In this note, a comprehensive analysis of tire damping effect on -optimal, multi-objective, and robust control of quarter-car suspensions excited by random road disturbances is provided. First, -optimal and convex multi-objective control problems are formulated and the latter problem is solved using linear matrix inequalities. Next, the multi-objective control problem is reformulated as a nonconvex and nonsmooth optimization problem with controller order restricted to be less than or equal to the quarter-car model order. For a range of orders, controllers are synthesized by using the HIFOO toolbox. Parametric studies of this note show that the effect of tire damping on the closed-loop performance of actively controlled suspension systems can be significant. Lastly, a robust controller with guaranteed performance over all polytopic suspension models with tire damping coefficient confined to a prescribed interval is synthesized.
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