Linear Parameter-Varying Model of an Electro-Hydraulic Variable Valve Actuator for Internal Combustion Engines

This paper presents a novel linear parameter-varying (LPV) model of an electro-hydraulic variable valve actuator (EHVVA) for internal combustion engines that is capable of continuously varying valve timing with dual-lift. The dual-lift is realized mechanically through a hydraulic lift control sleeve; valve opening (VO) terminal and closing seating velocities are regulated using a top or bottom snubber; and opening and closing timings, as well as lift profile area, are controlled by the valve actuation timing and hydraulic supply pressure. First, nonlinear mathematical system model is developed based on the Newton's law, orifice flow equation, and fluid constitutive law, where the fluid dynamics of the actuation solenoid valve, actuation piston, passages, and orifices, that influence the engine valve profile, are considered in detail. Second, to have an LPV control-oriented model, the order of nonlinear model is reduced and subsequently transformed into an LPV model with minimal deviation by carefully considering the system nonlinearities, time delay, and time-varying parameters. Calibration and validation experiments for both nonlinear and LPV models were performed on the test bench under different operational conditions. The key time-varying parameters, the time constant of the actuation piston top pressure and the discharge coefficient, are highly nonlinear as functions of temperature-sensitive fluid viscosity and are determined using the test data through the least-squares optimization. With the identified and calibrated model parameters, simulation results of both nonlinear and LPV models are in good agreement with the experimental ones under different operational conditions.