SEARCH · Engineering Papers

Results for “linear dynamical systems”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,333 records · Page 74

All sources NASA NTRS DOE OSTI

NASA NTRS1980

Singular perturbation equations for flexible satellites

Force equations of motion of the individual flexible elements of a satellite were obtained in a previous paper. Moment equations of motion of the composite bodies of a flexible satellite are to be developed using two sets of equations which form the basic system for any dynamic model of flexible satellites. This basic system consists of a set of N-coupled, nonlinear, ordinary, or partial differential equations, for a flexible satellite with n generalized, structural position coordinates. For single composite body satellites, N is equal to (n + 3); for dual-spin systems, N is equal to (n + 9). These equations involve time derivatives up to the second order. The study shows a method of avoiding this linearization by reducing the N equations to 3 or 9 nonlinear, coupled, first order, ordinary, differential equations involving only the angular velocities of the composite bodies. The solutions for these angular velocities lead to linear equations in the n generalized structural position coordinates, which can be solved by known methods.

Huang, T. C.↗

NASA NTRS1992

Force regulation in multiple-manipulator systems

A new intuitively appealing interpretation of the internal force in a multiple-arm system is presented. The static gravity-free case is considered where internal force has a well-founded physical meaning. The case is extended to the general dynamic case by removing the inertial force through balancing it with the minimum amount of contact force. The remaining component in the contact force is considered to be the sole contributor to the inertial force. Existing techniques for force control can be used to obtain various stabilizing force set point control laws. Particular attention is given to the motion control strategy for multiple arm systems. Three types of control laws, feedback linearization, arms-as-actuators, and passive control, are addressed. The first two techniques provide simplified control tuning but require much model information. The latter approach is considered to be very robust with respect to the model, but good transient performance is more challenging to obtain. It is suggested to combine one of the model-based approaches with the passive control approach.

Wen, John T.↗

NASA NTRS2004

Pilots Rate Augmented Generalized Predictive Control for Reconfiguration

The objective of this paper is to report the results from the research being conducted in reconfigurable fight controls at NASA Ames. A study was conducted with three NASA Dryden test pilots to evaluate two approaches of reconfiguring an aircraft's control system when failures occur in the control surfaces and engine. NASA Ames is investigating both a Neural Generalized Predictive Control scheme and a Neural Network based Dynamic Inverse controller. This paper highlights the Predictive Control scheme where a simple augmentation to reduce zero steady-state error led to the neural network predictor model becoming redundant for the task. Instead of using a neural network predictor model, a nominal single point linear model was used and then augmented with an error corrector. This paper shows that the Generalized Predictive Controller and the Dynamic Inverse Neural Network controller perform equally well at reconfiguration, but with less rate requirements from the actuators. Also presented are the pilot ratings for each controller for various failure scenarios and two samples of the required control actuation during reconfiguration. Finally, the paper concludes by stepping through the Generalized Predictive Control's reconfiguration process for an elevator failure.

Soloway, Don↗

NASA NTRS1991

Modeling the spatiotemporal organization of velocity storage in the vestibuloocular reflex by optokinetic studies

1. A generalized three-dimensional state space model of visual vestibular interaction was developed. Matrix and dynamical system operators associated with inputs from the semicircular canals, otolith velocity estimator, and the visual system have been incorporated into the model, which focus on their relationship to the velocity storage integrator. 2. A relationship was postulated between the eigenvalues and the direction of the eigenvectors of the system matrix and the orientation of the spatial vertical. It was assumed that the system matrix for a tilted position was a composition of two linear transformations of the system matrix for the upright position. One transformation modifies the eigenvalues of the system matrix, whereas another rotates the eigenvectors of the system matrix. The pitch and roll eigenvectors rotate with the head, whereas the yaw axis eigenvector remains approximately spatially invariant. 3. Based on the three-dimensional model, a computational procedure was formulated to identify the eigenvalues and eigenvectors of the system matrix with the use of a modification of the marquardt algorithm. With the use of data obtained from a monkey, it was shown that the three-dimensional behavior of velocity storage cannot be predicted solely in terms of its time constants, i.e., the inverse of its eigenvalues. With the use of the same eigenvalues the data could either be fit or not fit, depending on the eigenvector directions. Therefore, it is necessary to specify eigenvector directions when characterizing velocity storage in three dimensions. 4. Parameters found with the use of the Marquardt algorithm were incorporated into the model. Diagonal matrices in a head coordinate frame were introduced for coupling the visual system to the integrator and to the direct optokinetic pathway. Simulations of optokinetic nystagmus (OKN) and optokinetic after-nystagmus (OKAN) were run. The model predicted the behavior of yaw and pitch OKN and OKAN when the animal is upright. It also predicted the cross-coupling in the side down position. The trajectories in velocity space were also accurately simulated. 5. One of the predictions of the model is that when the stimulus direction is along an eigenvector, the trajectory in velocity space is a straight line. Using the "spectral width" of the residuals from a straight line sequence during OKAN, we developed a methodology to estimate how close the OKAN decay was to an eigenvector trajectory. 6. Thus we have developed a model-based approach for studying and interpreting the response characteristics of velocity storage in three dimensions.(ABSTRACT TRUNCATED AT 400 WORDS).

Non-NASA Center↗

NASA NTRS1979

Space construction base control system

Several approaches for an attitude control system are studied and developed for a large space construction base that is structurally flexible. Digital simulations were obtained using the following techniques: (1) the multivariable Nyquist array method combined with closed loop pole allocation, (2) the linear quadratic regulator method. Equations for the three-axis simulation using the multilevel control method were generated and are presented. Several alternate control approaches are also described. A technique is demonstrated for obtaining the dynamic structural properties of a vehicle which is constructed of two or more submodules of known dynamic characteristics.

Kaczynski, R. F.↗

NASA NTRS1986

Further investigation into calibration techniques for a magnetic suspension and balance system

Calibrations performed on three different magnetic cores for wind tunnel models suspended in the Southampton University Magnetic Suspension and Balance System (SUMSBS) are detailed. The first core investigated was the Southampton University pilot Superconducting Solenoid model, first flown in July 1983. Static calibrations of lift force, drag force and pitching moment, together with lift force and pitching moment calibrations determined by the dynamic method are detailed in this report. Other types of core investigated in a similar manner were conventional permanent magnets, Alnico and samarium-cobalt. All static calibrations gave a linear dependence of force on electromagnet current as expected. Dynamic calibrations are faster to perform but are proving to be not as easily analyzed as static calibrations. There are still some effects to be explained but dynamic lift calibration results were obtained agreeing to within 2 percent of the static calibration value.

Eskins, J.↗

NASA NTRS1986

The dynamics and control of a space platform connected to a tethered subsatellite

A mathematical model of the open and closed loop dynamics of a space tethered-platform-subsatellite system (TPS) is developed. The TPS consists of a rigid platform from which an (assumed massless) tether is deploying a subsatellite from an attachment point which is offset from the mass center of the platform. Control is provided by modulation of the tension level in the tether and by momentum-type platform-mounted devices. Control-law gains are obtained based on linear quadratic regulator techniques. Typical transient responses are presented.

Fan, R.↗

NASA NTRS1988

Digital active control law synthesis for aeroservoelastic systems

This paper presents a formulation for synthesis of digital active control laws for aeroservoelastic systems, which are typically modeled by large order equations in order to accurately represent the rigid and flexible body modes, unsteady aerodynamic forces, actuator dynamics, and gust spectra. The control law is expected to satisfy multiple design requirements on the dynamic loads, responses, actuator deflection and rate limitations, as well as maintain certain stability margins, yet should be simple enough to be implemented by an onboard digital microprocessor. The synthesis procedure minimizes a linear quadratic Gaussian type cost function, by updating selected free parameters of the control law, while satisfying a set of inequality constraints on the design loads, responses and stability margins. A stable classical control law or an estimator based full or reduced order control law can be used as an initial design starting point. The gradients of the cost function and the constraints, with respect to the digital control law design variables are derived analytically, to facilitate rapid convergence. Selected design responses can be treated as constraints instead of lumping them into the cost function, in order to satisfy individual root-mean-square load and response limitations. Constraints are also imposed on the minimum singular value requirements for stability robustness improvement.

Mukhopadhyay, Vivekananda↗

NASA NTRS1990

Parallelization of implicit finite difference schemes in computational fluid dynamics

Implicit finite difference schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods are considerably more difficult and non-intuitive. The parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta-diagonal matrices is discussed. Three-dimensional cases are emphasized and schemes that minimize the total execution time are presented. Partitioning and scheduling schemes for alleviating the effects of the global data dependencies are described. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed.

Decker, Naomi H.↗

NASA NTRS1992

Stability analysis of surface tension effects on a double-diffusive layer

The linear stability characteristics of a fluid layer with simultaneous temperature and concentration gradients in a reduced gravity field are examined. The surface tension of the fluid is assumed to be a linear function of temperature and concentration. It is concluded that a small amount of gravity may damp out oscillatory instability or may alter its dynamics so that instability appears as steady convection. The onset of salt-finger instability may be in the overstable mode due to the surface tension method. The Lewis and Prandtl numbers of the material have a strong influence on the stability boundaries and onset characteristics of the system.

Chen, C. F.↗

NASA NTRS2011

Emergency Entry with One Control Torque: Non-Axisymmetric Diagonal Inertia Matrix

In another work, a method was presented, primarily conceived as an emergency backup system, that addressed the problem of a space capsule that needed to execute a safe atmospheric entry from an arbitrary initial attitude and angular rate in the absence of nominal control capability. The proposed concept permits the arrest of a tumbling motion, orientation to the heat shield forward position and the attainment of a ballistic roll rate of a rigid spacecraft with the use of control in one axis only. To show the feasibility of such concept, the technique of single input single output (SISO) feedback linearization using the Lie derivative method was employed and the problem was solved for different number of jets and for different configurations of the inertia matrix: the axisymmetric inertia matrix (I(sub xx) > I(sub yy) = I(sub zz)), a partially complete inertia matrix with I(sub xx) > I(sub yy) > I(sub zz), I(sub xz) not = 0 and a realistic complete inertia matrix with I(sub xx) > I(sub yy) > I)sub zz), I(sub ij) not= 0. The closed loop stability of the proposed non-linear control on the total angle of attack, Theta, was analyzed through the zero dynamics of the internal dynamics for the case where the inertia matrix is axisymmetric (I(sub xx) > I(sub yy) = I(sub zz)). This note focuses on the problem of the diagonal non-axisymmetric inertia matrix (I(sub xx) > I(sub yy) > I(sub zz)), which is half way between the axisymmetric and the partially complete inertia matrices. In this note, the control law for this type of inertia matrix will be determined and its closed-loop stability will be analyzed using the same methods that were used in the other work. In particular, it will be proven that the control system is stable in closed-loop when the actuators only provide a roll torque.

Llama, Eduardo Garcia↗

NASA NTRS1989

Space Power Free-Piston Stirling Engine Scaling Study

The design feasibility study is documented of a single cylinder, free piston Stirling engine/linear alternator (FPSE/LA) power module generating 150 kW-electric (kW sub e), and the determination of the module's maximum feasible power level. The power module configuration was specified to be a single cylinder (single piston, single displacer) FPSE/LA, with tuning capacitors if required. The design requirements were as follows: (1) Maximum electrical power output; (2) Power module thermal efficiency equal to or greater than 20 percent at a specific mass of 5 to 8 kg/kW(sub e); (3) Heater wall temperature/cooler wall temperature = 1050 K/525 K; (4) Sodium heat-pipe heat transport system, pumped loop NaK (sodium-potassium eutectic mixture) rejection system; (5) Maximum power module vibration amplitude = 0.0038 cm; and (6) Design life = 7 years (60,000 hr). The results show that a single cylinder FPSE/LA is capable of meeting program goals and has attractive scaling attributes over the power range from 25 to 150 kW(sub e). Scaling beyond the 150 kW(sub e) power level, the power module efficiency falls and the power module specific mass reaches 10 kg/kW(sub e) at a power output of 500 kW(sub e). A discussion of scaling rules for the engine, alternator, and heat transport systems is presented, along with a detailed description of the conceptual design of a 150 kW(sub e) power module that meets the requirements. Included is a discussion of the design of a dynamic balance system. A parametric study of power module performance conducted over the power output range of 25 to 150 kW(sub e) for temperature ratios of 1.7, 2.0, 2.5, and 3.0 is presented and discussed. The results show that as the temperature ratio decreases, the efficiency falls and specific mass increases. At a temperature ratio of 1.7, the 150 kW(sub e) power module cannot satisfy both efficiency and specific mass goals. As the power level increases from 25 to 150 kW(sub e) at a fixed temperature ratio, power module efficiency is seen to increase slightly, but at the expense of increased specific mass. An empirical equation relating power module thermal efficiency as a function of power module specific mass, power output, and temperature ratio is developed. Alternative configurations to the single cylinder, direct coupled linear alternator approach are also evaluated, but are shown to have technical drawbacks that lessen their attractiveness. The dynamic balance assembly mass (moving mass and structure) represents 20 to 30 percent of the total single cylinder power module mass. Joining two modules in a balanced opposed configuration eliminates the need for the balancer, and a hot end junction can be made without significant addition of structural mass. Recommendations are made for evaluation of advanced heat pipe concepts, tests of radial flow heat exchangers, and evaluation of high temperature alternator materials.

Jones, D.↗

NASA NTRS1972

Characteristics of hingeless rotors with hub moment feedback controls including experimental rotor frequency response, Volume 1

Wind tunnel tests to determine the dynamic characteristics of hingeless rotors with hub moment feedback controls and to acquire experimental hingeless rotor transfer functions are discussed. Rotor transfer functions were calculated from data acquired during open loop frequency response tests. The transfer functions are linear and present the rotor longitudinal and lateral frequency responses to collective pitch, longitudinal cyclic pitch, and lateral cyclic pitch. The theoretical analysis was based on the rigid blade flapping model coupled with appropriate control system and cyclic pitch actuator equations of motion.

Kuczynski, W. A.↗

NASA NTRS1975

Sustained small oscillations in nonlinear control systems

Some results of bifurcation theory were used to study the existence of small-amplitude periodic behavior in launch vehicle dynamics, assuming that nonlinearity exists as a cubic term in the rudder response. The analysis follows closely Sattinger's (1973) approach to the theory of periodic bifurcations. The conditions under which a bifurcating branch of orbitally stable periodic solutions will exist are determined. It is shown that in more complicated cases, the conditions under which the system matrix has a pair of simple purely imaginary eigenvalues can be determined with the aid of linear stability techniques.

George, J. H.↗

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 NTRS1977

Efficient numerical treatment of periodic systems with application to stability problems

Two efficient numerical methods for dealing with the stability of linear periodic systems are presented. Both methods combine the use of multivariable Floquet-Liapunov theory with an efficient numerical scheme for computing the transition matrix at the end of one period. The numerical properties of these methods are illustrated by applying them to the simple parametric excitation problem of a fixed end column. The practical value of these methods is shown by applying them to some helicopter rotor blade aeroelastic and structural dynamics problems. It is concluded that these methods are numerically efficient, general and practical for dealing with the stability of large periodic systems.

Friedmann, P.↗

NASA NTRS1986

Ephemeris errors of GPS satellites

Numerical models are developed to examine the potential effects of solar radiation, the terrestrial gravitational field, and the estimated initial state of the Global Positioning System (GPS) satellites, along with the capability of current models to account for the effects on the ephemeris of the GPS constellation. Of particular interest is the accuracy of the satellite position predictions for applications in geodesy. The main characteristics of the GPS orbits are reviewed and linear combinations of possible errors for 3 day ephemerides are examined. It is shown that the effects of the forces on the GPS orbits will be dynamic, yet can be expressed simply enough to maintain positioning accuracy to 1 percent. The calculations can also take into consideration solar wind pressure on the solar panels.

Colombo, O. L.↗

NASA NTRS1988

Guaranteed properties for nonlinear gain scheduled control systems

An analysis is presented of two types of nonlinear gain-scheduled control systems: scheduling on a reference trajectory and scheduling on the plant output. Conditions are given which guarantee stability, robustness, and performance properties of the global gain-scheduled designs. These conditions confirm and formalize popular notions regarding gain-scheduled designs; e.g., that the scheduling variable should vary slowly and capture the plant's nonlinearities. These results extend the work of Shamma and Athans (1987), which addressed the case of linear plants whose dynamics depends on exogenous parameters.

Shamma, Jeff S.↗