# Review on System Identification and Mathematical Modeling of Flapping Wing Micro-Aerial Vehicles
## 3 System Identification and Mathematical Modeling of Flapping Wing Micro Air Vehicles (FWMAVs)
The review paper by [52] highlighted that the inertia effects of the wings on the main body were invoked in very few models of the flapping wing systems. The majority of the flapping angles of FWs remains greater than 20 degrees (see, for instance, [116]). Therefore, the small angle assumption (i.e., \(\sin(\theta)\approx\theta\)) is no longer valid, and consequently, the linearized dynamic model becomes inaccurate. The dynamic models of the FWs are generally highly nonlinear and time varying due to the aerodynamic forces on the wings that are typically predicted via the lift and drag coefficients of the quasi-steady aerodynamic model. These coefficients depend on the angle of attack, which may vary significantly during a single stroke. Various nonlinear modeling approaches have focused on the addition of a spring in the redesign and optimization of the elastic elements like actuators, wings, and linkages to further improve the capability of the system to be driven at resonances [16; 17; 18; 19]. Another strategy [20] considered wing, actuator, and transmission components, and developed an integrated nonlinear model, which considers all the changes made in the wing shape and linkage system. The change in the wing shape significantly affects the inertial properties and the aerodynamic damping forces, whereas the variation in the linkage mechanism affects the control input channels. Some useful linear models have also been developed that account for the nonlinear geometric and aerodynamic components [117; 118]. The developed nonlinear model sufficiently predicts the behavior of the FWMAVs with a considerable operating range. However, the accuracy in the model reduces when operated at high frequencies. The FWMAVs, as mentioned earlier, mimic either insect or bird flight. They are stabilized via active and passive stabilization strategies in different flight envelopes [10; 12; 30; 31; 32] through manually tuned controllers such as proportional-derivative (PD) and/or proportional-integral-derivative (PID) controllers. However, they are observed to be sensitive to external disturbances. Thus, it becomes quite challenging to keep them stable in broad flight envelopes. One reason for such difficulties is the absence of a sufficiently accurate nonlinear model that can describe the unsteady aerodynamics of the FWMAVs' flapping motions [119; 120] and the added inertia effect contribution to the MAVs dynamics [121]. In this context, a linear time invariant (LTI) model was developed in [121; 122; 123; 124] via the use of standard aircraft equations. Another approach, known as the multi-body approach, was introduced. However, such an approach for a time varying nonlinear model [121; 125] is not suitable for onboard processing. All the aforementioned approaches have significant shortcomings such as a lack of practical validation, limited only to computational environment and the repeatability of the data. Therefore, it is demanding to overcome such modeling difficulties in order to fully explore the capabilities of these fliers. In the subsequent subsections, we will focus on system identification strategies that have been applied for identifying parameters and mathematical models of FWMAVs. In presenting the review, we classify natural fliers and FWMAVs into two categories, the tailed and tailless fliers/FWMAVs. Various system identification techniques used in identifying the model parameters of fliers/FWMAVs in these two categories will be discussed.