Globally linearising control of linear time-fractional diffusion-advection-reaction systems

Abstract

The globally linearising control (GLC) structure is adopted to solve both the step tracking and disturbance rejection problems for distributed parameter system described by a time-fractional partial differential equation. The actuation is assumed to be distributed in the spatial domain while the controlled output is defined as a spatial weighted average of the state. First, following a similar reasoning to geometric control and based on the late lumping approach, an infinite dimensional state feedback that yields a fractional finite dimensional system in closed loop is developed. Then, the input of this resulting closed-loop system is defined by means of a robust controller to cope with step disturbances. Assuming that the output shaping function is non-vanishing, on the spatial domain, it is demonstrated that the GLC strategy is stable. Two applications examples are presented to show, through simulation runs, the stabilisation, step tracking and disturbance rejection capabilities of the GLC scheme.