Control-Oriented Modelling with Experimental Verification and Design of the Appropriate Gains of a PI Speed Ratio Controller of Chain CVTs

The continuously variable transmission (CVT) system represents one of the best solutions to minimize the fuel consumption for vehicles that are driven by an internal combustion engine or an electrical motor. Hence, the theoretical analysis of a chain CVT is crucial in the optimization of the design and control strategy. This paper is concerned with the transient dynamics of a chain CVT with a speed ratio controller adopted from the Carbone-Mangialardi-Mantriota model and its experimental verification. To this end, a theoretical model is developed with a PI speed ratio controller, considering the momentary solution of a first order differential equation governing the shifting speed, which represents the whole dynamics of the CVT. To verify the developed model, the experiments are carried out on a chain CVT test rig. It is observed that the numerical and experimental results are in good agreement, which implies that the developed model embedded in a speed ratio controller is appropriate to predict the shifting dynamics of the chain CVT. Afterwards, the developed model is used to design the appropriate PI gains by numerical experiments in order to obtain the same slope of the time response of speed ratio for different input angular velocities. Therefore, the same shifting speed can be secured for the different working conditions in this manner. This paper contains very important results for manufacturers about the control parameter and gain effect on the shifting dynamics of chain CVT, and the developed model can be used for different control algorithms in automotive applications.