Akgul, TugrulhanUnluturk, Ali2026-03-262026-03-2620252169-353610.1109/ACCESS.2025.36134602-s2.0-105017243224https://doi.org/10.1109/ACCESS.2025.3613460https://hdl.handle.net/20.500.14901/2620Akgul, Tugrulhan/0000-0001-7274-5843In this study, real vertical speed reducers (VSRs) were modeled according to the Institute of Transportation Engineers (ITE) standards and applied as road inputs to an active suspension system (ASS). Proportional-Integral-Derivative (PID), Fractional-Order-PID (FO-PID), Sigmoid-PID (S-PID), Sigmoid-Based Fractional-PID (SFO-PID), Exponential-PID (E-PID) and Linear Quadratic Regulator (LQR) controllers are designed for the ASS. The parameters of the controllers are optimized using methods such as Artificial Bee Colony (ABC), Golden Jackal Optimization (GJO), Mayfly Optimization (MFO), Particle Swarm Optimization (PSO), and Whale Optimization Algorithm (WOA). The root mean square (RMS) values of vertical body acceleration (VBA), vertical tire acceleration (VTA), suspension travel (SM), and dynamic load coefficients (DLC), which are the key performance indices of ASS, as well as error-performance indices such as integral of absolute value of error (IAE), integral of squared error (ISE), time integral of absolute value of error (ITAE), and time integral of squared error (ITSE), are compared with the advanced control methods and Passive Suspension (PS). The proposed MFO-E-PID provides 56.07% improvement in RMS values for VBA, 26.71% for VTA, 10.17% for SM, and 29.37% for DLC compared to PS; and 7.97% improvement in VBA, 3.99% for VTA, 2.37% for SM, and 2.77% for DLC compared to the second best, MFO-LQR. The MFO-E-PID method provided 30.45%, 49.99%, 23.58%, and 46.27% improvement in error-performance indices for IAE, ISE, ITAE, and ITSE, respectively, compared to PS; and 6.03%, 16.14%, 4.71%, and 17.20% improvement compared to MFO-LQR. Real-time tests have shown that MFO-E-PID improves ASS performance, safety, and comfort, and holds promise for future vehicles.eninfo:eu-repo/semantics/openAccessRoadsStandardsMathematical ModelsSafetyReal-Time SystemsPollution MeasurementMetaheuristicsAccidentsVehicle DynamicsRoot Mean SquareVertical Speed ReducersActive Suspension SystemOptimizationAdvanced ControlArticle