Genetic algorithm application in multi-objective optimization and decoupled sliding-Mode controller design on bus suspension system

Abstract

The study proposes a new method for optimizing and integrating control systems on the driver’s seat suspension to improve its performance. The first novelty is applying the genetic algorithm (GA) in the multi-objective optimization process to find the structure’s optimal parameters k_s and c_s that ensure the overall objective function J_x(w) of driver’s acceleration μ₁(x) and suspension’s relative displacement μ₂(x) minimized. J_x is formulated with the Weighted Square Sum model as the Pareto method. This process includes complex constraints on the comfort level, the vehicle’s body vertical stability, the guiding element’s deformation limits under different load conditions (no load, half load, full load), and road surfaces (transient, random). The second contribution is the integration of PID and SMC controllers into the suspension to reduce the vehicle’s body displacement x_s (m). The controllers’ parameters are also optimized simultaneously by GA, including K_P, K_I, K_D, N of PID, and p, η, Δ of SMC. The optimal values k_{s_opt} = 150000 (N/m) and c_{s_opt} = 10000 (Ns/m), respectively, in the cases of w = [0.5 0.6] corresponding to transient and random roads. The controllers helped improve x_s responses by over 40% with transient road and 65% with random road.