Mixed GL₂/H₂/GH₂control with pole placement and its application to vehicle suspension systems

This paper presents a multi-channel multi-objective synthesis framework, in which generalized L 2 (GL 2), H 2, and generalized H 2 (GH 2) criteria are specified for appropriate channels, and the poles of the closed-loop system are constrained within a subregion S(a, r,θ) of the left-half s-plane. The multi-objective framework is successfully applied to a seven degrees-of-freedom decoupled vehicle suspension system. The suspension control system has three channels: channel T 1, relating to ride comfort, is from road disturbances to vehicle body accelerations, the suspension travel channel, T 2, is from manoeuvre disturbances to suspension deflections, and channel T 0 is used to address system uncertainty. The control objective is to minimize a mixture of ||T 1|| H2 and ||T 2|| GH2 while guaranteeing that the closed-loop system is robustly stable, with poles located within a specified subregion S(a, r,θ). The simulation results demonstrate that this multi-objective control can improve vehicle ride comfort and decrease suspension travel simultaneously. In addition, the multi-objective synthesis framework provides a simple but effective trade-off between vehicle ride comfort and suspension travel.