The paper focuses on the design of nonlinear state feedback controllers to minimize the amplitude of limit cycle oscillations exhibited by nonlinear aeroelastic systems. Nonlinear normal modes are computed for the closed-loop system to represent the flutter mode dynamics using a single mode. The effectiveness of nonlinear normal modes as a tool to capture the limit cycle oscillation growth is demonstrated. The harmonic balance method is used to estimate the amplitude and frequency of the limit cycle oscillations exhibited by the flutter mode. Analytical estimates of sensitivities of limit cycle amplitude with respect to the introduced control parameters are derived and shown to match closely to the sensitivities computed numerically using the finite difference method on a time marching simulation of the complete aeroelastic system. A multi-objective optimization problem that minimizes the estimate of limit cycle oscillation amplitude and an approximate measure of control cost is solved using the analytical sensitivities. Numerical simulation results are used to verify that minimizing the estimate of the limit cycle amplitude of the flutter nonlinear normal mode corresponds closely to minimizing the simulated limit cycle amplitude of the complete aeroelastic system.
Actuator selection is a critical field in advanced aircraft design. This is especially true if Active Flutter Suppression (AFS) is desired, as sensitivities at both low and high frequency ranges become relevant. A three degree of freedom airfoil with flap model is analyzed to investigate the impact of actuator nonlinearities such as rate-limit and position saturation on the performance of AFS controllers subject to outer-loop input disturbance. A linear quadratic regulator (LQR) is used to ensure linear stability as well as to investigate nonlinear stability; i.e., response to large excitation. Simulations are performed in order to converge upon the input disturbance level (epsilon) needed to drive the flutter-suppressed system unstable in the presence of the aforementioned nonlinearities. The paper discusses the relationship between epsilon and actuator frequency and proposes varying LQR parameters to produce a more robust nonlinear control solution. Actuator selection based upon nonlinear limits, is shown to play a significant role in the nonlinear stability and AFS performance of the control system.
The interaction of an aircraft's structure and the ight dynamics is an increasing concern in modern aircraft. These interactions can cause instabilities such as body-freedom utter or can degrade the performance of a controller designed only considering the rigid body ight dynamics. Subscale vehicles could be used to understand the problem and validate the solutions, but current scaling methods are inadequate for these complex systems. To validate earlier theoretical scaling work, a subscale vehicle has been designed which shows signi cant coupling between the ight dynamics and structural dynamics. Output error system identi cation was used to identify a model from the ight test data. As expected, the new exible aircraft showed that if the dynamics are restricted to the short-period mode and the structural dynamics, then the Froude number has little e ect on the dynamics.
Introduction It has been appreciated by aeroelasticians for many years that results from the V -g or k method of flutter analysis may be difficult to interpret or even misleading. 1–3 The purpose of the present Note is to consider this difficulty with the k method in an especially simple setting, i.e. with steady-flow aerodynamics. As Pines showed many years ago in a different context, the use of highly simplified aerodynamics can be especially illuminating. In the special case of steady-flow aerodynamics and zero structural damping, the principal result of the present Note shows one way that the V -g or k method may lead to difficulties. For this special case, a particularly clear understanding of the nature of these difficulties can be obtained. This note adds a modest but new and, the authors believe, helpful addition to the rich literature on this perplexing issue. It is well known that k and p methods of calculating flutter speeds are quite different. 5
The paper presents a method to identify aerodynamic parameters from flight-test data, determine the uncertainty in the identified parameters, and estimate the model-form uncertainties in the aerody...
Summary Aeroelastic instabilities have long constrained the °ight envelope of many types ofaircraft and thus are considered important during the design process. As designersstrive to reduce weight and raise performance levels using directional material, thusleading to an increasingly °exible aircraft, there is a need for reliable (less conserva-tive yet accurate) analysis tools, which model all the important characteristics of the°uid-structure interaction problem. Such a model would be used in preliminary de-sign and control synthesis. Traditionally, the most accurate aeroelasticity results havecome from either an experimental investigation or more recently a complete numeri-cal simulation by coupling flnite element method and computational °uid dynamicsanalysis. Though such results are very accurate, can be obtained over a complete°ight regime and can include \higher-order phenomena and nonlinearities, they arealso very expensive, especially so in the initial phase of design, when a number ofdesign conflgurations may need to be analyzed.For a restricted problem, it is advantageous to take into account simpliflcationswhich do not compromise the quality of the results. This would reduce the order ofthe problem while retaining high fldelity. Such a model would lend itself to an easierparameter identiflcation and thus would be useful in design studies or in study ofhigher-order phenomenon.The focus of this research was to analyze a high-aspect-ratio wing aircraft °yingat low subsonic speeds. Such aircraft are designed for high-altitude, long-endurancexiii
A methodology is presented for the modeling of flexible horizontal-axis, wind-turbine systems. The multi-rigid-body portions of the system are modeled as a system of interconnected rigid bodies using Autolev, a symbolic manipulator ideally suited for dynamics of multi-rigid-body systems. The flexible portions of the wind-turbine system are represented as beam finite ele- ments. Equations are presented for the beam element, and the choices of generalized coordinates and general- ized speeds for the multi-rigid-body portion of the sys- tem are discussed. Finally, a method for the explicit linearization of the system equations is presented, along with a method for the unification of these equations into one framework.
A systematic approach for aeroelastic scaled-model design is developed. The method optimizes an incremental number of vibration eigenpairs, buckling eigenpairs, and optionally a linear static response of scaled models to match the scaled values of a target full-scale aircraft. A method for matching scaled modal mass, a required scaling parameter, is developed. The sources of local optima are identified and a tiered global-search-optimization procedure is incorporated. The approach is demonstrated on a joined-wing scaled-model-design problem. Costly nonlinear analysis is omitted from the evaluation of the objective function and constraints for optimization. The results produced scaled models that closely replicate the geometrically nonlinear target aeroelastic behavior.
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