Time scaling for motion control of a high-order and very fast dynamic system

This article delves into time scaling for a high-order and very fast dynamic system. A very fast system responds to a test input (e.g. a unit step input) with a very small settling time or rise time in the transient time evolution and its settling time or rise time could be in the scale of milliseconds or microseconds, and the positioning or tracking of a very fast system could be challenging. In general, simulations are needed to tune up or adjust the design and to support the theory or the experiment. The main contributions of this article are to show that for a high-order and very fast system, (i) simulations without time rescaling result in large numerical errors, and (ii) simulations with time rescaling lead to a very large decrease in numerical errors, and thus better representing the physical system. In this work, the time unit is rescaled from the unit of second to the unit of millisecond to effectively reduce the numerical error to achieve a very good tracking performance.