I came across an interesting Emerson Exchange presentation, Model Predictive Control for Integrating Processes, by Emerson’s Lou Heavner. You may recall Lou from several advanced control-related posts. Lou introduced the subject noting that historically, APC project engineers and consultants have tried to keep level control outside of the model predictive control (MPC) solution. Level control and control of other integrating processes tend to be poorly understood by many control engineers. His presentation sought to address the questions:

- Can you control level with MPC?
- How do you control level with MPC?

Liquid level processes and many gas pressure systems are examples of integrating processes where there is no natural equilibrium or steady state and therefore must be controlled. Deadtime may be present, but no 1^{st} order or higher order time constants are present in an open loop response.

Lou shared some application examples including hopper w/ loss-in-weight feeder and conveyor, distillation column bottom level and reflux accumulator level, evaporator level, and oil & gas production separator level. Conventional proportional-integral (PI) control has been used over the years for integrating processes where the closed loop time constant (Lambda) is set as large as possible to attenuate process variability. A smaller Lambda reduces process overshoot and shortens process response, but passes more of the variability “downstream”.

On a setpoint change in the control loop, Lambda is the time for PV to reach setpoint after a setpoint change. For a load change on the loop, Lambda is the time required to stop the change in the PV due to a step load change. The level will return to setpoint in about 6 x Lambda.

In using DeltaV Predict Pro for integrating processes, the factors you must consider include a feedback mechanism based on a model correction factor and rotation factor, a time to steady state (TSS) selection, MPC tuning based upon penalty on move (POM) and penalty on error (POE), multivariable interaction, and deadtime. In his presentation (see slide 13), Lou provided the equations for the model correction and rotation factors. The TSS setting defines the prediction horizon of the model. The POM effectively slows the control action of the manipulated variables (process inputs) and the POE acts conversely by penalizing the errors on the control and constraint variables (process outputs).

Lou shared his lessons learned with respect to these factors. The TSS is limited by deadtime and is normally set based on the responses of the self-regulating variables in multi-variable application. For MPC with integrating variables, he suggests starting with a TSS time that is at least six times the deadtime of the integrating variables, since increasing this time horizon helps reduce overshoot. Next, although counterintuitive, for integrating processes select a smaller POM to reduce overshoot and shorten response. The model correction and rotation factors have much less impact on the robustness of the model. Slides 16-21 show the effects of changes in overshoot and Lambda.

The answers are that yes you can control level with MPC by manipulating these factors based on your process response and deadtimes. There should be no hesitation about including integrating variables in the MPC problem, but if the self-regulating variables in the MPC require a relatively short TSS and relatively strong POM, then the levels may need to be taken out of the larger problem and controlled in a smaller MPC configured with only the integrating variable and a corresponding MV.

**Update: **I’ve updated the post by embedding the presentation and adding Lou’s changes to a few of the paragraphs.