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A method for optimally shifting the imaginary parts of the open-loop poles of a multivariable control system to the desirable closed-loop locations is presented. The optimal solution with respect to a quadratic performance index is obtained by solving a linear matrix Liapunov equation.
A reduced order Kalman Filter, based on a simplification of the Singular Evolutive Extended Kalman (SEEK) filter equations, is used to assimilate observed fields of the surface wind stress, sea surface temperature and sea level into the nonlinear coupled ocean-atmosphere model. The SEEK filter projects the Kalman Filter equations onto a subspace defined by the eigenvalue decomposition of the error forecast matrix, allowing its application to high dimensional systems. The Zebiak and Cane model couples a linear reduced gravity ocean model with a single vertical mode atmospheric model of Zebiak. The compatibility between the simplified physics of the model and each observed variable is studied separately and together. The results show the ability of the model to represent the simultaneous value of the wind stress, SST and sea level, when the fields are limited to the latitude band 10 deg S - 10 deg N. In this first application of the Kalman Filter to a coupled ocean-atmosphere prediction model, the sea level fields are assimilated in terms of the Kelvin and Rossby modes of the thermocline depth anomaly. An estimation of the error of these modes is derived from the projection of an estimation of the sea level error over such modes. This method gives a value of 12 for the error of the Kelvin amplitude, and 6 m of error for the Rossby component of the thermocline depth. The ability of the method to reconstruct the state of the equatorial Pacific and predict its time evolution is demonstrated. The method is shown to be quite robust for predictions I up to six months, and able to predict the onset of the 1997 warm event fifteen months before its occurrence.
A reduced order Kalman Filter, based on a simplification of the Singular Evolutive Extended Kalman (SEEK) filter equations, is used to assimilate observed fields of the surface wind stress, sea surface temperature and sea level into the nonlinear coupled ocean-atmosphere model of Zebiak and Cane. The SEEK filter projects the Kalman Filter equations onto a subspace defined by the eigenvalue decomposition of the error forecast matrix, allowing its application to high dimensional systems. The Zebiak and Cane model couples a linear reduced gravity ocean model with a single vertical mode atmospheric model of Zebiak. The compatibility between the simplified physics of the model and each observed variable is studied separately and together. The results show the ability of the model to represent the simultaneous value of the wind stress, SST and sea level, when the fields are limited to the latitude band 10 deg S - 10 deg N In this first application of the Kalman Filter to a coupled ocean-atmosphere prediction model, the sea level fields are assimilated in terms of the Kelvin and Rossby modes of the thermocline depth anomaly. An estimation of the error of these modes is derived from the projection of an estimation of the sea level error over such modes. This method gives a value of 12 for the error of the Kelvin amplitude, and 6 m of error for the Rossby component of the thermocline depth. The ability of the method to reconstruct the state of the equatorial Pacific and predict its time evolution is demonstrated. The method is shown to be quite robust for predictions up to six months, and able to predict the onset of the 1997 warm event fifteen months before its occurrence.
The dynamic response of a nonlinear, single degree of freedom structural system subjected to a physically white noise parametric excitation is investigated. The Ito stochastic calculus is employed to derive a general differential equation for the moments of the response coordinates. The differential equations of moments of any order are found to be coupled with higher order moments. A non-Gaussian closure scheme is developed to truncate the moment equations up to fourth order. The statistical of the stationary response are computed numerically and compared with analytical solutions predicted by a Gaussian closure scheme and the stochastic averaging method. It is found that the computed results exhibit the jump phenomenon which is typical of the characteristics of deterministic nonlinear systems. In addition, the numerical algorithm leads to multiple solutions all of which give positive mean squares. However, two of these solutions are found to violate the properties of high order moments. One solution preserves the moments properties and demonstrates that the system achieves a stationary response.
An efficient implicit finite-difference method is developed and tested for a global barotropic model. The scheme requires, at each time step, the solution of only one-dimensional block-tridiagonal linear systems. This additional computation is offset by the use of a time step chosen independently of the mesh spacing. The method is second-order accurate in time and fourth-order accurate in space. Present experience indicates that this implicit method is practical for numerical simulation on fine meshes.
In the development and testing of novel structural and controls concepts, such as morphing aircraft wings, appropriate models are needed for proper system characterization. In most instances, available system models do not provide the required additional degrees of freedom for morphing structures but may be modified to some extent to achieve a compatible system. The objective of this study is to apply wind tunnel data collected for an Unmanned Air Vehicle (UAV), that implements trailing edge morphing, to create a non-linear dynamics simulator, using well defined rigid body equations of motion, where the aircraft stability derivatives change with control deflection. An analysis of this wind tunnel data, using data extraction algorithms, was performed to determine the reference aerodynamic force and moment coefficients for the aircraft. Further, non-linear influence functions were obtained for each of the aircraft s control surfaces, including the sixteen trailing edge flap segments. These non-linear controls influence functions are applied to the aircraft dynamics to produce deflection-dependent aircraft stability derivatives in a non-linear dynamics simulator. Time domain analysis of the aircraft motion, trajectory, and state histories can be performed using these nonlinear dynamics and may be visualized using a 3-dimensional aircraft model. Linear system models can be extracted to facilitate frequency domain analysis of the system and for control law development. The results of this study are useful in similar projects where trailing edge morphing is employed and will be instrumental in the University of Maryland s continuing study of active wing load control.
A system composed of several interconnected elastic components that may experience large angular motion relative to each other during operation is referred to as a flexible multibody structure. Several formulations were proposed for the determination of the dynamic response of controlled flexible multibody structures. In general, these formulations consist of superposing elastic deformations of the component body onto the large rigid body motion of the component. It was shown that this particular methodology for combining linear structural deformations with nonlinear kinematics can lead to erroneous response predictions when either the beam member is very flexible or the rotational speed is high. In addition, previous formulations introduce constraint equations to define the interrelations among system components. This approach increases the number of equations that must be solved, and may result in contraint violation when numerical error accumulates during the integration process. In order to overcome the difficulties, a new approach was suggested. The approach is essentially a finite element formulation which takes advantage of the fact that many multibody structures are joint dominated. The Large Angle Transient Dynamic Analysis (LATDYN) program for clarity of documentation, ease of use, user friendliness, modeling generality, and accuracy of results was evaluated. This required gaining a working familiarity with the code and performing several case studies.
The requirements placed on an unsteady aerodynamic theory intended for turbomachinery aeroelastic applications are discussed along with a brief description of the various theoretical models that are available to address these requirements. The main emphasis is placed on the description of a linearized inviscid theory which fully accounts for the effects of a nonuniform mean or steady flow on unsteady aerodynamic response. Although this theory has been developed primarily for blade flutter prediction, more general equations are presented which account for unsteady excitations due to incident external aerodynamic disturbances as well as those due to blade motions. The resulting equations consist of a system of three field equations along with conditions imposed at blade, wake and shock surfaces and in the far field. These equations can be solved to determine the fluctuations in all fluid dynamic properties throughout the required solution domain. Example solutions are presented to demonstrate several effects associated with nonuniform steady flows on the linearized unsteady aerodynamic response to prescribed blade motions.
A stability and control augmentation system (SCAS) was designed based on a set of comprehensive performance criteria. Linear optimal control theory was applied to determine appropriate feedback gains for the stability augmentation system (SAS). The helicopter was represented by six-degree-of-freedom rigid body equations of motion and constant factors were used as weightings for state and control variables. The ratio of these factors was employed as a parameter for SAS analysis and values of the feedback gains were selected on this basis to satisfy three of the performance criteria for full and partial state feedback systems. A least squares design method was then applied to determine control augmentation system (CAS) cross feed gains to satisfy the remaining seven performance criteria. The SCAS gains were then evaluated by nine degree-of-freedom equations which include flapping motion and conclusions drawn concerning the necessity of including the pitch/regressing and roll/regressing modes in SCAS analyses.
Adaptive control techniques are studied for their future application to the control of large space structures, where uncertain or changing parameters may destabilize standard control system designs. The approach used is to examine an extended Kalman filter estimator, in which the state vector is augmented with the unknown parameters. The associated Riccatti equation is linearized about the case of exact knowledge of the parameters. By assuming that parameter variations occur slowly, the filter complexity is reduced further yet. Simulations on a two degree-of-freedom oscillator demonstrate the parameter-tracking capability of the filter, and an implementation on the JPL Flexible Beam Facility using an incorrect model shows the adaptive filter/optimal control to be stable where a standard Kalman filter/optimal control design is unstable.
A stabilization problem for Burgers' equation is considered. Using linearization, various controllers are constructed which minimize certain weighted energy functionals. These controllers produce the desired degree of stability for the closed-loop nonlinear system. A numerical scheme for computing the feedback gain functional is developed and several numerical experiments are performed to show the theoretical results.
The feasibility of space very long base interferometry (VLBI) observables for geodesy and geodynamics is investigated. A brief review of space VLBI systems from the point of view of potential geodetic application is given. A selected notational convention is used to jointly treat the VLBI observables of different types of baselines within a combined ground/space VLBI network. The basic equations of the space VLBI observables appropriate for convariance analysis are derived and included. The corresponding equations for the ground-to-ground baseline VLBI observables are also given for a comparison. The simplified expression of the mathematical models for both space VLBI observables (time delay and delay rate) include the ground station coordinates, the satellite orbital elements, the earth rotation parameters, the radio source coordinates, and clock parameters. The observation equations with these parameters were examined in order to determine which of them are separable or nonseparable. Singularity problems arising from coordinate system definition and critical configuration are studied. Linear dependencies between partials are analytically derived. The mathematical models for ground-space baseline VLBI observables were tested with simulation data in the frame of some numerical experiments. Singularity due to datum defect is confirmed.
The nonlinear multigrid is an efficient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble. In particular, we prove the convergence of the nonlinear V-cycle method for a class of mildly nonlinear second order elliptic boundary value problems which do not have full elliptic regularity.
We have performed numerical simulations of weakly and strongly magnetized relativistic jets embedded in a weakly and strongly magnetized stationary or mildly relativistic (0.5c) sheath using the RAISHIN code. In the numerical simulations a jet with Lorentz factor gamma=2.5 is precessed to break the initial equilibrium configuration. Results of the numerical simulations are compared to theoretical predictions from a normal mode-analysis of the linearized RMHD equations describing a uniform axially magnetized cylindrical relativistic jet embedded in a uniform axially magnetized moving sheath. The prediction of increased stability of a weakly-magnetized system with mildly relativistic sheath flow to Kelvin-Helmholtz instabilities and the stabilization of a strongly-magnetized system with mildly relativistic sheath flow is confirmed by the numerical simulations.
We have performed numerical simulations of weakly and strongly magnetized relativistic jets embedded in a weakly and strongly magnetized stationary or mildly relativistic (0.5c) sheath flow using the RAISHIN code. In the numerical simulations a jet with Lorentz factor gamma=2.5 is processed to break the initial equilibrium configuration. Results of the numerical simulations are compared to theoretical predictions from a normal mode analysis of the linearized RMHD equations describing a uniform axially magnetized cylindrical relativistic jet embedded in a uniform axially magnetized sheath flow. The prediction of increased stability of a weakly-magnetized system with mildly relativistic sheath flow to Kelvin-Helmholtz instabilities and the stabilization of a strongly magnetized system with mildly relativistic sheath flow is confirmed by the numerical simulations.
We have performed numerical simulations of weakly and strongly magnetized relativistic jets embedded in a weakly and strongly magnetized stationary or mildly relativistic'(0.5c) sheath flow using the RAISHIN code. In the numerical simulations a jet with Lorentz factor gamma=2.5 is processed to break the initial equilibrium configuration. Results of the numerical simulations are compared to theoretical predictions from a normal mode analysis of the linearized RMHD equations describing a uniform axially magnetized cylindrical relativistic jet embedded in a uniform axially magnetized sheath flow. The prediction of increased stability of a weakly-magnetized system with mildly relativistic sheath flow to Kelvin-Helmholtz instabilities and the stabilization of a strongly-magnetized system with mildly relativistic sheath flow is confirmed by the numerical simulations.
NASA's Digital Astronaut Project (DAP) implements well-vetted computational models to predict and assess spaceflight health and performance risks, and enhance countermeasure development. DAP provides expertise and computation tools to its research customers for model development, integration, or analysis. DAP is currently supporting the NASA Exercise Physiology and Countermeasures (ExPC) project by integrating their biomechanical models of specific exercise movements with dynamic models of the devices on which the exercises were performed. This presentation focuses on the development of a high fidelity dynamic module of the Advanced Resistive Exercise Device (ARED) on board the ISS. The ARED module, illustrated in the figure below, was developed using the Adams (MSC Santa Ana, California) simulation package. The Adams package provides the capabilities to perform multi rigid body, flexible body, and mixed dynamic analyses of complex mechanisms. These capabilities were applied to accurately simulate: Inertial and mass properties of the device such as the vibration isolation system (VIS) effects and other ARED components, Non-linear joint friction effects, The gas law dynamics of the vacuum cylinders and VIS components using custom written differential state equations, The ARED flywheel dynamics, including torque limiting clutch. Design data from the JSC ARED Engineering team was utilized in developing the model. This included solid modeling geometry files, component/system specifications, engineering reports and available data sets. The Adams ARED module is importable into LifeMOD (Life Modeler, Inc., San Clemente, CA) for biomechanical analyses of different resistive exercises such as squat and dead-lift. Using motion capture data from ground test subjects, the ExPC developed biomechanical exercise models in LifeMOD. The Adams ARED device module was then integrated with the exercise subject model into one integrated dynamic model. This presentation will describe the development of the Adams ARED module including its capabilities, limitations, and assumptions. Preliminary results, validation activities, and a practical application of the module to inform the relative effect of the flywheels on exercise will be discussed.
An algorithm is described that is based on the method of breaking the Laplace transform down into partial fractions which are then inverse-transformed separately. The sum of the resulting partial functions is the wanted time function. Any problems caused by equation system forms are largely limited by appropriate normalization using an auxiliary parameter. The practical limits of program application are reached when the degree of the denominator of the Laplace transform is seven to eight.