GA-LQR control for multi-objective optimization in inerter-based active suspension

Inerter-based active suspension systems have great potential for improving vehicle dynamic performance, but their controller design is still challenged by the conflicting requirements of ride comfort, handling stability, and control energy consumption. Conventional linear quadratic regulator control usually depends on empirical selection of weighting matrices and does not explicitly consider control power, which makes it difficult to achieve a satisfactory balance among body acceleration, suspension deflection, dynamic tire load, and actuator energy consumption. To address this issue, a quarter-car model equipped with an inerter element is established, and a Genetic Algorithm–Linear Quadratic Regulator (GA-LQR) control framework is developed for the active suspension system. In this method, the logarithmic parameters of the Linear Quadratic Regulator (LQR) weighting matrices are globally optimized by a genetic algorithm, so that body acceleration, suspension deflection, dynamic tire load, and control energy consumption can be considered simultaneously in the controller design. In this way, the traditional trial-and-error tuning of LQR weights is transformed into a systematic optimization process for multi-objective suspension control. Simulation results under random road excitation show that the proposed GA-LQR strategy provides better overall performance than both passive suspension and conventional LQR-controlled inerter suspension. Compared with standard LQR control, the proposed method reduces body acceleration by 39.01% and suspension deflection by 43.1%, while the corresponding reductions achieved by conventional LQR are 12.75% and 7.4%, respectively. In addition, tire-road contact stability is further improved. The results demonstrate that the GA-optimized weighting matrices can effectively improve the comprehensive performance of inerter-based active suspension systems and provide an effective control approach for vibration reduction with lower energy cost.