This dissertation presents shape and structural optimization studies on flapping wings for micro air vehicles. The design space of the optimization includes the wing planform and the structural properties that are relevant to the wing model being analyzed. The planform design is parameterized using a novel technique called modified Zimmerman, which extends the concept of Zimmerman planforms to include four ellipses rather than two. Three wing types are considered: rigid, plate-like deformable, and membrane. The rigid wing requires no structural design variables. The structural design variables for the plate-like wing are the thickness distribution polynomial coefficients. The structural variables for the membrane wing control the in-plane distributed forces which modulate the structural deformation of the wing. The rigid wing optimization is performed using the modified Zimmerman method to describe the wing. A quasi-steady aerodynamics model is used to calculate the thrust and input power required during the flapping cycle. An assumed inflow model is derived based on lifting-line theory and is used to better approximate the effects of the induced drag on the wing. A multi-objective optimization approach is used since more than one aspect is considered in flapping wing design. The the epsilon-constraint approach is used to calculate the Pareto optimal solutions that maximize the cycle-average thrust while minimizing the peak input power and the wing mass. An aeroelastic model is derived to calculate the aerodynamic performance and the structural response of the deformable wings. A linearized unsteady vortex lattice method is tightly coupled to a linear finite element model. The model is cost effective and the steady-state solution is solved by inverting a matrix. The aeroelastic model is used to maximize the thrust produced over one flapping cycle while minimizing the input power. / Ph. D.

Two micro air vehicles, namely Sapthami and Sapthami-flyer, are developed in this thesis. Their total weight is less than 200grams each. They fit inside a 30cm and 32cm sphere respectively and carry the commercially available Kestrel autopilot hardware. The vehicles have an endurance of around 20-30 minutes. The stall speed of Sapthami is around 7m/s and that of Sapthami-flyer is around 5m/s as found by nonlinear modeling. The low stall speed makes it possible for them to be launched by hand. This enhances their portability as they do not require any launching equipment. The vehicle installed with Kestrel autopilot system is capable of many modes of operations. It is capable of fully autonomous flight with the aid of a variety of sensors like the GPS unit, heading sensor, 2-axis magnetometer, 3-axis accelerometer and 3-axis gyros. The vehicle carrying the Kestrel autopilot hardware is capable of autonomous and semi-autonomous flights after installation and tuning of feedback loops. Sapthami, is a tailless flying wing with an inverse zimmermann profile. A flying wing is a preferred configuration for the MAV as it maximizes the lifting area for a given size constraint. For a maximum size constraint of 30cm and aspect ratio around 1, the vehicle operates at Reynolds number between 100,000 to 250,000, at flight velocity 7 m/s to 15 m/s. The Inverse Zimmerman profile has a higher lift coefficient, CL, in comparison to the other planforms such as rectangular, elliptical and Zimmermann, for aspect ratio 1 to 1.25 and tested at Reynolds number of 100,000. The configuration of Sapthami is clean as there is no fuselage and all the components like autopilot hardware and battery are housed inside the wing. A thick reflex Martin Hepperle (MH) airfoil MH18 is chosen which gives sufficient space to place the components. This airfoil is specially used for tailless configurations due to its negative camber at the trailing edge. This negative camber helps in reducing the negative pitching moment of the wing, since no separate horizontal tail is available on a tailless aircraft to compensate for it. The vehicle is fabricated using the blue foam, having a density of 30kg/m3 . The wing is fabricated by CNC machining after which slots are cut manually to embed the electronics. The vehicle is found to have stable flying characteristics. Limited flight trials are done for Sapthami. It takes large time to fabricate the vehicle due to limited availability of CNC machining facility. Therefore, a new tailless, wing-fuselage configuration, which can be fabricated with balsa wood, is designed. Sapthami-flyer is the second vehicle designed in this thesis. Its wing span is slightly more than Sapthami. Since it is a wing-fuselage configuration, therefore there is no need for a thick airfoil. Mark drela’s AG airfoils are found to have better lift than MH airfoils for the inverse Zimmerman profile. The thickness of the airfoils is reduced to 1% so that the wing can be made by a 1.5mm thick balsa sheet to reduce weight. The inverse Zimmermann profile wing with the AG09 airfoil is found to have best lift-to-drag ratio when compared to AG36, MH45 and MH18. The analysis is done using commercially available AVL software. AG09 with 1% thickness is used in the final configuration. This configuration has better short period damping than Sapthami. It also has slower modes of operation than Sapthami. The operating modes of most of the MAVs, including Sapthami and Sapthami-flyer, are lowly damped but fast. This makes it difficult for the pilot to fly the vehicle. To improve the flying qualities of the vehicle artificial stabilization is required. The feedback is implemented on the Kestrel autopilot hardware. It allows only PID based feedback structures to be implemented, hence gives no choice to the designer to implement higher order control. The digital integrator and differentiator implementation for feedback are non-ideal. This further reduces the effectiveness of control. The problem is dealt with by incorporating the additional dynamics introduced by these implementation while formulating the control problem. Further the modeling of the micro air vehicle is done by using vortex lattice simulation based softwares. The fidelity of the obtained dynamics is low. Therefore, there is high uncertainty in the plant model. The controller also needs to reject the wind gust disturbances which are of the order of the flight speed of the vehicle. All the above stated requirements from the control design can be best addressed by a robust control design. Sapthami-flyer uses aileron and elevator for control. There is no rudder in the configuration in order to reduce weight. In the longitudinal dynamics, pitch rate and pitch error feedback to elevator are used to increase the short period and phugoid damping respectively. In the lateral dynamics, a combination of roll rate, yaw rate and roll error feedback is given to aileron to improve the dutch roll damping and stabilize the spiral mode. The feedback loops for both longitudinal and lateral dynamics are multi-output single input design problems, therefore simultaneous tuning of loops is beneficial. The PID control is designed by first converting the actual plant to a static output feedback equivalent plant. The dynamics introduced by non-ideal differentiator and integrator implementation on the autopilot hardware are incorporated in the open loop static output feedback formulation. The robust pole placement for the SOF plant is done by using the modified iterative matrix inequality algorithm developed in this thesis. It is capable of multi-loop, multi-objective feedback design for SOF plants. The algorithm finds the optimal solution by simultaneously putting constraints on the H2 performance, pole placement, gain and phase margin of the closed loop system. The pole placement is done to minimize the real part of largest eigenvalue. A single controller is designed at a suit-able operating point and constraints are put on the gain and phase margin of the closed loop plant at other operating points. The designed controller is tested in flight on board Sapthami-flyer. The vehicle is also capable of tracking commanded pitch and roll attitude with the help of pitch error, roller or feedbacks. This is shown in the flight when the pilot leaves the RC stick and the vehicle tracks the desired attitude. The vehicle has shown improved flying characteristics in the closed loop mode.