This paper presents an active magnetic levitation application that exploits the measurement of coil current and flux density to determine the displacement of the mover. To this end, the nonlinear behavior of the plant and the physical sensing principle are modeled with a finite element approach at different air gap lengths and coil currents. A linear dynamic model is then obtained at the operating point as well as a linear relation for the displacement estimates. The effectiveness of the modeling approach and the performance of the sensing and control techniques are validated experimentally on an active magnetic levitation system. The results demonstrate that the solution is able to estimate the displacement of the mover with a relative error below 3% with respect to the nominal air gap. Additionally, this approach can be exploited for academic purposes and may serve as a reference to implement simple but accurate active magnetic levitation control using low-cost, off-the-shelf sensors.

This paper presents the study of linear Offset-Free Model Predictive Control (OF-MPC) for an Active Magnetic Bearing (AMB) application. The method exploits the advantages of classical MPC in terms of stability and control performance and, at the same time, overcomes the effects of the plant-model mismatch on reference tracking. The proposed approach is based on a disturbance observer with an augmented plant model including an input disturbance estimation. Besides the abovementioned advantages, this architecture allows a real-time estimation of low-frequency disturbance, such as slow load variations. This property can be of great interest for a variety of AMB systems, particularly where the knowledge of the external load is important to regulate the behavior of the controlled plant. To this end, the paper describes the modeling and design of the OF-MPC architecture and its experimental validation for a one degree of freedom AMB system. The effectiveness of the method is demonstrated in terms of the reference tracking performance, cancellation of plant-model mismatch effects, and low-frequency disturbance estimation.

The primary objective of a hybrid electric vehicle (HEV) is to optimize the energy consumption of the automotive powertrain. This optimization has to be applied while respecting the operating conditions of the battery. Otherwise, there is a risk of compromising the battery life and thermal runaway that may result from excessive power transfer across the battery. Such considerations are critical if factoring in the low battery capacity and the passive battery cooling technology that is commonly associated with HEVs. The literature has proposed many solutions to HEV energy optimization. However, only a few of the solutions have addressed this optimization in the presence of thermal constraints. In this paper, a strategy for energy optimization in the presence of thermal constraints is developed for P2 HEVs based on battery sizing and the application of model predictive control (MPC) strategy. To analyse this approach, an electro-thermal battery pack model is integrated with an off-axis P2 HEV powertrain. The battery pack is properly sized to prevent thermal runaway while improving the energy consumption. The power splitting, thermal enhancement and energy optimization of the complex and nonlinear system are handled in this work with an adaptive MPC operated within a moving finite prediction horizon. The simulation results of the HEV SUV demonstrate that, by applying thermal constraints, energy consumption for a 0.9 kWh battery capacity can be reduced by 11.3% relative to the conventional vehicle. This corresponds to about a 1.5% energy increase when there is no thermal constraint. However, by increasing the battery capacity to 1.5 kWh (14s10p), it is possible to reduce the energy consumption by 15.7%. Additional benefits associated with the predictive capability of MPC are reported in terms of energy minimization and thermal improvement.