Considering the time-delay in control input channel and the nonlinear spring stiffness characteristics of suspension, a quarter-vehicle magneto rheological active suspension nonlinear model with time-delay is established in this paper. Based on the time-delay nonlinear model, an adaptive neural network structure for magneto rheological active suspension is presented. By recognizing and training the adaptive neural network, the adaptive neural network active suspension controller is obtained. Simulation results show that the presented method can guarantee that the quarter-vehicle magneto rheological active suspension system has satisfying performance on the E_level very poor ground.

For engineering vehicles, farm tractors, military vehicles, and so on, the road conditions are usually very poor. Therefore, vibration problem is prominent particularly [

Vehicle suspension system is a complex dynamic system; the road input is a random process and has a strong uncertainty, while the system itself has strong nonlinearity characteristic; therefore, it is difficult to obtain ideal control effect by using conventional control methods [

The neural network is a kind of powerful tool to deal with uncertainty and nonlinearity; it can parallel computing and distribute information storage, while it has strong fault tolerance and self-learning ability. Hence, neural network is suitable for the complex system modeling and control [

In this paper, in order to reduce the vibration of magneto rheological active suspension system, adaptive neural network active suspension controller is designed. At first, a quarter-vehicle active suspension nonlinear model with time-delay is established by considering the time-delay in control input channel of magneto rheological active suspension system and the nonlinear spring stiffness characteristics of suspension. Then, an adaptive neural network structure for magneto rheological active suspension is presented according to the time-delay nonlinear model. Next, the adaptive neural network active suspension controller is obtained by recognizing and training the adaptive neural network. At last, E_level ground which is very poor road condition is considered for a quarter-vehicle magneto rheological active suspension system. Simulation shows that the presented method can guarantee that the system has satisfying performance.

The remainder of this paper is organized as follows. In Section

In this paper, quarter-vehicle model for active control of magneto rheological seat suspension system is studied. At the same time, the nonlinear stiffness characteristics of the suspension spring and control time-delay characteristics are considered. Figure

Quarter-vehicle model with a magneto rheological active suspension.

Among them,

Force-displacement curve of nonlinear spring.

Dynamic differential equation for the suspension system is

Adaptive neural network system structure is shown in Figure

Adaptive neural network structure.

In Figure

The road excitation can be viewed as a white noise signal and it is suitable to identify active suspension system by using nonlinear autoregressive moving average (NARMA) model; namely,

AN1 identifies the system model and multilayer feed-forward neural network was used by the network structure. Network is composed of two layers: the first layer is input layer and has

The structure of the neural network controller AN2 is shown in Figure

Adaptive neural network controller.

In order to obtain good performance, Marquardt back-propagation algorithm (MBP algorithm) which is of high training efficiency is used in training neural network identifier ANl. During training, the error between desired body acceleration and the output of neural network identifier ANl is as the input for MBP algorithm. And the weights and thresholds of AN1 keep unchanging.

Because the desired control signal is unknown at the very beginning, neural network controller AN2 is cascaded with neural network identifier AN1, as shown in Figure

The input-output relationship of the first layer is

The input-output relationship of the first layer is

To improve the training algorithm, the weights and thresholds are adjusted according to the following laws:

Consider the active suspension system [

For E_level ground, the road roughness power spectrum density is

Road excitation.

Figure

Training result.

Test result.

In order to make comparison, LQR controller is designed as well in this paper, and

Tire displacement.

Body acceleration.

Input force.

Figures

In this paper, an adaptive neural network control strategy is presented for a magneto rheological active suspension system with time-delay in control input channel and the nonlinear spring stiffness characteristics. On the basis of the time-delay nonlinear model and adaptive neural network structure, and by recognizing and training the adaptive neural network, the adaptive neural network active suspension controller is obtained. Simulation on a quarter-vehicle magneto rheological active suspension system under E_level ground shows that the proposed method can significantly reduce the peak values of tire displacement, body acceleration, and control signal, and the body acceleration and control signal are smoother.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported by Natural Science Foundation of China (51275249) and Talent Introduction Foundation of Engineering College Nanjing Agricultural University (Rcqd11-06).