Modeling and System Identification of an Ornithopter Flight Dynamics Model

Ornithopters are robotic flight vehicles that employ flapping wings to generate lift and thrust forces in a manner that mimics avian flyers. At the small scales and Reynolds numbers currently under investigation for miniature aircraft, where viscous effects deteriorate the performance of conventional aircraft, ornithopters achieve efficient flight by exploiting unsteady aerodynamic flow fields, making them well-suited for a variety of unmanned vehicle applications. Parsimonous dynamic models of these systems are requisite to augment stability and design autopilots for autonomous operation; however, flapping flight is fundamentally different than other means of engineered flight and requires a new standard model for describing the flight dynamics. This dissertation presents an investigation into the flight mechanics of an ornithopter and develops a dynamical model suitable for autopilot design for this class of system. A 1.22 m wing span ornithopter test vehicle was used to experimentally investigate flapping wing flight. Flight data, recorded in trimmed straight and level mean flight using a custom avionics package, reported pitch rates and heave accelerations up to 5.62 rad/s and 46.1 m/s^2 in amplitude. Computer modeling of the vehicle geometry revealed a 0.03 m shift in the center of mass, up to a 53.6% change in the moments of inertia, and the generation of significant inertial forces. These findings justified a nonlinear multibody model of the vehicle dynamics, which was derived using the Boltzmann-Hamel equations. Models for the actuator dynamics, tail aerodynamics, and wing aerodynamics, difficult to obtain from first principles, were determined using system identification techniques with experimental data. A full nonlinear flight dynamics model was developed and coded in both MATLAB and FORTRAN programming languages. An optimization technique is introduced to find trim solutions, which are defined as limit cycle oscillations in the state space. Numerical linearization about straight and level mean flight resulted in both a canonical time-invariant model and a time-periodic model. The time-invariant model exhibited an unstable spiral mode, stable roll mode, stable dutch roll mode, a stable short period mode, and an unstable short period mode. Floquet analysis on the identified time-periodic model resulted in an equivalent time-invariant model having an unstable second order and two stable first order modes, in both the longitudinal and lateral dynamics

Real-Time Parameter Estimation Using Output Error

Output-error parameter estimation, normally a post- ight batch technique, was applied to real-time dynamic modeling problems. Variations on the traditional algorithm were investigated with the goal of making the method suitable for operation in real time. Im- plementation recommendations are given that are dependent on the modeling problem of interest. Application to ight test data showed that accurate parameter estimates and un- certainties for the short-period dynamics model were available every 2 s using time domain data, or every 3 s using frequency domain data. The data compatibility problem was also solved in real time, providing corrected sensor measurements every 4 s. If uncertainty corrections for colored residuals are omitted, this rate can be increased to every 0.5 s

Position Corrections for Airspeed and Flow Angle Measurements on Fixed-Wing Aircraft

This report addresses position corrections made to airspeed and aerodynamic flow angle measurements on fixed-wing aircraft. These corrections remove the effects of angular rates, which contribute to the measurements when the sensors are installed away from the aircraft center of mass. Simplified corrections, which are routinely used in practice and assume small flow angles and angular rates, are reviewed. The exact, nonlinear corrections are then derived. The simplified corrections are sufficient in most situations; however, accuracy diminishes for smaller aircraft that incur higher angular rates, and for flight at high air flow angles. This is demonstrated using both flight test data and a nonlinear flight dynamics simulation of a subscale transport aircraft in a variety of low-speed, subsonic flight conditions

Random Noise Generation Using Fourier Series

This Note describes the Lanczos method for noise generation, and presents applications for aircraft simulation. Comparisons are made with conventional methods of noise generation, and it is shown that the noise sequences generated using the Lanczos method most often have more accurate statistical characteristics than those generated using the standard methods. Although the standard methods already produce high-quality noise sequences, using the Lanczos method to generate noise, when applicable, can realize a more accurate representation of the desired noise, and therefore lead to clearer insights into simulation analyses. It is hoped that others may find this description of the noise generation procedure and these simulation examples interesting and helpful for their own uses

A Learn-To-Fly Approach for Adaptively Tuning Flight Control Systems

A method is presented for adaptively tuning feedback control gains in a ight control sys- tem to achieve desired closed-loop performance. The method combines efficient parameter estimation for identifying closed-loop dynamics models, with online nonlinear optimization for sequentially perturbing and updating control gains to improve performance. Prior in- formation on stability and control derivatives is not needed, nor is any knowledge about the control system architecture. Following convergence, the optimized control gains (with uncertainties), the open-loop dynamics model, and the closed-loop dynamics model are available. The method is demonstrated for tuning a longitudinal stability augmentation system using a realistic nonlinear ight dynamics simulation of the NASA FASER airplane. Convergence was attained using five piloted maneuvers that spanned approximately one minute of ight test time. Although demonstrated for a relatively simple case, the method is general and can be applied to other aircraft, axes, performance metrics, and control systems

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

A Comparison of Three Random Number Generators for Aircraft Dynamic Modeling Applications

Three random number generators, which produce Gaussian white noise sequences, were compared to assess their suitability in aircraft dynamic modeling applications. The first generator considered was the MATLAB (registered) implementation of the Mersenne-Twister algorithm. The second generator was a website called Random.org, which processes atmospheric noise measured using radios to create the random numbers. The third generator was based on synthesis of the Fourier series, where the random number sequences are constructed from prescribed amplitude and phase spectra. A total of 200 sequences, each having 601 random numbers, for each generator were collected and analyzed in terms of the mean, variance, normality, autocorrelation, and power spectral density. These sequences were then applied to two problems in aircraft dynamic modeling, namely estimating stability and control derivatives from simulated onboard sensor data, and simulating flight in atmospheric turbulence. In general, each random number generator had good performance and is well-suited for aircraft dynamic modeling applications. Specific strengths and weaknesses of each generator are discussed. For Monte Carlo simulation, the Fourier synthesis method is recommended because it most accurately and consistently approximated Gaussian white noise and can be implemented with reasonable computational effort

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

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

Dynamic Modeling Accuracy Dependence on Errors in Sensor Measurements, Mass Properties, and Aircraft Geometry

A nonlinear simulation of the NASA Generic Transport Model was used to investigate the effects of errors in sensor measurements, mass properties, and aircraft geometry on the accuracy of dynamic models identified from flight data. Measurements from a typical system identification maneuver were systematically and progressively deteriorated and then used to estimate stability and control derivatives within a Monte Carlo analysis. Based on the results, recommendations were provided for maximum allowable errors in sensor measurements, mass properties, and aircraft geometry to achieve desired levels of dynamic modeling accuracy. Results using other flight conditions, parameter estimation methods, and a full-scale F-16 nonlinear aircraft simulation were compared with these recommendations