Self-Excited Limit Cycles in an Integral-Controlled System With Backlash

In this technical note, we study the properties of self-excited limit cycles in an integral-controlled system containing a play operator. A Newton-Raphson algorithm is formulated to calculate the limit cycles, and we prove that the amplitude and period of these limit cycles have linear relationships to system parameters. These results are confirmed in simulation, where we demonstrate the ability to predict the properties of the limit cycles.