Aero-Propulsive Modeling for eVTOL Aircraft Using Wind Tunnel Testing with Multisine Inputs
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system identification↗
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Dynamic Modeling using Output-Error Parameter Estimation based on Frequency Responses Estimated with Multisine Inputs
A method is developed for estimating model parameters, such as nondimensional stability and control derivatives, by fitting transfer function or state-space models to empirical frequency response data using the output-error approach. The frequency response data were computed using Fourier transforms of measured input and output data. The control surfaces were excited with periodic multisine inputs which facilitated time-ecient estimation of multiple-input multiple-output frequency responses. The method was applied to lateral data from a nonlinear flight dynamics simulation of the F-16 aircraft, and to longitudinal data from multiple repeated flight test maneuvers of the NASA T-2 subscale aircraft. Results using simulation data showed the frequency response method compared well to other standard methods for parameter estimation. In addition to including all the available inputs, outputs, and harmonic frequencies in the estimation, relatively small subsets of the measured data could also be used to focus on identifying specific parts of the model. Results from flight test data showed that parameter estimates and uncertainties determined from repeated maneuvers were accurate and in statistical agreement with each other.
Grauer, Jared A.↗
Aero-Propulsive Modeling for eVTOL Aircraft Using Wind Tunnel Testing with Multisine Inputs
A novel approach for modeling the aero-propulsive characteristics of an electric vertical takeoff and landing (eVTOL) aircraft was developed and demonstrated in wind tunnel testing. The approach was applied to the NASA LA-8 tandem tilt-wing eVTOL aircraft, using an efficient, hybrid experiment design composed of a static I-optimal response surface design for slowly-varying test variables, and dynamic orthogonal phase-optimized multisine excitations for the control surfaces and electric propulsors. Both the static and dynamic experiment designs were executed simultaneously to collect informative data for model identification. Statistically-weighted multivariate orthogonal function modeling was used to combine local modeling results computed in the frequency domain using data collected with dynamic excitations operating on the control effectors to form an aggregate aero-propulsive model. The final identified model exhibited good predictive capability when compared to validation data acquired separately from the data used to develop the model. The required test time using these new techniques was reduced by at least a factor of five compared to previous static wind tunnel testing for the LA-8 aircraft, while providing more informative data, greater parameterization flexibility, and high-quality models.
system identification↗
Aircraft System Identification from Multisine Inputs and Frequency Responses
The identification of aircraft flight dynamics is often performed using frequency responses, which are nonparametric models that quantify the steady-state magnitude and phase of a dynamic system response to sinusoidal inputs, as a function of frequency. Frequency responses are computed from measured input and output data, and then model parameters, such as stability and control derivatives, are estimated to best fit a parametric model to the empirical frequency response data. The utility of this approach is due to the familiarity of engineers with frequency responses, a number of theoretical and practical advantages under specific conditions, the availability of software packages, and many other reasons.
System identification↗
Aircraft System Identification from Multisine Inputs and Frequency Responses
A frequency-domain approach is described for estimating parameters, such as stability and control derivatives, in aircraft flight dynamic models from measured input and output data. The approach uses orthogonal phase-optimized multisines for moving the aircraft control effectors, Fourier analysis for computing multiple-input multiple-output frequency responses, and a maximum likelihood estimator called frequency response error (FRE) for determining values and uncertainties for the model parameters. The approach is demonstrated using flight test data for two subscale airplanes: the T-2 generic transport model and the X-56A aeroelastic demonstrator. Results and comparisons with the output-error method indicated that the approach produced accurate estimates of stability and control derivatives and their uncertainties from flight test data.
Grauer, Jared A.↗
Real-Time Estimation of Bare-Airframe Frequency Responses from Closed-Loop Data and Multisine Inputs
A method is presented for computing frequency responses of multiple-input multiple-output bare-airframe dynamics from flight test data containing feedback control and/or mixing of control effectors. Orthogonal phase-optimized multisines are used to simultaneously excite each input with unique harmonic frequencies, at which frequency responses are computed as ratios of output-to-input Fourier transform data. The confounding effects of feedback and mixing for frequency response estimation are resolved by interpolating the frequency responses among all the harmonic frequencies. The method can be run in batch for post-flight analysis, or in real time as the aircraft is flying. The effectiveness of the method was verified using closed-loop simulations of the subscale NASA T-2 generic transport airplane. The method was also demonstrated using flight test data from the X-56A MUTT aeroelastic airplane, which was flown with feedback control and mixing.
Jared A Grauer↗
Reduced-Order Aerodynamic Modeling Based on CFD Frequency Responses from Multisine Inputs
A system identification analysis was performed to determine reduced-order models of a computational fluid dynamics (CFD) solver for linear aeroelastic analysis and control design. The application was to the FUN3D code and the flexible half-span wind tunnel test article, in transonic flow conditions, used in the NASA-Boeing collaboration called the Integrated Adaptive Wing Technology Maturation (IAWTM) project. Multiple inputs (structural mode displacements and control surface deflections) were simultaneously excited with orthogonal phase-optimized multisines and multiple outputs (generalized aerodynamic forces) were recorded, from which the matrix of frequency responses were computed using a single CFD run. A state-space model was then fit to the frequency response data using a maximum-likelihood estimator.
System identification↗
Identification of Bare-Airframe Dynamics from Closed-Loop Data Using Multisine Inputs and Frequency Responses
Amethod is presented for computing multiple-input multiple-output frequency responses of bare-airframe dynamics for systems excited using orthogonal phase-optimized multisines and including correlated data arising from control mixing or feedback control. The estimation was posed as the solution to an underdetermined system of linear equations, for which additional information was supplied using interpolation of the frequency responses. A simulation model of the NASA T-2 aircraft having two inputs and two outputs was used to investigate the method in the open-loop configuration and under closed-loop control. The method was also applied to flight test data from the X-56A aeroelastic demonstrator having five inputs and ten outputs and flying under closed-loop control with additional control allocation mixing. Results demonstrated that the proposed method accurately estimates the bare airframe frequency responses in the presence of correlated data from control mixing and feedback control. Results also agreed with estimates obtained using different methods that are less sensitive to correlated inputs.
Grauer, Jared A.↗
Reduced-Order Aerodynamic Modeling Based on CFD Frequency Responses from Multisine Inputs
A system identification analysis was performed to determine a reduced-order model (ROM) of a computational fluid dynamics (CFD) solver in support of linear aeroservoelastic model development and feedback control design. The approach was applied to the FUN3D code for the half-span wind tunnel test article used in the NASA-Boeing collaboration called the Integrated Adaptive Wing Technology Maturation (IAWTM) project. In a transonic flow condition, multiple inputs (11 structural mode displacements and 3 control surface deflections) were simultaneously excited with orthogonal phase-optimized multisines while multiple outputs (the corresponding 14 generalized aerodynamic forces) were recorded. From these recorded times series, the matrix of frequency responses was computed and subsequently fit using rational function approximations (RFAs). It was found that the entire (14 x 14) matrix of frequency responses could be determined from a single CFD run and that results generally followed trends predicted using other methods. Differences were attributed to the modeling fidelity and nonlinearities from structural mode and control surface interactions at higher reduced frequencies. More accurate fits of the RFAs to the frequency response data were obtained by making two CFD runs, one with only structural mode excitations and one with only control surface excitations, which reduced the degree of nonlinearity in the modeling data.
Aeroservoelasticity↗
Evaluation of Piloted Inputs for Onboard Frequency Response Estimation
Frequency response estimation results are presented using piloted inputs and a real-time estimation method recently developed for multisine inputs. A nonlinear simulation of the F-16 and a Piper Saratoga research aircraft were subjected to different piloted test inputs while the short period stabilator/elevator to pitch rate frequency response was estimated. Results show that the method can produce accurate results using wide-band piloted inputs instead of multisines. A new metric is introduced for evaluating which data points to include in the analysis and recommendations are provided for applying this method with piloted inputs.
Grauer, Jared A.↗
System Identification for eVTOL Aircraft Using Simulated Flight Data
This paper describes a system identification method for electric vertical takeoff and landing (eVTOL) aircraft. The approach merges fixed-wing and rotary-wing modeling techniques with new strategies to develop a modeling method for eVTOL vehicles using flight test data. The eVTOL aircraft system identification approach is demonstrated through application to the NASA LA-8 tandem tilt-wing, distributed electric propulsion aircraft using a high-fidelity flight dynamics simulation. Orthogonal phase-optimized multisine inputs are applied to each control surface and propulsor at numerous flight conditions throughout the flight envelope to collect informative flight data. An aero-propulsive model is identified at each flight condition using the equation-error method in the frequency domain. The local model parameters are then blended to create a global model across the nominal flight envelope. Parameter estimation results are shown to provide a good fit to modeling data and have good prediction capability. The methodology is developed with a discussion of unique eVTOL vehicle aerodynamic characteristics and practical strategies intended to inform future flight-based system identification efforts for eVTOL aircraft.
system identification↗
Recent System Identification Research at NASA Langley Research Center
This talk summarizes some of the recent advances in system identification at NASA Langley Research Center. Efforts discussed were applied to aeroelastic models, aircraft with redundant inputs and feedback control active, and aircraft flying in turbulence. Topics mentioned include experiment design with orthogonal multisine inputs, frequency response estimation, maximum likelihood parameter estimation, and parameter estimation considering process noise.
NASA LaRC↗
Aero-Propulsive Damping Characterization for eVTOL Aircraft Using Free Motion Wind-Tunnel Testing
This paper describes an electric vertical takeoff and landing (eVTOL) aircraft system identification method applied using three degree-of-freedom (3DOF) free motion wind-tunnel testing. The approach, similar to flight-test system identification, allows for efficient mathematical model development of the aero-propulsive moments applied on an eVTOL vehicle, including aerodynamic damping effects. The approach is demonstrated using a subscale tiltrotor eVTOL aircraft mounted on a new 3DOF wind-tunnel apparatus. To execute the test, a model-based 3DOF control system is designed to track attitude commands and transition the aircraft based on the freestream dynamic pressure. While the flight controller is active, orthogonal phase-optimized multisine inputs are injected into the attitude command and control effector command signals to enable collection of informative data for model identification. Aero-propulsive models are then identified at several reference conditions in the transition flight envelope using the equation-error method in the frequency domain. The identified models are shown to have a good fit to the modeling data and good prediction capability of data not used for model identification. The method yields aerodynamic damping estimates using less wind-tunnel test time compared to traditional forced oscillation experiments and supplements static wind-tunnel testing to produce a comprehensive transition aero-propulsive model suitable for use in flight dynamics simulations.
RAVEN↗
Aircraft Fault Detection Using Real-Time Frequency Response Estimation
A real-time method for estimating time-varying aircraft frequency responses from input and output measurements was demonstrated. The Bat-4 subscale airplane was used with NASA Langley Research Center's AirSTAR unmanned aerial flight test facility to conduct flight tests and collect data for dynamic modeling. Orthogonal phase-optimized multisine inputs, summed with pilot stick and pedal inputs, were used to excite the responses. The aircraft was tested in its normal configuration and with emulated failures, which included a stuck left ruddervator and an increased command path latency. No prior knowledge of a dynamic model was used or available for the estimation. The longitudinal short period dynamics were investigated in this work. Time-varying frequency responses and stability margins were tracked well using a 20 second sliding window of data, as compared to a post-flight analysis using output error parameter estimation and a low-order equivalent system model. This method could be used in a real-time fault detection system, or for other applications of dynamic modeling such as real-time verification of stability margins during envelope expansion tests.
Grauer, Jared A.↗
Aeroelastic Modeling of X-56A Stiff-Wing Configuration Flight Test Data
Aeroelastic stability and control derivatives for the X-56A Multi-Utility Technology Testbed (MUTT), in the stiff-wing configuration, were estimated from flight test data using the output-error method. Practical aspects of the analysis are discussed. The orthogonal phase-optimized multisine inputs provided excellent data information for aeroelastic modeling. Consistent parameter estimates were determined using output error in both the frequency and time domains. The frequency domain analysis converged faster and was less sensitive to starting values for the model parameters, which was useful for determining the aeroelastic model structure and obtaining starting values for the time domain analysis. Including a modal description of the structure from a finite element model reduced the complexity of the estimation problem and improved the modeling results. Effects of reducing the model order on the short period stability and control derivatives were investigated.
Grauer, Jared A.↗
Advances in Aero-Propulsive Modeling for Fixed-Wing and eVTOL Aircraft Using Experimental Data
Small unmanned aircraft and electric vertical takeoff and landing (eVTOL) aircraft have recently emerged as vehicles able to perform new missions and stimulate future air transportation methods. This dissertation presents several system identification research advancements for these modern aircraft configurations enabling accurate mathematical model development for flight dynamics simulations based on wind-tunnel and flight-test data. The first part of the dissertation focuses on advances in flight-test system identification methods using small, fixed-wing, remotely-piloted, electric, propeller-driven aircraft. A generalized approach for flight dynamics model development for small fixed-wing aircraft from flight data is described and is followed by presentation of novel flight-test system identification applications, including: aero-propulsive model development for propeller aircraft and nonlinear dynamic model identification without mass properties. The second part of the dissertation builds on established fixed-wing and rotary-wing aircraft system identification methods to develop modeling strategies for transitioning, distributed propulsion, eVTOL aircraft. Novel wind-tunnel experiment designs and aero-propulsive modeling approaches are developed using a subscale, tandem tilt-wing, eVTOL aircraft, leveraging design of experiments and response surface methodology techniques. Additionally, a method applying orthogonal phase-optimized multisine input excitations to aircraft control effectors in wind-tunnel testing is developed to improve test efficiency and identified model utility. Finally, the culmination of this dissertation is synthesis of the techniques described throughout the document to form a flight-test system identification approach for eVTOL aircraft that is demonstrated using a high-fidelity flight dynamics simulation. The research findings highlighted throughout the dissertation constitute substantial progress in efficient empirical aircraft modeling strategies that are applicable to many current and future aeronautical vehicles enabling accurate flight simulation development, which can subsequently be used to foster advancement in many other pertinent technology areas.
system identification↗
Practical Aspects of Multiple-Input Design for Aircraft System Identification Flight Tests
Practical aspects of multiple-input design methods for aircraft system identification flight tests are discussed. The orthogonal optimized multisine multiple-input design technique is explained and demonstrated, along with useful variations. Practical implementation and application issues associated with applying orthogonal optimized multisine inputs in flight are explained, and solutions are demonstrated using flight data from full-scale and subscale aircraft, as well as simulated flight data from an F-16 nonlinear simulation. Topics include truncated and extended excitation inputs, variations for control effectors with limited movement capabilities, aircraft dynamic response to excitation inputs, pilot implementation, statistical uncertainty quantification, multiple-input efficiency and effectiveness, flight testing with active feedback control, frequency-response estimation, control actuator modeling, and control interaction effects. Examples demonstrate that the orthogonal optimized multisine input design method is a practical, versatile, and effective approach for designing multiple excitation inputs for aircraft system identification flight tests.
Multiple-Input Design↗
Aircraft Dynamic Modeling in Turbulence
A method for accurately identifying aircraft dynamic models in turbulence was developed and demonstrated. The method uses orthogonal optimized multisine excitation inputs and an analytic method for enhancing signal-to-noise ratio for dynamic modeling in turbulence. A turbulence metric was developed to accurately characterize the turbulence level using flight measurements. The modeling technique was demonstrated in simulation, then applied to a subscale twin-engine jet transport aircraft in flight. Comparisons of modeling results obtained in turbulent air to results obtained in smooth air were used to demonstrate the effectiveness of the approach.
Morelli, Eugene A.↗