Modified Polynomial Method to Synthesize a Control Algorithm for a System with Second-Order Inertia and Time Delay

The paper presents the procedure for tuning the PID controller to the object model with second-order inertia and time delay according to the method of the maximum degree of stability with iterations and the modified polynomial method. In industrial process automation, mathematical models attached to slow and very slow processes are approximated by mathematical model with second-order inertia and time delay. The modified polynomial method of tuning the PID algorithm to the control object model with first-order inertia and time delay is developed, which presents a simple procedure. To compare the obtained results, the method of the maximum degree of stability with iterations, the Ziegler-Nichols method of tuning the PID controller to the object model with second-order inertia and time delay is applied. Examples are examined and the results obtained when varying the parameters of the object model are analyzed. The advantages of the maximum degree of stability method with iterations and modified polynomial method are highlighted.