Tuning the PID Controller to the Model of Object with Inertia Second Order According to the Maximum Stability Degree Method with Iteration

Abstract

In this paper there was elaborate the procedure for tuning the PID controller to the object with inertia of the second order according to the maximum degree of stability method with iterations. The characteristic equation of the closed system is determined. By derivative operations on the unknown variable of the maximum degree, analytical expressions of the parameters of the PID controller are obtained as functions of the parameters of the object and the degree of stability. By graph-analytical procedures these functions are constructed by varying the argument. By procedures with iterations on these curves for the same value of the argument, sets of values of the parameters controller are chosen. The synthesized system is simulated and the system performances are evaluated. Two examples of objects with inertia less and greater than one according to the proposed method and the pole-zero allocation method by simulating on the computer system were examined. The parameters of the objects were varied and the robustness of the system at the unit step reference action was verified. The advantages of the proposed method are highlighted by reduced calculations and minimal time, which lead to the simplification of the procedure for tuning the controller for these objects.