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Are First Principle Models Used for Model Predictive Control?

The following discussion is part of an occasional series showcasing the ISA Mentor Program, authored by Greg McMillan, industry consultant, author of numerous process control books, 2010 ISA Life Achievement Award recipient, and retired Senior Fellow from Solutia, Inc. (now Eastman Chemical). Greg will be posting questions and responses from the ISA Mentor Program, with contributions from program participants.


The following question by Dr. Russ Rhinehart, Emeritus Professor at Oklahoma State University School of Chemical Engineering and key Mentor Program resource, is designed to start a conversation on what progress has been made in the use of first principle models for MPC.

Russ Rhinehart’s Question 

When I first started academic research into the use of first-principles (phenomenological, mechanistic) models in model-predictive control (MPC), alternately termed advanced process control (APC), there was only DMC and IdCom. I do believe that vendor development has continued and that now there are MPC products that use first-principles models (process simulators and such models) that express a mechanistic I/O relation between the process inputs and states and constraint variables. I recall that Shell’s SMOC-II is one that permits phenomenological models in the control forecast function, and I have a sense that Yokogawa’s PACE is another. In the mid-80s, I recall that an E&C company out of Houston was using SimSci models for control of customer columns (the computer in Houston received measurements from remote refineries, used the models, and sent setpoints pack to the plant controllers). 

Today, of course, many vendors are offering MPC products, but I understand that most use the traditional empirical linear models of the finite impulse response (FIR) type. I’m interested in learning of the commercial use of phenomenological dynamic models in MPC (multivariable, constraint-avoiding, response-shaping, horizon-predictive control). 

I understand that Adersa’s predictive functional control (PFC) can use first-principles models, and that the control objective is to find a step-and-hold process input to make the model match its setpoint at a future time (a coincidence point). However, this does not have the constraint-avoiding, response shaping property. 

As a parallel, Pavilion’s Perfector (now with Rockwell) uses nonlinear models for control in an MPC style, but I understand that these are empirical neural network models that mimic the steady state gains, and that the dynamics still represent a local linear response. I understand that Process2Control and CyboSoft each use a Neural Network to match empirical dynamic process data to develop a dynamic model. Universal Dynamics Brainwave uses Laguerre polynomials to adaptively model the empirical findings. 

I also recall vaguely that DOT Products had a controller (was it called STARR?) in which steady state gains were assigned by collective experience from process operators and engineers, then the dynamics could be empirically modeled with data from much reduced process step testing. I think it may have been acquired by Aspen Tech. 

Are there other commercial providers of MPC that use phenomenological dynamic models? 

Greg McMillan’s Answer 

I think there is a future for dynamic first-principle models to provide inferential measurements. There is a demonstrated opportunity for inferential measurements of cell growth rate and product formation rate for bioreactor profile control. An MPC can be setup to non-intrusively adapt the dynamic first-principle model to improve the fidelity of the dynamic model and the inferential measurements. 

The technology and opportunities are highlighted in the Control article, “Bioreactor control breakthroughs: Pharma industry turns to advanced measurements, simulation and modeling” and detailed in ISA book New Directions in Bioprocess Modeling and Control Second Edition. 

These first-principle models address the challenges in bioreactors, such as the multiplicative effects of kinetics, including limitation and inhibition factors and the extreme sensitivity and nonlinearity of temperature and pH effects. While DeltaV MPC and Mimic bioreactor models are ready to do this, we only have one customer pursuing this opportunity. I somehow need to develop an awareness of the incredibly large potential benefits. 

I do not know what progress other suppliers have made in offering first-principle dynamic models for providing inferential measurements for PID or MPC control. Of course, RTO has a long history of open equation steady state first-principle models. 

Mark Darby’s Answer 

I see mechanistic models used from time to time, but nothing has really stuck in the marketplace. ExxonMobil uses one for their polymer control as seen in the paper, “Evolution of an Industrial Nonlinear Model Predictive Controller” (Young, Bartusiak, and Fontaine). Part of the motivation was to use a common model to control multiple grades and use it across facilities. Honeywell took up support and applied it for several years but abandoned it. Probably says something about the effort or expertise. 

ExxonMobil still uses it, but they are the exception in polymers. Bartusiak published several papers on it; most control apps in polymers utilize a neural net for the steady-state nonlinearity and a combination of some dynamic balance equations and empirical dynamics. 

SMOC and now PACE are based on a linear state space model with some clever model updates based on intermediate variables (in addition to MVs and DVs), probably with some provision to handle NL static relationships. DMCplus and DMC3 support this. 

I've seen references to first principles models used for distillation control, but nothing I can point to that are used today. I agree with Greg's comments on the use of inferential measurements. I believe the future of MPC is hybrid models (part mechanistic, part empirical) if they can be developed quicker than 100% empirical, derived solely from testing. 

Matthew Howard’s Answer 

My company is currently operating an MPC solution purchased from a supplier that is entirely based on first principles. This solution automates the raw material and energy feeds into the ClO2 generator. The model produces “soft sensors” that estimate the important MV chemical concentrations in the generator. The models are using the stoichiometry of the reactions and the integrating nature of the vessel. It uses lab tests to check correct deviations in the model. There are questions about how accurate the tests truly are, but isn’t that always the case? 

I was impressed during startup that the supplier did no step test to develop models for this solution. They have had to do a fair amount of optimizing of their models, but the solution has run well overall. A previous MPC supplied by the same company was more traditional in its deployment, with a couple weeks of step tests to develop the models for the controller.

Greg McMillan
Greg McMillan
Greg McMillan has more than 50 years of experience in industrial process automation, with an emphasis on the synergy of dynamic modeling and process control. He retired as a Senior Fellow from Solutia and a senior principal software engineer from Emerson Process Systems and Solutions. He was also an adjunct professor in the Washington University Saint Louis Chemical Engineering department from 2001 to 2004. Greg is the author of numerous ISA books and columns on process control, and he has been the monthly Control Talk columnist for Control magazine since 2002. He is the leader of the monthly ISA “Ask the Automation Pros” Q&A posts that began as a series of Mentor Program Q&A posts in 2014. He started and guided the ISA Standards and Practices committee on ISA-TR5.9-2023, PID Algorithms and Performance Technical Report, and he wrote “Annex A - Valve Response and Control Loop Performance, Sources, Consequences, Fixes, and Specifications” in ISA-TR75.25.02-2000 (R2023), Control Valve Response Measurement from Step Inputs. Greg’s achievements include the ISA Kermit Fischer Environmental Award for pH control in 1991, appointment to ISA Fellow in 1991, the Control magazine Engineer of the Year Award for the Process Industry in 1994, induction into the Control magazine Process Automation Hall of Fame in 2001, selection as one of InTech magazine’s 50 Most Influential Innovators in 2003, several ISA Raymond D. Molloy awards for bestselling books of the year, the ISA Life Achievement Award in 2010, the ISA Mentoring Excellence award in 2020, and the ISA Standards Achievement Award in 2023. He has a BS in engineering physics from Kansas University and an MS in control theory from Missouri University of Science and Technology, both with emphasis on industrial processes.

Books:

Advances in Reactor Measurement and Control
Good Tuning: A Pocket Guide, Fourth Edition
New Directions in Bioprocess Modeling and Control: Maximizing Process Analytical Technology Benefits, Second Edition
Essentials of Modern Measurements and Final Elements in the Process Industry: A Guide to Design, Configuration, Installation, and Maintenance
101 Tips for a Successful Automation Career
Advanced pH Measurement and Control: Digital Twin Synergy and Advances in Technology, Fourth Edition
The Funnier Side of Retirement for Engineers and People of the Technical Persuasion
The Life and Times of an Automation Professional - An Illustrated Guide
Advanced Temperature Measurement and Control, Second Edition
Models Unleashed: Virtual Plant and Model Predictive Control Applications

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