Comparative analysis of the PID algorithm synthesis at the object model with astatism and dead time

Abstract

The paper presents the comparative analysis of the synthesis methods of the PID tuning algorithm for the model of the object with first degree astatism and dead time. In the practice of industrial and technological process automation, mathematical models attached to processes are considered models with first degree astatism and dead time. It analyzes the methods that can be applied for tuning algorithms to these types of process models. Systems with dead time transfer elements do not have finite dimensional systemic achievements, but have an infinite number of polyzeros. In practice, these models are approximated with rational forms known as Pade approximations with minimal and non-minimal phase. The method of tuning the PID controller shall be analyzed using analytical method of maximum degree of stability and method of maximum degree of stability with iterations. In the object model the dead time component is approximated with Pade approximations with minimal phase and for these models the PID algorithm is synthesized according to the method of the maximum degree with iterations. The PID algorithm is synthesized according to the proposed methods for two examples of values of the parameters of the model of the control object with astatism and dead time and the obtained results are analyzed. The advantages of the method of maximum stability with iterations are highlighted.