High-performance control of continuously variable transmissions

Nowadays, developments with respect to the pushbelt continuously variable transmission (CVT) are mainly directed towards a reduction of the fuel consumption of a vehicle. The fuel consumption of a vehicle is affected by the variator of the CVT, which transfers the torque and varies the transmission ratio. The variator consists of a metal V-belt, i.e., a pushbelt, which is clamped between two pulleys. Each pulley is connected to a hydraulic cylinder, which is pressurized by the hydraulic actuation system. The pressure in the hydraulic cylinder determines the clamping force on the pulley. The level of the clamping forces sets the torque capacity, whereas the ratio of the clamping forces determines the transmission ratio. When the level of the clamping forces is increased above the threshold for a given operating condition, the variator efficiency is decreased, whereas the torque capacity is increased. When the level of the clamping forces is decreased below the threshold for a given operating condition, the torque capacity is inadequate, which deteriorates the variator efficiency and damages the pulleys and the pushbelt. Since this threshold is not known, the level of the clamping forces is often raised for robustness, which reduces the variator efficiency. The challenge for the control system is to reduce the clamping forces towards the level for which the variator efficiency is maximized, although the variator efficiency is not measured. Furthermore, avoiding a failure of the variator in view of torque disturbances and tracking a transmission ratio reference are necessarily required. Two state-of-the-art control strategies are presently used, i.e., safety control and slip control. These control strategies involve limitations that follow from the model knowledge and/or the sensor use that underlies the control design. For this reason, the objectives of the research in this thesis are oriented towards improvements with respect to the model knowledge of both the hydraulic actuation system and the variator, which is subsequently exploited in the control design of both components, to improve the performance. The resources of the control designs are restricted to measurements from sensors that are standard. A cascade control configuration is proposed, where the inner loop controls the hydraulic actuation system and the outer loop controls the combination of the inner loop and the variator. The elements of the cascade control configuration are the subject of the research in this thesis. For the hydraulic actuation system, modeling via first principles and modeling via system identification are pursued. Modeling via first principles provides a nonlinear model, which is specifically suited for closed-loop simulation and optimization of design parameters. A modular approach is proposed, which reduces the model complexity, improves the model transparency, and facilitates the analysis of changes with respect to the configuration. The nonlinear model is validated by means of measurements from a commercial CVT. Modeling via system identification provides a model set, which is subsequently used for the hydraulic actuation system control design. A model set of high-quality is constructed, which is achieved by the design of the identification experiments that deals with the limited signal-to-noise ratio (SNR) that arises from actuators and sensors of low-quality. The hydraulic actuation system control design is multivariable, which is caused by the interaction between the hydraulic cylinders that is inherently introduced by the variator. Stability and performance are guaranteed for the range of operating conditions that is normally encountered, which is demonstrated with the experimental CVT. A variator control design is proposed that deals with both the transmission ratio and the variator efficiency in terms of performance variables, where the transmission ratio is measured, while the variator efficiency is not measured. The variator control design uses the standard measurement of the angular velocities, from which the transmission ratio is constructed, as well as the standard measurement of the pressure. Essentially, the variator control design exploits the observation that the maximum of the transmission ratio and the maximum of the variator efficiency are achieved for pressure values that nearly coincide. This observation is derived from both simulations with a nonlinear model and experiments with the experimental CVT. This motivates the use of the pressure-transmission ratio map, although the location of the maximum is not known. For this reason, the maximum of the input-output map is found by a so-called extremum seeking control (ESC) design, which aims to adapt the input in order to maximize the output. A robustness analysis shows that an input side disturbance that resembles a depression of the accelerator pedal and an output side disturbance that resembles the passage of a step bump are effectively handled. Finally, the ESC design is extended with a so-called tracking control (TC) design, which enables that optimizing the variator efficiency and tracking a transmission ratio reference are simultaneously achieved. The variator control design that is composed of the ESC design and the TC design is evaluated with the experimental CVT. Simulation of a driving cycle shows that the final variator control design outperforms the conventional variator control design in terms of the variator efficiency.