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Numerical experiments on the problem of moving a flexible beam are discussed. An optimal control problem is formulated and transcribed into a form which can be solved using semi-infinite optimization techniques. All experiments were carried out on a SUN 3 microcomputer.
Several models were built at NASA Langley and used to demonstrate the following nonlinear behavior: internal resonance in a free response, principal parametric resonance and subcritical instability in a cantilever beam-lumped mass structure, combination resonance in a parametrically excited flexible beam, autoparametric interaction in a two-degree-of-freedom system, instability of the linear solution, saturation of the excited mode, subharmonic bifurcation, and chaotic responses. A video tape documenting these phenomena was made. An attempt to identify a simple structure consisting of two light-weight beams and two lumped masses using the Eigensystem Realization Algorithm showed the inherent difficulty of using a linear based theory to identify a particular nonlinearity. Preliminary results show the technique requires novel interpretation, and hence may not be useful for structural modes that are coupled by a guadratic nonlinearity. A literature survey was also completed on recent work in parametrically excited nonlinear system. In summary, nonlinear systems may possess unique behaviors that require nonlinear identification techniques based on an understanding of how nonlinearity affects the dynamic response of structures. In this was, the unique behaviors of nonlinear systems may be properly identified. Moreover, more accutate quantifiable estimates can be made once the qualitative model has been determined.
The H and the related H(sub 2) controller design methodologies allow for the design of control systems that meet tracking requirements and, at the same time, maintain the binding disturbance rejection properties.
It has been demonstrated that a high frequency excitation (HFE) field significantly changes the fundamental properties of mechanical systems. The most important contribution of HFE is the stiffening effect of an elastic continuum in the direction of the wave vector. This effect allows control of stiffness in any selected direction by the corresponding changes in the intensity of HFE. This new approach can be effective for large flexible space structures. Such an approach may prove to be very practical in the sense that large structures need to be made as flimsy as possible for low cost under ordinary situations. However, for certain operations such as development, orbital transfer, docking, and other circumstances, it would be vital to have a means of temporarily stiffening certain structural members. If the structure was designed to meet these occasional loads without temporary stiffening, it would be considerably more massive and more expensive.
This project (NAG9-574) was meant to be a three-year research project. However, due to NASA's reorganizations during 1992, the project was funded only for one year. Accordingly, every effort was made to make the present final report as if the project was meant to be for one-year duration. Originally, during the first year we were planning to accomplish the following: we were to start with a three dimensional flexible manipulator beam with articulated joints and with a linear control-based controller applied at the joints; using this simple example, we were to design the software systems requirements for real-time processing, introduce the streamlining of various computational algorithms, perform the necessary reorganization of the partitioned simulation procedures, and assess the potential speed-up realization of the solution process by parallel computations. The three reports included as part of the final report address: the streamlining of various computational algorithms; the necessary reorganization of the partitioned simulation procedures, in particular the observer models; and an initial attempt of reconfiguring the flexible space structures.
Control systems design and hardware testing are addressed for an experimental structure that displays the characteristics of a typical flexible spacecraft. The results of designing and implementing various control design methodologies are described. The design methodologies under investigation include linear quadratic Gaussian control, static and dynamic dissipative controls, and H-infinity optimal control. Among the three controllers considered, it is shown, through computer simulation and laboratory experiments on the evolutionary structure, that the dynamic dissipative controller gave the best results in terms of vibration suppression and robustness with respect to modeling errors.
This paper presents a formulation for the modeling of a single-link flexible beam that is undergoing slewing motion at an actively controlled pinned end, where the other end of the beam is free. This pinned end, or slewing axis, is of fixed orientation such that the beam rotates in the horizontal plane. A geared dc electric motor is connected to the beam at the slewing axis. A position and a velocity sensor are placed at this hinged location, and their proportional feedback provides a position control system about the slewing axis. The motor characteristics, gear ratio, and the position feedback constant determine an equivalent rotational spring constant, often called the servo stiffness. This paper generalizes the structure's boundary conditions at the slewing axis to include the effects of the servo system. It is shown that the clamped-free beam assumption for the dynamics of the structure is a valid assumption if the ratio of the servo stiffness to beam flexibility is high. However, for moderate or low values of this ratio, the clamped-free beam leads to erroneous system models so that it becomes necessary to consider the effects of the driving servo on the dynamics of the flexible beam.
A generic procedure for the parameter optimization of a digital control law for a large-order flexible flight vehicle or large space structure modeled as a sampled data system is presented. A linear quadratic Guassian type cost function was minimized, while satisfying a set of constraints on the steady-state rms values of selected design responses, using a constrained optimization technique to meet multiple design requirements. Analytical expressions for the gradients of the cost function and the design constraints on mean square responses with respect to the control law design variables are presented.
A major challenge to the structural dynamicist is to validate mathematical models of large space structures which cannot be ground tested because of its size and/or flexibility. The paper presents a Multiple Boundary Condition Test (MBCT) approach which allows a systematic validation of the mathematical model by performing a number of ground tests on a large structure with variable boundary conditions. A numerical simulation is presented which illustrates the validity of the MBCT including some of the potential limitations.
Recently, a modal domain optical fiber sensor has been demonstrated as a sensor in a control system for vibration suppression of a flexible cantilevered beam. This sensor responds to strain through a mechanical attachment to the structure. Because this sensor is of the interferometric type, the output of the sensor has a sinusoidal nonlinearity. For small levels of strain, the sensor can be operated in its linear region. For large levels of strain, the detection electronics can be configured to count fringes. In both of these configurations, the sensor nonlinearity imposes some restrictions on the performance of the control system. In this paper we investigate the effects of these sensor nonlinearities on the control system, and identify the region of linear operation in terms of the optical fiber sensor parameters.
A computer program, ISAC, is described which calculates the stability and response of a flexible airplane equipped with active controls. The equations of motion relative to a fixed inertial coordinate system are formulated in terms of the airplane's rigid body motion and its unrestrained normal vibration modes. Unsteady aerodynamic forces are derived from a doublet lattice lifting surface theory. The theoretical basis for the program is briefly explained together with a description of input data and output results.
Distributed parameter modeling of structural dynamics has been limited to simple spacecraft configurations because of the difficulty of handling several distributed parameter systems linked at their boundaries. Although there is other computer software able to generate such models or complex, flexible spacecraft, unfortunately, neither is suitable for parameter estimation. Because of this limitation the computer software PDEMOD is being developed for the express purposes of modeling, control system analysis, parameter estimation and structure optimization. PDEMOD is capable of modeling complex, flexible spacecraft which consist of a three-dimensional network of flexible beams and rigid bodies. Each beam has bending (Bernoulli-Euler or Timoshenko) in two directions, torsion, and elongation degrees of freedom. The rigid bodies can be attached to the beam ends at any angle or body location. PDEMOD is also capable of performing parameter estimation based on matching experimental modal frequencies and static deflection test data. The underlying formulation and the results of using this approach for test data of the Mini-MAST truss will be discussed. The resulting accuracy of the parameter estimates when using such limited data can impact significantly the instrumentation requirements for on-orbit tests.
Preliminary attitude and articulation controller designs for the CRAF/Cassini spacecraft have prompted a consideration of potential interactions with structural dynamics and propellant motion. The two algorithms significantly affected are attitude control during main engine burns, and articulation control of the high-precision scan platform (HPSP). For main engine burns, the primary concerns are the sloshing of the bipropellant, which constitutes 70 percent of initial spacecraft mass, and the vibration of the three large appendages, especially the HPSP, on which the gyros are mounted. For the HPSP pointing algorithm, the main concern is the fairly large offset of the HPSP center-of-mass from the gimbals, which is motivated by other system and subsystem considerations. This offset results in significant coupling between HPSP articulation and HPSP boom structural dynamics. This paper surveys the operational scenarios of these algorithms, and the impacts of nonrigid dynamics on controller design and performance.
The method of active modal damping (AMD) is reviewed, and the pinhole/occulter facility (P/OF) is presented as a design example. This system is a large space system composed of a flexible beam, a gimbal-pointing system, and an optical alignment system mounted in the Shuttle cargo bay and excited by typical Shuttle disturbances. The AMD system performance is compared with that of a series-compensated control system.
One of the biggest challenges facing NASA's deep space exploration goals is structural mass. A long duration transit vehicle on a journey to Mars, for example, requires a large internal volume for cargo, supplies and crew support. As with all space structures, a large pressure vessel is not enough. The vehicle also requires thermal, micro-meteoroid, and radiation protection, a navigation and control system, a propulsion system, and a power system, etc. As vehicles get larger, their associated systems also get larger and more complex. These vehicles require larger lift capacities and force the mission to become extremely costly. In order to build large volume habitable vehicles, with only minimal increases in launch volume and mass, NASA is developing lightweight structures. Lightweight structures are made from non-metallic materials including graphite composites and high strength fabrics and could provide similar or better structural capability than metals, but with significant launch volume and mass savings. Fabric structures specifically, have been worked by NASA off and on since its inception, but most notably in the 1990's with the TransHAB program. These TransHAB developed structures use a layered material approach to form a pressure vessel with integrated thermal and micro-meteoroid and orbital debris (MMOD) protection. The flexible fabrics allow the vessel to be packed in a small volume during launch and expand into a much larger volume once in orbit. NASA and Bigelow Aerospace recently installed the first human-rated inflatable module on the International Space Station (ISS), known as the Bigelow Expandable Activity Module (BEAM) in May of 2016. The module provides a similar internal volume to that of an Orbital ATK Cygnus cargo vehicle, but with a 77% launch volume savings. As lightweight structures are developed, testing methods are vital to understanding their behavior and validating analytical models. Common techniques can be applied to fabric materials, such as tensile testing, fatigue testing, and shear testing, but common measurement techniques cannot be used on fabric. Measuring strain in a material and during a test is a critical parameter for an engineer to monitor the structure during the test and correlate to an analytical model. The ability to measure strain in fabric structures is a challenge for NASA. Foil strain gauges, for example, are commonplace on metallic structures testing, but are extremely difficult to interface with a fabric substrate. New strain measuring techniques need to be developed for use with fabric structures. This paper investigates options for measuring strain in fabric structures for both ground testing and in-space structural health monitoring. It evaluates current commercially available options and outlines development work underway to build custom measurement solutions for NASA's fabric structures.
An analytic redundancy management approach for on-line component failure detection is described and illustrated using a simulation of the NASA Langley Spacecaft Control Laboratory Experiment (SCOLE) research facility. The SCOLE experimental apparatus simulated is a functional model of the Space Shuttle with a large, flexible, offset-feed antenna cantilevered from the payload bay. This approach uses a single, active, Kalman filter selected from a bank of filters, each element of which was previously designed to accommodate a specific failure condition. The residuals of this active filter are processed through a sequential probability ratio test (SPRT) filter to identify the failure state of the system and, hence, closing the failure accommodation loop, to select the active filter. Results are presented that illustrate the ability of the system to detect and recover from failures introduced in the angular rate and linear acceleration sensors on the SCOLE facility.
The steady state solution of the linear quadratic optimal control problem with the constraint that only partial state information is available for feedback is derived. This development results in a systematic and computationally efficient approach for reducing the complexity of the control law for high order systems. Numerical examples and performance evaluation of (1) a simple fourth order system, and (2) a free-free flexible beam, are included.
Analysis extends technique for design of widely used type of vibration-isolating mounts for aircraft engines, in which rubber mounting pads located in plane behind center of gravity of enginepropeller combination. New analysis treats problem in statics. Results of simple approach useful in providing equations for design of vibrationisolating mounts. Equations applicable in usual situation in which engine-mount structure itself relatively light and placed between large mass of engine and other heavy components of airplane.