The energetic equivalence rule, which is based on a combination of metabolic theory and the self-thinning rule, is one of the fundamental laws of nature. However, there is a progressively increasing body of evidence that scaling relationships of metabolic rate vs. body mass and population density vs. body mass are variable and deviate from their respective theoretical values of 3/4 and −3/4 or −2/3. These findings questioned the previous hypotheses of energetic equivalence rule in plants. Here we examined the allometric relationships between photosynthetic mass (M p) or leaf mass (M L) vs. body mass (β); population density vs. body mass (δ); and leaf mass vs. population density, for desert shrubs, trees, and herbaceous plants, respectively. As expected, the allometric relationships for both photosynthetic mass (i.e. metabolic rate) and population density varied with the environmental conditions. However, the ratio between the two exponents was −1 (i.e. β/δ = −1) and followed the trade-off principle when local resources were limited. Our results demonstrate for the first time that the energetic equivalence rule of plants is based on trade-offs between the variable metabolic rate and population density rather than their constant allometric exponents.

The airspeed is an important feedback signal for flight control, and its measurement accuracy is related to the safety of aircraft, especially for hybrid vertical takeoff and landing (VTOL) unmanned aerial vehicles (UAV) in the transition phase. However, offline calibration of the pitot tube cannot fully simulate the situation in real cases, and this is why online calibration after installation is necessary. In addition, the environmental wind field creates a high risk for the conversion flight of a hybrid UAV, thus real-time wind field measurement of the flight field has great significance for the flight path planning of the conversion process. In this article, an innovative method for online calibration of pitot tube and wind field estimation is proposed. After establishing the extended Kalman filter (EKF) for estimation, an analysis method is proposed to analyze the observability of EKF under different flight strategies. Then, the hovering flight is selected as the experimental flight trajectory. The laboratory computer simulation and flight experiment results validate the theory and prove that the proposed method could re-calibrate the scale factor of the pitot tube and estimate the wind field.

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The wind field has a great influence on the control stability of Tilt-rotor unmanned aerial vehicle (UAV), especially during the takeoff and landing phase. The airspeed of UAV is so small during these phases that it cannot generate stable aerodynamic forces, which will significantly reduce the wind robustness of Tilt-rotor UAV. In this paper, the disturbance of wind field is analyzed from two perspectives: the wind field acting on the UAV fuselage, which is regarded as external interference, and the wind acting on the propeller, which is considered as modeling error. After analyzing the interference mechanism of wind field, a generalized extended state observer (GESO) and a H robust control method with mixed sensitivity are proposed, which could empower the Tilt-rotor UAV with good interference suppression ability as well as better performance tracking ability. Finally, the laboratory simulation and flight experiment are studied. The results validate the theory and prove that the proposed method could resist the interference of wind field and shows excellent control effect. INDEX TERMS Tilt-rotor, unmanned aerial vehicle, wind field disturbance, generalized extended state observer, robust control.