Revisiting the Kalman’s Conjecture to Stabilize the Motion of a DC Motor in the Presence of Stribeck Friction via PID Control

In absence of Stribeck friction, the application of PID to control the motion of a DC motor may lead to stable oscillation. The stable oscillation, in particular cases called limit cycle oscillation, occurs in low-speed control as well as in position control. In this research, the mitigation of stable oscillation has been performed from the perspective of Kalman’s conjecture. From the point of view of Kalman’s conjecture, the minimum required proportional gain in order to stabilize low-speed control has been derived. In addition, the minimum derivative gain and the maximum integrator gain necessary to stabilize position control are proposed. This research is complementary to previous research, which has applied the circle criterion for generating a stable PID strategy. The novelty of this research is that the PID strategy proposed in this research provides a more relaxed integrator gain requirement than the previous one, especially for low proportional gain. The findings of this research are beneficial for PID blind tuning since all stability requirements have been derived analytically.