RMP Lecture Notes

Modeling for Process Control

Very often engineers use "models" of a process to aid understanding. A model can be a description, a picture or physical model, or a mathematical or statistical construct that emulates the behavior of the real, physical system, although often in an idealized way.

The degree of complexity of a model is linked to decisions made in the modeling process. Sometimes it is desirable to start with a fundamental or first principles model -- modeling equations are developed starting from the material and energy balances, chemical and physical laws.

The steps in developing a fundamental model are:

Preparation
- Decide what kind of model is needed. What scale? How detailed? How accurate? What features cannot be neglected?
- Define and sketch the system.
- Select variables
Model Development
- Write balance equations (mass, component, energy) to describe the system.
- Write (descriptive) constitutive equations (transport, equilibrium, kinetic) needed to implement the balance equations.
- Check for consistency of units, independence of equations
Solution (Simulation)
- Solve the equations (analytically or numerically)
- Check and verify the solution

This type of model will emerge as a system of differential balance equations (ordinary or partial) accompanied by a set of algebraic constitutive equations. Depending on the intended use, the model can be adapted in several ways

made steady-state (time derivatives approach zero)
linearized
- differential equation form
- state-space form
- transformed to transfer function form

In other cases, the fundamental behavior of a process is poorly understood or prohibitively complex to model based on first principles. In these cases, models may be developed from experimental dynamic data. Developing a model from experimental data is often called process identification. Identification techniques can be very simple (process reaction curve analysis of step inputs) or complex (ARIMA modeling of PRBS inputs). Essentially, these approaches "curve fit" the data to produce what are sometimes called "Input/Output Models" or "Black Box" models.

The choice of a model type depends on the scale of the problem. You probably don't want to model molecular dynamics unless they make a difference!

References:

Luyben, W.L., Process Modeling, Simulation and Control for Chemical Engineers (2nd Edition), McGraw-Hill, 1990, pp. 15-17
Marlin, T.E., Process Control: Designing Processes and Control Systems for Dynamic Performance, McGraw-Hill, 1995, pp. 53-56.
Riggs, J.B., Chemical Process Control (2nd Edition), Ferret Publishing, 2001, pp. 97-98.

R.M. Price
Original: 9/29/93
Modified: 1/6/95, 12/18/95, 12/7/96, 1/8/97, 1/5/98; 5/1/2003