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Measurement-based control, utilizing an active feedback loop, is a standard tool in technology. Feedback control is also emerging as a useful and fundamental tool in quantum technology and in related fundamental studies, where it can be used to prepare and stabilize pure quantum states in various quantum systems. Feedback-cooling of center-of-mass micromechanical oscillators, which typically exhibit a high thermal noise far above the quantum regime has been particularly actively studied and has recently been shown to allow for ground-state cooling using optical measurements. Here, we realize measurement-based feedback operations in an electromechanical system, cooling the mechanical thermal noise down to 3 quanta, limited by added amplifier noise. Counter-intuitively, we also obtain significant cooling when the system is pumped at the blue optomechanical sideband, where the system is unstable without feedback.