Boris Moulin

Dynamic Response of Aeroservoelastic Systems to Gust Excitation

Frequency-domain and time-domain approaches to dynamic response analysis of aeroservoelastic systems to atmospheric gust excitations are presented. The discrete and continuous gust inputs are defined in either time-domain or stochastic terms. The various options are formulated in a way that accommodates linear control systems of the most general form. The frequency-domain approach is based on the interpolation of generalized aerodynamic force coefficient matrices and the application of Fourier transforms for time-domain solutions. The time-domain approach uses state-space formulation that requires the frequency-dependent aerodynamic coefficients to be approximated by rational functions of the Laplace variable. Once constructed, the state-space equations of motion are more suitable for time simulations and for the interaction with control design algorithms. However, there is some accuracy loss because of the rational approximation. The spiral nature in the complex plane of the gust-related aerodynamic terms is discussed, and means are provided for dealing with the associated numerical difficulties. A hybrid formulation that does not require the rational approximation of the gust coefficients is also presented for optional use in discrete gust response analysis. The various methods were utilized in the ZAERO software and applied to a generic transport aircraft model.

Gust loads alleviation using special control surfaces

Control laws are designed for the alleviation of dynamic gust loads on a wind-tunnel model of a transport aircraft using wing-mounted control surfaces. Three different control surfaces are used: the symmetrically actuated main ailerons, special underwing forward-positioned control surfaces at about 0.8 of the wingspan, and special wing-tip forward-positioned control surfaces. The 5.3-m-span cable-mounted wind-tunnel model was constructed at the TsAGI laboratories and is being tested as there part of the 3AS 5th Framework European Commission research project. The length of one-minus-cosine vertical gust velocity profile is tuned to yield maximal wing-root bending moment All the control laws are based on simple low-pass filters for easy and robust application in the wind tunnel. Each is based on single input of a wing-tip accelerometer, which is shown to react sufficiently before the peak of the wing-root bending moment

Robust Aeroservoelastic Design with Structural Variations and Modeling Uncertainties

An aeroservoelastic analysis procedure has been integrated with structural optimization and robust-control design tools. The multidisciplinary analysis and design process can address structural constraints, performance, and robust aeroservoelastic stability requirements simultaneously. The design process is expanded to account for structural variations and modeling uncertainties utilizing a reduced-order state-space model of the aeroelastic plant that is advantageous for efficient low-order controller design. Reduced-order modeling introduces unstructured modeling errors. Structural mass variations, such as those associated with a wide range of changeable external stores of a fighter aircraft, are also interpreted as model uncertainties. The models are expressed in a form compatible with standard robust control design procedures such as the μ synthesis and analysis technique incorporated in this study. The robust control system can then be included in an optimization process where more elaborate aeroelastic models are used for tuning selected structural variables and control gains for minimizing specific design objectives under stability, performance, and structural integrity requirements. To provide enhanced physical insight, the μ analysis procedure is supplemented by a technique for computing stability boundaries in multidimensional parametric uncertainty spaces that is based on the classical single-input/single-output gain-margin approach. The integrated design procedure is demonstrated with a realistic model of a fighter aircraft with four wing control surfaces and a wing-tip missile with variable inertial properties.

Models for Aeroservoelastic Analysis with Smart Structures

Modal-based mathematical models for the analysis of control-augmented aeroelastic systems are expanded to facilitate the use of distributed strain actuators. Smart actuators are constructed of structural elements, such as piezoelectric patches, that change their shape due to electric inputs. When embedded in the structure, the deforming smart elements introduce structural strains that change the shape of the structure and, consequently, the aerodynamic load distribution. The voltage‐strain relations, the overdetermined nature of the elastic actuator‐ structure equilibrium, the relatively large number of involved interface coordinates, and the high importance of local strains that typically limit the actuator performance require substantial modifications in the modeling process compared to that with common control-surface actuators. Fictitious masses are used in a way that causes the inclusion of important actuator strain information in the modal data with a minimal increase in the number of structural states. A control mode is defined by the static deformations due to a unit static voltage command. Huge dummy masses may be used to generate the control modes as part of a standard normal-modes analysis. State-space aeroservoelastic equations are constructed by the use of the minimum-state rational aerodynamic approximation approach. Two options are given for the introduction of control forces: a direct application of the forces, and an indirect application through the control mode. A numerical application for an unmanned aerial vehicle with a piezoelectric-driven control surface demonstrates the two options and shows that the control-mode option has some numerical advantages.

Aeroservoelastic Gust Response Analysis for the Design of Transport Aircrafts

Frequency-domain and time-domain approaches to the calculation of dynamic loads due to response of aeroservoelastic systems to atmospheric gust excitations are presented. The discrete and continuous gust inputs are defined in either time-domain or stochastic terms. The various options are formulated in a way that accommodates linear control systems of the most general form. The frequency-domain approach is based on the interpolation of generalized aerodynamic force coefficient matrices and the application of Fourier transforms for timedomain solutions. The time-domain approach uses state-space formulation that requires the frequency-dependent aerodynamic coefficients to be approximated by rational functions of the Laplace variable. Specific difficulties associated with the spiral nature in the complex plane of the gust-related aerodynamic terms is discussed and resolved. The two approaches are adapted for efficient application in realistic design environment with numerous combinations of flight conditions and weight configurations. An actual process of calculating gust-response design loads for the A400M transport aircraft is demonstrated, showing significant controlsystem effects.

Dynamic Gust Loads Analysis for Transport Aircraft with Nonlinear Control Effects

A process for calculating dynamic gust loads for structural design of transport aircraft with significant non-linear control-system effects is presented. The process is based on combinations of timeand frequency domain formulations of the equations of motion that facilitate the inclusion of nonlinear control elements. The frequency-domain approach is used for massive loads calculations using Fast Fourier Transform techniques. Special measures are employed for repeated analyses with many weight distributions and various gust excitations. Selected cases are repeated for the evaluation of the nonlinear control effects using time-domain, state-space linear models of the aeroelastic system combined with nonlinear control equations. The resulting time histories of the structural and control response in modal coordinates of the two approaches are then used for the calculation of structural loads using mode-displacement or summation-of-force techniques. The generation of aeroservoelastic time-domain models requires the approximation of the unsteady aerodynamic force coefficient matrices in the time domain. To avoid approximation errors associated with the gust force coefficients, the excitation forces are defined by a sequence of Fourier and Inverse-Fourier transforms. Convergence studies demonstrate the accuracy and efficiency of the various computation options with respect to the number of structural modes taken into account. The loads computation processes are demonstrated with discrete gust loads on the A400M military transport currently under development.

Extension of the g-Method Flutter Solution to Aeroservoelastic Stability Analysis

The g-method frequency-domain flutter solution technique is extended to include control-system effects for closed-loop aeroservoelastic stability analysis. The extension is based on expressing the aeroelastic equations of motion in a Laplacedomain state-space form where the aerodynamic coefficient matrices retain their transcendental dependency on the Laplace variable. The augmentation of these equations with controlsystem state-space models is straight forward. First-order approximations of the system matrix are used for formulating an iterative eigenvalue problem that is solved by a predictor-corrector frequency sweep technique that ensures process robustness. The numerical application is of rollcontrol design for a generic fighter aircraft with several wing control surfaces. The results demonstrate the accuracy and convenient applicability of the extended method. 1 Professor, Associate fellow AIAA; moti_karpel@technion.ac.il 2 Senior Researcher, Member AIAA; boris@aemoti2.technion.ac.il 3 Vice President, 7430E. Stetson Dr., Suite 205; pc@zonatech.com Introduction Linear flutter analysis of flight vehicles is commonly based on the stability boundaries of the frequencydomain aeroelastic equation of motion in modal coordinates. While the structural mass, damping and stiffness coefficient matrices are constant in this equation, the aerodynamic influence coefficient (AIC) matrix is a transcendental function of the frequency of oscillations, calculated for required non-dimensional frequency values by numerical procedures such as the doublet-lattice method and the harmonic gradient method. Consequently, frequency-domain flutter solvers are based on search algorithms that iterate between the system eigenvalues and the AIC matrix. A widely adopted method for flutter solution is the p-k method that was first introduced by Irwin and Guyett and has been generalized and modified to include a determinant-based search process by Hassig. Rodden et. al. added a damping dependent aerodynamic term that improved the search process. Rodden introduced the p-k method to MSC/NASTRAN with a lining-up procedure that matched the frequency values with the imaginary parts of the resulting eigenvalues. Chen extended the p-k concepts in the damping-perturbation gmethod that includes a first-order damping term that is rigorously derived from the Laplace-domain aerodynamics. While the p-k solver serches for one aeroelastic root per each modal coordinate taken into account, the g-solver search algorithm is capable of handling extra roots due to unsteady aerodynamic lag. Aeroservoelasticity (ASE) deals with the interaction of aeroelastic and control systems. The application of modern control design techniques requires the aeroservoelastic equations of motion to be cast in a first-order, time-domain (state-space) form. This representation requires the aerodynamic matrices to be approximated by rational functions in the complex Laplace domain. The resulting statespace equations can be easily augmented by standard control system models to provide ASE constant coefficient equations for which stability analysis is based on standard eigenvalue extraction routines, as utilized in the ZAERO code. The problem is that the aerodynamic approximation is sometimes of questionable accuracy. Hence, it is desired to be able to perform closed-loop flutter analysis in the frequency domain, with the original tabulated AIC matrices. The purpose of the this paper is to discuss the application of frequency-domain techniques to the ASE problem, explain why existing procedures often 1 44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Confere 7-10 April 2003, Norfolk, Virginia AIAA 2003-1512 Copyright

Active Alleviation of Gust Loads Using Special Control Surfaces

§¶ # The alleviation of dynamic gust loads on a transport aircraft using wing-mounted control surfaces is investigated. Three different wing-mounted control surfaces are considered: symmetrically-actuated ailerons, under-wing forward-positioned control surfaces at about 0.8 of the wing span, and wing-tip forward-positioned control surfaces. The main investigation is for a 1:10 cable-mounted wind-tunnel model of a transport aircraft that was constructed and tested at the TsAGI laboratories. The length of a one-minus-cosine vertical gust velocity profile is tuned to yield maximal wing-root bending moment. All the control laws are based on simple low-pass filters for easy and robust application in the wind tunnel. Each is based on a single input of a wing-tip accelerometer which is shown to react in time to allow the alleviation of the peak of the wing-root bending moment. All the three control means are shown to alleviate the extreme wing-root moments by 9-16% and the wing-tip accelerations by 26-33% at intermediate design flight velocities. The effects on section-loads envelopes at monitoring stations along the wing are also very favorable. The wing-tip and under-wing controls are found to be more effective than the existing aileron at these speeds. The ailerons become even less effective at higher speeds due to reduction in their aeroelastic effectiveness. The application of the same control concept to the full-scale aircraft model exhibits similar results. The effects of the designed control laws on the statistical response of the wing loads to continuous gusts are shown to be similar to their effects on discrete gusts.

Aeroservoelastic Modeling and Sensitivity Analysis with Strain Actuators

Mathematical models for the analysis and design of control-augmented aeroelastic systems are expanded to facilitate the use of distributed strain actuators in automated design processes. Strain actuators, such as piezoelectric patches, can change the shape of lifting surfaces by introducing structural strains due to electric voltage commands. The voltage-strain relations, the over-determined nature of the elastic actuator-structure equilibrium, the relatively large number of involved interface coordinates and the high importance of local strains that typically limit the actuator performance require substantial modiflcations in the modeling process compared to that with common control-surface actuators. A control mode is deflned by the static deformations due to a unit static voltage command. Huge dummy masses are used to generate the control modes and their mass coupling with the elastic modes as part of a standard normal-modes analysis. State-space aeroservoelastic equations are constructed using the minimum-state rational aerodynamic approximation approach. Analytical expressions are given for the sensitivity of the system coe‐cient matrices and the associated aeroservoelastic stability and response parameters with respect to the actuator properties. These sensitivities can be added to those with respect to other structural and control variables in gradient-based integrated design optimization processes. A numerical application of an unmanned aerial vehicle with a piezoelectric-driven control surface is given. The example demonstrates the modeling process, some aeroelastic response parameters to control commands, and the associated sensitivity analysis.

Flutter Analysis of Aircraft with External Stores Using Modal Coupling

A new modal coupling technique for efficient flutter and aeroservoelastic analyses of aircraft with multiple external-store configurations is presented. The aircraft is represented by a set of free-free normal modes obtained with large fictitious masses loading the interface coordinates to yield high-accuracy subsequent coupling results. Each store is represented by its own vibration modes obtained with a subset of statically determined interface coordinates clamped to the ground, and the remaining coordinates (if any) are loaded with large fictitious masses. The technique is formulated in a way that facilitates its application using standard options of common commercially available software packages. A finite element code is used to construct the aircraft and stores modal databases. A linear unsteady aerodynamics code is used to read the modal information, calculate the aerodynamic databases, construct and solve the aircraft-store coupling equations, and perform frequency-domain and state-space flutter analyses with or without control system effects