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NASA NTRS1984

An algorithm for maximum likelihood estimation using an efficient method for approximating sensitivities

An algorithm for maximum likelihood (ML) estimation is developed primarily for multivariable dynamic systems. The algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). The method determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort compared with integrating the analytically determined sensitivity equations or using a finite-difference method. Different surface-fitting methods are discussed and demonstrated. Aircraft estimation problems are solved by using both simulated and real-flight data to compare MNRES with commonly used methods; in these solutions MNRES is found to be equally accurate and substantially faster. MNRES eliminates the need to derive sensitivity equations, thus producing a more generally applicable algorithm.

Murphy, P. C.↗

NASA NTRS1993

Controls-structures-interaction dynamics during RCS control of the Orbiter/SRMS/SSF configuration

During the assembly flights of the Space Station Freedom (SSF), the Orbiter will either dock with the SSF and retract to the final berthed position, or will grapple the SSF using the Shuttle Remote Manipulator System (SRMS) and maneuver the SRMS coupled vehicles to their final berthed position. The SRMS method is expected to take approximately one to one and a half hours to complete and require periodic attitude corrections by either the Orbiter or the SSF reaction control system (RCS) or continuous control by a control moment gyro (CMG) system with RCS desaturation as required. Free drift of the attached vehicles is not currently thought to be acceptable because the desired system attitude will quickly deteriorate due to unbalanced gravity gradient and aerodynamic torques resulting in power generation problems, thermodynamic control problems, and communications problems. This paper deals with the simulation and control of the SRMS during trunnion/latch interaction dynamics and during RCS maneuvers. The SRMS servo drive joints have highly non-linear elastic characteristics which tend to degrade sensitive control strategies. In addition the system natural frequencies are extremely low and depend on the drive joint deflections and SRMS geometric position. The lowest mean period of oscillation for the Orbiter/SRMS/SSF(MB6) system in brakes hold mode positioned near the final berthed position is approximately 120 seconds. A detailed finite element model of the SRMS has been developed and used in a newly developed SRMS systems dynamics simulation to investigate the non-linear transient response dynamics of the Orbiter/SRMS/SSF systems. The present SRMS control strategy of brakes only recommended by the Charles Draper Labs is contrasted with a robust controller developed by the authors. The robust controller uses an optimal inear quadratic regulator (LQR) to optimally place the closed-loop poles of a multivariable continuous-time system within the common region of an open sector with the sector angle plus or minus 45 degrees from the negative real axis, and the left-hand side of a parallel to the imaginary axis in the complex s-plane. This guarantees that the critical damping ratio for the desired control modes is equal to or in excess of 0.707. The matrix sign function is used for solving the Riccati equations which appear in the controller design procedure. Fast and stable algorithms have recently been developed for the computation of the matrix sign function. Simulation results are given which demonstrate the potential CSI involvement for the current SRMS control system and the proposed control system.

Schliesing, J. A.↗

NASA NTRS2009

Complexity of Fit, with Application to Space Suits

Although fitting a garment is often considered more of an art than a science, experts suggest that a subjectively poor fit is a symptom of inappropriate ease, the space between the wearer and the garment. The condition of poor suit fit is a unique problem for the space program and it can be attributed primarily to: a) NASA s policy to accommodate a wide variety of people (males and females from 1st to 99th percentile range and with various shapes and sizes) and b) its requirement to deploy a minimum number of suit sizes for logistical reasons. These factors make the space suit fit difficult to assess, where a wide range of people must be fit by the minimum possible number of suits, and yet, fit is crucial for operability and safety. Existing simplistic sizing scheme do not account for wide variations in shape within a diverse population with very limited sizing options. The complex issue of fit has been addressed by a variety of methods, many of which have been developed by the military, which has always had a keen interest in fitting its diverse population but with a multitude of sizing options. The space program has significantly less sizing options, so a combination of these advanced methods should be used to optimize space suit size and assess space suit fit. Multivariate methods can be used to develop sizing schemes that better reflect the wearer population, and integrated sizing systems can form a compromise between fitting men and women. Range of motion and operability testing can be combined with subjective feedback to provide a comprehensive evaluation of fit. The amount of ease can be tailored using these methods, to provide enough extra room where it is needed, without compromising mobility and comfort. This paper discusses the problem of fit in one of its most challenging applications: providing a safe and comfortable spacesuit that will protect its wearer from the extreme environment of space. It will discuss the challenges and necessity of closely fitting its potential wearers, a group of people from a broad spectrum of the population, and will detail some of the methods that can be employed to ensure and validate a good fit.

Rajulu, Sudhakar↗

NASA NTRS2005

Fitting Nonlinear Curves by use of Optimization Techniques

MULTIVAR is a FORTRAN 77 computer program that fits one of the members of a set of six multivariable mathematical models (five of which are nonlinear) to a multivariable set of data. The inputs to MULTIVAR include the data for the independent and dependent variables plus the user s choice of one of the models, one of the three optimization engines, and convergence criteria. By use of the chosen optimization engine, MULTIVAR finds values for the parameters of the chosen model so as to minimize the sum of squares of the residuals. One of the optimization engines implements a routine, developed in 1982, that utilizes the Broydon-Fletcher-Goldfarb-Shanno (BFGS) variable-metric method for unconstrained minimization in conjunction with a one-dimensional search technique that finds the minimum of an unconstrained function by polynomial interpolation and extrapolation without first finding bounds on the solution. The second optimization engine is a faster and more robust commercially available code, denoted Design Optimization Tool, that also uses the BFGS method. The third optimization engine is a robust and relatively fast routine that implements the Levenberg-Marquardt algorithm.

Hill, Scott A.↗

NASA NTRS1987

Analysis models for the estimation of oceanic fields

A general model for statistically optimal estimates is presented for dealing with scalar, vector and multivariate datasets. The method deals with anisotropic fields and treats space and time dependence equivalently. Problems addressed include the analysis, or the production of synoptic time series of regularly gridded fields from irregular and gappy datasets, and the estimate of fields by compositing observations from several different instruments and sampling schemes. Technical issues are discussed, including the convergence of statistical estimates, the choice of representation of the correlations, the influential domain of an observation, and the efficiency of numerical computations.

Carter, E. F.↗

NASA NTRS1988

An application of eigenspace methods to symmetric flutter suppression

An eigenspace assignment approach to the design of parameter insensitive control laws for linear multivariable systems is presented. The control design scheme utilizes constrained optimization techniques to exploit the flexibility in eigenvector assignments to reduce control system sensitivity to changes in system parameters while maintaining performance requirements; it thus provides a systematic approach for choosing values for eigensystem design variables. The methods involve use of the singular value decomposition to provide an exact description of allowable eigenvectors in terms of a minimum number of design parameters. In a design example, the methods are applied to the problem of symmetric flutter suppression in an aeroelastic vehicle. In this example the flutter mode is sensitive to changes in dynamic pressure and eigenspace methods are used to enhance the performance of a stabilizing minimum energy/linear quadratic regulator controller and associated observer. Numerical results indicate that the methods provide feedback control laws that make the stability of the nominal closed loop systems less sensitive to changes in dynamic pressure, while maintaining acceptable control power and robustness constraints.

Fennell, Robert E.↗

NASA NTRS1996

Balanced Placement Of Vibration Sensors And Actuators

Mathematical approach that involves Hankel singular values leads to method for estimation of optimal placement of relatively few vibration sensors and actuators in multivariable flexible structure. Approach extends and complements previous developments regarding approximate decomposition, to Hankel singular values, of singular values of controllability and observability grammian matrices of multivariable flexible structure. Mathematical constructs also described in "Designing An Approximately Balanced LQG Compensator" (NPO-19000).

Gawronski, Wodek↗

NASA NTRS1985

An Algorithm for Efficient Maximum Likelihood Estimation and Confidence Interval Determination in Nonlinear Estimation Problems

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.

Murphy, Patrick Charles↗

NASA NTRSDate not supplied

Global Sensitivity Analyses for Test Planning with Black-Box Models for Mars Sample Return

This work describes sensitivity analyses performed on complex black-box models used to support experimental test planning under limited resources in the context of the Mars Sample Return program, which aims at bringing to Earth rock and atmospheric samples from Mars. We develop a systematic workflow that allows the analysts to simultaneously obtain quantitative insights on key drivers of uncertainty, on the direction of impact, and the presence of interactions. We apply novel optimal transport-based global sensitivity measures to tackle the multivariate nature of the output. On the modeling side, we apply multi-fidelity techniques that leverage low-fidelity models to speed up the calculations and make up for the limited amount of high-fidelity samples, while keeping these in the loop for accuracy guarantees. The sensitivity analysis reveals insights useful for the analysts to understand the model's behavior and identify the factors to focus on during testing in order to maximize the value of information extracted from them to ensure mission success when limited resources are available.

Giuseppe Cataldo↗

NASA NTRS1972

Near-earth orbital guidance and remote sensing

The curriculum of a short course in remote sensing and parameter optimization is presented. The subjects discussed are: (1) basics of remote sensing and the user community, (2) multivariant spectral analysis, (3) advanced mathematics and physics of remote sensing, (4) the atmospheric environment, (5) imaging sensing, and (6)nonimaging sensing. Mathematical models of optimization techniques are developed.

Powers, W. F.↗

NASA NTRS1991

Closed-form solutions for linear regulator design of mechanical systems including optimal weighting matrix selection

Vibration in modern structural and mechanical systems can be reduced in amplitude by increasing stiffness, redistributing stiffness and mass, and/or adding damping if design techniques are available to do so. Linear Quadratic Regulator (LQR) theory in modern multivariable control design, attacks the general dissipative elastic system design problem in a global formulation. The optimal design, however, allows electronic connections and phase relations which are not physically practical or possible in passive structural-mechanical devices. The restriction of LQR solutions (to the Algebraic Riccati Equation) to design spaces which can be implemented as passive structural members and/or dampers is addressed. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical system. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist.

Hanks, Brantley R.↗

NASA NTRS1978

Invariants of optimal minimal-order observer-based compensators

The relations characterizing the optimal minimal-order observer-based compensators for a linear time-invariant multivariable system with a random initial state (or, equivalently, known initial state and white plant-driving noise) have been reported by Miller (1973). In this note we establish in general that the plant transfer function uniquely determines the optimal compensator transfer function, and that this characterizes precisely the degrees of freedom in the compensator design; computational implications of this result are indicated.

Blanvillain, P. J.↗

NASA NTRS1991

The integrated manual and automatic control of complex flight systems

Research dealt with the general area of optimal flight control synthesis for manned flight vehicles. The work was generic; no specific vehicle was the focus of study. However, the class of vehicles generally considered were those for which high authority, multivariable control systems might be considered, for the purpose of stabilization and the achievement of optimal handling characteristics. Within this scope, the topics of study included several optimal control synthesis techniques, control-theoretic modeling of the human operator in flight control tasks, and the development of possible handling qualities metrics and/or measures of merit. Basic contributions were made in all these topics, including human operator (pilot) models for multi-loop tasks, optimal output feedback flight control synthesis techniques; experimental validations of the methods developed, and fundamental modeling studies of the air-to-air tracking and flared landing tasks.

Schmidt, David K.↗

NASA NTRS1981

An application of multivariable design techniques to the control of the national transonic facility

The digital versions of optimal linear regulator theory and eigenvalue placement theory are applied to the Mach number control loop of the National Transonic Facility cryogenic wind tunnel. The control laws developed are evaluated on a nonlinear simulation of the tunnel process for a typical est condition and are found to significantly reduce the open loop time required to achieve a Mach number set point.

Armstrong, E. S.↗

NASA NTRS1976

Invariants of optimal minimal-order observer-based compensators

The relations characterizing the optimal minimal-order observer-based compensators for a linear time-invariant multivariable system in a certain canonical form, with a random initial state (or equivalently, known initial state with white driving noise) have been reported by Miller and independently by others. In this note, we establish in general that the plant transfer function uniquely determines the optimal compensator transfer function, and that this characterizes precisely the degrees of freedom in the compensator design. Any two realizations of the optimal compensator dynamics yield the same performance.

Blanvillain, P.↗

NASA NTRS2014

Robust Modal Filtering and Control of the X-56A Model with Simulated Fiber Optic Sensor Failures

The X-56A aircraft is a remotely-piloted aircraft with flutter modes intentionally designed into the flight envelope. The X-56A program must demonstrate flight control while suppressing all unstable modes. A previous X-56A model study demonstrated a distributed-sensing-based active shape and active flutter suppression controller. The controller relies on an estimator which is sensitive to bias. This estimator is improved herein, and a real-time robust estimator is derived and demonstrated on 1530 fiber optic sensors. It is shown in simulation that the estimator can simultaneously reject 230 worst-case fiber optic sensor failures automatically. These sensor failures include locations with high leverage (or importance). To reduce the impact of leverage outliers, concentration based on a Mahalanobis trim criterion is introduced. A redescending M-estimator with Tukey bisquare weights is used to improve location and dispersion estimates within each concentration step in the presence of asymmetry (or leverage). A dynamic simulation is used to compare the concentrated robust estimator to a state-of-the-art real-time robust multivariate estimator. The estimators support a previously-derived mu-optimal shape controller. It is found that during the failure scenario, the concentrated modal estimator keeps the system stable.

Modal Filtering↗

NASA NTRS2016

Robust Modal Filtering and Control of the X-56A Model with Simulated Fiber Optic Sensor Failures

Modal Filtering↗

NASA NTRS1984

Quadratic optimal cooperative control synthesis with flight control application

An optimal control-law synthesis approach is presented that involves simultaneous solution for two cooperating controllers operating in parallel. One controller's structure includes stochastic state estimation and linear feedback of the state estimates, while the other controller involves direct linear feedback of selected system output measurements. This structure is shown to be optimal under the constraint of linear feedback of system outputs in one controller. Furthermore, it is appropriate for flight control synthesis where the full-state optimal stochastic controller can be adjusted to be representative of an optimal control model of the human pilot in a stochastic regulation task. The method is experimentally verified in the case of the selection of pitch-damper gain for optimum pitch tracking, where optimum implies the best subjective pilot rating in the task. Finally, results from application of the method to synthesize a controller for a multivariable fighter aircraft are presented, and implications of the results of this method regarding the optimal plant dynamics for tracking are discussed.

Schmidt, D. K.↗