Aerodynamic Parameters Estimation Using Radial Basis Function Neural Partial Differentiation Method

Aerodynamic parameter estimation involves modelling of force and moment coefficients and computation of stability and control derivatives from recorded flight data. This problem is extensively studied in the past using classical approaches such as output error, filter error and equation error methods. An alternative approach to these model based methods is the machine learning such as artificial neural network. In this paper, radial basis function neural network (RBF NN) is used to model the lateral-directional force and moment coefficients. The RBF NN is trained using k-means clustering algorithm for finding the centers of radial basis function and extended Kalman filter for obtaining the weights in the output layer. Then, a new method is proposed to obtain the stability and control derivatives. The first order partial differentiation is performed analytically on the radial basis function neural network approximated output. The stability and control derivatives are computed at each training data point, thus reducing the post training time and computational efforts compared to hitherto delta method and its variants. The efficacy of the identified model and proposed neural derivative method is demonstrated using real time flight data of ATTAS aircraft. The results from the proposed approach compare well with those from the other

Methods of system identification, parameter estimation and optimisation applied to problems of modelling and control in engineering and physiology

Mathematical and computer-based models provide the foundation of most methods of engineering design. They are recognised as being especially important in the development of integrated dynamic systems, such as “control-configured” aircraft or in complex robotics applications. These models usually involve combinations of linear or nonlinear ordinary differential equations or difference equations, partial differential equations and algebraic equations. In some cases models may be based on differential algebraic equations. Dynamic models are also important in many other fields of research, including physiology where the highly integrated nature of biological control systems is starting to be more fully understood. Although many models may be developed using physical, chemical, or biological principles in the initial stages, the use of experimentation is important for checking the significance of underlying assumptions or simplifications and also for estimating appropriate sets of parameters. This experimental approach to modelling is also of central importance in establishing the suitability, or otherwise, of a given model for an intended application – the so-called “model validation” problem. System identification, which is the broad term used to describe the processes of experimental modelling, is generally considered to be a mature field and classical methods of identification involve linear discrete-time models within a stochastic framework. The aspects of the research described in this thesis that relate to applications of identification, parameter estimation and optimisation techniques for model development and model validation mainly involve nonlinear continuous time models Experimentally-based models of this kind have been used very successfully in the course of the research described in this thesis very in two areas of physiological research and in a number of different engineering applications. In terms of optimisation problems, the design, experimental tuning and performance evaluation of nonlinear control systems has much in common with the use of optimisation techniques within the model development process and it is therefore helpful to consider these two areas together. The work described in the thesis is strongly applications oriented. Many similarities have been found in applying modelling and control techniques to problems arising in fields that appear very different. For example, the areas of neurophysiology, respiratory gas exchange processes, electro-optic sensor systems, helicopter flight-control, hydro-electric power generation and surface ship or underwater vehicles appear to have little in common. However, closer examination shows that they have many similarities in terms of the types of problem that are presented, both in modelling and in system design. In addition to nonlinear behaviour; most models of these systems involve significant uncertainties or require important simplifications if the model is to be used in a real-time application such as automatic control. One recurring theme, that is important both in the modelling work described and for control applications, is the additional insight that can be gained through the dual use of time-domain and frequency-domain information. One example of this is the importance of coherence information in establishing the existence of linear or nonlinear relationships between variables and this has proved to be valuable in the experimental investigation of neuromuscular systems and in the identification of helicopter models from flight test data. Frequency-domain techniques have also proved useful for the reduction of high-order multi-input multi-output models. Another important theme that has appeared both within the modelling applications and in research on nonlinear control system design methods, relates to the problems of optimisation in cases where the associated response surface has many local optima. Finding the global optimum in practical applications presents major difficulties and much emphasis has been placed on evolutionary methods of optimisation (both genetic algorithms and genetic programming) in providing usable methods for optimisation in design and in complex nonlinear modelling applications that do not involve real-time problems. Another topic, considered both in the context of system modelling and control, is parameter sensitivity analysis and it has been found that insight gained from sensitivity information can be of value not only in the development of system models (e.g. through investigation of model robustness and the design of appropriate test inputs), but also in feedback system design and in controller tuning. A technique has been developed based on sensitivity analysis for the semi-automatic tuning of cascade and feedback controllers for multi-input multi-output feedback control systems. This tuning technique has been applied successfully to several problems. Inverse systems also receive significant attention in the thesis. These systems have provided a basis for theoretical research in the control systems field over the past two decades and some significant applications have been reported, despite the inherent difficulties in the mathematical methods needed for the nonlinear case. Inverse simulation methods, developed initially by others for use in handling-qualities studies for fixed-wing aircraft and helicopters, are shown in the thesis to provide some important potential benefits in control applications compared with classical methods of inversion. New developments in terms of methodology are presented in terms of a novel sensitivity based approach to inverse simulation that has advantages in terms of numerical accuracy and a new search-based optimisation technique based on the Nelder-Mead algorithm that can handle inverse simulation problems involving hard nonlinearities. Engineering applications of inverse simulation are presented, some of which involve helicopter flight control applications while others are concerned with feed-forward controllers for ship steering systems. The methods of search-based optimisation show some important advantages over conventional gradient-based methods, especially in cases where saturation and other nonlinearities are significant. The final discussion section takes the form of a critical evaluation of results obtained using the chosen methods of system identification, parameter estimation and optimisation for the modelling and control applications considered. Areas of success are highlighted and situations are identified where currently available techniques have important limitations. The benefits of an inter-disciplinary and applications-oriented approach to problems of modelling and control are also discussed and the value in terms of cross-fertilisation of ideas resulting from involvement in a wide range of applications is emphasised. Areas for further research are discussed

Experimental Results of Concurrent Learning Adaptive Controllers

Commonly used Proportional-Integral-Derivative based UAV flight controllers are often seen to provide adequate trajectory-tracking performance only after extensive tuning. The gains of these controllers are tuned to particular platforms, which makes transferring controllers from one UAV to other time-intensive. This paper suggests the use of adaptive controllers in speeding up the process of extracting good control performance from new UAVs. In particular, it is shown that a concurrent learning adaptive controller improves the trajectory tracking performance of a quadrotor with baseline linear controller directly imported from another quadrotors whose inertial characteristics and throttle mapping are very di fferent. Concurrent learning adaptive control uses specifi cally selected and online recorded data concurrently with instantaneous data and is capable of guaranteeing tracking error and weight error convergence without requiring persistency of excitation. Flight-test results are presented on indoor quadrotor platforms operated in MIT's RAVEN environment. These results indicate the feasibility of rapidly developing high-performance UAV controllers by using adaptive control to augment a controller transferred from another UAV with similar control assignment structure.United States. Office of Naval Research. Multidisciplinary University Research Initiative (Grant N000141110688)National Science Foundation (U.S.). Graduate Research Fellowship Program (Grant 0645960)Boeing Scientific Research Laboratorie

Development of Robust Control Laws for Disturbance Rejection in Rotorcraft UAVs

Inherent stability inside the flight envelope must be guaranteed in order to safely introduce private and commercial UAV systems into the national airspace. The rejection of unknown external wind disturbances offers a challenging task due to the limited available information about the unpredictable and turbulent characteristics of the wind. This thesis focuses on the design, development and implementation of robust control algorithms for disturbance rejection in rotorcraft UAVs. The main focus is the rejection of external disturbances caused by wind influences. Four control algorithms are developed in an effort to mitigate wind effects: baseline nonlinear dynamic inversion (NLDI), a wind rejection extension for the NLDI, NLDI with adaptive artificial neural networks (ANN) augmentation, and NLDI with L1 adaptive control augmentation. A simulation environment is applied to evaluate the performance of these control algorithms under external wind conditions using a Monte Carlo analysis. Outdoor flight test results are presented for the implementation of the baseline NLDI, NLDI augmented with adaptive ANN and NLDI augmented with L1 adaptive control algorithms in a DJI F330 Flamewheel quadrotor UAV system. A set of metrics is applied to compare and evaluate the overall performance of the developed control algorithms under external wind disturbances. The obtained results show that the extended NLDI exhibits undesired characteristics while the augmentation of the baseline NLDI control law with adaptive ANN and L1 output-feedback adaptive control improve the robustness of the translational and rotational dynamics of a rotorcraft UAV in the presence of wind disturbances

A Data Driven Modeling Approach for Store Distributed Load and Trajectory Prediction

The task of achieving successful store separation from aircraft and spacecraft has historically been and continues to be, a critical issue for the aerospace industry. Whether it be from store-on-store wake interactions, store-parent body interactions or free stream turbulence, a failed case of store separation poses a serious risk to aircraft operators. Cases of failed store separation do not simply imply missing an intended target, but also bring the risk of collision with, and destruction of, the parent body vehicle. Given this risk, numerous well-tested procedures have been developed to help analyze store separation within the safe confines of wind tunnels. However, due to increased complexity in store separation configurations, such as rotorcraft and cavity-based separation, there is a growing desire to incorporate computational fluid dynamics (CFD) into the early stages of the store separation analysis. A viable method for achieving this objective is available through data-driven surrogate modeling of store distributed loads. This dissertation investigates the practicality of applying various data-driven modeling techniques to the field of store separation. These modeling methods will be applied to four demonstration scenarios: reduced order modeling of a moving store, design optimization, supersonic store separation, and rotorcraft store separation. For the first demonstration scenario, results are presented for three sub-tasks. In the first sub-task proper orthogonal decomposition (POD), dynamic mode decomposition (DMD), and convolutional neural networks (CNN) were compared for their capability to replicate distributed pressure loads of a pitching up prolate spheroid. Results indicated that POD was the most efficient approach for surrogate model generation. For the second sub-task, a POD-based surrogate model was derived from CFD simulations of an oscillating prolate spheroid subject to varying reduced frequency and amplitude of oscillation. The obtained surrogate model was shown to provide high-fidelity predictions for new combinations of reduced frequency and amplitude with a maximum percent error of integrated loads of less than 3\%. Therefore, it was demonstrated that the surrogate model was capable of predicting accurately at intermediate states. Further analysis showed a similar surrogate model could be generated to provide accurate store trajectory modeling under subsonic, transonic, and supersonic conditions. In the second demonstration scenario, a POD-based surrogate model is derived from a series of CFD simulations of isolated rotors in hover and forward flight. The derived surrogate models for hover and forward flight were shown to provide integrated load predictions within 1% of direct CFD simulation. Additionally, results indicated that computational expense could be reduced from 20 hours on 440 CPUs to less than a second on a single CPU. Given the reduction of cost and high fidelity of the surrogate model, the derived model was leveraged to optimize the twist and taper ratio of the rotor such that the efficiency of the rotor was maximized. For the third demonstration scenario, a POD and CNN surrogate model was derived for fixed-wing based supersonic store separation. Results demonstrated that both models were capable of providing high-fidelity predictions of the store\u27s distributed loads and subsequent trajectory. For the final demonstration scenario, a POD-based surrogate model was derived for the case of a store launching from a rotorcraft. The surrogate model was derived from three CFD simulations while varying ejection force. This surrogate model was then validated against CFD simulation of a new store ejection force. Results indicated that while the surrogate model struggled to provide detailed predictions of store distributed loads, mean load variations could be modeled well at a massively reduced computational cost. For each rotorcraft store separation CFD simulation, the computational cost required 10 days of simulation time across 880. While using the surrogate model, comparable predictions could be produced in under a minute on a single core. Overall findings from this study indicate that massive CFD generated data-sets can be efficiently leveraged to create meaningful surrogate models capable of being deployed to highly iterative design tasks relevant to store separation. Through further improvements, similar surrogate models can be combined with a control strategy to achieve trajectory optimization and control

Online parameter estimation of a miniature unmanned helicopter using neural network techniques

The online aerodynamic parameter estimation of a miniature unmanned helicopter using Neural Network techniques has been presented. The simulation model for the miniature helicopter was developed using the MATLAB/ SIMULINK software tool. Three trim conditions were analyzed: hover flight, 10m/s forward flight and 20m/s forward flight. Radial Basis Function (RBF) online learning was achieved using a moving window algorithm which generated an input-output data set at each time step. RBF network online identification was achieved with good robustness to noise for all flight conditions. However, the presence of atmospheric turbulence and sensor noise had an adverse effect on network size and memory usage. The Delta Method (DM) and the Modified Delta Method (MDM) was investigated for the NN-based online estimation of aerodynamic parameters. An increasing number high confidence estimated parameters could be extracted using the MDM as the helicopter transitioned from hover to forward flight

Parameter Estimation of Unstable Aircraft using Extreme Learning Machine

The parameter estimation of unstable aircraft using extreme learning machine method is presented. In the past, conventional methods such as output error method, filter error method, equation error method and non-conventional method such as artificial neural-network based methods have been used for aircraft’s aerodynamic parameter estimation. Nowadays, a trend of finding an accurate nonlinear function approximation is required to represent the aircraft’s equations-of-motion. Such type of nonlinear function approximation is usually achieved using artificial neural-network which is trained with the aircraft input-output flight data using a training algorithm. The accuracy of estimated parameters, which is achieved using the trained network, is highly dependent on the generalisation capability of the network which can be improved using extreme learning machine based network in contrast to artificial neural-network. To estimate the unstable aircraft parameters from the simulated flight data, Gauss-Newton based optimisation method has been used with a predefined aerodynamic model using the trained network. Further, the confidence of the estimated parameters has been shown in comparison to that of the standard parameter estimation methods in terms of the Cramer-Rao bounds

Multiple-Surrogate Approach to Helicopter Rotor Blade Vibration Reduction

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77383/1/AIAA-40291-933.pd

Optimal aeroelastic trim for rotorcraft with constrained, non-unique trim solutions

New rotorcraft configurations are emerging, such as the optimal speed helicopter and slowed-rotor compound helicopter which, due to variable rotor speed and redundant lifting components, have non-unique trim solution spaces. The combination of controls and rotor speed that produce the best steady-flight condition is sought among all the possible solutions. This work develops the concept of optimal rotorcraft trim and explores its application to advanced rotorcraft configurations with non-unique, constrained trim solutions. The optimal trim work is based on the nonlinear programming method of the generalized reduced gradient (GRG) and is integrated into a multi-body, comprehensive aeroelastic rotorcraft code. In addition to the concept of optimal trim, two further developments are presented that allow the extension of optimal trim to rotorcraft with rotors that operate over a wide range of rotor speeds. The first is the concept of variable rotor speed trim with special application to rotors operating in steady autorotation. The technique developed herein treats rotor speed as a trim variable and uses a Newton-Raphson iterative method to drive the rotor speed to zero average torque simultaneously with other dependent trim variables. The second additional contribution of this thesis is a novel way to rapidly approximate elastic rotor blade stresses and strains in the aeroelastic trim analysis for structural constraints. For rotors that operate over large angular velocity ranges, rotor resonance and increased flapping conditions are encountered that can drive the maximum cross-sectional stress and strain to levels beyond endurance limits; such conditions must be avoided. The method developed herein captures the maximum cross-sectional stress/strain based on the trained response of an artificial neural network (ANN) surrogate as a function of 1-D beam forces and moments. The stresses/strains are computed simultaneously with the optimal trim and are used as constraints in the optimal trim solution. Finally, an optimal trim analysis is applied to a high-speed compound gyroplane configuration, which has two distinct rotor speed control methods, with the purpose of maximizing the vehicle cruise efficiency while maintaining rotor blade strain below endurance limit values.Ph.D.Committee Chair: Dimitri N. Mavris; Committee Co-Chair: Daniel P Schrage; Committee Member: David A. Peters; Committee Member: Dewey H. Hodges; Committee Member: J.V.R. Prasa

Active control of turbulence-induced helicopter vibration

Helicopter vibration signatures induced by severe atmospheric turbulence have been shown to differ considerably from nominal, still air vibration. The perturbations of the transmission frequency have significant implications for the design of passive and active vibration alleviation devices, which are generally tuned to the nominal vibration frequency. This thesis investigates the existence of the phenomena in several realistic atmospheric turbulence environments, generated using Computational Fluid Dynamic (CFD) engineering software and assimilated within a high-fidelity rotorcraft simulation, RASCAL. The RASCAL simulation is modified to calculate blade element sampling of the gust, enabling thorough, high frequency analyses of the rotor response. In a final modification, a numerical, integration-based inverse simulation algorithm, GENISA is incorporated and the augmented simulation is henceforth referred to as HISAT. Several implementation issues arise from the symbiosis, principally because of the modelling of variable rotorspeed and lead-lag motion. However, a novel technique for increasing the numerical stability margins is proposed and tested successfully. Two active vibration control schemes, higher harmonic control 'HHC' and individual blade control 'IBC', are then evaluated against a 'worst-case' sharp-edged gust field. The higher harmonic controller demonstrates a worrying lack of robustness, and actually begins to contribute to the vibration levels. Several intuitive modifications to the algorithm are proposed but only disturbance estimation is successful. A new simulation model of coupled blade motion is derived and implemented using MATLAB and is used to design a simple IBC compensator. Following bandwidth problems, a redesign is proposed using H theory which improves the controller performance. Disturbance prediction/estimation is attempted using artificial neural networks to limited success. Overall, the aims and objectives of the research are met