Advances in experimental techniques and the ever-increasing fidelity of numerical simulations have led to an abundance of data describing fluid flows. This review discusses a range of techniques for analyzing such data, with the aim of extracting simplified models that capture the essential features of these flows, in order to gain insight into the flow physics, and potentially identify mechanisms for controlling these flows. We review well-developed techniques, such as proper orthogonal decomposition and Galerkin projection, and discuss more recent techniques developed for linear systems, such as balanced truncation and dynamic mode decomposition (DMD). We then discuss some of the methods available for nonlinear systems, with particular attention to the Koopman operator, an infinite-dimensional linear operator that completely characterizes the dynamics of a nonlinear system and provides an extension of DMD to nonlinear systems.

Model Reduction for Flow Analysis and Control

Bifurcation control deals with modification of bifurcation characteristics of a parameterized nonlinear system by a designed control input. Typical bifurcation control objectives include delaying t...

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Bifurcation control: theories, methods, and applications

Bifurcation analysis has previously been applied to the NASA Generic Transport Model (GTM) to provide insight into open-loop upset dynamics and also the impact on and sensitivity of such behaviour to closing the loop with a flight controller. However, these studies have not considered time delay in the system: this arises in all feedback controllers and has specific relevance when remotely piloting a vehicle such as the NASA AirSTAR GTM with ground-based controllers. Developments in the AirSTAR programme, in which a sub-scale generic airliner model will be tested for loss-of-control conditions over long ranges, raise the prospect of increased adverse effects of time delay relative to previous testing. This paper utilises bifurcation analysis, supplemented with time histories, on the GTM numerical model with a LQR-PI controller to evaluate the sensitivity of the closed-loop system stability to time delay. In this paper, the impact of time delays in both a fixed-gain and a gain-scheduled version of the controller is presented in terms of stability of nominal and off-nominal solutions.

Sensitivity of the Generic Transport Model upset dynamics to time delay

Synopsis: From the nostalgic remembrance of the first dynamic flight test this Survey Paper traces several milestones in the history of flight vehicle system identification. A comprehensive account of modern system identification techniques is provided. Several challenging examples bring out the fact that these techniques have reached a high level of maturity, making them a sophisticated and powerful tool not only for research purposes, but also to support the needs of the aircraft industry. This survey paper includes 183 references and provides a consolidated list of publications on the subject.

https://dlr.de/ft/en/portaldata/2/resources/dokumente/ft/jategaonkar/evol_sysid.pdf

Evolution of flight vehicle system identification

Bats have long captured the imaginations of scientists and engineers with their unrivaled agility and maneuvering characteristics, achieved by functionally versatile dynamic wing conformations as well as more than 40 active and passive joints on the wings. Wing flexibility and complex wing kinematics not only bring a unique perspective to research in biology and aerial robotics but also pose substantial technological challenges for robot modeling, design, and control. We have created a fully self-contained, autonomous flying robot that weighs 93 grams, called Bat Bot (B2), to mimic such morphological properties of bat wings. Instead of using a large number of distributed control actuators, we implement highly stretchable silicone-based membrane wings that are controlled at a reduced number of dominant wing joints to best match the morphological characteristics of bat flight. First, the dominant degrees of freedom (DOFs) in the bat flight mechanism are identified and incorporated in B2’s design by means of a series of mechanical constraints. These biologically meaningful DOFs include asynchronous and mediolateral movements of the armwings and dorsoventral movements of the legs. Second, the continuous surface and elastic properties of bat skin under wing morphing are realized by an ultrathin (56 micrometers) membranous skin that covers the skeleton of the morphing wings. We have successfully achieved autonomous flight of B2 using a series of virtual constraints to control the articulated, morphing wings.

A biomimetic robotic platform to study flight specializations of bats

Mathematical modeling of unsteady aerodynamic forces and moments plays an important role in aircraft dynamics investigation and stability analysis at high angles of attack. In this article the state-space representation of aerodynamic forces and moments for unsteady aircraft motion is proposed. Consideration of separated flow about an airfoil and flow with vortex breakdown about a slender delta wing gives the base for mathematical modeling using internal variables describing the flow state. Coordinates of separation points or vortex breakdown can be taken, e.g., as internal state-space variables. These variables are governed by some differential equations. Within the framework of the proposed mathematical model it is possible to achieve good agreement with different experimental data obtained in water and wind tunnels. These high angle-of-attack experimental results demonstrate considerable dependence of aerodynamic loads on motion time history.

State-Space Representation of Aerodynamic Characteristics of an Aircraft at High Angles of Attack

Application of bifurcation methods to nonlinear flight dynamics problems

An aircraft's performance and maneuvering capabilities in steady flight conditions are usually analyzed considering the steady states of the rigid-body equations of motion. A systematic way of computation of the set of all attainable steady states for a general class of helical trajectories is presented. The proposed reconstruction of attainable equilibrium states and their local stability maps provides a comprehensive and consistent representation of the aircraft flight and maneuvering envelopes. The numerical procedure is outlined and computational examples of attainable equilibrium sets in the form of two-dimensional cross sections of steady-state maneuver parameters are presented for three different aircraft models.

Evaluation of Aircraft Performance and Maneuverability by Computation of Attainable Equilibrium Sets

The use of nonlinear dynamics theory for the analysis of aircraft motion and the assessment of aircraft control systems is well known. In this paper the continuation and bifurcation methods are app...

Application of continuation and bifurcation methods to the design of control systems

A new five-degree-of-freedom rig for the dynamic wind-tunnel testing of aircraft models has been developed. The maneuver rig enables a large set of conventional and more-extreme aircraft maneuvers to be performed in the controlled environment of a wind tunnel, allowing direct physical simulation of in-flight maneuvers and the identification of aerodynamic models from aircraft-model time histories. A mathematical model of the rig has been developed for numerical simulation and identification purposes. The development of a quasi-steady aerodynamic model of the longitudinal motion for a subscale test aircraft is presented to illustrate rig capabilities. The longitudinal modes of motion are excited by a remotely controlled aircraft-model stabilator and dynamic-rig aerodynamic compensator deflections. Two rig configurations are considered: aircraft-model pitch only and aircraft-model pitch with heave, which is implemented via rig-pitch motion. The aircraft-model tail and wing in the mathematical model are cons...

Mikhail Goman

Papers

State-Space Representation of Aerodynamic Characteristics of an Aircraft at High Angles of Attack

Application of bifurcation methods to nonlinear flight dynamics problems

Evaluation of Aircraft Performance and Maneuverability by Computation of Attainable Equilibrium Sets

Application of continuation and bifurcation methods to the design of control systems

Multi-Degree-of-Freedom Wind-Tunnel Maneuver Rig for Dynamic Simulation and Aerodynamic Model Identification