Nonstationary LPV control for trajectory tracking: a double pendulum example

This article focusses on the implementation of recently developed nonstationary linear-parameter varying (NSLPV) control algorithms for the regulation of nonlinear systems about pre-specified trajectories. The trajectories of interest eventually settle into periodic orbits, and hence are duly called eventually periodic trajectories. Parameterising the nonlinear system equations about such trajectories results in eventually periodic NSLPV models, and then NSLPV controllers are designed for these models to ensure accurate trajectory tracking despite various disturbances and uncertainties. These control algorithms will be applied to control a double pendulum where a vessel containing fluid is rigidly attached to the end of the second link of the pendulum. The mass of the fluid varies in time and, together with its rate of variation, is available for measurement during plant operation.