Stability Analysis and Control Validation of DDEV in Handling Limit via SOSP: A Strategy Based on Stability Region

The stability region is an important criterion in the active safety system of vehicle. Extensive literatures have developed various stability regions for the centralized driving vehicle (CDV). However, seldom of them make a thorough analysis of the stability for distributed driving electric vehicle (DDEV). Especially when the direct yaw moment control (DYC) intervenes, the stability region of DDEV shows a huge difference compared with CDV. So far, most researches on the stability control of DDEV are still based on the traditional CDV stability region, which leads to the conservation of controller design. To this end, a dynamic and analytical stability region of DDEV is firstly developed in this paper. By employing sum of square programming (SOSP) algorithm, we choose a high-order Lyapunov function to make a precise estimation of the stability region. A novel DC shape function is proposed to reduce the conservation of estimation when DYC involves. To ensure the real-time performance for control application, Long Short Term Memory (LSTM) neural network is employed to fit the coefficients of Lyapunov function, as well as enable the dynamic shifting with driving conditions. Based on the aforementioned stability region, we develop a MPC controller to ensure the stability and tracking performance during handling limit. Both simulations and road tests demonstrate that the developed stability region could effectively restraint the vehicle states from diverging, which enhances vehicle maneuverability while ensuring vehicle stability.
Note to Practitioners
—Handling stability is a crucial factor which concerns the safety of vehicle. Almost all vehicles should be equipped with active safety system, such as Electronic Stability Program (ESP) of Bosch and Electronic Stability Controller (ESC) of GM. They collect the real-time vehicle states by the Built-in sensors. Meanwhile, they calculate the current stability margin according to the driver’s control input and analyze the deviation of the vehicle states to decide whether the active control is needed to maintain the stability of vehicle. This system is established well in CDV. However, for DDEV, it has another input of DYC in addition to wheel steering angle, which changes the dynamic characteristic of vehicle. This means that the stability margin of traditional ESP is inaccurate when the DYC intervenes, which will lead to the misjudgment of instability or the unsafety of vehicle. This paper develops an analytic stability region of DDEV and describes the stability margin with different values of DYC, which could adapt to varying conditions. This technology fills the gap of the stability determination of DDEV and has a good application prospect in the active safety system of DDEV.