Robust discrete-time deflection-limiting commands for flexible systems

Abstract

Properly shaped reference commands can greatly improve the performance of flexible systems. However, command profiles that move a system without residual vibration while simultaneously limiting transient deflection are very challenging to create. If the command generation problem is formulated and solved in the continuous-time domain, then a non-linear optimisation will generally be required to produce the command. The authors describe a method for creating deflection-limiting commands in the discrete-time domain. The major advantage of this method is that the problem is solved via linear optimisation. This reduces the computational complexity required to create deflection-limiting commands. Additionally, linear robustness constraints can be formulated, allowing for the development of robust deflection-limiting commands. The characteristics of the command profiles are presented as a function of transient deflection limit and the move distance. Experiments performed with an industrial bridge crane verify the usefulness of the proposed approach.