Designing functional observer-based compensators for time-varying distributed parameter systems

This paper presents a reduced order compensator for a class of SISO infinite dimensional systems. The compensator order is equal to the dimension of the input and is made possible via the use of a functional observer. A full state feedback controller is first designed and subsequently a functional observer is set-up to estimate such functional. When the estimated functional is used as the control signal, the resulting system is shown to be stable and match the performance of a full state feedback. As an added compensator improvement, the sensor is allowed to move, rendering the output operator time varying. Such a time variation results in a differential Sylvester equation. The results are also extended to the case of a time varying disturbance operator, often modelling a moving disturbance. Numerical results are included to demonstrate the performance improvement of the functional observer when a sensor is allowed to move.