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We present a theoretical scheme for ground state cooling of a mechanicalresonator in a membrane-in-middle optomechanical system (OMS) driven by twored-detuned drive fields. The details of dynamical evolution of OMS areprovided, and the effect of system conditions on cooling results aresystematically studied. Most importantly, the setups with two drives are foundto be capable of achieving better cooling results than the theoretical coolinglimit with single cavity. Even an improvement by one order of thermal phononnumber is possible with proper combination of the cavity damping rate and driveintensity.

Breaking optomechanical cooling limit by two drive fields on a membrane-in-middle system