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A new methodology is presented for model reduction of linear parabolic partial differential equations (PDEs) on general geometries using multivariate splines on triangulations. State-space descriptions are derived that can be used for control design. This method uses Galerkin projection with B-splines to derive a finite set of ordinary differential equations (ODEs). Any desired smoothness conditions between elements as well as the boundary conditions are flexibly imposed as a system of side constraints on the set of ODEs. Projection of the set of ODEs on the null space of the system of side constraints naturally produces a reduced-order model that satisfies these constraints. This method can be applied for both in-domain control and boundary control of parabolic PDEs with spatially varying coefficients on general geometries. The reduction method is applied to design and implement feedback controllers for stabilisation of a 1-D unstable heat equation and a more challenging 2-D reaction-convection-diffusion equation on an irregular domain. It is shown that effective feedback stabilisation can be achieved using low-order control models. [ABSTRACT FROM AUTHOR]

High-speed flight in GPS-denied environments is currently an important frontier in the research on autonomous flight of micro air vehicles. Autonomous drone races stimulate the advances in this area by representing a very challenging case with tight turns, texture-less floors, and dynamic spectators around the track. These properties hamper the use of standard visual odometry approaches and imply that the micro air vehicles will have to bridge considerable time intervals without position feedback. To this end, we propose an approach to trajectory estimation for drone racing that is computationally efficient and yet able to accurately estimate a micro air vehicle's state (including biases) and parameters based on sparse, noisy observations of racing gates. The key concept of the approach is to optimize unknown and difficult-to-observe state variables so that the observations of the racing gates best fit with the known control inputs, estimated attitudes, and the quadrotor dynamics and aerodynamics during a time window. It is shown that a gradient-descent implementation of the proposed approach converges ~4 times quicker to (approximately) correct bias values than a state-of-the-art 15-state extended Kalman filter. Moreover, it reaches a higher accuracy, as the predicted end-point of an open-loop turn is on average only ~20 cm away from the actual end-point, while the extended Kalman filter and the gradient descent method with kinematic model only reach an accuracy of ~50 cm. Although the approach is applied here to drone racing, it generalizes to other settings in which a micro air vehicle may only have sparse access to velocity and/or position measurements. [ABSTRACT FROM AUTHOR]

Despite significant interest in tailless flapping-wing micro aerial vehicle designs, tailed configurations are often favoured, as they offer many benefits, such as static stability and a simpler control strategy, separating wing and tail control. However, the tail aerodynamics are highly complex due to the interaction between the unsteady wing wake and tail, which is generally not modelled explicitly. We propose an approach to model the flapping-wing wake and hence the tail aerodynamics of a tailed flapping-wing robot. First, the wake is modelled as a periodic function depending on wing flap phase and position with respect to the wings. The wake model is constructed out of six low-order sub-models representing the mean, amplitude and phase of the tangential and vertical velocity components. The parameters in each sub-model are estimated from stereo-particle image velocimetry measurements using an identification method based on multivariate simplex splines. The computed model represents the measured wake with high accuracy, is computationally manageable and is applicable to a range of different tail geometries. The wake model is then used within a quasi-steady aerodynamic model, and combined with the effect of free-stream velocity, to estimate the forces produced by the tail. The results provide a basis for further modelling, simulation and design work, and yield insight into the role of the tail and its interaction with the wing wake in flapping-wing vehicles. It was found that due to the effect of the wing wake, the velocity seen by the tail is of a similar magnitude as the free stream and that the tail is most effective at 50-70% of its span. [ABSTRACT FROM AUTHOR]

The sensor based backstepping control law, based on the singular perturbation theory and Tikhonov's theorem, is a novel nonlinear incremental control approach. This Lyapunov function based method is not susceptible to model uncertainties since it uses measured state derivatives instead of an onboard model. Considering these merits, the sensor based backstepping method is extended to handle sudden structural changes in the fault-tolerant flight control of an overactuated Boeing 747-200 aircraft with the control allocation being considered. Because of the application of the backstepping technique, this double-loop joint sensor based backstepping attitude controller allows more interaction between its outer and inner loops compared to a standard nonlinear dynamic inversion angular control approach. The benchmark with engine separation and rudder runaway failure scenarios is employed to evaluate the new controller. The simulation results show that the new joint sensor based backstepping attitude controller can lead to an unbiased tracking error performance in the nominal condition and more consistent sideslip angles than those produced by the hybrid sensor based backstepping approach when the aircraft is under failures. [ABSTRACT FROM AUTHOR]

High-performance flight control systems based on the nonlinear dynamic inversion principle require highly accurate models of aircraft aerodynamics. In general, the accuracy of the internal model determines to what degree the system nonlinearities can be canceled; the more accurate the model, the better the cancellation, and with that, the higher the performance of the controller. In this paper, a new control system is presented that combines nonlinear dynamic inversion with multivariate simplex spline-based control allocation. Three control allocation strategies that use novel expressions for the analytic Jacobian and Hessian of the multivariate spline models are presented. Multivariate simplex splines have a higher approximation power than ordinary polynomial models and are capable of accurately modeling nonlinear aerodynamics over the entire flight envelope of an aircraft. This nonlinear spline based controller is applied to control a high-performance aircraft (F-16) with a large flight envelope. The simulation results indicate that perfect feedback linearization can be achieved throughout the entire flight envelope, leading to a significant increase in tracking performance compared with ordinary polynomial-based nonlinear dynamic inversion. [ABSTRACT FROM AUTHOR]

This paper presents an approach to the system identification of the Delfly II Flapping Wing Micro Air Vehicle (FWMAV) using flight test data. It aims at providing simple FWMAV aerodynamic models that can be used in simulations as well as in nonlinear flight control systems. The undertaken methodology builds on normal aircraft system identification methods and extends these with techniques that are specific to FWMAV model identification. The entire aircraft model identification cycle is discussed covering the set-up and automatic execution of the flight test experiments, the aircraft states, the aerodynamic forces and moments' reconstruction, the aerodynamic model structure selection, the parameter estimation and finally, the model validation. In particular, a motion capturing facility was used to record the flapper's position in time and from there compute the states and aerodynamic forces and moments that acted on it, assuming flap-averaged dynamics and linear aerodynamic model structures. It is shown that the approach leads to aerodynamic models that can predict the aerodynamic forces with high accuracy. Despite less accurate, the predictions of the aerodynamic moments still follow the general trend of the measured moments. Dynamic simulations based on the identified aerodynamic models show flight trajectories that closely match the ground truth spanning a number of flapping cycles. Finally, the dimensional aerodynamic forces and moments' coefficients of two of the identified aerodynamic models are presented. [ABSTRACT FROM AUTHOR]

Avoiding high computational loads is essential to online aerodynamic model identification algorithms, which are at the heart of any model-based adaptive flight-control system. Multivariate simplex B-spline methods are excellent function approximation tools for modeling the nonlinear aerodynamics of high-performance aircraft. However, the computational efficiency of the multivariate simplex B-spline method must be improved in order to enable real-time onboard applications, for example, in adaptive nonlinear flight-control systems. In this paper, a new recursive sequential identification strategy is proposed for the multivariate simplex B-spline method aimed at increasing its computational efficiency, thereby allowing its use in onboard system identification applications. The main contribution of this new method is a significant reduction of the computational load for large-scale online identification problems as compared to the existing multivariate simplex B-spline methods. The proposed method consists of two sequential steps for each time interval and makes use of a decomposition of the global problem domain into a number of subdomains, called modules. In the first step, the B-coefficients for each module are estimated using a least-squares estimator. In the second step, the local B-coefficients for each module are then smoothened into a single global B-coefficient vector using a linear minimum mean-square errors estimation. The new method is compared to existing batch and recursive multivariate simplex B-spline methods in a numerical experiment in which an aerodynamic model is recursively identified based on data from a NASA F-16 wind-tunnel model. [ABSTRACT FROM AUTHOR]

An accurate knowledge of the unsteady aerodynamic forces acting on a bio-inspired, flapping-wing micro air vehicle (FWMAV) is crucial in the design development and optimization cycle. Two different types of experimental approaches are often used: determination of forces from position data obtained from external optical tracking during free flight, or direct measurements of forces by attaching the FWMAV to a force transducer in a wind-tunnel. This study compares the quality of the forces obtained from both methods as applied to a 17.4 gram FWMAV capable of controlled flight. A comprehensive analysis of various error sources is performed. The effects of different factors, e.g., measurement errors, error propagation, numerical differentiation, filtering frequency selection, and structural eigenmode interference, are assessed. For the forces obtained from free flight experiments it is shown that a data acquisition frequency below 200 Hz and an accuracy in the position measurements lower than ± 0.2 mm may considerably hinder determination of the unsteady forces. In general, the force component parallel to the fuselage determined by the two methods compares well for identical flight conditions; however, a significant difference was observed for the forces along the stroke plane of the wings. This was found to originate from the restrictions applied by the clamp to the dynamic oscillations observed in free flight and from the structural resonance of the clamped FWMAV structure, which generates loads that cannot be distinguished from the external forces. Furthermore, the clamping position was found to have a pronounced influence on the eigenmodes of the structure, and this effect should be taken into account for accurate force measurements.