Tunable optical frequency combs offer a flexible solution for specific applications such as dual-comb spectroscopy, optical communications and microwave photonics, delivering improved precision, compatibility, and performance. However, previously, there has been a trade-off between reconfigurability and system simplicity in comb generation. Here, we present a fast-switched repetition rate frequency comb system that utilizes an electro-optic modulation time-lens technique with a high third-order nonlinear AlGaAsOI waveguide. Only one stage of modulator is used in the time-lens system which significantly reduces the complexity of the overall system. Our system allows for tuning of the center wavelength from 1542 nm to 1556 nm, as well as independent adjustment of the repetition rates from 18 GHz to 26.5 GHz, enabling fast-switching capabilities. Additionally, our system exhibits a high pump-to-comb conversion efficiency of up to 67.9%. It also demonstrates robustness to temperature changes and environmental instability. All the involved devices can be integrated onto a single chip, making this comb suitable for various applications.