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All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Parametric robust control and system identification: Unified approach

Despite significant advancement in the area of robust parametric control, the problem of synthesizing such a controller is still a wide open problem. Thus, we attempt to give a solution to this important problem. Our approach captures the parametric uncertainty as an H(sub infinity) unstructured uncertainty so that H(sub infinity) synthesis techniques are applicable. Although the techniques cannot cope with the exact parametric uncertainty, they give a reasonable guideline to model the unstructured uncertainty that contains the parametric uncertainty. An additional loop shaping technique is also introduced to relax its conservatism.

Keel, Leehyun↗
NASA NTRS2024

Aerothermal Analysis of the Rocket Lab Venus Probe Heatshield

This document provides an overview of the aerothermodynamic analyses performed by the Aerothermodynamics Branch at NASA Langley Research Center for the Rocket Lab Venus Probe (RLVP). In addition to defining the baseline heating environment to the heatshield, this document pursues the experimental validation of key physical models at RLVP-relevant conditions. This experimental validation analysis, which captures the model form uncertainty, is used as one of two primary components of the margin assessment, where the other component is the parametric uncertainty. These model form (experimental) and parametric uncertainty components are used to construct a spatial and time varying margin for the heating to the RLVP heatshield. The margin is evaluated as the sum of the parametric and model form uncertainty components. The model form uncertainty is defined as the difference between the RLVP-relevant measurements and their simulations, using the upper limit uncertainty bounds for both the measurements and simulations in the comparisons. The differences in the dominant physics in the stagnation region and flank lead to the separate RLVP-relevant measurements for assessing the model form uncertainty in these two regions. These regions are addressed as follows: Stagnation Region Heating Environment: For the high-temperature stagnation-region, both the radiative heating and impact of blowing on convective heating are significant, while the impacts of turbulence and roughness are negligible. Coupled radiation and ablation LAURA/HARA solutions with ray-tracing provide the radiative heating over the entire vehicle, including the contributions from the Venus atmosphere and ablation species. Non-ablating LAURA simulations provide the convective heating. During the material-response computation typically used for TPS sizing, this non-ablating convective heating is corrected for the impact of ablation using the blowing correction. Coupled ablation LAURA simulations that capture finite-rate sur-face processes show that this blowing correction may be non-conservative over most of the heatshield. This non-conservatism is due to hydrogen recombination in the finite-rate surface model, which tends to increase the coupled ablation convective heating to near the non-ablating values, therefore making any reduction in the non-ablating value through the blowing correction non-conservative. This non-conservatism due to H catalysis is captured in the parametric component of the margin. The best available ground-test measurements that capture the impact of blowing on stagnation region convective heating, at RLVP-relevant conditions, indicate that the current blowing reduction model is non-conservative by up to 20% at RLVP-relevant blowing rates (the coupled blowing simulations were also non-conservative). Because of the relatively low velocity of the ground tests and the non-Venus atmospheric chemistry, these measurements do not capture the chemistry and therefore do not inform the uncertainty due to H catalysis. However, they do capture the fluid mechanics of blowing. The non-conservatism of the blowing correction implied by these measurements is covered by the model form component of the margin, which leads to total margin values over 50%. For the radiative heating, the shock-tube informed bias approach suggests a model form uncertainty of roughly 20%, while the parametric uncertainty analysis suggests values over 100%. The combined stagnation-point radiation margin of over 100% leads to peak margined radiative heating values of over300 W/cm2, which remains small relative to the peak margined convective heating of nearly 2000 W/cm2. Based on this analysis, at the stagnation point, the peak margined heat rate is 2203 W/cm2 and the margined total heat load is 31.5 kJ/cm2 for the current nominal trajectory. Flank Heating Environment: The forebody flank (and near-shoulder) heating environment is dominated by the impact of turbulence, roughness augmentation, and ablation on the convective heating. An extensive collection of ground test measurements with RLVP-relevant turbulence and roughness is studied to show that the maximum difference between the simulated and measured convective heating is 5%. However, with the exception of the Holden measurements from the 1980s, these measurements do not include roughness elements extending into the supersonic region of the boundary layer, which is likely to occur for RLVP (due to the 45 degree sphere-cone geometry). The interaction between the supersonic flow and roughness could cause convective heating augmentation fundamentally different than for locally subsonic flow. Although these Holden measurements are consistent with the other measurements considered, another path was pursued to assure that the rough-ness height extending into supersonic flow does not fundamentally change the roughness augmentation. This additional path was a computational effort to resolve the roughness elements in the CFD grid, so that the interaction be-tween the roughness elements and locally supersonic flow may be simulated in detail. This roughness-resolved CFD simulation is feasible because of the RLVP forebody TPS’s patterned roughness, which may be approximated analytically, and because of the axisymmetric nominal flow field, which allows a narrow surface region to be simulated and therefore make the computational expense feasible. These grid-resolved roughness simulations, which are performed at actual RLVP flight conditions, result in heating augmentation values that are below the design approach for roughness augmentation. This provides evidence that the design approach for RLVP roughness augmentation is sufficient. Based on this analysis, at this flank or near-shoulder location, the peak margined total heat rate is 2088 W/cm2and the margined total heat load is 26.0 kJ/cm2for the current nominal trajectory. Heat flux, shear, pressure and heat transfer coefficient at the RLVP stagnation point and near shoulder location are evaluated for the entire trajectory, and curved fit to a functional form of F=AρB∞UC∞. These simplified relationships for the nominal and margined aerothermal environments are referred to as aerothermal indicators, and presented at the end of this document.

Christopher O Johnston↗
NASA NTRS2012

Robust Control Design for Uncertain Nonlinear Dynamic Systems

Robustness to parametric uncertainty is fundamental to successful control system design and as such it has been at the core of many design methods developed over the decades. Despite its prominence, most of the work on robust control design has focused on linear models and uncertainties that are non-probabilistic in nature. Recently, researchers have acknowledged this disparity and have been developing theory to address a broader class of uncertainties. This paper presents an experimental application of robust control design for a hybrid class of probabilistic and non-probabilistic parametric uncertainties. The experimental apparatus is based upon the classic inverted pendulum on a cart. The physical uncertainty is realized by a known additional lumped mass at an unknown location on the pendulum. This unknown location has the effect of substantially altering the nominal frequency and controllability of the nonlinear system, and in the limit has the capability to make the system neutrally stable and uncontrollable. Another uncertainty to be considered is a direct current motor parameter. The control design objective is to design a controller that satisfies stability, tracking error, control power, and transient behavior requirements for the largest range of parametric uncertainties. This paper presents an overview of the theory behind the robust control design methodology and the experimental results.

Kenny, Sean P.↗
NASA NTRS2012

UQTools: The Uncertainty Quantification Toolbox - Introduction and Tutorial

UQTools is the short name for the Uncertainty Quantification Toolbox, a software package designed to efficiently quantify the impact of parametric uncertainty on engineering systems. UQTools is a MATLAB-based software package and was designed to be discipline independent, employing very generic representations of the system models and uncertainty. Specifically, UQTools accepts linear and nonlinear system models and permits arbitrary functional dependencies between the system s measures of interest and the probabilistic or non-probabilistic parametric uncertainty. One of the most significant features incorporated into UQTools is the theoretical development centered on homothetic deformations and their application to set bounding and approximating failure probabilities. Beyond the set bounding technique, UQTools provides a wide range of probabilistic and uncertainty-based tools to solve key problems in science and engineering.

Kenny, Sean P.↗
NASA NTRS2012

Robustness Analysis and Optimally Robust Control Design via Sum-of-Squares

A control analysis and design framework is proposed for systems subject to parametric uncertainty. The underlying strategies are based on sum-of-squares (SOS) polynomial analysis and nonlinear optimization to design an optimally robust controller. The approach determines a maximum uncertainty range for which the closed-loop system satisfies a set of stability and performance requirements. These requirements, de ned as inequality constraints on several metrics, are restricted to polynomial functions of the uncertainty. To quantify robustness, SOS analysis is used to prove that the closed-loop system complies with the requirements for a given uncertainty range. The maximum uncertainty range, calculated by assessing a sequence of increasingly larger ranges, serves as a robustness metric for the closed-loop system. To optimize the control design, nonlinear optimization is used to enlarge the maximum uncertainty range by tuning the controller gains. Hence, the resulting controller is optimally robust to parametric uncertainty. This approach balances the robustness margins corresponding to each requirement in order to maximize the aggregate system robustness. The proposed framework is applied to a simple linear short-period aircraft model with uncertain aerodynamic coefficients.

Dorobantu, Andrei↗
NASA NTRS1993

On the apparent insignificance of the randomness of flexible joints on large space truss dynamics

Deployable periodic large space structures have been shown to exhibit high dynamic sensitivity to period-breaking imperfections and uncertainties. These can be brought on by manufacturing or assembly errors, structural imperfections, as well as nonlinear and/or nonconservative joint behavior. In addition, the necessity of precise pointing and position capability can require the consideration of these usually negligible and unknown parametric uncertainties and their effect on the overall dynamic response of large space structures. This work describes the use of a new design approach for the global dynamic solution of beam-like periodic space structures possessing parametric uncertainties. Specifically, the effect of random flexible joints on the free vibrations of simply-supported periodic large space trusses is considered. The formulation is a hybrid approach in terms of an extended Timoshenko beam continuum model, Monte Carlo simulation scheme, and first-order perturbation methods. The mean and mean-square response statistics for a variety of free random vibration problems are derived for various input random joint stiffness probability distributions. The results of this effort show that, although joint flexibility has a substantial effect on the modal dynamic response of periodic large space trusses, the effect of any reasonable uncertainty or randomness associated with these joint flexibilities is insignificant.

Koch, R. M.↗
NASA NTRS2004

Robust Control for The G-Limit Microgravity Vibration Isolation System

Many microgravity science experiments need an active isolation system to provide a sufficiently quiescent acceleration environment. The g-LIMIT vibration isolation system will provide isolation for Microgravity Science Glovebox experiments in the International Space Station. While standard control system technologies have been demonstrated for these applications, modern control methods have the potential for meeting performance requirements while providing robust stability in the presence of parametric uncertainties that are characteristic of microgravity vibration isolation systems. While H2 and H infinity methods are well established, neither provides the levels of attenuation performance and robust stability in a compensator with low order. Mixed H2/mu controllers provide a means for maximizing robust stability for a given level of mean-square nominal performance while directly optimizing for controller order constraints. This paper demonstrates the benefit of mixed norm design from the perspective of robustness to parametric uncertainties and controller order for microgravity vibration isolation. A nominal performance metric analogous to the mu measure for robust stability assessment is also introduced in order to define an acceptable trade space from which different control methodologies can be compared.

Whorton, Mark S.↗
NASA NTRS2003

Robust Control for Microgravity Vibration Isolation using Fixed Order, Mixed H2/Mu Design

Many space-science experiments need an active isolation system to provide a sufficiently quiescent microgravity environment. Modern control methods provide the potential for both high-performance and robust stability in the presence of parametric uncertainties that are characteristic of microgravity vibration isolation systems. While H2 and H(infinity) methods are well established, neither provides the levels of attenuation performance and robust stability in a compensator with low order. Mixed H2/H(infinity), controllers provide a means for maximizing robust stability for a given level of mean-square nominal performance while directly optimizing for controller order constraints. This paper demonstrates the benefit of mixed norm design from the perspective of robustness to parametric uncertainties and controller order for microgravity vibration isolation. A nominal performance metric analogous to the mu measure, for robust stability assessment is also introduced in order to define an acceptable trade space from which different control methodologies can be compared.

Whorton, Mark↗
NASA NTRS2009

Robust Landing Using Time-to-Collision Measurement with Actuator Saturation

This paper considers a landing problem for an MAV that uses only a monocular camera for guidance. Although this sensor cannot measure the absolute distance to the target, by using optical flow algorithms, time-to-collision to the target is obtained. Existing work has applied a simple proportional feedback control to simple dynamics and demonstrated its potential. However, due to the singularity in the time-to-collision measurement around the target, this feedback could require an infinite control action. This paper extends the approach into nonlinear dynamics. In particular, we explicitly consider the saturation of the actuator and include the effect of the aerial drag. It is shown that the convergence to the target is guaranteed from a set of initial conditions, and the boundaries of such initial conditions in the state space are numerically obtained. The paper then introduces parametric uncertainties in the vehicle model and in the time-to-collision measurements. Using an argument similar to the nominal case, the robust convergence to the target is proven, but the region of attraction is shown to shrink due to the existence of uncertainties. The numerical simulation validates these theoretical results.

parametric uncertainty↗
NASA NTRS2022

Uncertainty Models for the Hybrid Parametric Variation Method of Uncertainty Quantification; Analysis

There is some level of uncertainty in every finite element model (FEM), which flows to a level of uncertainty in predicted results. The purpose of uncertainty quantification (UQ) is to provide statistical bounds on prediction accuracy based on model uncertainty. This is distinct from model updating, which attempts to modify models to improve their accuracy. UQ does not improve the accuracy of models, but accepts that the models are inherently inaccurate and attempts to quantify the impact of that inaccuracy on predicted results. Previously, an alternate method for UQ, called the Hybrid Parametric Variation (HPV) method, was applied to Space Launch System (SLS) Hurty/Craig-Bampton (HCB) components to predict system-level statistics for launch vehicle attitude control transfer functions and core stage section loads due to buffet. The HPV method combines a parametric variation of the HCB fixed-interface (FI) modal frequencies with a nonparametric variation (NPV) method that randomly varies the HCB mass and stiffness matrices as Wishart random matrix distributions using random matrix theory (RMT). Alternatively, the most common method for modeling uncertainty in the structural dynamics community is a parametric approach, which varies physical parameters in the model. However, there are several disadvantages associated with the parametric method. Determining a reduced set of parameters that have a significant impact on the system response can be time consuming, and the selected parameter probability distributions are rarely reliably known. Therefore, in practice, the parameters are surrogates for the actual errors, and the link to parameter uncertainty is unknown. Another major drawback is that the uncertainty that can be represented is limited to the form of the nominal FEM. It is the experience of the authors that based on numerous aerospace programs, almost all FEM errors are in form rather than parameter values. This hypothesis is supported by the observation of the authors that it is almost never possible to ‘tune’ a FEM to match modal test results by only modifying model parameters. Model-form uncertainty cannot be directly represented by FEM input parameters nor included in a parametric approach. However, model-form uncertainty can be modeled using RMT, where a probability distribution is developed for the matrix ensemble of interest. The major advantage of the NPV method is that it covers errors in model form. The HPV method anchors uncertainty at the HCB component level to component modal test results by matching the HCB and test modes based on mode descriptions or other methods, and then applying differing levels of frequency variation. The specific variations depend on the confidence to which a component FEM has been validated through modal testing. The NPV method is layered on the frequency variation to match modal test self-orthogonality and cross-orthogonality (XO) results. Once the component uncertainty models are identified, they are assembled, and the uncertainty is propagated to the system level using a Monte Carlo (MC) analysis approach that generates statistics for system-level predictions This provides a UQ method that can be traced to test data, which can be updated as additional data and improved correlated models become available. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The second example is an application to a component that is design specific to the SLS. Based on this work and other assessments, the HPV method provides another tool to the toolset used for complex system UQ analysis. From experience gathered to date using the HPV method, additional design specific applications must be investigated to provide further confidence in the validity of the HPV method of UQ analysis.

Uncertainty quantification↗
NASA NTRSDate not supplied

SLS Integrated Modal Test Uncertainty Quantification using the Hybrid Parametric Variation Method

Uncertainty in structural loading during launch is a significant concern in the development of spacecraft and launch vehicles. Small variations in launch vehicle and payload mode shapes and their interaction can result in significant variation in system loads. In many cases involving large aerospace systems it is difficult, not economical, or impossible to perform a system modal test. However, it is still vital to obtain test results that can be compared with analytical predictions to validate models. Instead, the “Building Block Approach” is used in which system components are tested individually. Component models are correlated and updated to agree as best they can with test results. The Space Launch System consists of a number of components that are assembled into a launch vehicle. Finite element models of the components are developed, reduced to Hurty/Craig-Bampton models and assembled to represent different phases of flight. The only opportunity to obtain modal test data from an assembled Space Launch System will be during the Integrated Modal Test. There is always uncertainty in every model, which flows into uncertainty in predicted system results. Uncertainty Quantification is used to determine statistical bounds on prediction accuracy based on model uncertainty. For the Space Launch System, model uncertainty is at the Hurty/Craig-Bampton component level. Uncertainty in the Hurty/Craig-Bampton components is quantified using the hybrid parametric variation approach that combines parametric and nonparametric uncertainty. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. This type of uncertainty cannot be represented by variations infinite element model input parameters and thus cannot be included in a parametric approach. However, model-form uncertainty can be modeled using a nonparametric approach based on random matrix theory. The hybrid parametric variation method requires the selection of dispersion values for the Hurty/Craig-Bampton fixed-interface eigenvalues, and the Hurty/Craig-Bampton stiffness matrices. Component test/analysis frequency error is used to identify the fixed-interface eigenvalue dispersions, while test/analysis cross-orthogonality is used to identify stiffness dispersion values. The hybrid parametric variation uncertainty quantification approach is applied to the Space Launch System Integrated Modal Test configuration. Monte Carlo analysis is performed, and statistics are determined for modal correlation metrics, frequency response from Integrated Modal Test shakers to selected accelerometers, as well as other metrics for determining how well target modes are excited and identified. If the predicted uncertainty envelopes future Integrated Modal Test results, then there will be increased confidence in the utility of the component-based hybrid parametric variation uncertainty quantification approach.

Uncertainty Quantification↗
NASA NTRS1994

A Robust Control Design Framework for Substructure Models

A framework for designing control systems directly from substructure models and uncertainties is proposed. The technique is based on combining a set of substructure robust control problems by an interface stiffness matrix which appears as a constant gain feedback. Variations of uncertainties in the interface stiffness are treated as a parametric uncertainty. It is shown that multivariable robust control can be applied to generate centralized or decentralized controllers that guarantee performance with respect to uncertainties in the interface stiffness, reduced component modes and external disturbances. The technique is particularly suited for large, complex, and weakly coupled flexible structures.

Lim, Kyong B.↗
NASA NTRS1991

New bounds on parameter uncertainties for robust stability

The problem of robust stability in linear systems with parametric uncertainties is considered. A method is developed to determine bounds on uncertain parameters in the state-space model of the system, so that stability is preserved. Both continuous- and discrete-time systems are considered. Unlike previous results, the stability bounds are derived in terms of actual parameters instead of their absolute values, and consequently the stable region in the parameter space is not necessarily symmetric with respect to the origin. Furthermore, the uncertain parameters do not have to be linearly independent to each other.

Gao, Zhiqiang↗
NASA NTRS1992

Robust linear quadratic designs with respect to parameter uncertainty

The authors derive a linear quadratic regulator (LQR) which is robust to parametric uncertainty by using the overbounding method of I. R. Petersen and C. V. Hollot (1986). The resulting controller is determined from the solution of a single modified Riccati equation. It is shown that, when applied to a structural system, the controller gains add robustness by minimizing the potential energy of uncertain stiffness elements, and minimizing the rate of dissipation of energy through uncertain damping elements. A worst-case disturbance in the direction of the uncertainty is also considered. It is proved that performance robustness has been increased with the robust LQR when compared to a mismatched LQR design where the controller is designed on the nominal system, but applied to the actual uncertain system.

Douglas, Joel↗
NASA NTRS2008

Hard Constraints in Optimization Under Uncertainty

This paper proposes a methodology for the analysis and design of systems subject to parametric uncertainty where design requirements are specified via hard inequality constraints. Hard constraints are those that must be satisfied for all parameter realizations within a given uncertainty model. Uncertainty models given by norm-bounded perturbations from a nominal parameter value, i.e., hyper-spheres, and by sets of independently bounded uncertain variables, i.e., hyper-rectangles, are the focus of this paper. These models, which are also quite practical, allow for a rigorous mathematical treatment within the proposed framework. Hard constraint feasibility is determined by sizing the largest uncertainty set for which the design requirements are satisfied. Analytically verifiable assessments of robustness are attained by comparing this set with the actual uncertainty model. Strategies that enable the comparison of the robustness characteristics of competing design alternatives, the description and approximation of the robust design space, and the systematic search for designs with improved robustness are also proposed. Since the problem formulation is generic and the tools derived only require standard optimization algorithms for their implementation, this methodology is applicable to a broad range of engineering problems.

Crespo, Luis G.↗
NASA NTRS2008

Direct Adaptive Control of Systems with Actuator Failures: State of the Art and Continuing Challenges

In this paper, the problem of controlling systems with failures and faults is introduced, and an overview of recent work on direct adaptive control for compensation of uncertain actuator failures is presented. Actuator failures may be characterized by some unknown system inputs being stuck at some unknown (fixed or varying) values at unknown time instants, that cannot be influenced by the control signals. The key task of adaptive compensation is to design the control signals in such a manner that the remaining actuators can automatically and seamlessly take over for the failed ones, and achieve desired stability and asymptotic tracking. A certain degree of redundancy is necessary to accomplish failure compensation. The objective of adaptive control design is to effectively use the available actuation redundancy to handle failures without the knowledge of the failure patterns, parameters, and time of occurrence. This is a challenging problem because failures introduce large uncertainties in the dynamic structure of the system, in addition to parametric uncertainties and unknown disturbances. The paper addresses some theoretical issues in adaptive actuator failure compensation: actuator failure modeling, redundant actuation requirements, plant-model matching, error system dynamics, adaptation laws, and stability, tracking, and performance analysis. Adaptive control designs can be shown to effectively handle uncertain actuator failures without explicit failure detection. Some open technical challenges and research problems in this important research area are discussed.

Tao, Gang↗