Optimal Control for Cubic Strongly Nonlinear Vibration of Automobile Suspension

Abstract

An optimal control method is provided to mitigate the cubic strongly nonlinear vibration of vehicle suspension with velocity and displacement feedback controllers. The forced vibration of the vehicle suspension is studied utilizing the methods of modified Lindstedt-Poincaré and multiple scales. Ranges of feedback gains that can keep the vibration system stable are worked out by the stability conditions of eigenvalue equation. Taking the decay rate and the energy function as the objective functions and the ranges of stable vibration feedback gains as constrained conditions, the optimal feedback gains of velocity and displacement are calculated by the method of minimum method. The simulation results show that the control method can have optimal control results.

Approximating amplitude of a nonlinear oscillator at resonance

“…Observing the previous work done, the nonlinear vibration and control of the amplitude of an automobile system by minimizing energy were studied for under-damped systems. 1 The researchers have also shown that vibration attenuation depends mainly on the damping in a system. 5,12 In vehicle dynamics, the cubic damping ζ is not preferred.…”

“…The vehicle dynamics and vibration attenuation of a quarter-car system were investigated by minimizing energy and the effect of damping on the natural frequency and modal damping was studied. 1,2 The optimization of vehicle suspension for ride quality and tyre grip metrics and the optimization, control and stability of the vehicle system were also investigated by researchers. 3,4 The authors studied a shock absorber that attenuates the amplitude of the sprung mass at resonance.…”

A beam–ring circular truss antenna restrained by means of the negative speed feedback procedure

“…The results layout that the cubic speed input control strategy is effective in lessening the reaction response amplitude of the nonlinear plant just as dispensing with the numerous reactions. Liu et al (2014) controlled the cubic unequivocally nonlinear vibration of vehicle suspension with both speed and displacement feedback controllers by using the adjusted Lindstedt–Poincaré and multiple scale methodology. Amer and Agwa (2019) used two different controlling methods (linear and cubic) of velocity feedback to reduce the mechanical model system’s oscillation that is subjected to parametric forces via the perturbation technique.…”

Semi-active structural vibration control of base-isolated buildings using magnetorheological dampers

“…2–5,12 The semi-active concept was also successfully applied to a broad class of vehicle vibration isolation problems, ranging from tractors and other farm vehicles, to high-speed ground transportation vehicles. 13–15 Semi-active fluid dampers (oil dampers) are still the most common solution today when large forces are needed and have been widely used in civil engineering structures in Japan. 16 Examples are found for instance in the House of Creation and Imagination of Keio University (Yokohama), completed in 2000, 16 and in the 11-storey Keio University building—Mita South Building erected in 2005.…”