I am not sure exactly what you want, but if you want a 3rd order (or higher) problem to solve in a vehicle application I suggest a suspension system model consisting of a spring-mass-damper, where the spring is non-linear (F = -k*x + k2*x^2 + ...). That will increase the model order as you desire. Good luck.

The vehicle lateral dynamics model (single-track) is second-order. The path-following kinodynamic model is fourth-order.

See R. Rajamani, Vehicle dynamics and control, 2. ed. New York, NY Heidelberg: Springer, 2012.