The unstable model of the control object with inertia second order with known parameters is given. In order to tune the PID algorithm to these types of control models, several methods can be used as the root-locus allocation method etc., which lead to difficult calculations. The classical method of tuning the PID controller by the maximum stability degree to unstable control models with second order inertia is not applicable. For tuning the PID algorithm to the unstable object model, the algorithm was developed based on the maximum stability degree method with iterations. The advantages of the method of maximum stability degree with iterations are highlighted by reduced calculations in minimum time, which lead to the simplification of the procedure of according the PID algorithm for these classes of unstable control models of objects. In order to verify the obtained results when PID algorithm is tuned to the unstable models of control objects, an example of an automatic system was studied and simulated in MATLAB. Analyzing the obtained results when the PID algorithm was tuned  to the model of object by the maximum stability degree method with iterations, it was observed that: -  With the increase the degree of stability  increases the values of the parameters of the PID controller and the performances of the system the rice time  and the settling time  are reduced, and the overshoot is kept at the level . - With the increase of  it is reduced the performance and, conversely, the reduction of the  rises performance. - With the increase of  the performances also increase, and with the decrease of  the performances are reduced.