A non-linear mathematical model was built to represent the planetary magnetic gear motor in a vehicle steering system. In view of period doubling, quasi-period and chaotic motions in the steering process of the steering system under some parameters and operation conditions, a numerical simulation analysis was conducted on chaotic behavior arising in the model for the steering system based on the maximum Lyapunov exponent. Furthermore, the system was designed through complementary sliding-mode control and its performance was improved by combining this with an adaptive recurrent cerebellar-modelarticulation controller. This suppresses chaos in the lateral motion of vehicles, and improves the safety and stability of the steering system in the process of vehicle driving, proving the eff ectiveness of the proposed control strategy.