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NASA NTRS1993

Simulation of linear mechanical systems

A dynamics and controls analyst is typically presented with a structural dynamics model and must perform various input/output tests and design control laws. The required time/frequency simulations need to be done many times as models change and control designs evolve. This paper examines some simple ways that open and closed loop frequency and time domain simulations can be done using the special structure of the system equations usually available. Routines were developed to run under Pro-Matlab in a mixture of the Pro-Matlab interpreter and FORTRAN (using the .mex facility). These routines are often orders of magnitude faster than trying the typical 'brute force' approach of using built-in Pro-Matlab routines such as bode. This makes the analyst's job easier since not only does an individual run take less time, but much larger models can be attacked, often allowing the whole model reduction step to be eliminated.

Sirlin, S. W.↗

NASA NTRS1972

Control system optimization studies. Volume 2: High frequency cutoff filter analysis

The problem of digital implementation of a cutoff filter is approached with consideration to word length, sampling rate, accuracy requirements, computing time and hardware restrictions. Computing time and hardware requirements for four possible programming forms for the linear portions of the filter are determined. Upper bounds for the steady state system output error due to quantization for digital control systems containing a digital network programmed both in the direct form and in the canonical form are derived. This is accomplished by defining a set of error equations in the z domain and then applying the final value theorem to the solution. Quantization error was found to depend upon the digital word length, sampling rate, and system time constants. The error bound developed may be used to estimate the digital word length and sampling rate required to achieve a given system specification. From the quantization error accumulation, computing time and hardware point of view, and the fact that complex poles and zeros must be realized, the canonical form of programming seems preferable.

Fong, M. H.↗

NASA NTRS1978

Random motion analysis of flexible satellite structures

A singular perturbation formulation is used to study the responses of a flexible satellite when random measurement errors can occur. The random variables, at different instants of time, are assumed to be uncorrelated. Procedures for obtaining maxima and minima are described, and a variation of the linear method is developed for the formal solution of the two-point boundary-value problems represented by the variational equations. Random and deterministic solutions for the structural position coordinates are studied, and an analytic algorithm for treating the force equation of motion is developed. Since the random system indicated by the variational equation will always be asymptotically unstable, any analysis of stability must be based on the deterministic system.

Huang, T. C.↗

NASA NTRS1985

Vibration/Libration Interaction Dynamics During the Orbiter Based Deployment of Flexible Members

Essential features of a general formulation for studying librational dynamics of a large class of spacecraft during deployment of flexible members are reviewed. The formulation is applicable to a variety of missions ranging from deployment of antennas, booms and solar panels to manufacturing of trusses for space platforms using the space shuttle. The governing nonlinear, non-autonomous and coupled equations of motion are extremely difficult to solve even with the help of a computer, not to mention the cost involved. To get some appreciation as to the complex interactions between flexibility, deployment and attitude dynamics as well as to help pursue stability and control analysis, the equations are linearized about their nominal deflected equilibrium configuration. The procedure is applied to the Space Shuttle based deployment of boom and plate-like members. Results suggest substantial influence of the inertia parameter, flexural rigidity of the appendages, orbit eccentricity, deployment velocity, initial conditions, etc. on the system response. The results should prove useful in planning of the Orbiter based experiments aimed at assessing effectiveness of procedures for studying dynamics and control of flexible orbiting members.

Modi, V. J.↗

NASA NTRS1985

Two-phase flows within systems with ambient pressure

In systems where the design inlet and outlet pressures are maintained above the thermodynamic critical pressure, it is often assumed that two phase flows within the system cannot occur. Designers rely on this simple rule of thumb to circumvent problems associated with a highly compressible two phase flow occurring within the supercritical pressure system along with the uncertainties in rotordynamics, load capacity, heat transfer, fluid mechanics, and thermophysical property variations. The simple rule of thumb is adequate in many low power designs but is inadequate for high performance turbomachines and linear systems, where two phase regions can exist even though outlet pressure is greater than critical pressure. Rotordynamic-fluid-mechanic restoring forces depend on momentum differences, and those for a two phase zone can differ significantly from those for a single-phase zone. Using the Reynolds equation the angular velocity, eccentricity, geometry, and ambient conditions are varied to determine the point of two phase flow incipience.

Hendricks, R. C.↗

NASA NTRS1986

Heat and mass transfer in porous media phase separation at temperatures below the lambda-point of He-4

Newtonian fluid motion, coupled to heat transfer via latent heat of phase transition, is well known from numerous studies of condensation and boiling. Considerably less knowledge is available for vapor-liquid phase separation in the absence of gravity effect on the transport phenomena. The present studies are focused on heat and mass transfer associated with vapor-liquid phase separation required for long-term storage of the cryogen liquid He II in space vessels. Though space conditions are the dominant mode of interest in advanced equipment, e.g. IR telescopes, the systems may be operated in principle during terrestrial conditions. The latter are considered in the present work. It emphasizes the linear regime including an extrapolation based on variable thermophysical properties. Data taken with a phase separation approach show departures from the linear regime prediction. They agree with a transport equation proposed for the nonlinear, turbulent regime.

Yuan, S. W. K.↗

NASA NTRS1991

Second-order discrete Kalman filtering equations for control-structure interaction simulations

A general form for the first-order representation of the continuous, second-order linear structural dynamics equations is introduced in order to derive a corresponding form of first-order Kalman filtering equations (KFE). Time integration of the resulting first-order KFE is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete KFE involving only symmetric, N x N solution matrix.

Park, K. C.↗

NASA NTRS1993

Analyzing Martian winds and tracer concentrations using Mars Observer data

During the courses of a day, the Mars Observer spacecraft will acquire globally distributed profiles of the martian atmosphere. It is highly desirable that this data be assembled into synoptic weather maps (complete specifications of the atmospheric pressure, temperature, and winds at a given time), which can in turn be used as starting points in the study of many meteorological phenomena. Unfortunately, the special nature of the Mars Observer data presents several challenges above and beyond the usual difficult problem of data initialization. Mars Observer atmospheric data will consist almost exclusively of asynoptic vertical profiles of temperatures (or radiances) and pressures, whereas winds are generally in balance with horizontal gradients of these quantities (which will not be observed). It will therefore be necessary to resort to dynamical models to analyze the wind fields. As a rule, data assimilation into atmospheric models can result in the generation of spurious gravity waves, so special steps must be taken to suppress these. In addition, the asynoptic nature of the data will require a four-dimensional (space and time) data assimilation scheme. The problem is to find a full set of meteorological fields (winds and temperatures) such that, when marched forward in time in the model, they achieve a best fit (in the weighted least-squares sense) to the data. The proposed solution is to develop a model especially for the Mars Observer data assimilation problem. Gravity waves are filtered from the model by eliminating all divergence terms from the prognostic divergence equation. This leaves a diagnostic gradient wind relation between the rotational wind and the temperature field. The divergent wind is diagnosed as the wind required to maintain the gradient wind balance in the presence of the diabatic heating. The primitive equations of atmospheric dynamics (with three principal dependent variables) are thus reduced to a simpler system with a single prognostic equation for temperature - the variable that will be best observed. (This balance system was apparently first derived by Charney as a first-order Rossby number expansion of the equations of motion). Experience with a full primitive equation model of the martian atmosphere indicates that a further simplification is possible: at least for short-term integrations, the model can be linearized about the zonally symmetric basic state.

Houben, Howard C.↗

NASA NTRS1994

Dynamic analysis of a magnetic bearing system with flux control

Using measured values of two-dimensional forces in a magnetic actuator, equations of motion for an active magnetic bearing are presented. The presence of geometric coupling between coordinate directions causes the equations of motion to be nonlinear. Two methods are used to examine the unbalance response of the system: simulation by direct integration in time; and determination of approximate steady state solutions by harmonic balance. For relatively large values of the derivative control coefficient, the system behaves in an essentially linear manner, but for lower values of this parameter, or for higher values of the coupling coefficient, the response shows a split of amplitudes in the two principal directions. This bifurcation is sensitive to initial conditions. The harmonic balance solution shows that the separation of amplitudes actually corresponds to a change in stability of multiple coexisting solutions.

Knight, Josiah↗

NASA NTRS1995

Roll-yaw control at high angle of attack by forebody tangential blowing

The feasibility of using forebody tangential blowing to control the roll-yaw motion of a wind tunnel model is experimentally demonstrated. An unsteady model of the aerodynamics is developed based on the fundamental physics of the flow. Data from dynamic experiments is used to validate the aerodynamic model. A unique apparatus is designed and built that allows the wind tunnel model two degrees of freedom, roll and yaw. Dynamic experiments conducted at 45 degrees angle of attack reveal the system to be unstable. The natural motion is divergent. The aerodynamic model is incorporated into the equations of motion of the system and used for the design of closed loop control laws that make the system stable. These laws are proven through dynamic experiments in the wind tunnel using blowing as the only actuator. It is shown that asymmetric blowing is a highly non-linear effector that can be linearized by superimposing symmetric blowing. The effects of forebody tangential blowing and roll and yaw angles on the flow structure are determined through flow visualization experiments. The transient response of roll and yaw moments to a step input blowing are determined. Differences on the roll and yaw moment dependence on blowing are explained based on the physics of the phenomena.

Pedreiro, N.↗

NASA NTRS1995

Roll-Yaw control at high angle of attack by forebody tangential blowing

Pedreiro, N.↗

NASA NTRS2002

Reentry Vehicle Flight Controls Design Guidelines: Dynamic Inversion

This report addresses issues in developing a flight control design for vehicles operating across a broad flight regime and with highly nonlinear physical descriptions of motion. Specifically it addresses the need for reentry vehicles that could operate through reentry from space to controlled touchdown on Earth. The latter part of controlled descent is achieved by parachute or paraglider - or by all automatic or a human-controlled landing similar to that of the Orbiter. Since this report addresses the specific needs of human-carrying (not necessarily piloted) reentry vehicles, it deals with highly nonlinear equations of motion, and then-generated control systems must be robust across a very wide range of physics. Thus, this report deals almost exclusively with some form of dynamic inversion (DI). Two vital aspects of control theory - noninteracting control laws and the transformation of nonlinear systems into equivalent linear systems - are embodied in DI. Though there is no doubt that the mathematical tools and underlying theory are widely available, there are open issues as to the practicality of using DI as the only or primary design approach for reentry articles. This report provides a set of guidelines that can be used to determine the practical usefulness of the technique.

Ito, Daigoro↗

NASA NTRS2014

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part I: Linear Theory

Conical shell theory and piston theory aerodynamics are used to study the aeroelastic stability of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). Structural models of the TPS consist of single or multiple orthotropic conical shell systems resting on several circumferential linear elastic supports. The shells in each model may have pinned (simply-supported) or elastically-supported edges. The Lagrangian is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the equations of motion. The natural modes of vibration and aeroelastic stability boundaries are found by calculating the eigenvalues and eigenvectors of a large coefficient matrix. When the in-flight configuration of the TPS is approximated as a single shell without elastic supports, asymmetric flutter in many circumferential waves is observed. When the elastic supports are included, the shell flutters symmetrically in zero circumferential waves. Structural damping is found to be important in this case. Aeroelastic models that consider the individual TPS layers as separate shells tend to flutter asymmetrically at high dynamic pressures relative to the single shell models. Several parameter studies also examine the effects of tension, orthotropicity, and elastic support stiffness.

Goldman, Benjamin D.↗

NASA NTRSDate not supplied

Three-Dimensional Nonequilibrium Boundary Layer Stability & Transition Analysis For Martian Entry

In this work, we apply the boundary layer stability code LASTRAC, modified to include chemical and thermal nonequilibrium capabilities, to a simulated test case based on literature, with three-dimensional effects. LASTRAC provides Parabolized Stability Equations (PSE)as well as Linear Stability Theory (LST) to predict the stability of a boundary layer and transition with semiempirical eN methods. Tests of the Mars Science Laboratory (MSL)indicated a range of laminar to transitional flow conditions. In order to reduce the weight of Thermal Protection Systems (TPS), reliable prediction of transition and an understanding of the environmental factors that contribute to transition are necessary. This work is a step towards addressing this need, including the effects of thermochemical nonequilibrium but neglecting radiation, ablation, and ionization effects. Our results indicate that an oblique first mode produces maximum N-Factors on the symmetry plane, however with N-Factors too small to explain transition. Although we are able to show nonequilibrium three-dimensional PSE results inCO2, further study with improved mean flow solutions, accounting for some of the uncertainties inherent in this analysis, or evaluation of alternative transition mechanisms is needed to explain transition in the wind tunnel cases examined here.

H L Kline↗

NASA NTRS1976

A method for the analysis of nonlinearities in aircraft dynamic response to atmospheric turbulence

An analytical method is developed which combines the equivalent linearization technique for the analysis of the response of nonlinear dynamic systems with the amplitude modulated random process (Press model) for atmospheric turbulence. The method is initially applied to a bilinear spring system. The analysis of the response shows good agreement with exact results obtained by the Fokker-Planck equation. The method is then applied to an example of control-surface displacement limiting in an aircraft with a pitch-hold autopilot.

Sidwell, K.↗

NASA NTRS1978

A user oriented microcomputer facility for designing linear quadratic Gaussian feedback compensators

A laboratory design facility for digital microprocessor implementation of linear-quadratic-Gaussian feedback compensators is described. Outputs from user interactive programs for solving infinite time horizon LQ regulator and Kalman filter problems were conditioned for implementation on the laboratory microcomputer system. The software consisted of two parts: an offline high-level program for solving the LQ Ricatti equations and generating associated feedback and filter gains and a cross compiler/macro assembler which generates object code for the target microprocessor system. A PDP 11/70 with a UNIX operating system was used for all high level program and data management, and the target microprocessor system is an Intel MDS (8080-based processor). Application to the control of a two dimensional inverted pendulum is presented and issues in expanding the design/prototyping system to other target machine architectures are discussed.

Houpt, P. K.↗

NASA NTRS1978

Investigation of ODE integrators using interactive graphics

In the present paper, two FORTRAN programs are described which use an interactive graphic terminal to generate accuracy and stability plots for a given multistep integrator of ordinary differential equations (ODE). One program treats the fixed-stepsize linear case with complex variable solutions, and generates plots to show accuracy and error response to step driving function of a numerical solution. It also generates the linear stability region. The other program generates an analog with an accuracy plot. Both systems are capable of computing method coefficients from a simple specification of the method. Example plots are given.

Brown, R. L.↗

NASA NTRS1986

Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems

An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

Gibson, J. S.↗