Journal Title

120th ASEE Annual Conference & Exposition

Publication Date



An introductory control systems course can be challenging to undergraduate students due to its fairly sophisticated mathematical nature. For example, it can be difficult to comprehend how even a system composed of perfect components could have a steady-state error. To help students understand such non-intuitive concepts, it is beneficial to offer them a visual example that involves a familiar scenario. This paper describes a car race analogy which leverages these twocomplementary techniques in a one semester course for juniors and seniors in automatic control systems.

The analogy consists of two competing cars of differing masses and air drags with various inputs via the gas pedal. Equations of motion are presented for the displacement, velocity, and acceleration for step, ramp, and parabolic inputs. MATLAB® software is used to solve the equations and plot the results for analysis and comparison. This familiar illustrative scenario allows students to discover easily and quickly how steady-state differences (analogous to errors) depend on the nature of the system and its type of input. It also demonstrates the effects of some easily understood corrective actions to reduce or eliminate the differences and reinforces understanding of the derivative-integral relationships between the displacement, velocity, and acceleration responses.

The graphical nature of this illustration fits well with the visual learning style of many students. Through this multi-faceted investigative analogy, they gain an intuitive understanding of steady-state errors as a complement to the traditional mathematical treatment. Results of avoluntary survey completed by the students indicated that they found the car race analogy helpful in understanding the origin and nature of steady-state errors in control systems.


Engineering mathematics; Engineering--Study and teaching; Engineering students

Publication Information

120th ASEE Annual Conference & Exposition, 2013, 1-18.

© 2013 ASEE

Archived version is the final published version.



Document Type

Conference Presentation