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Vol. 36 (2000) No. 6 P 527-533



This paper describes modeling of a gear ratio servo system of a belt-drive continuously variable transmission (CVT) and design of controllers for the system. It is found through experiments that the servo dynamics is modeled as a first-order system with time delay. Its time constant is given as a function of gear ratio, shift direction, and line pressure of the hydraulic system. The steady-state gain varies depending on the distance between the primary and secondary pulleys or stepper motor position. The steady-state gain variation with the stepper motor position is compensated for by inverse mapping from gear ratio to stepper motor position. Thereby the system can be modeled as a first-order-delay system with a constant steady-state gain. The control system consists of a first-order feedforward controller with a scheduled parameter and a proportional-plus-integral-type feedback controller. The feedforward controller gives desired dynamic characteristics, while compensating for time constant variation of the plant by scheduling the control parameter. The feedback controller guarantees stability of the closed-loop system in the presence of the time-constant uncertainty. The feedback controller also provides the system with robustness against other uncertainties such as time delay, parameter variation due to aging, errors between scheduled and real parameters, etc. Robust performance of the control system is verified through μ-analysis and the control effectiveness is demonstrated through computer simulation and driving tests.

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