Research on LQR control of nonlinear active suspension cooperatively optimized by differential geometry and genetic algorithms

With the continuous advancement of the automotive industry’s demand for driving comfort and handling stability, active suspension systems have become a research hotspot due to their ability to achieve effective balancing among multiple performance metrics. However, traditional active suspension control algorithms face challenges such as insufficient modeling accuracy and excessive reliance on empirical parameter optimization when dealing with nonlinear systems. To address these issues, this study proposes an improved linear quadratic regulator (LQR) control strategy that integrates differential geometry theory and genetic algorithm (GA) optimization to enhance the control performance of nonlinear active suspension systems. First, a quarter-car nonlinear active suspension model is established using differential geometry theory, effectively preserving the system’s nonlinear characteristics and improving modeling precision. Building on this foundation, an enhanced LQR controller is designed, combined with the global optimization capability of the genetic algorithm, to construct a fitness function based on multiple suspension performance metrics. This approach achieves automated optimization of the weight coefficient matrix and multi-objective balancing. To validate the effectiveness of the proposed control strategy, comparative simulations under discrete impact road and Class C random road conditions are conducted using the MATLAB-Simulink platform. Results demonstrate that, compared to PID control, the GA-LQR strategy reduces the root mean square (RMS) values of body vertical acceleration, suspension dynamic deflection, and tire dynamic displacement by 6.94%, 57.72%, and 4.4%, respectively, under discrete impact road conditions. Under Class C road conditions, these reductions further increase to 22.1%, 63.6%, and 16.25%. This study provides a high-performance and robust control strategy for nonlinear suspension systems, laying a theoretical foundation for improving overall vehicle performance and driving handling stability.