Differential Flatness of Single-Input Commensurate Delay Systems With Applications to Trajectory Planning, Tracking, and Transformation to Fully Actuated Systems

This paper studies the differential flatness of time-delay systems (TDSs). Based on factorizations in the pseudo-polynomials ring, a flat output for the single-input linear commensurate TDS (namely, the delays in the system are multiplies of a certain unit delay) is constructed explicitly. Then the TDS can be converted into a high-order fully actuated system (HOFAS) model with the generalized state as the flat output, and the finite spectrum assignment (FSA) problem can be solved immediately by using the HOFAS approach, which provides some new insight into the study of the FSA problem. By parameterizing the considered TDS via the constructed flat output and applying the interpolation theory, the state trajectory planning problem and state tracking problem are solved, resulting a two-degree-of-freedom (2DOF) controller. Numerical examples demonstrates the effectiveness of the presented approach.