Radio frequency fingerprint (RFF) identification represents a promising technique for lightweight device authentication. However, current research on RFF primarily focuses on the close-set recognition assumption. Moreover, the high computational complexity and excessive latency during the identification stage represent an intolerable burden for Internet of Things (IoT) devices. In this paper, we propose a deep-learning-based RFF identification framework in relation to open-set scenarios. Specifically, we leverage a simulated training scheme, in which we strategically designate certain devices as simulated unknowns. This allows us to fine-tune our extractor to better handle open-set recognition. Additionally, we construct an exemplar set that only contains representative RFF features to further reduce time consumption in the identification stage. The experiments are carried out on a hardware platform involving LoRa devices and using a USRP N210 software-defined radio receiver. The results show that the proposed framework can achieve 90.23% accuracy for rogue device detection and 93.85% accuracy for legitimate device classification. Furthermore, it is observed that using an exemplar set consisting of half the total data size can reduce the time overhead by 58% compared to using the entire dataset.