Rollover prevention control of vehicles with crosswind disturbance

Abstract

In this paper, we propose a design method for a rollover prevention controller using front and rear wheel steering that takes into account the variation of vehicle velocity. First, we propose a new description for vehicles. The description is suitable for controller design in case when vehicle velocity varies. Next, based on the description, we develop a new rollover prevention control scheme. In the vehicle control system using the developed controller, the lateral acceleration tracks the estimated crosswind disturbance in the case of the high risk of rollover so that the risk of rollover can be reduced. Finally, numerical simulations are carried out to demonstrate the usefulness of the proposed controller.

Appendix

The equation of motion for ${\varvec{q}}_{\phi } \left( t \right)$ is given by [12]

$$ \begin{aligned} \dot{\user2{q}}_{\phi } \left( t \right) & = \frac{{m_{{\text{s}}} h_{{\text{s}}} }}{{I_{\phi } }}{\varvec{b}}_{{\text{s}}} {\varvec{b}}_{{\text{u}}}^{T} {\varvec{a}}\left( t \right) \\ & \; + \left( {{\varvec{b}}_{{\text{u}}} {\varvec{b}}_{{\text{s}}}^{T} - \frac{1}{{I_{\phi } }}{\varvec{b}}_{{\text{s}}} {\varvec{g}}_{{\text{s}}}^{T} } \right){\varvec{q}}_{\phi } \left( t \right) + {\varvec{b}}_{{{\text{d2}}}} d_{{\text{w}}} \left( t \right). \\ \end{aligned} $$

(29)

From Eqs. (1), (2) and (29), we have

$$ \begin{aligned} \dot{\user2{a}}\left( t \right) + \alpha {\varvec{a}}\left( t \right) & = \left( { - v_{x}^{ - 1} A_{21} + A_{22} } \right){\varvec{q}}_{y} \left( t \right) \\ & - \left( {v_{x}^{ - 1} A_{31} + \frac{{m_{{\text{s}}} h_{{\text{s}}} }}{{I_{{\text{m}}} }}{\varvec{b}}_{{\text{u}}} {\varvec{g}}_{{\text{s}}}^{T} A_{5} } \right){\varvec{a}}\left( t \right) + A_{4} {\varvec{q}}_{\phi } \left( t \right) \\ & + B_{{{\text{p2}}}} \left\{ {{\varvec{b}}_{{\text{u}}} \delta_{{\text{c}}}^{*} \left( t \right) + {\varvec{\mu}}\left( t \right)} \right\} + \left[ {\begin{array}{*{20}c} {{\varvec{b}}_{{{\text{d3}}}} } & {{\varvec{b}}_{{{\text{d1}}}} } \\ \end{array} } \right]{\varvec{d}}_{{\text{w}}} \left( t \right). \\ \end{aligned} $$

(30)

From Eqs. (1), (29) and (30), the dynamic equation (3) can be derived.