(373y) Data-Driven Method for Real Time Optimization of Mode-Based Processes

In the past few decades the process industry observed an increased demand for more efficient, reliable and cost-effective operations. One of the most prominent industrial technologies for bolstering economic gains is the Real Time Optimization (RTO). Traditionally, RTO has been performed using steady-state phenomenological models of the process plant, along with an economic objective function that captures market prices and external conditions. This is expected since achieving the optimum while satisfying the nonlinear process constraints comprises one of the foundations of the methodology. However, model-based methods carry some well-known issues, e.g. difficulty in developing a model for complex systems, the need to constantly address plant-model mismatch, and the high computational cost for regularly solving the optimization problem, especially when dealing with uncertainty. In this work we study the problem of performing real-time optimization based solely on process data.

The first methodologies for addressing data-based optimization from an RTO perspective may be traced back to Extremum Seeking Control (ESC), which was originally introduced as the main alternative for adaptive control (Ariyur and Krstic, 2003). This class of methods aim at tracking the steady-state optimum of an output variable online and have the important feature of inherent robustness to certain types of uncertainty. A recent application of this method to a wastewater-treatment process reveals that the method presents multiple possible stationary solutions, limiting the domain of attraction of the true optimum (Trollberg et al., 2014). This highlights the need for further theoretical results and specific application studies for the perturbation-based ESC method. On the other hand, in the RTO community most studies related to the utilization of data focus on the adaptation of the phenomenological models to account for plant-model mismatch and other types of uncertainty by modifying model parameters, constraints and gradients of the optimization problem, or the offline controller design (Chachuat et al., 2009). A method more focused toward the model-free paradigm is the NCO (necessary conditions of optimality) tracking, which ensures that the plant optimum is reached by setting the NCO components as controlled variables with null setpoint (François et al., 2005).

The present work focuses on achieving a local optimum within a defined search region around a specific operating mode of a process. Many relevant industrial processes operate around certain predefined modes, which can be identified from process data in an unsupervised learning fashion. Convex or linear regions enclosing the operating mode search space are estimated, which simplify the underlying optimization problem and allow a faster solution. The proposed methodology incorporates features of both ESC and model adaptation strategies, in specific NCO tracking. The search for the optimum is carried out using a derivative-free based method and different perturbation signals are analyzed with respect to the quality of feedback data they provide. To illustrate its main features the methodology is applied to a simple case study consisting of a continuous stirred tank reactor (CSTR) employing regulatory PI controllers.

References

Ariyur K B, Krstic M. Real-time optimization by extremum seeking control. Wiley-Interscience, 2003.

Chachuat B, Srinivasan B, Bonvin D. Adaptation strategies for real-time Optimization. Computers & Chemical Engineering, 33 (10), 1557-1567, 2009.

François G, Srinivasan B, Bonvin D. Use of measurements for enforcing the necessary conditions of optimality in the presence of constraints and uncertainty, Journal of Process Control 15 701–712, 2005.

Trollberg O, Carlsson B, Jacobsen E W. Extremum seeking control of the CANON process – Existence of multiple stationary solutions. Journal of Process Control, 24.2, 348–356, 2014.