The existing available research outcomes on vibration attenuation control for time-delay feedback indicate that, for the delay dynamic vibration absorber with fixed time-delay control parameters, under harmonic excitation, a good vibration attenuation control effect occurs on the vibration of the main system. However, the effect is not obvious for complex excitation. Aiming at the above problems, in a short time interval, a harmonic excitation with the same displacement size as the complex excitation was established. Then, by calculating its equivalent amplitude and equivalent frequency, a harmonic equivalent method for complex excitation was proposed in this paper. The time-delay parameters were adjusted according to the equivalent frequency of harmonic equivalent excitation in real time; therefore, a good vibration attenuation control effect was obtained through the delay dynamic vibration absorber in the discrete time interval. In this paper, research on a time-varying delay dynamic vibration absorber was conducted by taking the two-degree-of-freedom vibration system with a delay dynamic vibration absorber as an example. The simulation results show that the proposed control method can reduce the vibration of the main system by about 30% compared with the passive vibration absorber. This can obviously improve the performance of the time-delay dynamic vibration absorber. It provides a new technical idea for the design of vehicle active frame system.

To overcome the increase in the unsprung mass and deformation of the magnet gap for in-wheel-motor-propelling systems, a novel topology scheme had been presented in previous work. In this study, an optimal matching design between the suspension and the rubber bushing is employed for the novel system to reduce the effect of the road surface roughness on the magnet gap as much as possible, on the basis of good ride quality and comfort. First, the half-vehicle model of the scheme is set up. Second, the objective function is developed using the weighting coefficient method to obtain a balanced consideration of the magnet gap deformation, the body's pitch angle acceleration and the vertical vibration acceleration which takes the road condition, the vehicle speed and the load condition into account. The suspension's dynamic travel, the dynamic load of the tyres, the damping parameters of the suspension, the bushing stiffness, the bushing damping and the bushing deformation are selected as the constraint conditions. Third, the design optimization for matching is carried out with the following excitation sources: the road surface roughness and the unbalanced magnetic force. Finally, a comparative analysis of the three optimization indices is performed before and after the optimization. The results show that, after optimal matching, all vibration response variables demonstrate measurable improvements. The magnet gap deformation achieves the greatest improvement, followed by the vertical vibration acceleration and the body's pitch angle acceleration. The magnet gap deformation is improved by 42.4%, 45.4% and 44.99% under the no-load condition, the half-load condition and the full-load condition respectively, and the deformation of the rubber bushings satisfies the required design. The performance improvement is significant. The optimal matching method can be used to solve research problems involving the magnet gap deformation and the ride comfort of in-wheel-motor-driven vehicles, while at the same time offering a method for design optimization.

Vehicles driving on the road continuously suffer low-frequency and high-intensity road excitation, which can cause the occupant feelings of tension and dizziness. To solve this problem, a three-degree-of-freedom vehicle suspension system model including vehicle seat is established and a linear function equivalent excitation method is proposed. The optimization of the random excitation is transformed into the optimization of constant force in a discrete time interval, which introduces the adaptive weighted particle swarm optimization algorithm to optimize the delay and feedback gain parameters in the feedback control of time delay. In this paper, the stability switching theory is used for the first time to analyze the stability interval of 3-DOF time-delay controlled active suspension, which ensures the stability of the control system. The numerical simulation results show that the algorithm can reduce vertical passenger acceleration and vehicle acceleration, respectively, by 13.63% and 28.38% on average, and 29.99% and 47.23% on random excitation, compared with active suspension and passive suspension based on inverse control. The effectiveness of the method to suppress road random interference is verified, which provides a theoretical reference for further study of suspension performance optimization with time-delay control.

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.

With the application of an active control unit in the suspension system, the phenomenon of time delay has become an important factor in the control system. Aiming at the application of time-delay feedback control in vehicle active suspension systems, this paper has researched the dynamic behavior of semivehicle four-degree-of-freedom structure including an active suspension with double time-delay feedback control, focusing on analyzing the vibration response and stability of the main vibration system of the structure. The optimal objective function is established according to the amplitude-frequency characteristics of the system, and the optimal time-delay control parameters are obtained by using the particle swarm optimization algorithm. The stability for active suspension with double time-delay feedback control by frequency-domain scanning method is analyzed, and the simulation model of active suspension with double time delay based on feedback control is finally established. The simulation results show that the active suspension with double time-delay feedback control could reduce the body’s vertical vibration acceleration, pitch acceleration, and other indicators significantly, whether under harmonic excitation or random excitation. So, it is indicating that the active suspension with double time-delay feedback control has a better control effect in improving the ride comfort of the car, and it has important reference value for further research on suspension performance optimization.