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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records

Short-time Lyapunov exponent analysis

A new technique for analyzing complicated fluid flows in numerical simulations has been successfully tested. The analysis uses short time Lyapunov exponent contributions and the associated Lyapunov perturbation fields. A direct simulation of the Taylor-Couette flow just past the onset of chaos demonstrated that this new technique marks important times during the system evolution and identifies the important flow features at those times. This new technique will now be applied to a 'minimal' turbulent channel.

Vastano, J. A.↗

Short-time Lyapunov exponent analysis and the transition to chaos in Taylor-Couette flow

The physical mechanism driving the weakly chaotic Taylor-Couette flow is investigated using the short-time Liapunov exponent analysis. In this procedure, the transition from quasi-periodicity to chaos is studied using direct numerical 3D simulations of axially periodic Taylor-Couette flow, and a partial Liapunov exponent spectrum for the flow is computed by simultaneously advancing the full solution and a set of perturbations. It is shown that the short-time Liapunov exponent analysis yields more information on the exponents and dimension than that obtained from the common Liapunov exponent calculations. Results show that the chaotic state studied here is caused by a Kelvin-Helmholtz-type instability of the outflow boundary jet of Taylor vortices.

Vastano, John A.↗

Sensitivity analysis of Lyapunov and Riccati equations with application to controls-structures integrated design

Controls-structure integrated design is a complicated multidisciplinary design optimization problem which involves the state equations pertaining to open-loop eigenvalues and control laws. In order to alleviate the intensity of the computation, this study uses the adjoint variable method to derive sensitivity equations for the eigenvalue, Liapunov, and Riccati equations. These individual sensitivity equations are then combined together to form the multidisciplinary sensitivity equations for the control structure integrated design problems. A set of linear sensitivity equations, proportional in number to the number of performance functions involved in the optimization process, are solved. This proposed approach may provide a great saving in computer resources. The validity of the newly developed sensitivity equations is verified by numerical examples.

Hou, Gene↗

Optimal Variable-Structure Control Tracking of Spacecraft Maneuvers

An optimal control approach using variable-structure (sliding-mode) tracking for large angle spacecraft maneuvers is presented. The approach expands upon a previously derived regulation result using a quaternion parameterization for the kinematic equations of motion. This parameterization is used since it is free of singularities. The main contribution of this paper is the utilization of a simple term in the control law that produces a maneuver to the reference attitude trajectory in the shortest distance. Also, a multiplicative error quaternion between the desired and actual attitude is used to derive the control law. Sliding-mode switching surfaces are derived using an optimal-control analysis. Control laws are given using either external torque commands or reaction wheel commands. Global asymptotic stability is shown for both cases using a Lyapunov analysis. Simulation results are shown which use the new control strategy to stabilize the motion of the Microwave Anisotropy Probe spacecraft.

John L. Crassidis↗

A Coupled Nonlinear Spacecraft Attitude Controller and Observer with an Unknown Gyro Misalignment and Gyro Bias

A nonlinear control scheme for attitude control of a spacecraft is combined with a nonlinear gyro misalignment and bias observer for the case of constant gyro misalignment and bias. A persistency of excitation analysis shows the observer gyro bias estimates converge to the true bias values exponentially fast. The convergence of the misalignment estimates is also presented. Then; the resulting coupled, closed loop dynamics are proven by a Lyapunov analysis to be globally stable, with asymptotically perfect tracking. The analysis is extended to consider the effects of noise in addition to the gyro misalignment and bias. A simulation of the proposed observer-controller design is given for a rigid spacecraft tracking a specified, time-varying attitude sequence to illustrate the theoretical claims.

Thienel, Julie↗

A Nonlinear, Six-Degree of Freedom Precision Formation Control Algorithm, Based on Restricted Three Body Dynamics

Precision Formation Flying is an enabling technology for a variety of proposed space-based observatories, including the Micro-Arcsecond X-ray Imaging Mission (MAXIM), the associated MAXIM pathfinder mission, and the Stellar Imager. An essential element of the technology is the control algorithm. This paper discusses the development of a nonlinear, six-degree of freedom (6DOF) control algorithm for maintaining the relative position and attitude of a spacecraft within a formation. The translation dynamics are based on the equations of motion for the restricted three body problem. The control law guarantees the tracking error convergences to zero, based on a Lyapunov analysis. The simulation, modelled after the MAXIM Pathfinder mission, maintains the relative position and attitude of a Follower spacecraft with respect to a Leader spacecraft, stationed near the L2 libration point in the Sun-Earth system.

Bauer, Frank↗

Adaptive Control for Linear Uncertain Systems with Unmodeled Dynamics Revisited via Optimal Control Modification

This paper presents the optimal control modification for linear uncertain plants. The Lyapunov analysis shows that the modification parameter has a limiting value depending on the nature of the uncertainty. The optimal control modification exhibits a linear asymptotic property that enables it to be analyzed in a linear time invariant framework for linear uncertain plants. The linear asymptotic property shows that the closed-loop plants in the limit possess a scaled input-output mapping. Using this property, we can derive an analytical closed-loop transfer function in the limit as the adaptive gain tends to infinity. The paper revisits the Rohrs counterexample problem that illustrates the nature of non-robustness of model-reference adaptive control in the presence of unmodeled dynamics. An analytical approach is developed to compute exactly the modification parameter for the optimal control modification that stabilizes the plant in the Rohrs counterexample. The linear asymptotic property is also used to address output feedback adaptive control for non-minimum phase plants with a relative degree 1.

Unmodeled Dynamics↗

Shape Servoing of Deformable Objects using Adaptive Deformation Model Estimation

In this paper, we propose an adaptive shape servoing method to deform a soft object into a desired 3-D shape. The high dimensional representation and the unknown deformation properties of the soft object pose a challenge to actively manipulate its shape. To address this issue, we develop a method to compute the deformation Jacobian matrix in real-time. The Jacobian is estimated using a set of basis functions and its corresponding parameters to capture the dynamics of the system and relate the applied input motion to changes in the soft object's shape. An integral concurrent learning (ICL) based adaptive update law is derived using Lyapunov analysis to estimate the deformation parameters and prove its convergence. A physics-based simulation is used to validate the proposed method and controller by performing manipulation tasks with different desired configurations. The performance is compared with a standard gradient update law to demonstrate the accuracy and robustness of our approach.

Vrithik Raj Guthikonda↗

Passive Roll Stabilization of the Near Earth Asteroid Scout Solar Sail Mission

The Near Earth Asteroid (NEA) Scout is a small satellite, solar sail mission set to launch on Artemis I. Analysis of the NEA Scout solar radiation pressure model determined that, for certain solar incidence angles, there exists at least one locally stable equilibrium point about the “roll” axis, or the axis normal to the solar sail plane. This analysis is extended to three other geometrically similar solar sail models, and a Lyapunov stability analysis is conducted demonstrating that the stable equilibria are locally stable for the majority of roll angles in a wide range of solar incidence angles. Under certain assumptions, it is possible that only two axis control is required for non-spinning solar sails. If the roll axis is controlled, an active rate damping controller can be designed to asymptotically stabilize the system. Simulation results are presented that follow the stability analysis, where in the homogenous case, the system enters a limit cycle and, in the actively damped case, the system asymptotically converges to the equilibrium point.

Ivan Rodrigues Bertaska↗

Parameter Transient Behavior Analysis on Fault Tolerant Control System

In a fault tolerant control (FTC) system, a parameter varying FTC law is reconfigured based on fault parameters estimated by fault detection and isolation (FDI) modules. FDI modules require some time to detect fault occurrences in aero-vehicle dynamics. This paper illustrates analysis of a FTC system based on estimated fault parameter transient behavior which may include false fault detections during a short time interval. Using Lyapunov function analysis, the upper bound of an induced-L2 norm of the FTC system performance is calculated as a function of a fault detection time and the exponential decay rate of the Lyapunov function.

Belcastro, Christine↗

Neural Network Based Modeling and Analysis of LP Control Surface Allocation

This paper presents an approach to interpretive modeling of LP based control allocation in intelligent flight control. The emphasis is placed on a nonlinear interpretation of the LP allocation process as a static map to support analytical study of the resulting closed loop system, albeit in approximate form. The approach makes use of a bi-layer neural network to capture the essential functioning of the LP allocation process. It is further shown via Lyapunov based analysis that under certain relatively mild conditions the resulting closed loop system is stable. Some preliminary conclusions from a study at Ames are stated and directions for further research are given at the conclusion of the paper.

Langari, Reza↗

Development of An Intelligent Flight Propulsion Control System

The initial design and demonstration of an Intelligent Flight Propulsion and Control System (IFPCS) is documented. The design is based on the implementation of a nonlinear adaptive flight control architecture. This initial design of the IFPCS enhances flight safety by using propulsion sources to provide redundancy in flight control. The IFPCS enhances the conventional gain scheduled approach in significant ways: (1) The IFPCS provides a back up flight control system that results in consistent responses over a wide range of unanticipated failures. (2) The IFPCS is applicable to a variety of aircraft models without redesign and,(3) significantly reduces the laborious research and design necessary in a gain scheduled approach. The control augmentation is detailed within an approximate Input-Output Linearization setting. The availability of propulsion only provides two control inputs, symmetric and differential thrust. Earlier Propulsion Control Augmentation (PCA) work performed by NASA provided for a trajectory controller with pilot command input of glidepath and heading. This work is aimed at demonstrating the flexibility of the IFPCS in providing consistency in flying qualities under a variety of failure scenarios. This report documents the initial design phase where propulsion only is used. Results confirm that the engine dynamics and associated hard nonlineaaities result in poor handling qualities at best. However, as demonstrated in simulation, the IFPCS is capable of results similar to the gain scheduled designs of the NASA PCA work. The IFPCS design uses crude estimates of aircraft behaviour. The adaptive control architecture demonstrates robust stability and provides robust performance. In this work, robust stability means that all states, errors, and adaptive parameters remain bounded under a wide class of uncertainties and input and output disturbances. Robust performance is measured in the quality of the tracking. The results demonstrate the flexibility of the IFPCS architecture and the ability to provide robust performance under a broad range of uncertainty. Robust stability is proved using Lyapunov like analysis. Future development of the IFPCS will include integration of conventional control surfaces with the use of propulsion augmentation, and utilization of available lift and drag devices, to demonstrate adaptive control capability under a greater variety of failure scenarios. Further work will specifically address the effects of actuator saturation.

Calise, A. J.↗

MRAC with Time-Varying Reference Model from Convex Combination

An extension of model reference adaptive control is presented that accommodates use of a time-varying reference model. Specifically, the reference model is taken to be a time-varying convex combination of two linear, time-invariant models. The design is intended to act as a way to smoothly transition between two different reference models without resorting to a scheduled switch. It also provides the ability to use an interpolated reference model when the plant is operating between design points. The time variation of the combination must satisfy some requirements to ensure stability but is otherwise user choice. Subject to these requirements, bounded tracking error behavior is demonstrated via Lyapunov stability analysis for the single-input, single-output, output feedback case. Tracking error convergence is asymptotic when time variation ceases. The proposed design is demonstrated in simulation of a numerical model.

Hashemi, Kelley E.↗

Simultaneous Trajectory Tracking Control and Online Mass Estimation for a Regolith Excavating Robot via Integral Concurrent Learning

An adaptive controller is developed for a regolith excavation robot to determine the mass of excavated material and to account for the effects of gravity and friction while on the surface of other celestial bodies. A data-based integral concurrent learning (ICL) parameter update law accounts for and estimates the unknown mass, gravity, and friction parameters. A Lyapunov-based analysis proves that the trajectory tracking error and the parameter estimate errors exponentially converge to zero. An estimation of the mass of regolith excavated by the robot is calculated from the estimated parameters. A simulation study is performed to show the performance of the developed technique. Simulation results show that for 3 kilograms of excavated material, the mass estimate has an error of 4.9 grams.

Max L. Greene↗

Shape Servoing of Deformable Objects Using Model Estimation and Barrier Lyapunov Function

An adaptive shape servoing control method is presented in this article to manipulate a deformable object into a desired shape in 3-D. A finite-point-based representation of the deformable object is used and the deformation Jacobian matrix is approximated using Fourier series basis functions. The unknown parameters of the deformation Jacobian are learned by using the velocity applied to a control point on the object and corresponding change of positions of the points describing the entire object. An integral concurrent learning (ICL)-based parameter update law is designed along with a constrained controller to satisfy the state constraints on the motion of the control point using Barrier Lyapunov function analysis. ICL-based parameter update law uses data history of velocity and corresponding positions of the points along with their current values. An efficient algorithm to update the history stack using singular value maximization is proposed based on the structure of the regressor matrix. Simulations using a physical simulator and experiments using a robot platform are performed to validate the performance of the proposed controller on two different deformable objects.

Vrithik Raj Guthikonda↗

A unified perspective on robot control - The energy Lyapunov function approach

A unified framework for the stability analysis of robot tracking control is presented. By using an energy-motivated Lyapunov function candidate, the closed-loop stability is shown for a large family of control laws sharing a common structure of proportional and derivative feedback and a model-based feedforward. The feedforward can be zero, partial or complete linearized dynamics, partial or complete nonlinear dynamics, or linearized or nonlinear dynamics with parameter adaptation. As result, the dichotomous approaches to the robot control problem based on the open-loop linearization and nonlinear Lyapunov analysis are both included in this treatment. Furthermore, quantitative estimates of the trade-offs between different schemes in terms of the tracking performance, steady state error, domain of convergence, realtime computation load and required a prior model information are derived.

Wen, John T.↗

Evaluating the Stability of NASA's Space Launch System with Adaptive Augmenting Control

NASA's baseline Space Launch System (SLS) flight control system (FCS) design includes an adaptive augmenting control (AAC) component that modifies the attitude control system response to provide the classical gain-scheduled control architecture with additional performance and robustness. The NASA Engineering and Safety Center (NESC) teamed with the Space Launch System (SLS) Program to perform a comprehensive assessment of the stability and robustness of the FCS with AAC. This paper provides an overview of the approach, specific analysis techniques, and outcomes that were particularly relevant for the SLS Program. Multiple analysis techniques that specifically target the nonlinear AAC were commissioned as part of this assessment, which was completed outside of the Program's standard design analysis cycle. The following analyses were included, with each technique adding its own valuable insights: Lyapunov-based stability analysis, classical stability analysis with static AAC gain variations, circle criterion-based analysis of the FCS with a time-varying element, time-domain stability margin assessment, Monte Carlo simulations with expanded dispersions, and an extensive set of stressing cases. Several of the completed analyses focused on determining whether the inclusion of AAC introduced risk to the FCS, while others quantified the benefits of the adaptive augmentation.

Tannen S Vanzwieten↗

Comparison of continuous and discrete adaptive identification algorithms

Discretization of a popular continuous-time control algorithm is effected and an equivalent discrete-time identification law developed and compared to a published discrete identification algorithm developed from Lyapunov Theory. Results are compared as regards asymptotic stability as insured using Lyapunov theory. Some analysis and design guidelines are proposed as regards implementation and practical utility.

Colburn, B. K.↗