Third order motion profile

In motion control, a common need is to move a system from one steady position to another (point-to-point motion). Following the fastest possible motion within an allowed maximum value for speed, acceleration, and jerk, will result in a third-order motion profile as illustrated below:

Jerk systems

A jerk system is a system whose behavior is described by a jerk equation, which is an equation of the form (Sprott, 2003):

• Sprott, Julien Clinton (2003). Chaos and Time-Series Analysis. Oxford University Press. ISBN 0-19-850839-5 and ISBN 978-0-19-850839-7.
• Am. J. Phys., Vol. 65, No. 6, Pg. 538, June 1997