Limit Cycle Analysis for Drive Systems with Backlash Nonlinearity using an Eigenvalue Method

This paper proposes an analysis of limit cycles for drive systems with backlash nonlinearity using an eigenvalue method. The analysis of limit cycles by means of eigenvalue analysis has the advantage that several nonlinearities can be treated simultaneously, e.g. simultaneous occurrence of backlash and friction. Here, a speed-controlled drive system is investigated. At first, a nonlinear state space model for the drive is set up in combination with the control algorithm. Afterwards, the resulting limit cycles of the controlled system are examined by means of the harmonic balance, which specifies the describing function of the nonlinearity for the eigenvalue analysis. Finally, the analytically calculated limit cycle is experimentally validated using a prototype dual-mass system, with backlash.