A drifting model for the resonant frequency and retardation amplitude of a photo-elastic modulator (PEM) in the photo-elastic modulated Fourier transform spectrometer (PEM-FTs) is presented. A multi-parameter broadband-matching driving control method is proposed to improve the thermal stability of the PEM interferometer. The automatically frequency-modulated technology of the driving signal based on digital phase-locked technology is used to track the PEM's changing resonant frequency. Simultaneously the maximum optical-path-difference of a laser's interferogram is measured to adjust the amplitude of the PEM's driving signal so that the spectral resolution is stable. In the experiment, the multi-parameter broadband-matching control method is applied to the driving control system of the PEM-FTs. Control of resonant frequency and retardation amplitude stabilizes the maximum optical-path-difference to approximately 236 μm and results in a spectral resolution of 42 cm-1. This corresponds to a relative error smaller than 2.16% (4.28 standard deviation). The experiment shows that the method can effectively stabilize the spectral resolution of the PEM-FTs.