تثبیت حلقه های کنترل متشکل از فرآیند FOPDT و کنترل کننده PID پارامتر وابسته

In this paper, problem of stability analysis of the control loops consisting of first-order plus dead time (FOPDT) processes and proportional-integrative-derivative (PID) controllers is studied, where the controller coefficients are functions of one or more independent parameters. An effective procedure is presented to determine a stability region in the independent parameters space. This method does not require complex numerical calculations such as solving nonlinear equations. It is based on usage of a two-valued indicator function and by using that, a stability region is easily determined. In order to clarify that, why the stability region needs to be specified in the “independent parameters space” an optimal method is given to design the PID controller for the FOPDT processes, as an instance. In this optimal method the controller coefficients are obtained as the functions of a free parameter, where this parameter needs to be chosen by the designer such that it should be near to the maximum operating frequency of the system, besides on the other hand the closed-loop system to be stable. In the end, two illustrative examples are given in order to show the usefulness and effectiveness of the proposed method, and to compare the obtained stability regions with the whole stability regions.