# Chemical Process Control

## What is Process Control?

The manipulation of an object (actuation device) to maintain a parameter within an acceptable deviation from an ideally required condition. At it's core, process control is the transfer of variability from on variable to another.

There are two basic process control philosophies, feedback and feedforward control.

### Feedback Control

In feedback control, the controlled variable is measured and compared with a set-point. The deviation between the controlled variable and the set-point is the error signal. The error signal is then used to reduce the deviation of controlled variable from set-point.

#### Direct Acting Control

If the controlled variable increases as the manipulated variable increases, then direct acting control is used.

## Mathematical Modeling

### Conservation Laws

The conservation laws on mass, energy and momentum are fundamental bases for the development of models of chemical processes. The general form of the law for a variable , when applied to a control volume (CV) is

${\displaystyle {\frac {d(X~IN~to~CV)}{dt}}-{\frac {d(X~OUT~of~CV)}{dt}}+{\frac {d(GENERATION~OF~X~within~CV)}{dt}}-{\frac {d(DISAPPEARANCE~of~X~within~CV)}{dt}}={\frac {d(ACCUMULATION~of~X~within~CV)}{dt}}}$

When applied to mass this becomes the Law of Conservation of Mass. Assuming no nuclear reactions take place, then the rate of generation or disappearance of mass is zero. Hence, we have

${\displaystyle {\frac {d(Mass~IN)}{dt}}-{\frac {d(Mass~OUT)}{dt}}={\frac {d(ACCUMULATION~of~Mass)}{dt}}}$

In symbols we may say

${\displaystyle {\dot {m}}_{in}-{\dot {m}}_{out}={\frac {dM}{dt}}}$

where M stands for the total mass within the CV

## Glossary

Actuator
The mechanical device that cause the activation or movement of a final control element.
Direct Synthesis
Final Control Element
A physical device whose activation or movement causes a change in a dynamic process. In process control, the most common final control elements are control valves.
Frequency Domain
Internal Model Control
IMC-PID Tuning
A method for PID tuning that selects tuning parameters to approximate an IMC-derived controller.
An integral transformation from time domain to Laplace domain. Given a function of time ${\displaystyle f(t)}$, the Laplace transform is given by the following
${\displaystyle F(s)=\int _{0}^{\infty }\!f(t)\;e^{-st}dt}$
The use of ${\displaystyle F(s)}$ to represent the Laplace transform of ${\displaystyle f(t)}$ is a common convention; however, in dynamics and control it is common to use ${\displaystyle f(t)}$ and ${\displaystyle f(s)}$ to represent a time-domain function and its Laplace transform, respectively.