Output predictor control for unstable linear systems with input delay

Abstract

   The classical output control problem for a linear system with an input delay and constant known parameters is considered. The plant may be unstable, making most of the known methods ineffective or unconstructive. A new control algorithm based on the Luenberger observer and the Smith predictor is proposed, incorporating correction terms defined by simple expressions that eliminate the need for complex calculations. The resulting regulator has a linear structure; however, the correction term provides for a periodic reset of the corresponding regulator variable. It is analytically proven that a closed system of a plant with an input delay and a modified Smith predictor is globally exponentially stable. The resulting method for controlling systems with an input delay surpasses all analogues known to the authors in terms of simplicity of implementation and effective performance for unstable systems. In future works, this approach will be extended to nonlinear and parametrically uncertain systems with an input delay.