Safety of a quarter-vehicle car through negative derivative feedback controller

Abstract

The aim of this paper is presenting the acts of a resonant control technique called Negative Derivative Feedback (NDF) controller on a quarter-vehicle car subjected to principal parametric excitation. This control technique is useful and effective as it helps to avoid any dangerous vibrations caused during its operation. Therefore, we considered the NDF controller that plays an important role in it. Moreover, robustness to natural frequency variation has been investigated for the first time on a quarter-vehicle car system. The multiple scale homotopy (MSH) approach has been used for solving the equations of the controlled system mathematically. At the studied resonance case Ω=2,ω=1, the acts of actual various parameters and system conduct are calculated. Frequency-response equations (FREs) governing the controlled system vibration amplitude have been derived. The simulation outcomes were completed with the help of MATLAB 7.0 programs. A comparison between PPF and NDF controllers has been made in the vibration system to show the best controller. Numerical outcomes reveal that the best one in removing the oscillations and decreasing the value of amplitudes is the NDF controller. Furthermore, after adding this controller, its gains lessened the steady-state amplitudes of the model in a minor time. In addition, this controller made the structure more stable than those of other controllers. The impacts of the effective parameters on the controlled system have been discovered. The different response curves for the framework when the controller is off and on action have been plotted by the obtained frequency-response equation displaying the stable and unstable zones. Finally, the obtained numerical results have shown an outstanding agreement per the analytical ones.