Establishing a prediction model, with linearity and few dof (degree of freedom), is a key step for the design of a control algorithm based on the modern control theory. In this paper, such a model is needed for active suppression of vehicle longitudinal low‐frequency vibration. However, many dynamic processes in the vehicle have different effects on the vibration. Therefore, a detailed coupling model is firstly established, considering the dynamics of the torsional vibrations of the driveline and the tire, the tire force nonlinearity, and the vehicle vertical and pitch vibrations. Based on this model, sensitivity analysis is conducted and the results show that the tire slip, the torsional stiffness of the half‐shaft, and the tire have great influences on the longitudinal vibration. Then a three‐dof model is obtained by linearizing the tire slip into damping. A parameter estimation method is designed to obtain the model parameters. Finally, the model is validated. The time domain response, error analysis, and frequency response results demonstrate that the 3‐dof model has a good consistency with the detailed coupling model. It is suitable as a control‐oriented model.

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.

This paper presents an optimal tracking control of engine valve timing for an electro-hydraulic variable valve actuator utilizing the adaptively estimated supply pressure that is the main source for valve timing variation. The system supply pressure is online estimated through a model-guided adaptive estimator with one-step prediction capability. The estimation model consists of a static guidance model, an in-event valve model, and a one-step prediction model. Using the estimation model, the adaptive estimator generates a nominal estimation with accelerated convergence, estimates the pressure residual error using in-event dynamics, and provides one-step forward pressure prediction along with the resulting pressure fluctuation. The linear quadratic tracking (LQT) control is used to track the desired valve timing based on an event-by-event valve model, where the adaptively estimated pressure variation is used as the feedforward control in the LQT control to improve the tracking accuracy and a Kalman filter is used to estimate the system states for the LQT state feedback control. The parameter estimation and control algorithms are validated through both the simulation and test bench studies by comparing different estimation and control schemes. Both the steady-state and transient operational conditions are investigated, and the effectiveness of the proposed adaptive LQT valve timing control is demonstrated.

In this article, a model predictive control strategy is presented for an all-speed governor of heavy-duty vehicles that satisfies the requirements of fast tracking and fuel economy. The control-oriented torque-based engine model is used for the design of a model predictive control–based speed tracking control algorithm. Two methods for improving the speed tracking and fuel economy synthesis are presented, which include engine load estimation and variable weighting factor. The engine speed and fuel mass are used to estimate the real-time engine torque. The variable weighting factor based on the driver’s intention is used to adjust the control algorithm in MATLAB/Simulink. The simulation results show that the tracking performance and fuel economy of the model predictive controller are better than that of a proportional–integral–derivative controller.