Application of constrained H∞ control for a half-car model of an active suspension system equipped with inerter

In this study, a multi-objective robust H
2
/H
∞
controller for a half-car model of an active inerter-based suspension system in the presence of external disturbance has been investigated. Its main goal is to improve the inherent trade-offs between ride quality, handling performance, and suspension travel and to guarantee the allowable level for suspension stroke and energy consumption. Inerters have been widely used to suppress undesirable vibrations of various types of mechanical structures. The advantage of inerters is that the realized equivalent mass ratio (inertance over primary structure mass) is greater than its actual mass ratio, leading to higher performance for the same effective mass. First, the dynamics and state space of the active inerter-based suspension system for a half-car model have been achieved. In order to attain the defined objectives, and ensure that the closed-loop system achieves the prescribed disturbance attenuation level, the Lyapunov stability function, and linear matrix inequality (LMI) techniques have been utilized to satisfy the multi-objective robust H
2
/H
∞
criterion. Furthermore, to limit the gain of the controller, some LMIs have been added. In the case of feasibility, sufficient LMI conditions by solving a convex optimization problem afford the stabilizing gain of the constrained robust state-feedback controller. Numerical simulations show that the active inerter-based suspension system performs much better than a passive suspension with inerter and active suspension without inerter