Longitudinal mode model-based controller design for tailless flapping wing robot with loop shaping compensator.

In this study, the stable proportional-derivative (PD) controller gains for pitch control (longitudinal control) are obtained using the linearized and non-coupled longitudinal-mode flight dynamics model of the tailless, hover-capable, flapping wing robot named KUBeetle. To acquire a more realistic longitudinal model of KUBeetle, we incorporated the dynamics of the sensors, filters, and servo. Then, the range of PD controller gains that yield stable and sufficient stability robustness are determined using the Routh-Hurwitz, root locus, and H norm stability analyses. We observed that the stability of the closed loop controller is affected significantly by the dynamics that are incorporated. The PD controller gain with good robustness is selected based on the stability analysis. However, the low frequency gain of the PD controller was too small to attain the setpoint, although the stability margin was sufficiently high. A loop shaping compensator is designed and added to the control loop to improve the low frequency gain while sustaining the stability margin. The frequency and time domain analyses reveal that the proposed control loop can be used for stabilizing KUBeetle. To test the performance experimentally, we implemented the control loop in an onboard control system, which includes a microprocessor and MEMS sensors. The experimental results closely matched the simulation results, demonstrating that the proposed controller could maintain stability in a real system with high flapping noises.