Analytical Cost Function-Based Optimization of Time Delay Parameter in a Nonlinear Quarter-Vehicle Suspension

This study develops a weighted cost function-based optimization framework for tuning the time delay parameter in a nonlinear vehicle suspension with time-delayed acceleration feedback control. A quarter-vehicle model is first established to characterize suspension dynamics. The steady-state response is derived analytically using the harmonic balance method, while a stability analysis of the linearized system delineates the feasible ranges of time delay and feedback gain coefficient. A composite cost function is then formulated by integrating weighted contributions from the sprung mass acceleration, suspension dynamic deflection, and tire dynamic load. Optimization of the time delay parameter is carried out for both positive and negative feedback control configurations. A comparative performance evaluation between constant and frequency-dependent time delay strategies is conducted across the human-sensitive frequency band (4-8 Hz). Numerical simulations validate the theoretical predictions, demonstrating average reductions of 45.97% in the cost function, 35.54% in the sprung mass acceleration, and 30.65% in the tire dynamic load. Although a slight increase in the suspension dynamic deflection is observed, the results confirm that optimized time delay can simultaneously improve ride comfort and driving safety.