Backstepping sliding-mode control for active suspension system matching mechanical elastic wheel with uncertainties

For the purpose of anti-puncture and lightweight, a new type of mechanical elastic wheel (MEW) is constructed. However, the large radial stiffness of MEW has a negative effect on ride comfort. To make up for the disadvantage, this paper proposes a novel control strategy consisting of backstepping control and integral sliding-mode control, considering the uncertainties of active suspension and MEW. First, an active suspension system matching MEW is established, discussing the impact of uncertainties. The nonlinear radial characteristic of MEW is fitted based on the previous experiment results. Then, in order to derive ideal motions, an ideal suspension system combining sky-hook and ground-hook damping control is introduced. Next, ignoring the nonlinear characteristics and external random disturbance, a backstepping controller is designed to track ideal variables. Combined with the backstepping control law, an integral sliding-mode control strategy is given, further taking parameter uncertainty and external disturbance into account. To tackle chattering problem, an adaptive state variable matrix is applied. By using Lyapunov stability theory, the whole scheme proves to be robust and convergent. Finally, co-simulations with Carsim and MATLAB/Simulink are carried out. By analyzing the simulation results, it can be concluded that the vehicle adopting backstepping sliding-mode control performs best, with excellent real-time performance and robustness.

Decoupling control of active suspension and four-wheel steering based on Backstepping-ADRC with mechanical elastic wheel

Mechanical elastic wheel (MEW) has the advantages of explosion-proof and prick-proof, which is conducive to the safety and maneuverability of the vehicle. However, the research on the performance of the full vehicle equipped with MEW is rare. Considering the particular properties of the radial and cornering stiffness of MEW, this paper aims to take into account both ride comfort and yaw stability of the vehicle equipped with the MEW through a nonlinear control method. Firstly, a 9-DOF nonlinear full vehicle model with the MEW tire model is constructed. The tire model is fitted based on experimental data, which corrects the impacts of vertical load on the cornering characteristic of the MEW. Then the full vehicle system is decoupled into four subsystems with a single input and a single output each according to active disturbance rejection control (ADRC) technology. In this process, the coupling relationship between different motions of the original system is regarded as the disturbance. Afterward, a novel nonlinear extended state observer is proposed, which has a similar structure of traditional linear extended state observer but smaller estimation error. Next, the control law of Backstepping-ADRC for different subsystems are derived respectively based on the Lyapunov theory. For the first time, the Backstepping-ADRC method is applied to the decoupling control of four-wheel steering and active suspension systems. Furthermore, the parameters of the controllers are adjusted through a multi-objective optimization scheme. Finally, simulation results validate the effectiveness and robustness of the proposed controller, especially when encountering some disturbances. The indices of vehicle body attitude and ride comfort are improved significantly, and also the yaw stability is guaranteed simultaneously.

Radial stiffness analysis of circular ring with uncertain boundary conditions: Mechanical elastic wheel as an example

The paper studies the radial stiffness of mechanical elastic wheel (MEW), which is regarded as a circular ring with uncertain boundary conditions for the first time, and proposes a ring-chain model to solve the radial stiffness of the ring. Different from assuming the boundary conditions by experience or building finite element model with complex processes from previous researches, the ring-chain model coupling circular ring model and dynamics of multi-rigid body is accurate and simple to find the loaded positions of ring and make the boundary conditions clear. The results show that the ring-chain model can be solved to get the deformations and loaded positions of ring, the radial stiffness of MEW is large, and the radial displacement of MEW increases non-linearly. The results are consistent with that from finite element model under the same settings, but the time cost of ring-chain model is less. In addition, the influence factors of ring radial stiffness are also found and analyzed. The method presented in this paper can provide data for the response analyses of vehicle and references for the analysis of circular ring with uncertain boundary conditions.