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A compact in-line fiber-based polarization controller (FPC) made of a rotatable fiber squeezer is investigated in detail with the Mueller matrix model established based on the generalized principal state of polarization (PSP). The PSP caused by the fiber squeezing is in the equator plane, which turns around S3 axis on the Poincaré sphere when rotating the squeezer. Subsequently, a programmable polarization control method is proposed to realize the polarization conversion between arbitrary polarization states, in which only two parameters of phase shift and rotation angle need to be controlled. This type of FPC, which has a highly compact structure, lower insertion loss, and can be directly embedded into any fiber devices without any extra delay, will be an ideal PC for high-speed optical communication and all-optical signal processing. [ABSTRACT FROM AUTHOR]