In this paper, a new method to manage the stabilization and control problems of n-dimensional linear systems plus dead time, which includes one, two, or three unstable poles, is proposed. The control methodology proposed in this work is an Observer-based Proportional-Integral-Derivative (PID) strategy, where an observer and a PID controller are used to relocate the original unstable open-loop poles to stabilize the resultant closed-loop system. The observer provides an adequate estimation of the delayed-free variables and the PID uses the delay-free variables estimated by the proposed observer. Also, step-tracking is achieved in the overall control scheme. Necessary and sufficient conditions are presented to ensure closed-loop stability based on the open loop parameters of the system. The observer-based PID strategy considers five to seven constant parameters to obtain a stable closed-loop system. A general procedure to implement the proposed control strategy is presented and its performance is evaluated by means of numerical simulations.

This work considers the stabilization of a high-order system with time delay; an observer–predictor scheme is designed to estimate an internal signal of the system that is not available for measurement: this internal signal is the output before being delayed. By using the estimated signal, it is possible to design a controller for the delay-free system. The key point to carrying out this estimation strategy is to obtain conditions assuring that the estimated signal converges to the internal variable of the system. A necessary and sufficient condition to achieve an appropriate convergence in the proposed observer–predictor scheme is given. In addition, an analysis of the disturbance rejection and robustness with respect to the delay term is provided. The correct functioning of this scheme is verified through an example.

This work considers the stabilization problem for unstable linear input-delay systems. The main idea of the paper is to use a finite-dimensional approximation for the delay operator, which is based on non-overlapping partitions of the time delay. Subsequently, each individual delay is approximated by means of a classical Pade approximation, resulting the overall approximation in a high-order Pade approximation that converges to the delay operator. By departing from a state- space realization of the approximate process, a linear observer is used to estimate the delay-free output, which is used within a compensation scheme to stabilize the process output. The resulting control strategy has the structure of an observer-based Smith prediction scheme. Numerical results on three examples show that i) the finer the time delay partition, the better the control performance, and ii) high-order compensators can be required to stabilize certain unstable processes.