DYNAMICS AND CONTROL OF FLEXIBLE AIRCRAFT
2018-2019 Assignment: Distributed Propulsion 1.1
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e.a.
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Ti
Ti
Ti+1
Mi+1
V∞
A straight semi-span wing of semi-span band chord c, clamped at the root, carries an arbitrary number of
propellers, each of which is approximated as a lumped force and moment. The thrust of each propeller is
Ti=Ti0+ ∆Ti. The moment is Mi=Mi0+ ∆Mi. The moment perturbation, ∆Mi, is associated with the
thrust perturbation, ∆Ti, namely ∆Mi=k∆Ti(what is the value of k?).
Define the number of propellers and their location along the wing. Propellers are offset from the wing’s
elastic axis; their center of mass is moved forward with respect to the wing’s elastic axis. Each propeller axis
may have a different rotation with respect to the plane of the wing, such that differential thrust changes
between adjacent propellers result in a net transverse force.
The wing structure is modeled as a beam, with out-of-plane bending and torsional stiffness distributions
EJ and GJ , mass per unit span m, and polar inertia Jp, referred to the center of mass (c.m.), which is offset
at a distance daft of the elastic axis (e.a.).
The aerodynamics model will be described later.
The objective is to design a controller for flutter suppression and/or load alleviation that uses the thrust
perturbation of the propellers as actuators. The sensors and the dynamics of the actuators will be
selected and defined later.
To support the design of the controller, we need to develop an appropriate dynamic model of the system.
Outline:
1. Model the wing structure using beam finite elements. Discretize it such that the propellers are
connected to nodes.
2. Add the propellers to the structural model considering their:
•mass and inertia, which contribute to the overall mass matrix;
•prestress contribution resulting from the reference thrust, Ti0, which contributes to the overall
stiffness matrix;
•gravity contribution to the stiffness matrix (e.g. pendulum-like, when appropriate).
3. Produce a reduced order model (ROM), using a limited number of low-frequency modes and using any
technique of preference to improve the quality of the ROM when engine and propeller lumped forces
are taken into account.
4. Determine the right-hand side of the problem as the matrix that produces the generalized forces acting
on the system as a function of the thrust increments, ∆Ti.
Additional tasks will be specified as soon as the related topics are dealt with in class.
Note: define and comment any missing data.
