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A characteristic model based all-coefficient adaptive control law was recently implemented on an experimental test rig for high-speed energy storage flywheels suspended on magnetic bearings. Such a control law is an intelligent control law, as its design does not rely on a pre-established mathematical model of a plant but identifies its characteristic model while the plant is being controlled. Extensive numerical simulations and experimental results indicated that this intelligent control law outperforms a μ-synthesis control law, originally designed when the experimental platform was built in terms of their ability to suppress vibration on the high-speed test rig. We further establish, through an extensive simulation, that this intelligent control law possesses considerable robustness with respect to plant uncertainties, exteal disturbances, and time delay.