Finite-dimensional robust controller design for infinite-dimensional systems

Abstract

Time delay occurs in many systems like control systems, process control applications, and large-scale mechanical structures. Due to the infinite-dimensional nature of delays, their controller design is more complicated since many traditional control methods depending on rational models of the plant. The Smith Predictor has been widely studied as a control structure for delay systems. It compensates for dead time by separating the nominal plant dynamics from the delay element. Despite the simple structure and effectiveness, the Classical Smith Predictor has some limitations, such as its sensitivity to modeling errors and the assumption that the plant model is precisely known. This study presents and extension to the classical Smith predictor and examines the robust stabilization of a specific category of multi-input-multi-output (MIMO) infinite dimensional linear time-invariant systems. Significant practical applications include finite dimensional MIMO systems that experience time delays in either the input or output channels. Controllers are developed by using a stable transfer matrix created using tangential Nevanlinna-Pick interpolation. The structure of the controller can be viewed as an extension of Smith predictors tailored for systems with time delays. A finite dimensional approximation of the controller and its effects on the robust stability of the feedback system are also addressed, accompanied by four numerical examples.