Have you ever wondered why we discard process knowledge and revert to Laplace transforms and linear models for control when first-principles models can work?

So did I.

As a process engineer in industry, I used first-principles models (also called mechanistic, phenomenological and engineers’ models) to support both process design and online analysis. They embody the functional relations between process variables and may have a few coefficients (like tray efficiency, reactivity, or friction factors) whose values could be adjusted to match process operating data. I found them very functional.  

When my career migrated to process control activities, I realized that proportional-integral control presumes that process gain and time constraints are unchanging, and I had to learn the various techniques for first-order plus dead time modeling, controller tuning, gain scheduling, interaction decoupling and such. These advanced regulatory control (ARC) compensations for process behavior are grounded in the linear mathematics of deviation variables in Laplace transforms.

These were great solutions for the analog device era, but for the digital era, using first-principles models would be simpler to implement, more effective in countering process behaviors, and more compatible with the process engineer’s training. Seeing the digital revolution starting, I left industry to start an academic career where I could explore how to use first-principles models in process control.  

I found several techniques—generic model control (GMC), simple model-based control (MBC), process-model-based control (PMBC), predictive functional control (PFC) and nonlinear horizon predictive control (nHPC)—and tested them on diverse pilot-scale process units and some commercial pH and plasma reactor processes. The algorithms range from relatively simple to implement to no more complicated than today’s model-predictive advanced process control (APC). 

A Practical Application of First-Principles Models

Here is an application I explored: We had a packed tower absorber (8 inches in diameter and 15 feet high with two 6-foot-tall packed sections) in the unit operations lab that students were using to generate data to analyze liquid-gas absorption. We wanted to manipulate the inlet gas rate to control the column pressure drop to all possible values below flooding and over the entire liquid flow rate range. There are two major sources of nonlinearity in this process. The differential pressure-to-flowrate relation is substantially quadratic, and the flow control valve has a quick opening installed characteristic. Tuning a proportional-integral controller at the mid-range for satisfactory response led to unacceptable aggressiveness at the upper and lower ranges. In addition, the column differential pressure depends on the void fraction, which is a complicated combination of liquid and gas flow rates and liquid hold-up. Modeling the ideal pressure drop to the inlet flow rate and the flow rate to the valve position was relatively elementary. Also, we used online data to adjust a model coefficient related to the pressure loss coefficient.  

Control was demonstrated in the servo and regulatory modes for no wind-up at constrained conditions and bumpless transfer. Model adaptation was demonstrated and shown to provide process insight, such as the onset of flooding. The controllers were the inverse of the first-principles models and had only one tuning coefficient each. Control was effective over the entire operating range. The controller was developed by graduate students (relative novices) as one of about six projects in a summer session laboratory course. In addition to solving the control issues, it reinforced the mechanistic understanding of the process. The results were reported in Govindarajan et al., “Cascaded Process Model Based Control: Packed Absorption Column Application,” ISA Transactions, Vol. 53, No. 2, 2014, 391−401. 

We should not discard first-principles process knowledge and revert to linear Laplace transform methods in the digital age. This experiment, and others, demonstrate that first principles models are ready for prime time in process control.   

Dr. Rhinehart’s new book, “Nonlinear Model-Based Control: Using First-Principles Models in Process Control,” explains these advanced modeling techniques and guides readers in developing models and setting up and troubleshooting the controllers.

Author Q&A

Read more from Dr. Rhinehart in this author Q&A about the new book and his career in industrial automation.