Modeling and Control of an Articulated Multibody Aircraft

Abstract

Insects use dynamic articulation and actuation of their abdomen and other appendages to augment aerodynamic flight control. These dynamic phenomena in flight serve many purposes, including maintaining balance, enhancing stability, and extending maneuverability. The behaviors have been observed and measured by biologists but have not been well modeled in a flight dynamics framework. Biological appendages are generally comparatively large, actuated in rotation, and serve multiple biological functions. Technological moving masses for flight control have tended to be compact, translational, internally mounted and dedicated to the task. Many flight characteristics of biological flyers far exceed any technological flyers on the same scale. Mathematical tools that support modern control techniques to explore and manage these actuator functions may unlock new opportunities to achieve agility. The compact tensor model of multibody aircraft flight dynamics developed here allows unified dynamic and aerodynamic simulation and control of bioinspired aircraft with wings and any number of idealized appendage masses. The demonstrated aircraft model was a dragonfly-like fixed-wing aircraft. The control effect of the moving abdomen was comparable to the control surfaces, with lateral abdominal motion substituting for an aerodynamic rudder to achieve coordinated turns. Vertical fuselage motion achieved the same effect as an elevator, and included potentially useful transient torque reactions both up and down. The best performance was achieved when both moving masses and control surfaces were employed in the control solution. An aircraft with fuselage actuation combined with conventional control surfaces could be managed with a modern optimal controller designed using the multibody flight dynamics model presented here.

Complex Eigenvalue Analysis of Multibody Problems via Sparsity-Preserving Krylov–Schur Iterations

“…By expanding the evaluation of the partial derivatives of F to all the terms contained in it the following result is obtained where all the derivatives of the forces have been meaningfully collected into more readable stiffness K and damping R matrices: M(q)δ q + R(q, q)δ q + K(q, q, q, γ)δq + C q (q, t) T δγ = 0 C q (q, t)δq = 0 (5) (6) In the formula above, the damping matrix R comes from the linearization of internal/external forces f about q, plus the linearization of f g , the quadratic part of the inertial forces; hence,…”

“…In this case, one needs to implement a complex-valued eigenvalue problem, where the imaginary and real parts of the eigenvalues give an indication of the damping factor and, consequently, an indication about the impending instability [4,5]. Finally, we can mention that, in the field of control theory, often a state-space representation of the linearized system is required, and this is another problem that motivates the research of efficient methods to recover the eigenvalues of the multibody system [6,7].…”

Attitude Control of Ornithopter Wing by Using a MIMO Active Disturbance Rejection Strategy

“…For example, the Proportional-Integral-Derivative (PID) controller and its variants are the commonly used schemes for flight control in real-world applications [ 7 , 8 , 37 , 38 ]. Classical optimal techniques such as Linear Quadratic Regulator (LQR), Linear Quadratic Integrator (LQI), and Model Predictive Control (MPC) are also adopted as control solutions [ 39 , 40 ]. Robust control schemes such as also appear in literature as a choice.…”

“…, then the control law of Equation (43) and Extended State Observer (ESO) with gains described in Equation (40), Equations ( 41) and (42) Remark 3. The mathematical developments that result in Theorem 1 were applied in a MIMO system composed of three second-order equations.…”

Complex Eigenvalue Analysis of Multibody Problems via Sparsity-Preserving Krylov-Schur Iterations

“…In this case, one needs to implement a complex-valued eigenvalue problem, where the imaginary and real parts of the eigenvalues give an indication of the damping factor and, consequently, an indication about the impending instability [4] [5] . Finally we can mention that, in the field of control theory, often a state space representation of the linearized system is required, and this is another problem that motivates the research of efficient methods to recover the eigenvalues of the multibody system [6] [7] . Motivated by the above mentioned applications, in this paper we discuss the numerical difficulties related to the computation of eigenvalues and eigenvectors in multi-flexiblebody systems under the most general assumptions: we assume that the system can present singular modes (also called rigid body or free-free modes), we consider the optional presence of damping, hence leading to complex-valued eigenpairs, we consider an arbitrary number of parts and constraints, and we assume that the size of the system could be arbitrarily large.…”