Model identification and backstepping control of a continuously variable transmission system

This paper develops a continuous-time model and controller for the drivetrain dynamics and hydraulics governing the ratio dynamics of a metal V-belt continuously variable transmission (CVT). In developing the drivetrain dynamics, the separate notions of geometric ratio and speed ratio and their relation to each other through the output power efficiency of the CVT are introduced. A data driven model is then created to represent the relationship between ratio dynamics and control hydraulics. The controller developed uses backstepping to effectively track a desired engine speed. Exact local asymptotic stability conditions for the controller are presented. A simulation incorporating the entire drive train and vehicle dynamics demonstrates good closed loop behavior of the controlled system.