A Study on the Internal Relationship among Smith Predictor, Dahlin Controller & PID

It is now common knowledge that the PID (proportional-integral-derivative) is not suitable for controlling long time delay processes and the conventional Smith predictor is sensitive to model mismatch and has poor disturbance rejection capability. By illustrating the design procedure of the H_infin Smith predictor and H₂ Smith predictor first proposed by Zhang [9], who designed an analytical Smith predictor in terms of H_infin or H₂ theory, the internal relationship among the Smith predictor, Dahlin controller and practical PID is established. The range of the filtering time constant lambda is derived theoretically and a set of analytical tuning formulae is proposed. This paper also takes a different viewpoint on the applicability and robustness of PID and the Smith predictor. An illustrative simulation example gives a persuasive view to the conclusions drawn in this paper.