Synthesis of the PID Algorithm for Models of Objects with Double Astatism and Dead Time

Abstract

The paper summarizes the tuning algorithm for models of objects with inertia and astatism of the second degree and dead time, which describe the dynamics of various technical objects and technological processes. These models of tuned objects have the original double pole and a negative pole and an infinity of poly-zeros due to the dead time component. In order to tune the PID controller algorithm to the model of the given object, the algorithm was elaborated based on the analytical method of the maximum degree of stability. The dead time component approximates by the Pade approximants with nonminimal phase. For the approximate object model, the PID algorithm is synthesized using the maximum degree method with iterations. In order to verify the results obtained at the synthesis of the PID algorithm by the analytical method and method with iterations of the maximum degree of stability, the synthesis of the tuned algorithm was performed using the method of polynomial equations. An example of a system with the control object model and the controller synthesized according to these methods with computer simulation in the MATLAB package was examined and the system performance was analyzed. The advantages of the method of the maximum degree of stability with iterations through reduced calculations and minimum time are highlighted, which lead to the simplification of the procedure for tuning the PID algorithm for these object models and higher system robustness.