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A multiflexible body dynamics code intended for fast turnaround control design trades is described. Nonlinear rigid body dynamics and linearized flexible dynamics combine to provide efficient solution of the equations of motion. Comparison with results from the DISCOS code provide verification of accuracy.
The rigid body dynamics and control of the tether, subsatellite and space platform are analyzed, during deployment, stationkeeping and retrieval phases using the Linear Quadratic Regulator (LQR) approach, accounting for the mass of the tether as well as a three dimensional offset of its point of attachment. The strategies employ tension in the tether line, thrusters, motion of the offset of the tether attachment point or their hybrid combinations. An assessment of the relative merit suggests the thruster-offset hybrid controller to be the most effective in damping given disturbances.
This paper outlines the development of a mathematical model that is expected to be useful for rotorcraft flying qualities research. A computer model is presented that can be applied to a range of different rotorcraft configurations. The algorithm computes vehicle trim and a linear state-space model of the aircraft. The trim algorithm uses non linear optimization theory to solve the nonlinear algebraic trim equations. The linear aircraft equations consist of an airframe model and a flight control system dynamic model. The airframe model includes coupled rotor and fuselage rigid body dynamics and aerodynamics. The aerodynamic model for the rotors utilizes blade element theory and a three state dynamic inflow model. Aerodynamics of the fuselage and fuselage empennages are included. The linear state-space description for the flight control system is developed using standard block diagram data.
Understanding the contact dynamics of nonspherical particles is crucial for accurately modeling colloidal and granular systems where shape anisotropy dictates structural organization and transport properties. We here introduce an energy-conserving contact dynamics framework for arbitrary convex rigid-body particles by implementing vertex–boundary interactions in 2D and vertex–surface and edge–edge detection in 3D. The established formulation enables continuous force evaluation and prevents particle overlap while conserving total energy during translational and rotational motion. We demonstrate the framework’s stability and its utility to capture packing behavior, anisotropic diffusion, and equations of state of polygonal and polyhedral particles as examples. The framework establishes a robust and extensible foundation for investigating nonequilibrium dynamics of complex nonspherical particulate systems, enabling enhanced understanding of phenomena across spatiotemporal scales in self- and directed-assembly, granular flows, and hydrodynamics, potentially coupled with interactions that represent underlying physical mechanisms.
The Space Technology 7 experiment will perform an on-orbit system-level validation of two specific Disturbance Reduction System technologies: a gravitational reference sensor employing a free-floating test mass and a set of micro-Newton colloidal thrusters. The ST7 Disturbance Reduction System is designed to maintain the spacecraft s position with respect to a free-floating test mass to less than 10 nm/the square root of Hz over the frequency range of 1 to 30 mHz. This requirement will help ensure that the residual accelerations on the test masses (beyond gravitational acceleration) will be below the ST7 goal of 300 (1 + [f/3 mHz](sup 2)) pm/s(sup 2)/the square root of Hz. This paper presents the overall design and analysis of the spacecraft drag-free and attitude controllers being designed by NASA s Goddard Space Flight Center. These controllers close the loop between the GRS and the micro-Newton colloidal thrusters. The ST7 DRS comprises three control systems: the attitude control system to maintain a sun-pointing attitude, the drag free control to center the spacecraft about the test masses, and the test mass suspension control. There are five control modes in the operation of the ST7-DRS, starting from the attitude-only mode and leading to the challenging science mode. The design and analysis of each of the control modes are presented. An 18-DOF model is developed to capture the essential dynamics of the ST7-DRS package. It includes all rigid-body dynamics of the spacecraft and two test masses (three translations and three rotations for the spacecraft and each of the test masses). Actuation and measurement noise and major disturbance sources acting on the spacecraft and test masses are modeled.
Multidisciplinary tools for prediction of single rectangular-tail buffet are extended to single swept-back-tail buffet in transonic-speed flow, and multidisciplinary tools for prediction and control of twin-tail buffet are developed and presented. The configuration model consists of a sharp-edged delta wing with single or twin tails that are oriented normal to the wing surface. The tails are treated as cantilevered beams fixed at the root and allowed to oscillate in both bending and torsion. This complex multidisciplinary problem is solved sequentially using three sets of equations on a dynamic single or multi-block grid structure. The first set is the unsteady, compressible, Reynolds-averaged Navier-Stokes equations which are used for obtaining the flow field vector and the aerodynamic loads on the tails. The Navier-Stokes equations are solved accurately in time using the implicit, upwind, flux-difference splitting, finite volume scheme. The second set is the coupled bending and torsion aeroelastic equations of cantilevered beams which are used for obtaining the bending and torsion deflections of the tails. The aeroelastic equations'are solved accurately in time using, a fifth-order-accurate Runge-Kutta scheme. The third set is the grid-displacement equations and the rigid-body dynamics equations, which are used for updating the grid coordinates due to the tail deflections and rigid-body motions. The tail-buffet phenomenon is predicted for highly-swept, single vertical tail placed at the plane of geometric symmetry, and for highly-swept, vertical twin tails placed at three different spanwise separation distances. The investigation demonstrates the effects of structural inertial coupling and uncoupling of the bending and torsion modes of vibration, spanwise positions of the twin-tail, angle of attack, and pitching and rolling dynamic motions of the configuration model on the tail buffet loading and response. The fundamental issue of twin-tail buffet alleviation is addressed using two active flow-control methods. These methods are the tangential leading-edge blowing and the flow suction from the leading-edge vortex cores along their paths. Qualitative and quantitative comparisons with the available experimental data are presented. The comparisons indicate that the present multidisciplinary aeroelastic analysis tools are robust, accurate and efficient.
A mathematical model was developed to simulate the staging dynamics of a proposed space shuttle configuration. Included in the mathematical model is the kinematics and dynamics of the staging mechanism, thrust forces and thrust vector control, rigid-body dynamics, and structural dynamics of both the booster and orbiter stages of the configuration. The mathematical model was incorporated into a computer program so that the staging maneuver could be simulated. Results of the simulations are presented.
Comparative evaluation of seven insensitive synthesis techniques applied to the control of the longitudinal axis and symmetric flexure modes of the C-5A aircraft is described. These techniques have the common goal of achieving insensitivity to parameter uncertainties and unmodeled dynamics. For this comparison, the 'complete' model was assumed to consist of rigid body dynamics, fifteen flexure modes, unsteady aerodynamics, gust dynamics, and first order actuators for two control inputs. Thirteen flexure modes and the unsteady aerodynamics were treated as neglected dynamics. Dynamic pressure, structural frequency and damping, and the stability derivative were treated as uncertain parameters. Design specifications consisted of a transient response criterion, statistical response criteria, eigenvalue criteria and stability margins. A nominal controller designed without regard to sensitivity served as a benchmark for performance comparisons of the insensitive controllers.
The Articulated Total Body (ATB) model is a computer sumulation program which was originally developed for the study of aircrew member dynamics during ejection from high-speed aircraft. This model is totally three-dimensional and is based on the rigid body dynamics of coupled systems which use Euler's equations of motion with constraint relations of the type employed in the Lagrange method. In this paper the use of the ATB model as a robot dynamics simulation tool is discussed and various simulations are demonstrated. For this purpose the ATB model has been modified to allow for the application of torques at the joints as functions of state variables of the system. Specifically, the motion of a robotic arm with six revolute articulations with joint torques prescribed as functions of angular displacement and angular velocity are demonstrated. The simulation procedures developed in this work may serve as valuable tools for analyzing robotic mechanisms, dynamic effects, joint load transmissions, feed-back control algorithms employed in the actuator control and end-effector trajectories.
This paper presents the overall design and analysis process of the spacecraft controller being developed at NASA's Goddard Space Flight Center to close the loop between the GRS and the micro-newton colloidal thrusters. The essential dynamics of the ST7-DRS are captured in a simulation including eighteen rigid-body dynamic degrees of freedom: three translations and three rotations for the spacecraft and for each test mass. The ST7 DRS comprises three control systems: the attitude control system (ACS) to maintain a sun-pointing attitude; the drag free control (DFC) to center the spacecraft about the test masses; and the test mass suspension control. This paper summarizes the control design and analysis of the ST7-DRS 18-DOF model, and is an extension of previous analyses employing a 7-DOF planar model of ST-7.
The Lunar Reconnaissance Orbiter (LRO) undergoes a series of thruster maneuvers to attain lunar orbit. The first of the series of lunar orbit insertion (LOI) maneuvers is crucial to the success of the mission. Therefore, it is important to characterize the disturbances acting on the spacecraft during this phase of the mission. This paper focuses on the internal disturbance force caused by fuel slosh and its impact on attitude control. During the first LOI maneuver (LOI-1), approximately 50% of the total fuel mass is used or roughly 25% of the spacecraft s wet mass, during the 38-minute burn. The forces imparted on the spacecraft from the fuel are dependent on the fill level of the two fuel tanks. During LOI-1, the fill level in both tanks varies greatly and thus so does the disturbance level caused by the fuel. It is therefore necessary to account for the time-varying mass properties of the spacecraft and the effects of the varying fuel levels during the entire 38-minute maneuver. Two simulations are developed in Mathworks s Simulink to analyze the fuel slosh effect. The first model, a baseline model, is a rigid body dynamics model where the fuel slosh is not modeled. The second is a multibody model, developed using a multibody dynamics toolbox, where each of the two fuel tanks and the remaining spacecraft body are treated as separate rigid bodies. The simulations are executed in a piece-wise fashion to account for the time-varying mass properties, and to accommodate the multibody toolbox. Disturbances caused by fuel slosh during both lunar and mission orbit insertions will be analyzed through simulation of different dynamics models. Results of the analysis will show the effects of the slosh disturbance on the spacecraft s attitude.
In the dynamic formulation of holonomic and nonholonomic systems based on D'Alembert-Lagrange equation, the forces of constraints are maintained in the dynamic equations by introducing auxiliary variables, called Lagrange multipliers. This approach introduces a set of generalized reaction forces associated with the system generalized coordinates. Different sets of variables can be used as generalized coordinates and accordingly, the generalized reactions associated with these generalized coordinates may not be the actual reaction forces at the joints. In rigid body dynamics, the generalized reaction forces and the actual reaction forces at the joints represent equipollent systems of forces since they produce the same total forces and moments at and about any point on the rigid body. This is not, however, the case in deformable body analyses wherein the generalized reaction forces depend on the system generalized reference and elastic coordinates. In this paper, a method for determining the actual reaction forces at the joints from the generalized reaction forces in deformable multibody systems is presented.
The Modeling and Control for Agile Aircraft Development project (MCAAD) seeks to reduce the time spent on wind tunnel testing and computational fluid dynamic modeling when developing control laws for new commercial and military aircraft. MCAAD uses advanced dynamic modeling procedures coupled with real-time control design which can reduce the time and cost spent on traditional aircraft development methods. This is done in-flight by using a real-time modeling procedure where programmed test inputs (PTI) deflect the aircraft control surfaces, and the responses are measured in order to create a dynamic model. This paper presents an 𝐻∞-based linear parameter-varying (LPV) control law designed on a nonlinear rigid-body dynamic model which commands control surface deflections at frequencies above the PTI frequency band. Thus the controller will not suppress the response due to the PTI. The LPV controller is compared with a previously designed Nonlinear Dynamic Inversion (NDI) controller and the coherence between the commanded control surface deflections and the PTI is plotted for both controllers. The LPV controller is shown to distort the PTI less than the NDI controller.
A computational procedure suitable for the solution of equations of motions for flexible multibody systems has been developed. A fully nonlinear continuum approach capable of accounting for both finite rotations and large deformations has been used to model a flexible beam component. The beam kinematics are referred directly to an inertial reference frame such that the degrees of freedom embody both the rigid and flexible deformation motions. As such, the beam inertia expression is identical to that of rigid body dynamics. The nonlinear coupling between gross body motion and elastic deformation is contained in the internal force expression. Numerical solution procedures for the integration of spatial kinematic systems can be directily applied to the generalized coordinates of both the rigid and flexible components. An accurate computation of the internal force term which is invariant to rigid motions is incorporated into the general solution procedure.
Dynamic stability analysis of the Multi-Purpose Crew Vehicle (MPCV) is performed us-ing the US3D flow solver and a plugin library to solve rigid-body dynamics, Free-Flight CFD(FF-CFD). Previous efforts investigated the free-flight behavior of higher speed, open-backaeroshell shapes. Three primary experimental sources are used to evaluate the predictivecapability of the FF-CFD solver in the low supersonic range (Mach≈1). First, the ballisticrange results obtained at the HFFAF facility at NASA Ames is used to verify the six degree-of-freedom (6-DoF) dynamic capability of the FF-CFD solver. Next, FF-CFD simulationsare preformed using restricted motion and the resultant trajectories are post-processed toobtain pitch damping coefficient as a function of angle-of-attack. The comparison of thepitch damping results obtained with one degree-of-freedom (1-DoF) FF-CFD compare wellwith experimental fits derived from ballistic range data. Finally, the atmospheric flight ca-pability of FF-CFD is compared to data from the Ascent Abort-2 (AA-2) flight experiment.Two simulations were performed using forced and forced-free flight to investigate surfacepressure predictive capability and free-flight aerodynamic performance through a varyingatmosphere at low speed (Mach 0.6-0.2). Surface pressure predicted with FF-CFD agreeswell with experimental trends, with slight over-prediction near the end of the trajectory.The total angle-of-attack for the free-flight portion agrees well with experimental data.
This grant provided for the demonstration of coupled controls, body dynamics, and fluids computations in a workstation cluster environment; and an investigation of the impact of peer-peer communication on flow solver performance and robustness. The findings of these investigations were documented in the conference articles.The attached publication, 'Towards Distributed Fluids/Controls Simulations', documents the solution and scaling of the coupled Navier-Stokes, Euler rigid-body dynamics, and state feedback control equations for a two-dimensional canard-wing. The poor scaling shown was due to serialized grid connectivity computation and Ethernet bandwidth limits. The scaling of a peer-to-peer communication flow code on an IBM SP-2 was also shown. The scaling of the code on the switched fabric-linked nodes was good, with a 2.4 percent loss due to communication of intergrid boundary point information. The code performance on 30 worker nodes was 1.7 (mu)s/point/iteration, or a factor of three over a Cray C-90 head. The attached paper, 'Nonlinear Fluid Computations in a Distributed Environment', documents the effect of several computational rate enhancing methods on convergence. For the cases shown, the highest throughput was achieved using boundary updates at each step, with the manager process performing communication tasks only. Constrained domain decomposition of the implicit fluid equations did not degrade the convergence rate or final solution. The scaling of a coupled body/fluid dynamics problem on an Ethernet-linked cluster was also shown.
During the space power facility jettison tests, the non-domed half of the Centaur standard shroud was allowed to completely separate from its hinge connection and was caught in a horizontal catch net. A rigid body dynamic analysis that was performed to predict the half shroud prior to and after net contact is presented. Analytical predictions of the longitudinal and circumferential bending moments imposed on the half shroud by the catch net and the net pressure on the half shroud corrugated skin are also presented.
The fuel-to-dry-mass ratio of spacecraft continues to grow as new human spaceflight missions target destinations from Earth. Large amounts of liquid propellant can lead to significant coupling between the rigid-body dynamics of the spacecraft and the motion of the fuel within its storage tank. The present work gives an overview of the dynamic features and a flowchart for a method of simulating the motion of a spacecraft with fuel slosh inside a cylindrical, domed tank in a low-g environment. The method involves modeling the liquid propellant as a particle that transfers momentum to the spacecraft through perfectly inelastic collisions with the tank wall. The foundation of the modeling methodology is the approach taken during the Apollo program used to predict the effect of fuel slosh on the complex motion exhibited by the Service Module following separation from the Crew Module. This paper discusses the motivation, methodology, and conclusions from the Apollo-era method, and subsequently builds upon it by incorporating corrections to the derivation of the dynamics and filling in the gaps due to unavailability of the detailed contractor report and simulation code. The results presented in this paper provide an example that demonstrates the effect that fuel slosh can have on the trajectory of a spacecraft in a low-g environment.