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Control system eliminates or reduces flexibility effects on the manual and automatic control of large flexible vehicles. It extracts rigid-body and flexible-body motion and adapts well when a flexible-body frequency coincides or nearly coincides with the control mode frequency.
Consideration of the uncontrolled vehicle stability and control moment gyro (CMG) wobble damping of two typical modular-spinning-space-station configurations. General stability trends are established as a function of structural parameters. Results of investigations using a unique CMG wobble damping concept are presented, and requirements are formulated. Modifications to the basic control law required as a result of structural flexibility are described. The majority of the analyses were performed with the aid of a digital simulation of the flexible body dynamics. The description of the vehicles, the flexible body simulation, and the CMG wobble damping concept are presented. Previously established theory is supported insofar as the stabilization and control problems associated with a minimum inertia type spinning spacecraft are shown to be significantly greater than those of a maximum inertia vehicle. For example, the maximum inertia configuration investigated is stable for all structural flexibility conditions studied, while the stability of the minimum inertia configuration is dependent upon the distribution of energy dissipating material throughout the structure.
A flexible fin device for mounting on an aircraft to effect spin recovery is described. The device may be selectively deployed to provide a triangular planform of flexible material to provide spin recovery, and retracted for compact storage during non-use. A single flexible fin may be deflected in a specific direction depending on direction of spin rotation, or two flexible fins forming an inverted V configuration may be used. The device is mounted on the underbody of the aircraft.
The dynamics of rotational motion of a spinning orbiting spacecraft consisting of two rigid bodies connected by a flexible joint and arbitrary number of flexible appendages (two of which are flexible massless booms having masses on their tips) is analyzed. Active attitude control is provided by momentum exchange devices (e.g. control moment gyroscopes) or a mass expulsion system. The linearized equations of motion describing the vehicle are presented, and a large scale digital simulation that has been developed at the Marshall Space Flight Center is presented. A simplified model of the geometrically complex vehicle is selected to make it analytically tractable. The simplified model consists of a single rigid core body with two attached flexible massless booms having tip masses. The states of the vehicle are defined as small perturbations about its steady-state spin. An analysis is performed to determine the domain of stability.
The principal limitation on the accuracy of the hydrogen maser as a primary frequency standard has been the irreproducibility of the frequency shift caused by collisions of the radiating atoms with the walls of the vessel containing them. The flexible bulb-large storage box hydrogen maser allows correction for this wall shift within a single device, sidestepping the reproducibility problem, and reducing the frequency error from the wall shift to the level imposed by the device's stability. The principles of the device are discussed including the flexible bulb technique and the complications caused by a multiple region storage bulb. The stability of the device is discussed including a comparison with an ordinary hydrogen maser. Data is presented from a working flexible bulb-large storage box hydrogen maser demonstrating the feasibility of the device and showing some of its operating characteristics. The flexibility of the device is demonstrated by showing how the device's added degrees of freedom allow measurement of parameters unmeasurable in an ordinary hydrogen maser.
The equations of motion for a system of coupled flexible bodies, rigid bodies, point masses, and symmetric wheels were derived. The equations were cast into a partitioned matrix form in which certain partitions became nontrivial when the effects of flexibility were treated. The equations are shown to contract to the coupled rigid body equations or expand to the coupled flexible body equations all within the same basic framework. Furthermore, the coefficient matrix always has the computationally desirable property of symmetry. Making use of the derived equations, a comparison was made between the equations which described a flexible body model and those which described a rigid body model of the same elastic appendage attached to an arbitrary coupled body system. From the comparison, equivalence relations were developed which defined how the two modeling approaches described identical dynamic effects.
Several studies in which analytical procedures were used to obtain balancing criteria for flexible rotors are described. General response data for a uniform rotor in damped flexible supports were first obtained for plain cylindrical bearings, tilting pad bearings, axial groove bearings, and partial arc bearings. These data formed the basis for the flexible rotor balance criteria presented. A procedure by which a practical rotor in bearings could be reduced to an equivalent uniform rotor was developed and tested. It was found that the equivalent rotor response always exceeded to practical rotor response by more than sixty percent for the cases tested. The equivalent rotor procedure was then tested against six practical rotor configurations for which data was available. It was found that the equivalent rotor method offered a procedure by which balance criteria could be selected for practical flexible rotors, using the charts given for the uniform rotor.
A scheme for the control and maneuvering of a large flexible spacecraft by means of two flexible AMCD's using noncontacting magnetic suspension is presented. The system consists of a flexible vehicle, two flexible rings and a magnetic suspension and driving assembly. The necessary skewing of the rings for maneuvering of the vehicle is accomplished by moving the pairs of magnets along tracks distributed around the circumference of the vehicle. The equations of motion for each subsystem are derived by the Lagrangian approach. Attitude motions are described in terms of quasi-coordinates. For small vehicle angular rates and rings attitude motions, an ordering scheme can be used to separate the equations of motion according to the magnitude of the terms. The ordered equations of motion lead to a linear time-variant optimal control problem for the maneuvering of the spacecraft.
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.
The uncontrolled dynamics of an orbiting flexible beam in the presence of solar radiation pressure forces is considered. The effect of solar radiation forces and moments on the rigid and flexible modes of a free-free flexible beam is evaluated. It is found that moments result only from the flexible symmetric modal deformations. For small pitch amplitudes, and at near geosynchronous altitudes the solar radiation moments due to the deformations of the beam are seen to be greater than those due to the gravity-gradient. Within the linear range, simulated steady state dynamic responses show that the induced pitch amplitudes can be more significant than the induced amplitudes of the modal shape functions.
In order to analyze the dynamic behavior of the first stage compressor/fan of the 'E3' turbofan engine, a classical structural dynamics approach is employed to couple the motions of a flexible bladed disk to a rotating flexible shaft. The analysis accounts for flexible disk displacements which are transverse to the plane of rotation, and radial as well as tangential, and also accounts for rigid disk translations along, and rotations about, axes normal to the undeformed shaft axes. In the case of a wide range of E3 engine shaft flexibilities and speeds, some of the one-diametral node frequencies are shown to be affected by shaft degrees of freedom whose stiffness values are in general range of design practice. Coriolis forces are also found to significantly affect natural frequencies where strong coupling between certain modes is present.
A full scale prototype flexible radiator panel was designed, built and tested. The panel, has approximately 173 sq ft of radiating area and is designed to reject 1.33 kW of heat to a 0 F sink with a 100 F fluid inlet. The panel is constructed from a flexible Teflon/silver mesh fin surrounding 1/8 inch Teflon tubes. The prototype panel is stowed on a 10 inch diameter by 4 foot wide drum. (It rolls up to a diameter of 17 inches when fully stowed). Deployment of the soft tube prototype is via two four inch diameter Kevlar/Mylar inflation tubes with flat springs incorporated in each tube. Nitrogen is normally used for the deployment with approximately 1 psi required. The springs retract the panels when the inflation tubes are deflated. Another method of deployment available for the soft tube flexible is a motor driven deployable boom. This eliminates the need for expendables when the panel area is varied during the mission for heat load control. The soft tube panel is designed for a 90% probability of no punctured tube in a 30 day mission. The acceptable working fluids for this soft tube flexible are Coolanol 15, Coolanol 20 and Glycol/water (a eutectic mixture).
Quick, precise control of a flexible manipulator in a space environment is essential for future Space Station repair and satellite servicing. Numerous control algorithms have proven successful in controlling rigid manipulators wih colocated sensors and actuators; however, few have been tested on a flexible manipulator with noncolocated sensors and actuators. In this thesis, a model reference adaptive control (MRAC) scheme based on command generator tracker theory is designed for a flexible manipulator. Quicker, more precise tracking results are expected over nonadaptive control laws for this MRAC approach. Equations of motion in modal coordinates are derived for a single-link, flexible manipulator with an actuator at the pinned-end and a sensor at the free end. An MRAC is designed with the objective of controlling the torquing actuator so that the tip position follows a trajectory that is prescribed by the reference model. An appealing feature of this direct MRAC law is that it allows the reference model to have fewer states than the plant itself. Direct adaptive control also adjusts the controller parameters directly with knowledge of only the plant output and input signals.
An analysis is made of the dynamics of a thin, homogeneous, flexible square plate exposed to solar radiation disturbance. It is shown that only the first three flexible modes of the plate generate a first order net moment about the center of mass and that the solar radiation pressure does not influence the flexible modes of the plate for small-amplitude vibrations. In the absence of control, for a symmetrical homogeneous square platform, the solar radiation induces a steady angular drift about one of the body principal axes. For extremely flexible platforms, nominally oriented in the local horizontal plane, appreciable rigid modal amplitudes can be induced due to solar radiation, even in the presence of both active and passive control. Optimal control law and feedback gain values are obtained using linear quadratic Gaussian methods.
This paper presents the application of a model reference adaptive control (MRAC) algorithm to flexible aircraft flight control. The algorithm is an adaptive version of the Command Generator Tracking (CGT) control technique. This technique forces a dynamic system to follow a reduced-order model, allowing it to cope with the problem of unmodeled dynamics. The studies were made via simulation, using for the plant an aircraft dynamic model similar to the B1 bomber. This model is of a large aircraft with a reasonable amount of structural flexibility. In particular, flight configurations were analyzed where the influence of the flexible modes make it difficult to control the aircraft. The results indicate that the algorithm has good robustness properties vis-a-vis unmodeled dynamics and can force the flexible aircraft to follow rigid body responses.
As spacecraft structural concepts increase in size and flexibility, the vibration frequencies become more closely-spaced. The identification and control of such closely-spaced frequencies present a significant challenge. To validate system identification and control methods prior to actual flight, simpler space structures will be flown. To challenge the above technologies, it will be necessary to design these structures with closely-spaced or coupled vibration modes. Thus, there exists a need to develop a systematic method to design a structure which has closely-spaced vibration frequencies. This paper describes an optimization procedure which is used to design a large flexible structure to have closely-spaced vibration frequencies. The procedure uses a general-purpose finite element analysis program for the vibration and sensitivity analyses and a general-purpose optimization program. Results are presented from two studies. The first study uses a detailed model of a large flexible structure to design a structure with one pair of closely-spaced frequencies. The second study uses a simple equivalent beam model of a large flexible structure to obtain a design with two pairs of closely-spaced frequencies.
The utilization of piezoelectric actuators in controlling the structural vibrations of flexible beams is examined. A Modified Independent Modal Space Control (MIMSC) method is devised to enable the selection of the optimal location, control gains and excitation voltage of the piezoelectric actuators in a way that would minimize the amplitudes of vibrations of beams to which these actuators are bonded, as well as the input control energy necessary to suppress these vibrations. The developed method accounts for the effects that the piezoelectric actuators have on changing the elastic and inertial properties of the flexible beams. Numerical examples are presented to illustrate the application of the developed MIMSC method in minimizing the structural vibrations of beams of different materials when subjected to different loading and end conditions using ceramic or polymeric piezoelectric actuators. The obtained results emphasize the importance of the devised method in designing more realistic active control systems for flexible beams, in particular, and large flexible structures in general.
The significance of hub flexibility in the nonlinear static and dynamic analyses of advanced turboprop blades is assessed. The chosen blade is the 0.175 scale model of the GE-A7-B4 unducted fan blade. A procedure for coupling the effective hub stiffness matrix to an MSC/NASTRAN finite element model is defined and verified. A series of nonlinear static and dynamic analyses are conducted on the blade for both rigid and flexible hug configurations. Results indicate that hub flexibility is significant in the nonlinear static and dynamic analyses of the GE-A7-B4. In order to insure accuracy in analyses of other blades, hub flexibility should always be considered.