method (Qin and Badgwell, 2003). Some important factors in the success of MPC are its inherent robustness to disturbances and plant-model mismatch, and the ability to track setpoints without offset (Rawlings et al., 2020, pp. 46-59, 204-214). As is often noted by industrial practitioners, MPC can be quite forgiving with respect to model errors, aging of the plant, changes in environmental conditions, and changes in operating conditions. As such, practitioners have long achieved sufficient performance with heuristic or out-of-date models, without rigorous methods of identifying both plant and disturbance models. As stake holders continue to demand greater performance from their processes, however, they require a system of best practices for identifying plant and disturbance models.

Traditionally, MPC implementations have relied on linear finite impulse response (FIR) plant models (Qin and Badgwell, 2003). Over the last two decades, however, recent MPC products have shifted away from FIR models and towards linear state-space models (Darby and Nikolaou, 2012). This shift is motivated by a number of shortcomings of the FIR approach, most notably: (1) the inability to handle unstable and integrating systems without modification, (2) the overparameterization of the underlying linear system (especially for slow processes), (3) the difficulty of formulating estimators, and (4) the fact that FIR models are a special case of the linear state-space model (Lee et al., 1994; Lundström et al., 1995).

To identify the plant model, practitioners typically fit a linear model to step response data (Caveness and Downs, 2005). However, this does not provide the noise covariance estimates required to design an estimator for MPC implementation. While subspace methods—such as canonical variate analysis (CVA) (Larimore, 1983), N4SID (Van Overschee and De Moor, 1994), or MOESP (Verhaegen, 1994)—are sometimes used to identify estimate the process and measurement noise covariances, these methods can only identify controllable and observable realizations (Qin, 2006), and the disturbance model contains uncontrollable integrating modes (Muske and Badgwell, 2002; Pannocchia and Rawlings, 2003). Disturbance models may be tuned under strong assumptions on the process and measurement noises (Lee et al., 1994; Lee and Yu, 1994), but the required assumptions are not general, producing suboptimal estimator performance. Autocovariance least squares can identify the complete disturbance model, but it has a high computational cost for minimum variance estimates (Odelson et al., 2006; Zagrobelny and Rawlings, 2015). Kuntz and Rawlings (2022) presented the first identification algorithm that provides estimates of both the state-space model coefficients and the disturbance noise covariance required to implement an offset-free MPC.

In this study, we present a closed-loop extension of the algorithm proposed in Kuntz and Rawlings (2022) and demonstrate its efficacy in an industrial case study. Our method systematizes the identification of new offset-free MPC models and design of new MPC estimators, allowing practitioners save time and achieve optimal estimator performance. To do this, we combine the plant modeling and disturbance modeling steps by passing information about state estimates between identification steps. Because state information is passed between steps, each step can be formulated as a linear regression problem for which closed-form solutions are readily available (Rao, 1973; Anderson, 2003). The plant modeling step is a regularized version of the closed-loop identification procedure outlined by Larimore (1983, 1997, 2005). To validate the viability of our method in the wider chemical process industries, we performed a case study on an existing process at Eastman Chemical’s Kingsport, Tennessee location. The newly identified model shows clear improvement from the older step-response model, and the closed-loop performance is improved as measured by the controlled variable tracking error. Moreover, we used a closed-loop experimental design that is desirable to operations engineers for its simplicity, safety, and ability to produce predictably high-quality data. The case study serves as a template for using this new method to improve existing MPC performance.

References

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