# Fundamentals of Mathematical Modeling, Simulation, and Process Control

• Ricardo Simpson
• Sudhir K. Sastry
Chapter

## Abstract

Believe it or not, we have extensively, unconsciously, exposed you to, practiced, and developed mathematical models throughout this book. The first exposure to mathematical modeling was probably in (Sect. ), where we introduced the ideal gas law. In Sect. , you were exposed to several mathematical models that are very common in chemical and bioprocess engineering. Then, in several of the subsequent chapters, we utilized mathematical models. For example, in , we used different mathematical models that are frequently utilized in, for example, thermodynamics, heat transfer, and mass transfer.

First, the main purpose of this chapter is to understand and discover, through examples, the importance of mathematical modeling and to start constructing simple mathematical models. The second purpose is introduce you to process and bioprocess simulation. Again, in the case of simulation, you already have been exposed to and practiced simulation through exercises in previous chapters. For example, in (Sect. , problem 3), it was proved that two continuous bioreactors in series (total volume V) were more effective than one continuous bioreactor of volume V.

Due to the descriptive nature of this chapter, quantitative problems have not been included, but five conceptual questions are analyzed and discussed.

## Keywords

Bioprocess Engineer Proportional Integral Derivative Supervisory Control Simple Mathematical Model Pressure Relief Valve
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

1. Simpson, R., Almonacid, S., and Teixeira, A. 2002. Optimization criteria for batch retort battery design and operation in food canning-plants. J. Food Proc. Eng., 25, 515–538.

1. Teacher package: Mathematical Modeling http://plus.maths.org/content/os/issue44/package/index
2. Introduction to Modeling Lesson https://www.youtube.com/watch?v=GnlgGmLNn5o
3. C Batch Process Control System http://www.youtube.com/watch?v=IlH-tSxlTRE
4. PID Control - A brief introduction https://www.youtube.com/watch?v=UR0hOmjaHp0