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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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68 records · Page 4

Optimal limited state variable feedback controllers for linear systems.

Optimized static and dynamic linear system compensator designs with a priori fixed dimensions are discussed. Expressions are derived to determine the parameters of these designs, including the fixed-gain output feedback, the time-varying output feedback, and time-invariant compensation. A relevant deterministic off-line optimization problem is formulated, and the properties of a solution to the problem are analyzed. A unified design philosophy for limited state-variable control problems of essentially deterministic systems is developed. The philosophy incorporates design constraints, a careful selection of performance criteria, and interpretation of the results.

Levine, W. S.↗

A new approach to the design of time-varying control systems with application to the Space Shuttle Boost

A general approach to the analysis and design of closed-loop control for slowly time-varying linear systems is presented. The approach uses the method of generalized multiple scales in which slow and fast dynamics are systematically separated by employing different 'clocks' which measure time at varying rates. The clocks, which are necessarily nonlinear functions of time, are chosen in such a manner that the system dynamics are asymptotically invariant with respect to the new time scale. A transfer function relating the output to the input for general linear slowly time-varying systems is developed and represents the actual system under certain conditions. The clock function is shown to satisfy an algebraic characteristic equation and can be determined in terms of the coefficients. The approach can be viewed as an extension of time-invariant linear feedback control theory.

Ramanth, R. V.↗

Identifiability of unknown noise covariance matrices for some special cases of a linear, time-invariant, discrete-time dynamic system

Two off-line schemes are proposed for the identification of unknown noise covariance matrices Q and R of a discrete-time dynamic system. The first scheme is based on a maximum a posteriori cost function utilizing smoothed state estimates, while the second is based on a maximum likelihood cost function utilizing filtered state estimates. Sensitivity of the cost functions to Q and R is analyzed for the following cases: (1) single-input single-output systems; (2) multiinput single-output systems; and (3) single-input multioutput systems with a diagonal R. Identifiability criteria are presented for the cases considered and demonstrated by examples.

Tsang, W. L.↗

Control-System Design Program

Control-theory design package, Optimal Regulator Algorithms for Control of Linear Systems (ORACLS), developed to aid in design of controllers and optimal filters for systems modeled by linear, time-invariant differential and difference equations. Optimal linear quadratic regulator theory, Linear-Quadratic-Gaussian (LQG) problem, most widely accepted method of determining optimal control policy. Provides for solution to time-in-variant continuous or discrete LQG problems. Attractive to control-system designer providing rigorous tool for dealing with multi-input and multi-output dynamic systems in continuous and discrete form. CDO version written in FORTRAN IV. VAX version written in FORTRAN 77.

Frisch, Harold P.↗

Passivity In Analysis Of Robustness Of A Control System

Robustness margin (measure of degree of passivity) defined. Paper presents new approach to analysis of stability of multivariable feedforward-and-feedback control system consisting of exponentially stable linear time-invariant (LTI) feedforward subsystem and nonlinear time-varying (NTV) or dynamic feedback subsystem. New method based on notion of passivity, quantified by robustness margin. Margin provides bound on magnitudes of perturbations, below which perturbations will not make system unstable.

Wen, John Ting-Yung↗

Absolute Stability And Hyperstability In Hilbert Space

Theorems on stabilities of feedback control systems proved. Paper presents recent developments regarding theorems of absolute stability and hyperstability of feedforward-and-feedback control system. Theorems applied in analysis of nonlinear, adaptive, and robust control. Extended to provide sufficient conditions for stability in system including nonlinear feedback subsystem and linear time-invariant (LTI) feedforward subsystem, state space of which is Hilbert space, and input and output spaces having finite numbers of dimensions. (In case of absolute stability, feedback subsystem memoryless and possibly time varying. For hyperstability, feedback system dynamical system.)

Wen, John Ting-Yung↗

Model reduction using new optimal Routh approximant technique

An optimal Routh approximant of a single-input single-output dynamic system is a reduced-order transfer function of which the denominator is obtained by the Routh approximation method while the numerator is determined by minimizing a time-response integral-squared-error (ISE) criterion. In this paper, a new elegant approach is presented for obtaining the optimal Routh approximants for linear time-invariant continuous-time systems. The approach is based on the Routh canonical expansion, which is a finite-term orthogonal series of rational basis functions, and minimization of the ISE criterion. A procedure for combining the above approach with the bilinear transformation is also presented in order to obtain the optimal bilinear Routh approximants of linear time-invariant discrete-time systems. The proposed technique is simple in formulation and is amenable to practical implementation.

Hwang, Chyi↗

PLATSIM: An efficient linear simulation and analysis package for large-order flexible systems

PLATSIM is a software package designed to provide efficient time and frequency domain analysis of large-order generic space platforms implemented with any linear time-invariant control system. Time domain analysis provides simulations of the overall spacecraft response levels due to either onboard or external disturbances. The time domain results can then be processed by the jitter analysis module to assess the spacecraft's pointing performance in a computationally efficient manner. The resulting jitter analysis algorithms have produced an increase in speed of several orders of magnitude over the brute force approach of sweeping minima and maxima. Frequency domain analysis produces frequency response functions for uncontrolled and controlled platform configurations. The latter represents an enabling technology for large-order flexible systems. PLATSIM uses a sparse matrix formulation for the spacecraft dynamics model which makes both the time and frequency domain operations quite efficient, particularly when a large number of modes are required to capture the true dynamics of the spacecraft. The package is written in MATLAB script language. A graphical user interface (GUI) is included in the PLATSIM software package. This GUI uses MATLAB's Handle graphics to provide a convenient way for setting simulation and analysis parameters.

Maghami, Periman↗

Stable Inversion for Nonlinear Nonminimum-Phase Time Varying Systems

In this paper, we extend stable inversion to nonlinear time-varying systems and study computational issues; the technique is applicable to minimum-phase as well as nonminimum-phase systems. The inversion technique is new, even in the linear time-varying case, and relies on partitioning (the dichotomic split of) the linearized system dynamics into time-varying, stable, and unstable, submanifolds. This dichotomic split is used to build time-varying filters which are, in turn, the basis of a contraction used to find a bounded inverse input-state trajectory. Finding the inverse input-state trajectory allows the development or exact-output tracking controllers. The method is local to the time-varying trajectory and requires that the internal dynamics vary slowly; however, the method represents a significant advance relative to presently available tracking controllers. Present techniques are restricted to time-invariant nonlinear systems and, in the general case, track only asymptotically.

Devasia, S.↗

Integral Twist Actuation of Helicopter Rotor Blades for Vibration Reduction

Active integral twist control for vibration reduction of helicopter rotors during forward flight is investigated. The twist deformation is obtained using embedded anisotropic piezocomposite actuators. An analytical framework is developed to examine integrally-twisted blades and their aeroelastic response during different flight conditions: frequency domain analysis for hover, and time domain analysis for forward flight. Both stem from the same three-dimensional electroelastic beam formulation with geometrical-exactness, and axe coupled with a finite-state dynamic inflow aerodynamics model. A prototype Active Twist Rotor blade was designed with this framework using Active Fiber Composites as the actuator. The ATR prototype blade was successfully tested under non-rotating conditions. Hover testing was conducted to evaluate structural integrity and dynamic response. In both conditions, a very good correlation was obtained against the analysis. Finally, a four-bladed ATR system is built and tested to demonstrate its concept in forward flight. This experiment was conducted at NASA Langley T~ansonic Dynamics Tunnel and represents the first-of-a-kind Mach-scaled fully-active-twist rotor system to undergo forward flight test. In parallel, the impact upon the fixed- and rotating-system loads is estimated by the analysis. While discrepancies are found in the amplitude of the loads under actuation, the predicted trend of load variation with respect to its control phase correlates well. It was also shown, both experimentally and numerically, that the ATR blade design has the potential for hub vibratory load reduction of up to 90% using individual blade control actuation. Using the numerical framework, system identification is performed to estimate the harmonic transfer functions. The linear time-periodic system can be represented by a linear time-invariant system under the three modes of blade actuation: collective, longitudinal cyclic, and lateral cyclic. A vibration minimizing controller is designed based on this result, which implements classical disturbance rejection algorithm with some modifications. The controller is simulated numerically, and more than 90% of the 4P hub vibratory load is eliminated. By accomplishing the experimental and analytical steps described in this thesis, the present concept is found to be a viable candidate for future generation low-vibration helicopters. Also, the analytical framework is shown to be very appropriate for exploring active blade designs, aeroelastic behavior prediction, and as simulation tool for closed-loop controllers.

Shin, SangJoon↗

Direct Optimal Control of Duffing Dynamics

The "direct control method" is a novel concept that is an attractive alternative and competitor to the differential-equation-based methods. The direct method is equally well applicable to nonlinear, linear, time-varying, and time-invariant systems. For all such systems, the method yields explicit closed-form control laws based on minimization of a quadratic control performance measure. We present an application of the direct method to the dynamics and optimal control of the Duffing system where the control performance measure is not restricted to a quadratic form and hence may include a quartic energy term. The results we present in this report also constitute further generalizations of our earlier work in "direct optimal control methodology." The approach is demonstrated for the optimal control of the Duffing equation with a softening nonlinear stiffness.

Oz, Hayrani↗

A High-Order, Linear Time-Invariant Model for Application to Higher Harmonic Control and Flight Control System Interaction

This research describes a new methodology for the extraction of a high-order, linear time invariant model, which allows the periodicity of the helicopter response to be accurately captured. This model provides the needed level of dynamic fidelity to permit an analysis and optimization of the AFCS and HHC algorithms. The key results of this study indicate that the closed-loop HHC system has little influence on the AFCS or on the vehicle handling qualities, which indicates that the AFCS does not need modification to work with the HHC system. However, the results show that the vibration response to maneuvers must be considered during the HHC design process, and this leads to much higher required HHC loop crossover frequencies. This research also demonstrates that the transient vibration responses during maneuvers can be reduced by optimizing the closed-loop higher harmonic control algorithm using conventional control system analyses.

Cheng, Rendy P.↗

Template Matching Approach to Signal Prediction

A new approach to signal prediction and prognostic assessment of spacecraft health resolves an inherent difficulty in fusing sensor data with simulated data. This technique builds upon previous work that demonstrated the importance of physics-based transient models to accurate prediction of signal dynamics and system performance. While models can greatly improve predictive accuracy, they are difficult to apply in general because of variations in model type, accuracy, or intended purpose. However, virtually any flight project will have at least some modeling capability at its disposal, whether a full-blown simulation, partial physics models, dynamic look-up tables, a brassboard analogue system, or simple hand-driven calculation by a team of experts. Many models can be used to develop a predict, or an estimate of the next day s or next cycle s behavior, which is typically used for planning purposes. The fidelity of a predict varies from one project to another, depending on the complexity of the simulation (i.e. linearized or full differential equations) and the level of detail in anticipated system operation, but typically any predict cannot be adapted to changing conditions or adjusted spacecraft command execution. Applying a predict blindly, without adapting the predict to current conditions, produces mixed results at best, primarily due to mismatches between assumed execution of spacecraft activities and actual times of execution. This results in the predict becoming useless during periods of complicated behavior, exactly when the predict would be most valuable. Each spacecraft operation tends to show up as a transient in the data, and if the transients are misaligned, using the predict can actually harm forecasting performance. To address this problem, the approach here expresses the predict in terms of a baseline function superposed with one or more transient functions. These transients serve as signal templates, which can be relocated in time and space against the signal background. One then has the ability to reconstruct a signal regardless of the precise timing of the transients. During operation, one applies the actual start times of spacecraft activities as they occur, and produces a reconstructed, accurate predict in real-time. This general approach is valid under two important conditions. First, the transients themselves must be time-invariant. Second, the transients must be reasonably consistent with respect to different operating points. Both of these assumptions are generally valid, but in the case of a complicated system with numerous types of overlapping transients, this approach may not be effective. Fortunately, there tend to be few transients in spacecraft telemetry of sensor quantities or low-level health and status information because these signals rarely reflect multiple different types of operation. Furthermore, if the predict is at least reasonably close to actual operation, the shift either in time, or in the operating point when the transient occurs - is likely to be small. The proposed approach considers three ways to recognize a transient. The first and most reliable is to use a different signal that identifies operating mode - often the transient will be correlated to a change in operating mode, and this change can usually be detected positively from discrete signals in spacecraft telemetry. If there is no useful mode signal, the second option is to identify the transient template by hand, and detect the onset of the transient using a curve-fitting approach. Finally, if one elects not to choose by hand, there is an option for automatic selection. This technique has been applied to sensor data from several JPL missions and industrial applications, demonstrating an improvement in accurate prediction of future behavior and early detection of system problems. This technique is applicable to practically any time-varying, quantitative sensor measurement.

Mackey, Ryan↗

Identifiability of Additive, Time-Varying Actuator and Sensor Faults by State Augmentation

Recent work has provided a set of necessary and sucient conditions for identifiability of additive step faults (e.g., lock-in-place actuator faults, constant bias in the sensors) using state augmentation. This paper extends these results to an important class of faults which may affect linear, time-invariant systems. In particular, the faults under consideration are those which vary with time and affect the system dynamics additively. Such faults may manifest themselves in aircraft as, for example, control surface oscillations, control surface runaway, and sensor drift. The set of necessary and sucient conditions presented in this paper are general, and apply when a class of time-varying faults affects arbitrary combinations of actuators and sensors. The results in the main theorems are illustrated by two case studies, which provide some insight into how the conditions may be used to check the theoretical identifiability of fault configurations of interest for a given system. It is shown that while state augmentation can be used to identify certain fault configurations, other fault configurations are theoretically impossible to identify using state augmentation, giving practitioners valuable insight into such situations. That is, the limitations of state augmentation for a given system and configuration of faults are made explicit. Another limitation of model-based methods is that there can be large numbers of fault configurations, thus making identification of all possible configurations impractical. However, the theoretical identifiability of known, credible fault configurations can be tested using the theorems presented in this paper, which can then assist the efforts of fault identification practitioners.

Upchurch, Jason M.↗