Delay Systems, The Smith Predictor Control Model Mismatch Under Stability Study

Smith Predictor was proposed to resolve time delay term in the closed loop characteristic equation of time delay system. But Smith predictor has a disadvantage that it requires accurate system models, and it is very sensitive to modeling errors. Modified Smith Predictor cannot remove the inherent weakness that it depends on the precise models of the system. PID controller and its variations are the most popular in today's industrial world. However, it has long been suggested that this controller structure is less appropriate for the control of processes with a dominant time delay. Smith Predictor is often used in the control of systems with dominant time delay with PID as its controller.In this work, Stabilization of a class of time delay system controlled by Smith predictor strategy is researched when the predictor model is mismatched. For the first order with time delay system, when predictor model's static gain, time coefficient, or the time delay coefficient is mismatched, the distribution of the stabilizing PI or PD controller's Parameters in parameter space is analytically examined by a method that is based on the generalized Hermite-Biehler theorem that can be applied to quasi-polynomials. Stabilizing parameter distribution in PID parameter space of 3-Dimensions is also examined in the case of that model's static gain is mismatched.Particularly, two terms of time delay are involved in the system when Time delay coefficient is mismatched, which is difficult to deal with in stability analysis. In this work, a method which is also based on the generalized Hermite-Biehler theorem is applied to find Proportional controller gain stabilization condition thereby.Simulations are presented in each case aforementioned to illustrate conclusions.