Research on GA-LQR control of air suspension damping for hub motor-driven electric vehicles
To address the challenges of energy shortages and environmental pollution, electric vehicles ( Evs ) have emerged as energy-efficient, and environmentally friendly transportation solutions. Evs using hub motors have gained keen academic interest worldwide thanks to their compact structures, flexible driving, and high transmission efficiency. However, the installation of hub motors causes such issues as increased unsprung mass and motor excitation, further undermining the performances of both Evs and hub motors. Addressing the exacerbated negative vibrations in hub motor-driven Evs caused by the offset of the rotor axis within the motor leads to changes in the air gap magnetic field and unbalanced electromagnetic forces. This paper conducts research by employing Evs equipped with hub motors and air suspension systems. A genetic algorithm-based Linear Quadratic Regulator ( GA-LQR ) air suspension control method is proposed to mitigate the deterioration of suspension performance resulted from the introduction of hub motors. Based on the theory of air gap magnetic field in hub motors and in consideration of the effect of road conditions on the eccentricity of the rotor in hub motors, a model of air gap magnetic field distribution is built to calculate the unbalanced electromagnetic forces under eccentric conditions. By analyzing the coupling mechanism between the hub motor and the air suspension, an eight-degree-of-freedom half-car dynamic model of a hub motor-driven electric vehicle incorporating both the hub motor and the air suspension system is developed. Considering the lag of the vehicle's wheelbase, a road excitation model is established. Real vehicle tests are conducted on randomly generated road surfaces to validate the accuracy of the dynamic model. The test data are compared with simulation data in both the time and frequency domains. Simulations are conducted to study the vertical vibration characteristics of the Evs under dual excitation from unbalanced electromagnetic forces and road inputs, and the impact of unbalanced electromagnetic forces on the vertical vibration of the vehicle is analyzed. To improve suspension performance and alleviate adverse vibrations from the hub motor, Linear Quadratic Regulator ( LQR) control theory is proposed based on the half-car system dynamic model and optimal control. The magneto-rheological dampers in the air suspension are employed as control objects, and a cost function is built by vehicle performance indicators, suspension travel and damper damping force as constraints. To address the subjective influence on the weighting matrices Q and R in the LQR controller, a genetic algorithm is employed for global search optimization. The GA-LQR controller for the hub motor-driven electric vehicle is built in Matlab/Simulink. Simulation analysis of the controller is conducted at different road surface grades at constant speeds and under different speeds on the same road surface grade to validate the effectiveness of the proposed control strategy. The simulation results obtained from both the time and frequency domains show the GA-LQR-controlled air suspension significantly improves the vertical acceleration of the vehicle body, hub motor eccentricity, tire dynamic load, and pitch acceleration of the vehiclecompared with those of passive suspension and LQR-controlled air suspension. It effectively suppresses the adverse vibrations caused by hub motor eccentricity and greatly enhances Evs' travel comforts.
air suspensionhub motorunbalanced electromagnetic forcesGA-LQR controlEVs
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