**Introduction**

Updated 2024-06-16

Process-model based control (PMBC) uses an engineer’s first-principles model for automatic control. This was the concept that I envisioned toward the end of my 13 years in the chemical industry, a vision inspired by 70’s digital revolution in control systems. At the same time, many others throughout the world had similar visions and developed several practicable control approaches.

At that time, we were using first-principles (mechanistic) models for process design and on-line process analysis. Why discard that knowledge and use linear empirical models for control, when we could use familiar nonlinear models? Why distract an engineer to understand Laplace mathematics when the first-principles models represent the mechanisms and provide utility for many purposes? Here is a list of advantages of using first-principles models in control:

- Retain and reinforce mechanistic process understanding.
- Useful for training, trouble shooting, diagnosis, process improvement.

- Consistent control over the entire operating range.
- Control is naturally nonlinear with interaction pairing/decoupling and feedforward compensation.

- Monitoring process attributes, such as fouling, efficiency, or reactivity.
- Useful to forecast maintenance scheduling, and ever-changing constraint conditions.

- Simplicity of tuning.
- Only one tuning coefficient per CV.

- Don’t distract engineering staff to learn abstract mathematics.
- Such as NN, Laplace transforms, linear algebra, etc. The models use the engineers’ mathematics.

- Ease Design Constraints.
- Nonlinear control does not require linear or high-volume processes. Tanks can be horizontal. FCV pressure drop does not have to be 50% of dynamic losses. Heat integrated processes are facilitated.

- “The ONE MODEL to rule them all.”
- Control, design, analysis, training, supervisory optimization

- Simplicity of model calibration.
- There are only a few adjustable model coefficients, compared to 10 to 100 for equivalent performance. This means minimal process experimentation. And the model may already be available.

I left industry to pursue these possibilities, and Process-Model-Based Control (PMBC) is the result of explorations in my 31-year academic career, which included substantial testing on pilot-scale and industrial processes. ISA (the International Society for Automation) recently published my book on Nonlinear Model-Based Control Using First Principles Models. And ISA’s Automation.com hosts an article explaining PMBC on a 2×2 process.

This set of pages shares some of the material.

In a single-loop application, PMBC could replace PID control as a single-input single-output (SISO) controller, or alternate model-based type controllers such as internal-model, neural-network, or fuzzy-logic. It can receive multiple inputs to handle disturbances in a manner similar to ratio or feedforward (MISO). It can also do square and non-square MIMO applications, along with auxiliary variable constraints.

A feature of PMBC is that selected coefficients in the model representing non-stationary process features can be adjusted incrementally, on-line, to have the model evolve with the process (representing fouling factors, efficiency, yield, etc.). This provides additional information for the human supervisor about the state of the process, what is possible during constraints, and an updated model for supervisory process optimization.

Demonstrated here with simulators as one-step-ahead control of a MISO and a square MIMO application, PMBC can be imbedded in a MIMO, horizon-predictive, constraint-avoiding controller (termed either Advanced Process Control – APC, or Model-Predictive Control – MPC). The structure and implementation of both the simpler one-step-ahead and the more complicated MPC are discussed in the materials you can download here. For much greater detail, I recommend my book Nonlinear Model-Based Control Using First-Principles Models, released in early 2024 by the International Society for Automation (www.isa.org).

The use of first-principles models has been demonstrated on numerous commercial and pilot-scale applications – pH, distillation, heat exchange, fluid flow, plasma reaction, and pressure. Recent publications include: Manimegalai-Sridhar, U.; A. Govindarajan, and R. R. Rhinehart, “Demonstration of Leapfrogging for Implementing Nonlinear Horizon Predictive Control on a Heat Exchanger”, __ISA Transactions__, Vol 60 (2016) pp 218-227; Govindarajan, A., S. K. Jayaraman, V. Sethuraman, P. R. Raul, and R. R. Rhinehart, “Cascaded Process Model Based Control: Packed Absorption Column Application”, __ISA Transactions__, Vol. 53, No. 2, 2014, 391-401; and Raul, P. R., H. Srinivasan, S. Kulkarni, M. Shokrian, G. Shrivastava, and R. R. Rhinehart, “Comparison of Model-Based and Conventional Controllers on a Pilot-Scale Heat Exchanger” __ISA Transactions__, Vol. 52, No. 3, 2013, pp. 391-405.

This document r3eda site Simple PMBC 2016-06-11 provides an introduction to SISO or MISO PMBC (one-step ahead control action), which I feel process control engineers can implement in-house. This simulator r3eda PMBC Car Speed Control LF to Solve for u implicit 2017-04-23 demonstrates a SISO PMBC with model adaptation on an automobile speed control. And, this simulator Hot and Cold Mixing 2018-09-17 demonstrates a 2×2 MIMO control of hot and cold water mixing where optimization handles the balance of temperature an flow rate control when constraints are encountered.

This document from my keynote presentation at the XVIII Control Instrumentation System Conference (CISCON-2021) explains how to set up MPC (horizon predictive, constraint handling control) using first-principles models MPC Using First-Principles Models.

Other relatively simple model-based approaches that use first-principles models are GMC (generic model control, from the minds of Peter Lee and Gerry Sullivan) and PFC (predictive functional control, from Jacques Richalet). GMC using a steady state model could be classified as PI control with output characterization (a nonlinear transformation) by the inverse of the model. Advantages are the simplicity of a steady state model and familiarity with tuning and modifying PI. PFC uses a dynamic model and iterative use of the model to make some future value forecast of the model hit a coincidence point. The time of the coincidence point is set to be after delays or inverse action, perhaps 80% of the settling time. The advantages of PFC are that it can handle ill-behaved dynamics as well as nonlinearity. But the disadvantage is that with a nonlinear model, the control action is calculated iteratively (either by root-finding or optimization). If there is inconsequential impact of either delay or inverse period, PMBC with a single step toward the setpoint is simpler. If there is a delay or inverse action, first-principles models in a MPC structure can see past the delay or inverse period, plan action now to avoid future constraints, and balance MV action with CV performance. The incremental model adjustment of PMBC that lets the model adapt to process changes, can also be implemented with GMC, PFC, and MPC models. I think that each of these methods have credible industrially-relevant demonstrations of practicability, are effective, and are simpler than many other approaches to nonlinear control that have been revealed in the scientific literature.