Observer-Based PD Controller for a Class of High Order Linear Unstable Delayed Systems

In this paper it is considered the stabilization and control of a class of high order linear systems that are subject to constant time delay at the input-output channel. In particular, systems with two unstable poles and any number of real or complex conjugate stable poles are studied. To improve the solutions existing in the literature, a new proposal for the solution of the considered problem is taken into account consisting in the design of an observer and a ProportionalDerivative PD controller to assure stable closedloop performance, establishing by means of a frequency analysis necessary and sufficient conditions for the proposed control strategy. The proposal novelty is the inclusion of the PD control action in the observer that allows to estimate internal signals used in the solution. This configuration offers advantages in the time delay size that can be handled and on the control performance of the closed loop system. A practical design procedure is presented to determine the value of the controller gains. Numerical simulations examples are presented to show the operation of the proposal.