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NASA NTRS1999

Feasibility of Decentralized Linear-Quadratic-Gaussian Control of Autonomous Distributed Spacecraft

A distributed satellite formation, modeled as an arbitrary number of fully connected nodes in a network, could be controlled using a decentralized controller framework that distributes operations in parallel over the network. For such problems, a solution that minimizes data transmission requirements, in the context of linear-quadratic-Gaussian (LQG) control theory, was given by Speyer. This approach is advantageous because it is non-hierarchical, detected failures gracefully degrade system performance, fewer local computations are required than for a centralized controller, and it is optimal with respect to the standard LQG cost function. Disadvantages of the approach are the need for a fully connected communications network, the total operations performed over all the nodes are greater than for a centralized controller, and the approach is formulated for linear time-invariant systems. To investigate the feasibility of the decentralized approach to satellite formation flying, a simple centralized LQG design for a spacecraft orbit control problem is adapted to the decentralized framework. The simple design uses a fixed reference trajectory (an equatorial, Keplerian, circular orbit), and by appropriate choice of coordinates and measurements is formulated as a linear time-invariant system.

Carpenter, J. Russell↗

NASA NTRS2015

Optimization for Load Alleviation of Truss-Braced Wing Aircraft with Variable Camber Continuous Trailing Edge Flap

This paper focuses on load alleviation optimization for a high aspect ratio truss braced wing (TBW) aircraft. The TBW aircraft model is based on the Subsonic Ultra Green Aircraft Research (SUGAR) concept developed by Boeing, with the wing structures of the model modified to include a novel aerodynamic control surface known as the Variable Camber Continuous Trailing Edge Flap (VCCTEF). The purpose of the study is to investigate the effectiveness of a Performance Adaptive Aeroelastic Wing (PAAW) technology, specifically the VCCTEF, for alleviating load on the TBW wing during flight maneuver. The specific flight maneuver under consideration in this study is a 2.5g pull-up maneuver. Constrained gradient-based optimization is conducted to tailor the deflections of the VC- CTEF such that bending moment along the wing is minimized at the 2.5g pull-up flight condition. Aerodynamic modeling for this study is conducted using a vortex-lattice method code called Vorlax. A non-linear finite element analysis (FEA) method is constructed for analyzing the structural deformation and resulting bending moment along the wing of the aircraft with the inclusion of effects from tension-stiffening due to axial loading in the truss. This study is the first phase of several, and involves optimization of a rigid wing aircraft for preliminary analysis. Future studies will incorporate flexible wing structures with aeroelastic interactions and deformations. The results of this first phase positively demonstrate the potential of utilizing the novel control surface on modern aircraft wing designs for shaping control in order to provide load alleviation during flight maneuver.

Lebofsky, Sonia↗

NASA NTRS2015

Progress Towards Improved Analysis of TES X-ray Data Using Principal Component Analysis

The traditional method of applying a digital optimal filter to measure X-ray pulses from transition-edge sensor (TES) devices does not achieve the best energy resolution when the signals have a highly non-linear response to energy, or the noise is non-stationary during the pulse. We present an implementation of a method to analyze X-ray data from TESs, which is based upon principal component analysis (PCA). Our method separates the X-ray signal pulse into orthogonal components that have the largest variance. We typically recover pulse height, arrival time, differences in pulse shape, and the variation of pulse height with detector temperature. These components can then be combined to form a representation of pulse energy. An added value of this method is that by reporting information on more descriptive parameters (as opposed to a single number representing energy), we generate a much more complete picture of the pulse received. Here we report on progress in developing this technique for future implementation on X-ray telescopes. We used an 55Fe source to characterize Mo/Au TESs. On the same dataset, the PCA method recovers a spectral resolution that is better by a factor of two than achievable with digital optimal filters.

Low-temperature detectors A[center dot] Transition↗

NASA NTRSDate not supplied

Parametric Mechanism Design Through Numerical Optimization and Physics Simulation

Design-Build-Test approaches for developing spaceflight hardware are prohibitively time and cost intensive and often lead to suboptimal mechanism designs. Approaches that couple machine learning and high-fidelity physics simulation could eliminate the need for hardware prototyping and dramatically accelerate the engineering design cycle, ultimately reducing cost. This work presents a modular NASA-developed toolchain to optimize hardware mechanisms in a virtual environment using numerical optimization and multi-body physics simulation. The toolchain enables multi-objective optimization, generates parametric CAD files that can be further post-processed by an end user, and can be expanded to optimize full systems and non-mechanical parameters such as feedback control variables. We demonstrate the toolchain through an independently verifiable design problem that optimizes wheel radius to achieve a desired linear velocity in a rigid-body physics environment when the wheel rotates at a constant angular speed, and then post-process the parametric CAD file of the optimal design generated by the tool before ultimately manufacturing it via 3D printing. We end with a discussion of how the toolchain can incorporate other analysis tools, including finite element analysis, computational fluid dynamics, and granular media simulations.

Optimization↗

NASA NTRSDate not supplied

An Optimization-Based Toolchain for Parametric Mechanism Design

Optimization↗

NASA NTRSDate not supplied

A Nonlinear Schur Complement Solver for CFD-Based Multidisciplinary Models

CFD-based multidisciplinary models are the fundamental building blocks of multidis- ciplinary design optimization frameworks. Linear and nonlinear solutions of these coupled models are difficult, especially when the Jacobian matrices represent a saddle point problem, where a block-diagonal corresponding to a discipline is non-invertible. These scenarios necessitate the use of a coupled solver algorithm such as the Newton’s method instead of the popular block Gauss– Seidel-based methods because of this non-invertible block. To address this challenge, we introduce a nonlinear Schur complement solver suitable for CFD-based multidisciplinary models. The solver leverages the specialized linear and nonlinear solvers of the CFD code, and therefore, does not require the solution of a large coupled linear system as the coupled Newton’s method. Further- more, because the solver primarily uses the specialized linear and nonlinear solvers of the CFD code, it does not suffer from the same robustness limitations as the coupled Newton’s method. In this work, we will implement this solver in NASA’s OpenMDAO framework and demonstrate its effectiveness using a CFD-based aeropropulsive model. The solver will contribute to the develop- ment of aeropropulsive design optimization and CFD-based design optimization methods with the ultimate goal of accelerating the design and integration of advanced propulsion systems.

Nonlinear Solvers↗

NASA NTRS2005

Experimental Feedback Control of Flow Induced Cavity Tones

Discrete-time, linear quadratic methods were used to design feedback controllers for reducing tones generated by flow over a cavity. The dynamics of a synthetic jet actuator mounted at the leading edge of the cavity as observed by two microphones in the cavity were modeled over a broad frequency range using state space models computed from experimental data. Variations in closed loop performance as a function of model order, control order, control bandwidth, and state estimator design were studied using a cavity in the Probe Calibration Tunnel at NASA Langley. The controller successfully reduced the levels of multiple cavity tones at the tested flow speeds of Mach 0.275, 0.35, and 0.45. In some cases, the closed loop results were limited by excitation of sidebands of the cavity tones, or the creation of new tones at frequencies away from the cavity tones. Nonetheless, the results validate the combination of optimal control and experimentally-generated state space models, and suggest this approach may be useful for other flow control problems. The models were not able to account for non-linear dynamics, such as interactions between tones at different frequencies.

Cabell, Randolph H.↗

NASA NTRS2020

Pterodactyl: Development and Comparison of Control Architectures for a Mechanically Deployed Entry Vehicle

The Pterodactyl project, seeks to advance the current state-of-the-art for entry vehicles by developing novel guidance and control technologies for Deployable Entry Vehicles (DEVs) that can be applied to various entry vehicle configurations. This paper details the efforts on the NASA-funded Pterodactyl project to investigate and implement multiple control techniques for an asymmetric mechanical DEV. We design multiple control architectures for a Pterodactyl Baseline Vehicle (PBV) and evaluate their performance in achieving varying guidance commands during entry. The control architectures studied are (i) propulsive control systems such as reaction control systems and (ii) non-propulsive control systems such as aerodynamic control surfaces and internal moving masses. For each system, state-feedback integral controllers based on linear quadratic regulator (LQR) optimal control methods are designed to track guidance commands of either (i) bank angle or (ii) angle of attack and sideslip angle as determined by the desired guidance trajectory. All control systems are compared for a lunar return reference mission and by providing a comparative analysis of these systems, configurations, and performance, the efforts detailed in this paper and the Pterodactyl project as a whole will help entry vehicle system designers determine suitable control architectures for integration with DEVs and other entry vehicle types.

Okolo, Wendy A.↗

NASA NTRS1966

Estimation of the state of a nonlinear process in the presence of nongaussian noise and disturbances.

Optimum estimate of nonlinear process in presence of non-Gaussian noise and disturbances, deriving algorithm for correcting approximation

OPTIMIZATION↗

NASA NTRS2002

Transient Vibration Prediction for Rotors on Ball Bearings Using Load-dependent Non-linear Bearing Stiffness

Rolling-element bearing forces vary nonlinearly with bearing deflection. Thus an accurate rotordynamic transient analysis requires bearing forces to be determined at each step of the transient solution. Analyses have been carried out to show the effect of accurate bearing transient forces (accounting for non-linear speed and load dependent bearing stiffness) as compared to conventional use of average rolling-element bearing stiffness. Bearing forces were calculated by COBRA-AHS (Computer Optimized Ball and Roller Bearing Analysis - Advanced High Speed) and supplied to the rotordynamics code ARDS (Analysis of Rotor Dynamic Systems) for accurate simulation of rotor transient behavior. COBRA-AHS is a fast-running 5 degree-of-freedom computer code able to calculate high speed rolling-element bearing load-displacement data for radial and angular contact ball bearings and also for cylindrical and tapered roller beatings. Results show that use of nonlinear bearing characteristics is essential for accurate prediction of rotordynamic behavior.

Fleming, David P.↗

NASA NTRS1978

Optimal control of a supersonic inlet to minimize frequency of inlet unstart

A preliminary investigation into the use of modern control theory for the design of controls for a supersonic inlet is described. In particular, the task of controlling a mixed-compression supersonic inlet is formulated as a linear optimal stochastic control and estimation problem. An inlet can exhibit an undesirable instability due to excessive inlet normal shock motion. For the optimal control formulation of the inlet problem, a non quadratic performance index, which is equal to the expected frequency of inlet unstarts, is used. This physically meaningful performance index is minimized for a range of inlet disturbance and measurement noise covariances.

Lehtinen, B.↗

NASA NTRS1991

Two Point Exponential Approximation Method for structural optimization of problems with frequency constraints

The point exponential approximation method was introduced by Fadel et al. (Fadel, 1990), and tested on structural optimization problems with stress and displacement constraints. The reports in earlier papers were promising, and the method, which consists of correcting Taylor series approximations using previous design history, is tested in this paper on optimization problems with frequency constraints. The aim of the research is to verify the robustness and speed of convergence of the two point exponential approximation method when highly non-linear constraints are used.

Fadel, G. M.↗

NASA NTRS2011

On Time Delay Margin Estimation for Adaptive Control and Optimal Control Modification

This paper presents methods for estimating time delay margin for adaptive control of input delay systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent an adaptive law by a locally bounded linear approximation within a small time window. The time delay margin of this input delay system represents a local stability measure and is computed analytically by three methods: Pade approximation, Lyapunov-Krasovskii method, and the matrix measure method. These methods are applied to the standard model-reference adaptive control, s-modification adaptive law, and optimal control modification adaptive law. The windowing analysis results in non-unique estimates of the time delay margin since it is dependent on the length of a time window and parameters which vary from one time window to the next. The optimal control modification adaptive law overcomes this limitation in that, as the adaptive gain tends to infinity and if the matched uncertainty is linear, then the closed-loop input delay system tends to a LTI system. A lower bound of the time delay margin of this system can then be estimated uniquely without the need for the windowing analysis. Simulation results demonstrates the feasibility of the bounded linear stability method for time delay margin estimation.

Nguyen, Nhan T.↗

NASA NTRS2001

Computationally efficient control allocation

A computationally efficient method for calculating near-optimal solutions to the three-objective, linear control allocation problem is disclosed. The control allocation problem is that of distributing the effort of redundant control effectors to achieve some desired set of objectives. The problem is deemed linear if control effectiveness is affine with respect to the individual control effectors. The optimal solution is that which exploits the collective maximum capability of the effectors within their individual physical limits. Computational efficiency is measured by the number of floating-point operations required for solution. The method presented returned optimal solutions in more than 90% of the cases examined; non-optimal solutions returned by the method were typically much less than 1% different from optimal and the errors tended to become smaller than 0.01% as the number of controls was increased. The magnitude of the errors returned by the present method was much smaller than those that resulted from either pseudo inverse or cascaded generalized inverse solutions. The computational complexity of the method presented varied linearly with increasing numbers of controls; the number of required floating point operations increased from 5.5 i, to seven times faster than did the minimum-norm solution (the pseudoinverse), and at about the same rate as did the cascaded generalized inverse solution. The computational requirements of the method presented were much better than that of previously described facet-searching methods which increase in proportion to the square of the number of controls.

Durham, Wayne↗

NASA NTRS2001

Integrated Modeling for the Next Generation Space Telescope "Yardstick" Concept

The so-called NASA "Yardstick" design concept for the Next Generation Space Telescope presents unique challenges for systems-level analysis. Simulations that integrate controls, optics, thermal, and structural models are required to evaluate baseline performance, study design sensitivities, and perform design optimization. An integrated modeling approach was chosen using a combination of commercial off-the-shelf and "in-house" developed codes. The resulting capability provides a foundation for linear and non-linear analysis, using both the time and frequency-domain methods. It readily allows various combinations of design parameters and environmental loads to be evaluated directly in terms of key science-related metrics, in this case the scalar RMS (root mean square) line-of-sight and RMS wavefront errors. This presentation first addresses the development of the component, or discipline, models for the Yardstick design. It will then proceed to present the integration of the component models, using linear-systems approaches, in order to support two of the most critical baseline performance analyses: jitter and thermal-elastic stability of the optical telescope assembly (OTA). The results of the jitter analysis indicate that disturbances from the reaction wheels coupled with the lightly-damped and highly-flexible structure present significant challenges to the baseline line-of-sight control architecture. Vibration isolation will be required to meet jitter error requirements. The results of the thermal-elastic analysis indicate that the mirror segment displacements due to ground-to-orbit cool-down of the telescope are within the expected capture range of the segment rigid-body control actuators. This means we will be able to align and phase the primary mirror. However, the results for the analysis of the thermal transient response following an attitude maneuver (slew) show that this telescope design is not sufficiently stable, passively, to meet the wavefront error requirements. Structural re-design is one possibility; alternatively, active thermal control of the OTA may be considered. The Yardstick integrated models were successfully used to demonstrate the feasibility of two thermal control strategies.

Mosier, Gary E.↗

NASA NTRS1995

Non-LTE line-blanketed model atmospheres of hot stars. 1: Hybrid complete linearization/accelerated lambda iteration method

A new munerical method for computing non-Local Thermodynamic Equilibrium (non-LTE) model stellar atmospheres is presented. The method, called the hybird complete linearization/accelerated lambda iretation (CL/ALI) method, combines advantages of both its constituents. Its rate of convergence is virtually as high as for the standard CL method, while the computer time per iteration is almost as low as for the standard ALI method. The method is formulated as the standard complete lineariation, the only difference being that the radiation intensity at selected frequency points is not explicity linearized; instead, it is treated by means of the ALI approach. The scheme offers a wide spectrum of options, ranging from the full CL to the full ALI method. We deonstrate that the method works optimally if the majority of frequency points are treated in the ALI mode, while the radiation intensity at a few (typically two to 30) frequency points is explicity linearized. We show how this method can be applied to calculate metal line-blanketed non-LTE model atmospheres, by using the idea of 'superlevels' and 'superlines' introduced originally by Anderson (1989). We calculate several illustrative models taking into accont several tens of thosands of lines of Fe III to Fe IV and show that the hybrid CL/ALI method provides a robust method for calculating non-LTE line-blanketed model atmospheres for a wide range of stellar parameters. The results for individual stellar types will be presented in subsequent papers in this series.

Hubeny, I.↗

NASA NTRS2017

Switching State-Feedback LPV Control with Uncertain Scheduling Parameters

This paper presents a new method to design Robust Switching State-Feedback Gain-Scheduling (RSSFGS) controllers for Linear Parameter Varying (LPV) systems with uncertain scheduling parameters. The domain of scheduling parameters are divided into several overlapped subregions to undergo hysteresis switching among a family of simultaneously designed LPV controllers over the corresponding subregion with the guaranteed H-infinity performance. The synthesis conditions are given in terms of Parameterized Linear Matrix Inequalities that guarantee both stability and performance at each subregion and associated switching surfaces. The switching stability is ensured by descent parameter-dependent Lyapunov function on switching surfaces. By solving the optimization problem, RSSFGS controller can be obtained for each subregion. A numerical example is given to illustrate the effectiveness of the proposed approach over the non-switching controllers.

Switching LPV control↗

NASA NTRS2020

Squash-Box Feasibility Driven Differential Dynamic Programming

Recently, Differential Dynamic Programming (DDP) and other similar algorithms have become the solvers of choice when performing non-linear Model Predictive Control (nMPC) with modern robotic devices. The reason is that they have a lower computational cost per iteration when compared with off-the-shelf Non-Linear Programming (NLP) solvers, which enables its online operation. However, they cannot handle constraints, and are known to have poor convergence capabilities. In this paper, we propose a method to solve the optimal control problem with control bounds through a squashing function (i.e., a sigmoid, which is bounded by construction). It has been shown that a naive use of squashing functions damage the convergence rate. To tackle this, we first propose to add a quadratic barrier that avoids the difficulty of the plateau produced by the sigmoid. Second, we add an outer loop that adapts both the sigmoid and the barrier; it makes the optimal control problem with the squashing function converge to the original control-bounded problem. To validate our method, we present simulation results for different types of platforms including a multi-rotor, a biped, a quadruped and a humanoid robot.

Navarro, Angel Santamaria↗