Robust digital tracking with perturbation estimation via the Euler operator

A model reference control (MRC) method is presented for linear, time-invariant systems with unknown dynamics. The class of systems investigated can be described by where ΔA, ΔB and d(t) are unknown dynamics and unexpected disturbances, respectively. The design method is described in the discrete time form using the Euler operator, which approaches the Laplace operator as the sampling interval, T, approaches zero. The control is constructed, based on the estimation of system perturbations using time delay control (TDC), under the following two assumptions: (1) the dynamics stemming from the perturbations are considerably slower than the discretization frequency, 1/T; and (2) the control has access to all the plant states. The controller is tested through simulation and experiment. The theoretical and experimental results indicate that the proposed method has potential applications for controlling servo-mechanisms subjected to unknown and unexpected disturbances.