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Success Stories in Control: Nonlinear Dynamic Inversion Control

NASA plays an important role in advancing the state of the art in flight control systems. In the case of Nonlinear Dynamic Inversion (NDI) NASA supported initial implementation of the theory in an aircraft and demonstration in a space vehicle. Dr. Dale Enns of Honeywell Aerospace Advanced Technology performed this work in cooperation with NASA and under NASA contract. Honeywell and Lockheed Martin were subsequently contracted by AFRL to create "Design Guidelines for Multivariable Control Theory". This foundational work directly contributed to the advancement of the technology and the credibility of the control law as a design option. As a result Honeywell collaborated with Lockheed Martin to produce a Nonlinear Dynamic Inversion controller for the X-35 and subsequently Lockheed Martin did the same for the production Lockheed Martin F-35 vehicle. The theory behind NDI is to use a systematic generalized approach to controlling a vehicle. Using general aircraft nonlinear equations of motion and onboard aerodynamic, mass properties, and engine models specific to the vehicle, a relationship between control effectors and desired aircraft motion can be formulated. Using this formulation a control combination is used that provides a predictable response to commanded motion. Control loops around this formulation shape the response as desired and provide robustness to modeling errors. Once the control law is designed it can be used on a similar class of vehicle with only an update to the vehicle specific onboard models.

Bosworth, John T.

Nonlinear dynamic theory for photorefractive phase hologram formation

A nonlinear dynamic theory is developed for the formation of photorefractive volume phase holograms. A feedback mechanism existing between the photogenerated field and free-electron density, treated explicitly, yields the growth and saturation of the space-charge field in a time scale characterized by the coupling strength between them. The expression for the field reduces in the short-time limit to previous theories and approaches in the long-time limit the internal or photovoltaic field. Additionally, the phase of the space charge field is shown to be time-dependent.

Kim, D. M.

Nonlinear dynamics in cardiac conduction

Electrical conduction in the heart shows many phenomena familiar from nonlinear dynamics. Among these phenomena are multiple basins of attraction, phase locking, and perhaps period-doubling bifurcations and chaos. We describe a simple cellular-automation model of electrical conduction which simulates normal conduction patterns in the heart as well as a wide range of disturbances of heart rhythm. In addition, we review the application of percolation theory to the analysis of the development of complex, self-sustaining conduction patterns.

NASA Discipline Cardiopulmonary

Nonlinear dynamics of charged particles in the magnetotail

An important region of the earth's magnetosphere is the nightside magnetotail, which is believed to play a significant role in energy storage and release associated with substorms. The magnetotail contains a current sheet which separates regions of oppositely directed magnetic field. Particle motion in the collisionless magnetotail has been a long-standing problem. Recent research from the dynamical point of view has yielded considerable new insights into the fundamental properties of orbits and of particle distribution functions. A new framework of understanding magnetospheric plasma properties is emerging. Some novel predictions based directly on nonlinear dynamics have proved to be robust and in apparent good agreement with observation. The earth's magnetotail may serve as a paradigm, one accessible by in situ observation, of a broad class of boundary regions with embedded current sheets. This article reviews the nonlinear dynamics of charged particles in the magnetotail configuration. The emphasis is on the relationships between the dynamics and physical observables. At the end of the introduction, sections containing basic material are indicated.

Chen, James

Nonlinear dynamics and predictability in the atmospheric sciences

Systematic applications of nonlinear dynamics to studies of the atmosphere and climate are reviewed for the period 1987-1990. Problems discussed include paleoclimatic applications, low-frequency atmospheric variability, and interannual variability of the ocean-atmosphere system. Emphasis is placed on applications of the successive bifurcation approach and the ergodic theory of dynamical systems to understanding and prediction of intraseasonal, interannual, and Quaternary climate changes.

Ghil, M.

Bifurcation techniques for nonlinear dynamic analysis of compressor stall phenomena

Compressor stall phenomena is analyzed from nonlinear control theory viewpoint, based on bifurcation-catastrophe techniques. This new approach appears promising and offers insight into such well known compressor instability problems as surge and rotating stall; furthermore it suggests strategies for recovery from stall. Three interlocking dynamic nonlinear state space models are developed. It is shown that the problem of rotating stall can be viewed as an (induced) bifurcation of solution of the unstalled model. Hysteresis effect is shown to exist in the stall/recovery process. Surge cycles are observed to develop for some critical parameter values. It is shown that the oscillatory behavior is due to development of limit cycles, generated by Hopf bifurcation of solutions. Both stable and unstable limit cycles are observed. To further illustrate the usefulness of the methodology some partial computation of domains of attraction of equilibria is carried out, and parameter sensitivity analysis is performed.

Razavi, H. C.

Nonlinear Dynamic Control Derivative Analysis for Aircraft with Application to Transonic Truss-Braced Wing

This paper presents the development of a nonlinear dynamic control derivative estimation method. A nonlinear aerodynamic model is developed to account for the effects of large control surface deflections on aircraft aerodynamic forces and moments. A series of unsteady RANS CFD simulations is performed to simulate the control surface oscillations at various reduced frequencies. The time-domain data are transformed into the frequency-domain data by a Fourier series analysis. Transfer functions of the dynamic control derivatives are then estimated by a frequency-domain regression. The method is applied to the Transonic Truss-Braced Wing (TTBW) to estimate the dynamic control derivatives for the elevator, aileron, and rudder.

Aircraft Control Derivatives

Finite Element Analysis of the TRUST Nonlinear Dynamics Testbed

This paper builds on prior work conducted within the Los Alamos National Laboratory (LANL) Testbeds to Reduce Uncertainty in Simulations and Tests (TRUST) program. Specifically, it builds on finite element (FE) modeling efforts for the TRUST program’s Nonlinear Dynamics (ND) testbed. Historically, the FE model for the ND testbed has exclusively utilized a Lanczos eigensolver that linearly extracts the system’s natural frequencies. This paper investigates the Abaqus 2024’s explicit dynamic solver, which implements a central difference explicit solver. The central difference method used in Abaqus can capture nonlinear material responses in structural dynamic simulations making it suitable for the ND FE model.

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