Robust stabilization of interval plants with time delay

Abstract

In this work it is presented a new method to tune PID controllers for processes that have uncertainty in its parameters. This uncertainty is represented by interval plants, which mathematically describes the process to be controlled. The tuning methodology is based on the use of well-known rules of Ziegler and Nichols, which are generalized to systems that have parametric uncertainty, which is the main contribution of the research. Furthermore, it is a tzime delay in the system output, which may be due to an inherent delay in the mathematical model or time delay caused by delay in the computation time for devices, sensors or actuators. The methodology is based on the construction of the “Value Set” for the characteristic equation of the close loop control system, which, aided by the Zero Exclusion Principles, it provides a simple graphical tool by which you can obtain the parameters (ultimate gain) and (ultimate period), and with this parameters it is possible to tune the PID controller for the system with uncertainty and time delay. This prevents that the system loses stability due to the parametric uncertainty.