A sampled-data singularly perturbed boundary control for a heat conduction system with noncollocated observation

This note presents a sampled-data strategy for a boundary control problem of a heat conduction system modeled by a parabolic partial differential equation (PDE). Using the zero-order-hold, the control law becomes a piecewise constant signal, in which a step change of value occurs at each sampling instant. Through the 'lifting' technique, the PDE is converted into a sequence of constant input problems, to be solved individually for a sampled-data formulation. The eigenspectrum of the parabolic system can be partitioned into two groups: a finite number of slow modes and an infinite number of fast modes, which is studied via the theory of singular perturbations. Controllability and observability of the sampleddata system are preserved, irrelevant to the sampling period. A noncollocated output-feedback design based upon the state observer is employed for set-point regulation. The state observer serves as an output-feedback compensator with no static feedback directly from the output, satisfying the so-called 'low-pass property'. The feedback controller is thus robust against the observation error due to the neglected fast modes. Index Terms--Boundary control, distributed parameter system (DPS), sampled-data systems, singular perturbation.