Nonlinear Observer for Bounded Jacobian Systems, With Applications to Automotive Slip Angle Estimation

Real-time knowledge of the slip angle in a vehicle is useful in many active vehicle safety applications, including yaw stability control, rollover prevention, and lane departure avoidance. Sensors that can directly measure slip angle are too expensive for ordinary automotive applications. This technical note develops a new nonlinear observer design technique for estimation of slip angle using inexpensive sensors normally available for yaw stability control applications. The approach utilized is to use the mean value theorem to express the nonlinear error dynamics as a convex combination of known matrices with time varying coefficients. A modified form of the mean value theorem for vector nonlinear systems is presented. The observer gains are then obtained by solving linear matrix inequalities (LMIs). The developed approach can also enable observer design for a large class of differentiable nonlinear systems with a globally (or locally) bounded Jacobian. The developed nonlinear observer is evaluated through experimental tests on a Volvo XC90 sport utility vehicle. Detailed experimental results show that the developed nonlinear observer can reliably estimate slip angle for a variety of test maneuvers on road surfaces with different friction coefficients.