Boundary Sliding Mode Control of a Diffusion Process under Sampling and Hold: Chattering Analysis

This paper investigates discretization chattering effects in a distributed-parameter process governed by the diffusion PDE and equipped with a sliding-mode-based boundary controller. The collocated measurement is sampled in time and the boundary control signal is applied through a zero-order-hold element. The limit cycle modes constituting the chattering effects are determined exactly by exploiting the difference equation method, yielding their period and spatially dependent amplitude. Simulation results show that the theoretically determined limit cycle modes occur in the closed-loop system.