A Brillouin optical time-domain analysis (BOTDA) method based on a closed-loop control system is proposed to track fast variations of the Brillouin frequency shift along the sensing fiber. Whilst the method eliminates the gain spectral scanning, the exact distributed Brillouin frequency profile is retrieved directly from the output of a closed-loop controller with no need of post-processing. Moreover, as the operating frequency is being continuously updated to follow the Brillouin frequency change, an unlimited temperature or strain measurement range can be achieved. Both theoretical analysis and experimental results validate that the closed-loop controlled BOTDA acts as a low-pass filter that considerably rejects the noise from photodetector, with an efficiency which fundamentally outperforms basic averaging. By optimizing the closed-loop parameters, the measurement time is reduced from a few minutes to a couple of seconds compared with standard BOTDA, i.e., two orders of magnitude improvement in terms of measurement speed, while keeping the same accuracy and measurement conditions. If the sampling time interval that is limited by our instrument can be further reduced, the method offers the potentiality of km-range sensing with sub-second measurement time, with an unmatched favorable trade-off between measurand accuracy and closed-loop delay.