Abstract

Citation

Researchers should cite this work as follows:

• Bryan, K. (2023). 1-155-CruiseControl-ModelingScenario. SIMIODE, QUBES Educational Resources. doi:10.25334/EKE2-KC61

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Article Context

Description

Many physical systems are well-modeled by ordinary differential equations (ODEs) and it is frequently the case that the goal of such a model is to facilitate control of the relevant physical system, in order to steer the system to some desired behavior. A good example is the cruise control found in modern automobiles. The purpose of a cruise control is to maintain the car's motion at a constant speed, even as the vehicle encounters hills, wind, or other alterations in the environment. Cruise control has been a feature on cars for over 60 years, and modern cruise control not only modulates the car's throttle, but also the brakes.

In this project we illustrate the design of a proportional-integral-derivative (PID) cruise control algorithm for an automobile. PID control is one of the most common techniques in control engineering and makes a wonderful application of the Laplace transform that goes beyond the standard ``let's solve some ODEs'' problems found in standard ODE texts.

A computer algebra system is helpful for this project, which can be done in class, or perhaps better yet, started in class as part of a homework assignment.