Mark H Lowenberg

Sensitivity of the Generic Transport Model upset dynamics to time delay

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.

Bifurcation Analysis of the NASA GTM with a View to Upset Recovery

The loss of control in-flight of civil airliners is a matter of great concern to the aviation industry. Loss of control in-flight often involves so called ‘upset’ conditions and, hence, the ability to recover from upset will reduce the frequency of loss of control incidents. This paper presents the use of bifurcation analysis, complemented by time-history simulations, to understand the flight dynamics of the open loop NASA Generic Transport Model with a view to identifying the attractors of the dynamical system that underlie upset behaviour. A number of drivers for potential upset conditions have been discovered which include non-oscillatory spirals and oscillatory spins. Time-histories of the upset conditions yield the response characteristics associated with these upset scenarios.

Tailored Dynamic Gain-Scheduled Control

This paper advances the theoretical basis and application of dynamic gain-scheduled control, a novel method for the control of nonlinear systems, to an aircraft model. Extensions of this method involving multivariable gain scheduling and continuation tailoring are developed. The idea behind this method is to schedule the control law gains with a fast-varying state rather than with a slow-varying state or an input parameter. This approach is advantageous because it is then possible to schedule the gains with a state that is dominant in the mode that we are most interested in controlling. The use of this type of gain scheduling is shown to improve the transient response of the aircraft model when stepping between trim conditions and to reduce control surface movement, thus reducing the potential for saturation problems. Hidden coupling terms that introduce unwanted dynamics when scheduling gains with a fast state (rather than the input design parameter) are eliminated directly by applying a transformation to the classical parameter-scheduled gain distributions that are calculated using optimal control theory. A highly nonlinear unmanned combat air vehicle model is used to demonstrate the design process.

Upset Dynamics of an Airliner Model: A Nonlinear Bifurcation Analysis

Despite the significant improvement in safety linked to the fourth generation of airliners, the risk of encountering upset conditions remains an important consideration. Upset, which may arise from faults, external events, or inappropriate pilot inputs, can induce a loss-of-control incident if the pilot does not respond in the correct manner. Any initiative aimed at preventing such events requires an understanding of the fundamental aircraft behavior. This paper presents the use of bifurcation analysis, complemented by time-history simulations, to understand the flight dynamics of the open-loop NASA generic transport model by identifying the attractors of the dynamical system that govern upset behavior. A number of drivers for potential upset conditions have been identified, including nonoscillatory spirals and oscillatory spins. The analysis shows that these spirals and spins are connected in two-parameter space and that, by an inappropriate pilot reaction to the spiral, it is possible to enter the oscil...

Bifurcation and Stability Analysis of Aircraft Turning on the Ground

During ground maneuvers a loss of lateral stability due to the saturation of the main landing gear tires can cause the aircraft to enter a skid or a spin. The lateral stability is governed not only by aspects of the gear design, such as its geometry and tire characteristics, but also by operational parameters: for example, the weather and taxiway condition. In this paper, we develop an improved understanding and new presentation of the dynamics of an aircraft maneuvering on the ground, ultimately aimed at optimization and automation of ground operations. To investigate turning maneuvers, we apply techniques from dynamic systems theory to a modified version of a nonlinear computer model of an A320 passenger aircraft developed by the Landing Gear Group at Airbus in the United Kingdom. Specifically, we present a bifurcation analysis of the underlying solution structure that governs the dynamics of turning maneuvers with dependence on the steering angle and thrust level. Furthermore, a detailed study of the behavior when lateral stability is lost focuses on how the tire saturation at different wheel sets leads to qualitatively different types of overall behavior. The presented bifurcation diagrams identify parameter regions for which undesirable behavior is avoidable, and thus they form a foundation for defining the safe operating limits during turning maneuvers.

Influence of Variable Side-Stay Geometry on the Shimmy Dynamics of an Aircraft Dual-Wheel Main Landing Gear

Commercial aircraft are designed to fly but also need to operate safely and efficiently as vehicles on the ground. During taxiing, take-off, and landing the landing gear must operate reliably over a wide range of forward velocities and vertical loads. Specifically, it must maintain straight rolling under a wide variety of operating conditions. It is well known, however, that under certain conditions the wheels of the landing gear may display unwanted oscillations, referred to as shimmy oscillations, during ground maneuvers. Such oscillations are highly unwanted from a safety and a ride-comfort perspective. In this paper we conduct a study into the occurrence of shimmy oscillations in a main landing gear (MLG) of a typical midsize passenger aircraft. Such a gear is characterized by a main strut attached to the wing spar with a side-stay that connects the main strut to an attachment point closer to the fuselage center line. Nonlinear equations of motion are developed for the specific case of a two-wheeled M...

Experimental analysis and modeling of limit cycles in a dynamic wind-tunnel rig

Large-amplitude self-sustaining periodic oscillations have been observed in an unforced pitch-axis single-degree-of-freedom dynamic wind-tunnel rig. These limit-cycle oscillations and the associated bifurcations are caused by aerodynamic phenomena and have been studied by constructing experimental bifurcation diagrams, where a system parameter (horizontal tailplane deflection) is varied quasi statically and the steady-state response of the system recorded. An innovative strategy based on these bifurcation diagrams is then used to identify a mathematical model of the rig aerodynamics over a wide operating region

Numerical Continuation Applied to Landing Gear Mechanism Analysis

A method of investigating quasi-static mechanisms is presented and applied to an overcenter mechanism and to a nose landing gear mechanism. The method uses static equilibrium equations along with equations describing the geometric constraints in the mechanism. In the spirit of bifurcation analysis, solutions to these steady-state equations are then continued numerically in parameters of interest. Results obtained from the bifurcation method agree with the equivalent results obtained from two overcenter mechanism dynamic models (one state-space and one multibody dynamic model), while a considerable computation time reduction is demonstrated with the overcenter mechanism. The analysis performed with the nose landing gear model demonstrates the flexibility of the continuation approach, allowing conventional model states to be used as continuation parameters without a need to reformulate the equations within the model. This flexibility, coupled with the computation time reductions, suggests that the bifurcation approach has potential for analyzing complex landing gear mechanisms.

Operational Parameter Study of Aircraft Dynamics on the Ground

The dynamics of passenger aircraft on the ground are influenced by the nonlinear characteristics of several components, including geometric nonlinearities, aerodynamics, and interactions at the tire-ground interface. We present a fully parameterized mathematical model of a typical passenger aircraft that includes all relevant nonlinear effects. The full equations of motion are derived from first principles in terms of forces and moments acting on a rigid airframe, and they include implementations of the local models of individual components. The overall model has been developed from and validated against an existing industry-tested SIMMECHANICS model. The key advantage of the mathematical model is that it allows for comprehensive studies of solutions and their stability with methods from dynamical systems theory, particularly, the powerful tool of numerical continuation. As a concrete example, we present a bifurcation study of how fixed-radius turning solutions depend on the aircrafts steering angle and center of gravity position. These results are represented in a compact form as surfaces of solutions, on which we identify regions of stable turning and regions of laterally unstable solutions. The boundaries between these regions are computed directly, and they allow us to determine ranges of parameter values for safe operation. The robustness of these results under the variation in additional parameters, specifically, the engine thrust and aircraft mass, are investigated. Qualitative changes in the structure of the solutions are identified and explained in detail. Overall our results give a complete description of the possible turning dynamics of the aircraft in dependence on four parameters of operational relevance.

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

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...