Time Domain Analysis of the Smith Predictor in Case of Parameter Uncertainties: A Case Study

Time domain representation of the original Smith Predictor is presented for systems with feedback delays. It is shown that if the parameters in the internal model of the predictor are not equal to the parameters of the real system, then the dimension of the closed loop system is double of the dimension of the open-loop system. Furthermore, the time-domain representation of the corresponding control law involves terms of integrals with respect to the past similarly to the Finite Spectrum Assignment control technique. The results are demonstrated for a second order system (pendulum) subjected to the Smith Predictor. It is demonstrated that stability diagrams can be constructed using the D-subdivision method and Stepan’s formulas. The sensitivity of the stability properties with respect to the parameter uncertainties in the predictor’s internal model is analyzed. It is shown that the original Smith Predictor can stabilize unstable plants for some extremely detuned internal model parameters. Thus the general concept that the Smith Predictor is not capable to stabilize unstable systems is technically not true.