Observer-based sampled-data control of unstable process with time delay

A sampled-data control scheme is developed for an unstable time-delayed process, in order to circumvent the limitation on stabilizability (de Paor 1985, de Paor and O'Malley 1989, de Paor and Egan 1989) imposed by the parameter ϵ = λL, where λ > 0 is the unstable pole location in the s-domain and L is process latency. A Luen-berger observer is used for initial assignment of eigenvalues, with disturbance-rejecting PI or PID control then added. The adverse effect of ϵ on disturbance rejection is highlighted. This parameter is seen as a genuine index of difficulty in control, whichever approach is adopted. The effect of derivative action on stability is considered via root locus; no compelling case for its incorporation is established.