IHB method for response computation of a class of second-order hysteretic nonlinear control systems under a sinusoidal excitation

Aiming at a class of hysteretic nonlinear control systems, their hysteresis characteristics and linear characteristics could be separated, a model based on backlash neutral network was adopted to approach the hysteresis nonlinear characteristics of the systems. After the dynamic model was established. The incremental harmonic balance (IHB) method was used to solve the forced vibration response of this hysteretic control system with a proportional controller. Floquet theory was applied to analyze the stability of the periodic solution of the systems. The proposed approach was verified with Runge-Kutta numerical integration. The effects of the parameters of the controller on the system performance were analyzed.