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H.J. Tol
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A compensator strategy based on the linearized Navier–Stokes equations, aimed to suppress Tollmien–Schlichting waves naturally occurring in low freestream turbulence conditions, is experimentally demonstrated. Experiments have been conducted on a flat-plate geometry under the influence of an externally imposed adverse pressure gradient. A Kalman filter is used to estimate the effect of upstream disturbances based on pressure information from a single wall-embedded microphone. This information is used by the controller to cancel the incoming perturbations using a surface dielectric barrier discharge plasma actuator. The estimates obtained from the Kalman filter are compared with experimental data obtained using particle image velocimetry. It is shown that the Kalman filter is able to estimate the spatiotemporal behavior of the perturbation field even though it relies on a priori assumptions on the upstream disturbance environment. The performance of the controller and its robustness to varying freestream velocities are analyzed in comparison with open-loop continuous forcing. It is shown that the controller is able to additionally reduce the fluctuating pressure power at the most amplified frequencies with more than one order of magnitude and is capable of reducing the standard deviation of the downstream sensor signal between 30 and 60% for a range of offdesign freestream velocities.
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A compensator strategy based on the linearized Navier–Stokes equations, aimed to suppress Tollmien–Schlichting waves naturally occurring in low freestream turbulence conditions, is experimentally demonstrated. Experiments have been conducted on a flat-plate geometry under the influence of an externally imposed adverse pressure gradient. A Kalman filter is used to estimate the effect of upstream disturbances based on pressure information from a single wall-embedded microphone. This information is used by the controller to cancel the incoming perturbations using a surface dielectric barrier discharge plasma actuator. The estimates obtained from the Kalman filter are compared with experimental data obtained using particle image velocimetry. It is shown that the Kalman filter is able to estimate the spatiotemporal behavior of the perturbation field even though it relies on a priori assumptions on the upstream disturbance environment. The performance of the controller and its robustness to varying freestream velocities are analyzed in comparison with open-loop continuous forcing. It is shown that the controller is able to additionally reduce the fluctuating pressure power at the most amplified frequencies with more than one order of magnitude and is capable of reducing the standard deviation of the downstream sensor signal between 30 and 60% for a range of offdesign freestream velocities.
This paper investigates the use of point wall pressure measurements for output feedback control of Tollmien–Schlichtingwaves in Falkner–Skan boundary layers.Anewapproach is presented for input–outputmodeling of the linear dynamics of the fluid system and the integration withH2∕Linear Quadratic Gaussian reduced-order control design. The pressure output at the wall is related with the global perturbation velocity field through the linearized pressure Poisson equation. A Kalman filter is subsequently used to obtain time-resolved estimates of the velocity field using pressure information at discrete points at the wall. The estimated field is in turn used to calculate an optimal state feedback control to suppress the instabilities. The controller is designed in a feedforward, a feedback, and a combined feedforward/feedback actuator/sensor configuration. It is shown that combined feedforward/feedback control gives the best tradeoff between robust performance and robust stability in the presence of uncertainties in the Reynolds number and the pressure gradient. Robust performance in off-design conditions is enhanced compared to feedforward control, whereas robust stability is enhanced compared to feedback control.
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This paper investigates the use of point wall pressure measurements for output feedback control of Tollmien–Schlichtingwaves in Falkner–Skan boundary layers.Anewapproach is presented for input–outputmodeling of the linear dynamics of the fluid system and the integration withH2∕Linear Quadratic Gaussian reduced-order control design. The pressure output at the wall is related with the global perturbation velocity field through the linearized pressure Poisson equation. A Kalman filter is subsequently used to obtain time-resolved estimates of the velocity field using pressure information at discrete points at the wall. The estimated field is in turn used to calculate an optimal state feedback control to suppress the instabilities. The controller is designed in a feedforward, a feedback, and a combined feedforward/feedback actuator/sensor configuration. It is shown that combined feedforward/feedback control gives the best tradeoff between robust performance and robust stability in the presence of uncertainties in the Reynolds number and the pressure gradient. Robust performance in off-design conditions is enhanced compared to feedforward control, whereas robust stability is enhanced compared to feedback control.
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.
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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.
Doctoral thesis
(2018)
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Henry Tol
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.
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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.
In existing modular adaptive control approaches, the effects of external disturbances such as atmospheric turbulence are often not considered. In real-life flight applications, stochastic atmospheric disturbances can severely degrade the performance of these approaches, resulting in undesired and unpredictable control behavior. In this paper, robust adaptation laws are developed within the framework of multivariate-spline-based adaptive control. This new approach, referred to as robust spline-based adaptive nonlinear dynamic inversion (R-SANDI), integrates nonlinear dynamic inversion (NDI) and spline-model-based control allocation with a robust real-time aerodynamic model identification routine. The latter is based on the conditional estimation of the deterministic and the disturbance effect. The developed method is applied to control a F-16 aircraft subject to significant aerodynamic uncertainties and turbulence. Simulation results show that the developed control system outperforms a previously proposed deterministic spline-based adaptive NDI controller, which is shown to become unstable in the presence of turbulence. The new controller is able to adapt to large uncertainties within the onboard aerodynamic model, even in the co-existence of high turbulence levels. This enhances flight performance, safety and survivability and facilitates future real-life flight applications in high performance aircraft.
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In existing modular adaptive control approaches, the effects of external disturbances such as atmospheric turbulence are often not considered. In real-life flight applications, stochastic atmospheric disturbances can severely degrade the performance of these approaches, resulting in undesired and unpredictable control behavior. In this paper, robust adaptation laws are developed within the framework of multivariate-spline-based adaptive control. This new approach, referred to as robust spline-based adaptive nonlinear dynamic inversion (R-SANDI), integrates nonlinear dynamic inversion (NDI) and spline-model-based control allocation with a robust real-time aerodynamic model identification routine. The latter is based on the conditional estimation of the deterministic and the disturbance effect. The developed method is applied to control a F-16 aircraft subject to significant aerodynamic uncertainties and turbulence. Simulation results show that the developed control system outperforms a previously proposed deterministic spline-based adaptive NDI controller, which is shown to become unstable in the presence of turbulence. The new controller is able to adapt to large uncertainties within the onboard aerodynamic model, even in the co-existence of high turbulence levels. This enhances flight performance, safety and survivability and facilitates future real-life flight applications in high performance aircraft.
A new framework is presented for estimation and control of instabilities in wall-bounded shear flows described by the linearised Navier-Stokes equations. The control design considers the use of localised actuators/sensors to account for convective instabilities in an optimal control framework. External sources of disturbances are assumed to enter the control domain through the inflow. A new inflow disturbance model is proposed for external excitation of the perturbation modes that contribute to transition. This model allows efficient estimation of the flow perturbations within the localised control region of a conceptually unbounded domain. The state-space discretisation of the infinite-dimensional system is explicitly obtained, which allows application of linear control theoretic tools. A reduced-order model is subsequently derived using exact balanced truncation that captures the input/output behaviour and the dominant perturbation dynamics. This model is used to design an optimal controller to suppress the instability growth. The two-dimensional non-periodic channel flow is considered as an application case. Disturbances are generated upstream of the control domain and the resulting flow perturbations are estimated/controlled using point wall shear measurements and localised unsteady blowing and suction at the wall. The controller is able to cancel the perturbations and is robust to both unmodelled disturbances and sensor inaccuracies. For single-frequency and multiple-frequency disturbances with low sensor noise a nearly full cancellation is achieved. For stochastic forced disturbances and high sensor noise an energy reduction in perturbation wall shear stress of 96Â % is shown.
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A new framework is presented for estimation and control of instabilities in wall-bounded shear flows described by the linearised Navier-Stokes equations. The control design considers the use of localised actuators/sensors to account for convective instabilities in an optimal control framework. External sources of disturbances are assumed to enter the control domain through the inflow. A new inflow disturbance model is proposed for external excitation of the perturbation modes that contribute to transition. This model allows efficient estimation of the flow perturbations within the localised control region of a conceptually unbounded domain. The state-space discretisation of the infinite-dimensional system is explicitly obtained, which allows application of linear control theoretic tools. A reduced-order model is subsequently derived using exact balanced truncation that captures the input/output behaviour and the dominant perturbation dynamics. This model is used to design an optimal controller to suppress the instability growth. The two-dimensional non-periodic channel flow is considered as an application case. Disturbances are generated upstream of the control domain and the resulting flow perturbations are estimated/controlled using point wall shear measurements and localised unsteady blowing and suction at the wall. The controller is able to cancel the perturbations and is robust to both unmodelled disturbances and sensor inaccuracies. For single-frequency and multiple-frequency disturbances with low sensor noise a nearly full cancellation is achieved. For stochastic forced disturbances and high sensor noise an energy reduction in perturbation wall shear stress of 96Â % is shown.
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.
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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.
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.
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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.
Journal article
(2016)
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HJ Tol, CC de Visser, LG Sun, EJ van Kampen, QP Chu
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 reconfigured using incoming observations, the remainder of the model remains unchanged and can be used as an a priori source of information. This prevents the occurrence of sudden fundamental changes in the global model structure, which are experienced when using ordinary polynomials.
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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 reconfigured using incoming observations, the remainder of the model remains unchanged and can be used as an a priori source of information. This prevents the occurrence of sudden fundamental changes in the global model structure, which are experienced when using ordinary polynomials.