H.J. Tol

Nonlinear Multivariate Spline-Based Control Allocation for High-Performance Aircraft

High performance flight control systems based on the nonlinear dynamic inversion (NDI) 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 NDI with multivariate simplex spline based control allocation. We present three control allocation strategies which use novel expressions for the analytical Jacobian and Hessian of the multivariate spline models. 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 new method, indicated as SNDI, is applied to control a high performance aircraft (F-16) with a large flight envelope. The simulation results indicate that the SNDI controller can achieve feedback linearization throughout the entire flight envelope, leading to a significant increase in tracking performance compared to ordinary polynomial based NDI.

Multivariate Spline-Based Adaptive Control of High-Performance Aircraft with Aerodynamic Uncertainties

In this paper, a new modular adaptive control system is presented to compensate for aerodynamic uncertainties in high-performance flight control systems. This approach combines nonlinear dynamic inversion with multivariate spline-based adaptive control allocation. A new real-time identification routine for multivariate splines is presented to compensate for aerodynamic uncertainties in the control allocation system. This method, indicated as spline-based adaptive nonlinear dynamic inversion, is applied to control an F-16 aircraft subject to significant aerodynamics uncertainties. Simulation results indicate that the new controller can tune itself each time a model error is detected and has superior adaptability compared to an ordinary polynomial-based adaptive controller. Multivariate splines have sufficient flexibility and approximation power to accurately model nonlinear aerodynamics over the entire flight envelope. As a result, the global model remains intact. Although a part of the model is being reco...

Model Reduction of Parabolic PDEs using Multivariate Splines

ABSTRACT 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.

Nonlinear and Fault-Tolerant Flight Control Using Multivariate Splines

This paper presents a study on fault tolerant flight control of a high performance aircraft using multivariate splines. The controller is implemented by making use of spline model based adaptive nonlinear dynamic inversion (NDI). This method, indicated as SANDI, combines NDI control with nonlinear control allocation based on an onboard aerodynamic spline model and a real-time identification routine. The controller is tested for an aileron hardover failure and structural damages which change the global aerodynamic properties of the aircraft. It is shown that the controller can quickly tune itself in failure conditions without the need of failure detection and monitoring algorithms. Instead, self-tuning innovation based forgetting is applied to reconfigure the onboard aerodynamic model. The controller is able to tune itself each time a model error is detected and does not require any external triggers for re-identification. Multivariate splines have a high local approximation power and are able to accurately model nonlinear aerodynamics over the entire flight envelope of an aircraft. As a result the identification routine gives a robust adaption of the aerodynamic model in case of a failure.

Multivariate Simplex Spline Based Nonlinear Dynamic Inversion Control of High Performance Aircraft

High performance flight control systems based on the nonlinear dynamic inversion (NDI) 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 cancelled; the more accurate the model, the better the cancellation, and with that, the higher the performance of the controller. In this paper, a multivariate simplex spline based NDI control system is presented which is applied to control a high performance aircraft (F-16) with a large flight envelope. Simplex splines have a much higher approximation power than ordinary polynomial models, and are capable of accurately modelling nonlinear aerodynamics over the entire flight envelope of an aircraft. The new control approach is applied to a high-fidelity F-16 simulation model. The simulation results indicate that the simplex spline based NDI controller can achieve perfect feedback linearization through the entire flight envelope, and as a result provide accurate global tracking performance.

Finite-dimensional approximation and control of shear flows

Dynamical systems theory can significantly contribute to the understanding and control of fluid flows. Fluid dynamical systems are governed by the Navier-Stokes equations, which are continuous in both time and space, resulting in a state space of infinite dimension. To incorporate tools from systems theory it has become common practise to approximate the infinite-dimensional system by a finite-dimensional lumped system. Current techniques for this reduction step are data driven and produce models which are sensitive to the simulation or experimental conditions. This dissertation proposes a rigorous and practical methodology for the derivation of accurate finite-dimensional approximations and output feedback controllers directly from the governing equations. The approach combines state-space discretisation of the linearised Navier-Stokes equations with balanced truncation to design experimentally feasible low-order controllers. The approximation techniques can be used to design any suitable linear controller. In this study the reduced-order controllers are designed within an H2 optimal control framework to account for external disturbances and measurement noise. Application is focused on control of laminar wall-bounded shear flows to delay the classical transition process initially governed by two-dimensional convective perturbations, to extend laminar flow and reduce skin friction drag. The controllers are successfully tested in the vertical wind tunnel at the TU Delft.

Effectivity and efficiency of selective frequency damping for the computation of unstable steady-state solutions

Selective Frequency Damping (SFD) is a popular method for the computation of globally unstable steady-state solutions in fluid dynamics. The approach has two model parameters whose selection is generally unclear. In this article, a detailed analysis of the influence of these parameters is presented, answering several open questions with regard to the effectiveness, optimum efficiency and limitations of the method. In particular, we show that SFD is always capable of stabilising a globally unstable systems ruled by one unsteady unstable eigenmode and derive analytical formulas for optimum parameter values. We show that the numerical feasibility of the approach depends on the complex phase angle of the most unstable eigenvalue. A numerical technique for characterising the pertinent eigenmodes is presented. In combination with analytical expressions, this technique allows finding optimal parameters that minimise the spectral radius of a simulation, without having to perform an independent stability analysis. An extension to multiple unstable eigenmodes is derived. As computational example, a two-dimensional cylinder flow case is optimally stabilised using this method. We provide a physical interpretation of the stabilisation mechanism based on, but not limited to, this Navier–Stokes example.

Control of fluid flows using multivariate spline reduced order models

This paper presents a study on control of fluid flows using multivariate spline reduced order models. A new approach is presented for model reduction of the incompressible Navier-Stokes equations using multivariate splines defined on triangulations. State space descriptions are derived that can be used for control design. This paper considers the linearised Navier-Stokes equations in velocity-pressure formulation. The pressure is elimi- nated from the equations by using a space of velocity fields which are divergence free. The divergence free condition along with the smoothness across the domain and the bound- ary conditions are imposed as a linear system of side constraints. The projection of the system on the null space of these constraints significantly reduces the dimension of the model while satisfying these constraints. The reduction method is applied to design and implement feedback controllers for stabilization of disturbances in a Poiseuille flow. It is shown that effective feedback stabilization can be achieved using low order control models.