Vibration control of semi-active suspension system with magnetorheological damper based on hyperbolic tangent model

In this article, the nonlinear damping characteristics of magnetorheological damper are expressed with hyperbolic tangent model to simulate its mechanical experimental results. The fitted hyperbolic tangent model can represent hysteretic behavior for magnetorheological damper exactly. Based on the hyperbolic tangent model, a quarter-car model with magnetorheological damper is established, and a new hybrid fuzzy and fuzzy proportional-integral-derivative (HFFPID) controller integrated with hybrid fuzzy control and fuzzy proportional-integral-derivative control is developed to improve the semi-active suspension performance, which can overcome the absence of precise mathematical model. Furthermore, numerical simulations for fuzzy proportional-integral-derivative (PID), hybrid fuzzy proportional-integral-derivative (HFPID), and HFFPID controllers are investigated to demonstrate the effectiveness of the proposed approaches. The simulation results show that the body acceleration, suspension deflection, and tyre displacement can be reduced more effectively using HFFPID controller under sinusoidal road excitation. It can be further concluded that the suspension performance is improved more effectively by using HFFPID controller under random road excitation, especially in the peak points.