On the Relation Between the Smith Predictor and Algebraic Control Approach for Time Delay Systems: A Case Study

The Smith predictor is a well-established model-based strategy for eliminating or attenuating a dead-time effect on the control feedback loop. A controlled system model and a dead-time estimation represent crucial parts of the predictor structure that, however, are usually inaccurate. The design problem becomes more challenging when internal (state) delays also appear. An algebraic approach in a specific ring of quasi-polynomial meromorphic functions was proposed recently to design controllers for linear systems with internal delays. This contribution intends to compare these two design principles and find an equivalence between them from the viewpoint of closed-loop transfer functions. The sufficient stability condition for the Smith predictor structure is formulated, and necessary and sufficient conditions for constant-wise reference tracking and load disturbance attenuation are generally derived. A specific case of controlling a heating-cooling process for more complex (linear-wise) external signals is studied, and simple numerical robustness tests are performed. A concluding research outlook based on the obtained results is proposed as well.