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 dasialiftingpsila 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 sampled-data 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 dasialow-pass propertypsila. The feedback controller is thus robust against the observation error due to the neglected fast modes.