## 1 Introduction
Stabilizing tailless FWMAVs is a significantly important objective in the development of tailless FWMAVs for flying. Owing to the inherent instability of tailless FWMAVs, feedback controllers are required to stabilize them during flight. In comparison, tailed FWMAVs, such as the Microbat [40], Delfly II [41], TL-Flowerfly [42], Konkuk University Biomimetic Ornithopter [43], H2 Bird Ornithopter [44], and Robird [45], have an inherent stability [46] so that they can maintain equilibrium without any active manipulation of wing or tail kinematics. Recent findings on Hawkmoth [47] have indicated that the vibration of flapping wings potentially contributes to the improved stability of large insects and FWMAVs through a passive vibrational stabilization mechanism. Owing to their feasibility and simplicity, proportional-integral-derivative (PID) feedback controllers and their simple variants are often implemented, particularly during the early development of tailless FWMAVs [19; 30; 37; 38]. More complex variants of PID feedback controllers incorporating different strategies (such as neural network [48], particle swarm optimization [49], and dominant pole placement [50]) and autotuning algorithms (such as optimal approach [51; 52] and fuzzy adaptive [53]) are being developed for various applications. As with many biomimetic robots, tailless FWMAVs have less complicated body structures and control mechanisms than their biological counterparts. Thus, they can be considered as simplified versions of insects. However, owing to the nonlinear, time-varying, and periodic nature of these systems, describing the mechanics of tailless FWMAVs is still a considerable challenge. In addition, as tailless FWMAVs have different wing configurations [54; 55; 56; 57], actuators, and control mechanisms [19; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39], they cannot be fully generalized. Many efforts have been made to model the flapping kinematics, aerodynamics, and flight dynamics of flyers and FWMAVs. They are derived computationally or experimentally with various assumptions, ranging from time-invariant linear to nonlinear time-periodic models [58; 59; 60]. One of the main purposes of obtaining a dynamic model is to design a flight controller with various control techniques and schemes, such as PID [34; 61], linear-quadratic-Gaussian [62], state feedback [63; 64], nonlinear [65; 66; 67], sliding mode [68; 69], robust [70; 71], adaptive [72], adaptive neural network [73; 74], and model-free [75]. While many dynamic models and controllers have been successfully developed, only a limited number have been implemented on tailless FWMAVs because some tailless FWMAVs cannot generate sufficient lift to perform free flight for implementation and verification. In this study, the system identification of a tailless FWMAV called KUBeetle was conducted to improve the previously derived longitudinal mode extended dynamic model [34] and obtain a more accurate dynamic model to design a controller. The fabrication of tailless FWMAVs with successful flight makes it possible for system identification based on measured input and output data to be conducted [65; 66; 77; 78; 79; 80; 81; 82]. This approach can potentially identify real dynamics and address the design changes of tailless FWMAVs to obtain a dynamic model with a high degree of similarity to actual systems. In a previous study [65], three single-axis closed-loop system identifications of the robotic hummingbird were conducted using a gimbal system and a Vicon motion tracking system with step reference command as the input. A second-order system was used to describe the pitch, roll, and yaw dynamic. A theoretical linear model for the piezo actuator positioning of Robobee wings' [76] was developed using an off-board displacement laser sensor. The identified model had an error of around 5%, but it was restricted to the wing driving system. A longitudinal gray box model system identification using open-loop system identification procedures was conducted on Delfly Nimble [77].