Linear system control via saturating dynamic actuators global output-reference tracking

The problem of controlling cascade systems, involving in series a saturating actuator and a linear plant, is revisited. Presently, the actuator is described with a more realistic model that accounts not only for its saturating nature but also for its dynamics. Furthermore, the considered model emphasises the internal feedback interaction (between saturation and dynamics) that characterises most real-life actuators. The control objective is 2-fold: (i) stabilising the whole actuator-plant association; (ii) and enforcing the plant input de accurately match any bounded reference signal. To this end, a two-loop controller is developed following a backstepping-like design procedure. Accordingly, the outer regulator is first synthesised, to meet the output-reference tracking objective. During this synthesis stage the actuator output is considered as a virtual control signal. The control law obtained at this stage will serve as a reference trajectory for the actuator output. In the second stage, the inner regulator is designed to make the actuator output tracks its reference trajectory. The cascade controller thus developed is formally shown to meet its control objectives, that is, bounded input bounded output (BIBO) stability and perfect asymptotic matching of any reference signal that is compatible with the actuator saturation.