Management of angular speed sensors for control at the power-zero condition of a continuously variable transmission: A describing-function approach

Abstract

This paper focuses on the control at the power-zero condition of a power-split continuously variable transmission (CVT) used in agricultural tractors. The power-zero condition requires the controller to regulate the transmission ratio to zero, independently of the input engine speed. This is particularly useful when the tractor is operated uphill or downhill, in order to keep the vehicle still without using brakes. As the considered CVT is tailored to low-power tractors used in orchards and vineyards, this is indeed a very important functioning mode. Specifically, it is shown how the control problem is deeply interleaved with the choice of the appropriate angular speed sensors used for computing the transmission ratio and the algorithm used to process their output for computing the angular speed. An innovative analysis on the estimation error and the time delay of the two main speed estimation algorithms is developed. In particular, it is proven that the delay introduced by the speed sensor can cause an undesired limit-cycle behaviour in the closed-loop system. The existence and stability properties of such a limit cycle are assessed with a describing-function approach, and a strategy to suppress the limit cycle is proposed.