Linear-Parameter-Varying Control of an Improved Three-Degree-of-Freedom Aeroelastic Model

Abstract

Introduction Aeroelasticity is a broad term that describes the often complex interactions between aerodynamics and structural mechanics. The active control of aeroelastic phenomena is of particular research interest as it can lead to a reduction in weight and an increase in performance of an airframe. For more background on the analysis and control of aeroelastic systems, the reader is referred to the article by Mukhopadhyay [1]. A two degree-of-freedom wing section that is allowed to pitch and plunge due to supporting translational and torsional springs has often been used as a testbed for novel aeroelastic control methodologies. Two such apparatus are commonly used for the experimental validation of these methodologies; the Benchmark Active Control Technologies (BACT) wing [1, 2], and the Nonlinear Aeroelastic Test Apparatus (NATA) [3, 4]. This work focusses on the NATA platform, and presents an improved dynamic model along with a dynamic-less state-feedback Linear Parameter Vary-1 ing (LPV) controller which self-schedules with airspeed, U , and experimental results showing the suppression of limit-cycle oscillations. Many practical and theoretical studies based on the NATA use the two degree-of-freedom models as published in Platanitis and Strganac [4]. However, this model does not correctly model the inertia from the portion of the carriage that rotates, and the control surface dynamics, which in this case are too slow to be neglected. The improved three degree-of-freedom dynamic model presented in this work captures these effects, and will benefit future theoretical and experimental research based on the NATA and similar platforms. Using a H 2 representation of the standard Linear Quadratic Regulator (LQR) control problem, a state-feedback controller of the form u = K(U)x is synthesized using Linear Matrix Inequalities (LMIs) as a generalized LPV control problem. This controller assumes thatU is much slower than the airfoil dynamics and can be approximated as equal to zero, and that once stable, the torsional stiffness nonlinearity present in Strganac, Ko, and Thompson [3] has little influence, hence can be approximated as k α (α) = k α. 2 Model Consider the typical-section airfoil shown in Figure 1, with three degrees-offreedom; pitch, α, plunge, h, and trailing-edge surface deflection, β. The wing section is forced by an aerodynamic lift force, L, and moment, M , coupled to the free-stream conditions and the dynamic state of the airfoil. The wing section is divided into three distinct bodies; a translational body of mass m h which corresponds to the non-rotational component of the carriage in the experimental apparatus (Section 3), the rotational wing body of mass m α and inertia I α , which corresponds to the main wing body plus the rotational component of the carriage in the experimental apparatus, and the rotational trailing-edge section of mass m β and inertia I β. The trailing-edge servo motor provides a torque between the wing body and the trailing-edge section. These

Tensor-Product-Model-Based Control of a Three Degrees-of-Freedom Aeroelastic Model

“…However, Controller 3 has to stabilize the system with an additional nonlinearity caused by the friction. Control performance: The control performance can be compared with the results presented in [15], where The LQR controller was designed for the same three DoF aeroelastic wing section.…”

“…One of the most recent models of the three DoF aeroelastic wing section based on real measurements, which was adopted in this investigation, was presented and deeply elaborated in [11,15] [15] by curve tting on the measured displacement-moment data for a nonlinear spring k α (α) = 25.55 − 103.19α + 543.24α 2 . It is important to emphasize that the order of the polynomial dening k α (α) does not inuence the control design methodology, see later.…”

“…The details and denition of each system parameter can be found in [15] and they have the (6) is given for any parameter as the parameter-varying convex combination of LTI system matrices S ∈ R O×I .…”

“…where M eom , C eom , K eom and F eom are the mass, damping, stiness and forcing matrices of the equation of motion [15].…”

“…Based on [15], it is assumed that the trailing-edge servo-motor dynamics can be represented using a second-order system of the form:…”