**Introduction**

Updated 2021-10-06

Process-model based control (PMBC) uses an engineer’s first-principles model for automatic control. This was the concept that I had during my 13 years in the chemical industry. We used engineer’s 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? The challenges were to determine how to remove steady state off-set, what to use for the control objective, and how to tune the controllers. PMBC is the result of my explorations in my 29-year academic career, which includes substantial testing on pilot-scale and industrial processes.

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, with constraints.

The advantages of PMBC are that it uses the engineer’s process understanding – not a linear model, not a purely empirical model, and not a set of linguistic rules. PMBC preserves and enhances process understanding, and the same model for control can be used for process design, on-line process analysis, and training. PMBC provides a model that is functional over the entire range of operating conditions. 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.

Although demonstrated here 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).

PMBC has been demonstrated on numerous pilot-scale applications – pH, distillation, heat exchange, fluid flow, 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 that 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.

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 either delay or inverse period, PMBC with a single step toward the setpoint is simpler. If there is a delay or inverse action, PMBC in a model-predictive control structure can see past the delay or inverse period and also avoid 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 and PFC models. I think that each of these three 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.