This work considers the problem of stabilization and control of a class of unstable first order linear systems subject to a relatively large input–output delay. As a first step, the conditions to ensure the stability of the system in closed loop with an output injection strategy are presented. In a second step, the stability conditions are used to design an observer-based scheme that provides a forward output estimation together with a feedback compensation to guarantee prediction convergence. The robustness of the overall observer-based strategy is analyzed when considering uncertainties on the magnitude of the time delay associated with the plant and the one considered on the design of the observer. A stability region as a function of these two time delays is obtained. The proposed prediction scheme is complemented by the use of a PI compensator to track step reference signals and to reject step disturbances.

Induction motors (IM) have been a fundamental part of industrial applications for over a century and the number of their applications continues to expand. A significant amount of the world’s total energy expense is consumed by this kind of motor. Hence, it is very important to increase the energy efficiency of these machines. Due to its good performance, field-oriented control (FOC) is the most common strategy to control IM. FOC requires references for stator current and rotor magnetic fluxes. For velocity regulation, a velocity reference is used instead of a stator current reference. However, at motor start-up or when a change of torque is required, it would be convenient for these references to be variable in order to reduce energy consumption. In this work, it is shown that this is indeed the case, and a technique to find optimal time-variable references for stator currents and magnetic rotor fluxes to reduce energy consumption is proposed. It is shown that, depending on the mechanical load, an energy reduction of 20–45% can be achieved.

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.