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NASA NTRS2008

Low-Impact Mating System for Docking Spacecraft

A document describes a low-impact mating system suitable for both docking (mating of two free-flying spacecraft) and berthing (in which a robot arm in one spacecraft positions an object for mating with either spacecraft). The low-impact mating system is fully androgynous: it mates with a copy of itself, i.e., all spacecraft and other objects to be mated are to be equipped with identical copies of the system. This aspect of the design helps to minimize the number of unique parts and to standardize and facilitate mating operations. The system includes a closed-loop feedback control subsystem that actively accommodates misalignments between mating spacecraft, thereby attenuating spacecraft dynamics and mitigating the need for precise advance positioning of the spacecraft. The operational characteristics of the mating system can be easily configured in software, during operation, to enable mating of spacecraft having various masses, center-of-gravity offsets, and closing velocities. The system design provides multi-fault tolerance for critical operations: for example, to ensure unmating at a critical time, a redundant unlatching mechanism and two independent pyrotechnic release subsystems are included.

Lewis, James L.↗

NASA NTRS2011

Optical Sensors for Monitoring Gamma and Neutron Radiation

For safety and efficiency, nuclear reactors must be carefully monitored to provide feedback that enables the fission rate to be held at a constant target level via adjustments in the position of neutron-absorbing rods and moderating coolant flow rates. For automated reactor control, the monitoring system should provide calibrated analog or digital output. The sensors must survive and produce reliable output with minimal drift for at least one to two years, for replacement only during refueling. Small sensor size is preferred to enable more sensors to be placed in the core for more detailed characterization of the local fission rate and fuel consumption, since local deviations from the norm tend to amplify themselves. Currently, reactors are monitored by local power range meters (LPRMs) based on the neutron flux or gamma thermometers based on the gamma flux. LPRMs tend to be bulky, while gamma thermometers are subject to unwanted drift. Both electronic reactor sensors are plagued by electrical noise induced by ionizing radiation near the reactor core. A fiber optic sensor system was developed that is capable of tracking thermal neutron fluence and gamma flux in order to monitor nuclear reactor fission rates. The system provides near-real-time feedback from small- profile probes that are not sensitive to electromagnetic noise. The key novel feature is the practical design of fiber optic radiation sensors. The use of an actinoid element to monitor neutron flux in fiber optic EFPI (extrinsic Fabry-Perot interferometric) sensors is a new use of material. The materials and structure used in the sensor construction can be adjusted to result in a sensor that is sensitive to just thermal, gamma, or neutron stimulus, or any combination of the three. The tested design showed low sensitivity to thermal and gamma stimuli and high sensitivity to neutrons, with a fast response time.

Boyd, Clark D.↗

NASA NTRS1994

System identification of the Large-Angle Magnetic Suspension Test Fixture (LAMSTF)

The Large-Angle Magnetic Suspension Test Fixture (LAMSTF), a laboratory-scale research project to demonstrate the magnetic suspension of objects over wide ranges of attitudes, has been developed. This system represents a scaled model of a planned Large-Gap Magnetic Suspension System (LGMSS). The LAMSTF consists of a small cylindrical permanent magnet suspended element which is levitated above a planar array of five electromagnets mounted in a circular configuration. The cylinder is a rigid body and can be controlled to move in five independent degrees of freedom. Six position variables are sensed indirectly by using infrared light-emitting diodes and light-receiving phototransistors. The motion of the suspended cylinder is in general nonlinear and hence only the linear, time-invariant perturbed motion about an equilibrium state is considered. One of the main challenges in this project is the control of the suspended element over a wide range of orientations. An accurate dynamic model plays an essential role in controller design. The analytical model is first derived and open-loop characteristics discussed. The system is shown to be highly unstable and requires feedback control for system identification. Projection filters are first proposed to identify the state space model from closed-loop input/output test data in the time domain. This method is then extended to identify linear systems from the frequency test data. A canonical transformation matrix is also derived to transform the identified state space model into the physical coordinate. The LAMSTF system is stabilized by using a linear quadratic regulator (LQR) feedback controller for closed-loop identification. The rate information is obtained by calculating the back difference of the sensed position signals. Only the closed-loop random input/output data are recorded. Preliminary results from numerical simulations demonstrate that the identified system model is fairly accurate from either time domain or frequency-domain data. Experiments will be performed to validate the proposed closed-loop identification algorithms.

Huang, Jen-Kuang↗

NASA NTRS2018

Output Feedback Adaptive Control of Non-Minimum Phase Systems Using Optimal Control Modification

This paper describes output feedback adaptive control approaches for non-minimum phase SISO systems with relative degree 1 and non-strictly positive real (SPR) MIMO systems with uniform relative degree 1 using the optimal control modification method. It is well-known that the standard model-reference adaptive control (MRAC) cannot be used to control non-SPR plants to track an ideal SPR reference model. Due to the ideal property of asymptotic tracking, MRAC attempts an unstable pole-zero cancellation which results in unbounded signals for non-minimum phase SISO systems. The optimal control modification can be used to prevent the unstable pole-zero cancellation which results in a stable adaptation of non-minimum phase SISO systems. However, the tracking performance using this approach could suffer if the unstable zero is located far away from the imaginary axis. The tracking performance can be recovered by using an observer-based output feedback adaptive control approach which uses a Luenberger observer design to estimate the state information of the plant. Instead of explicitly specifying an ideal SPR reference model, the reference model is established from the linear quadratic optimal control to account for the non-minimum phase behavior of the plant. With this non-minimum phase reference model, the observer-based output feedback adaptive control can maintain stability as well as tracking performance. However, in the presence of the mismatch between the SPR reference model and the non-minimum phase plant, the standard MRAC results in unbounded signals, whereas a stable adaptation can be achieved with the optimal control modification. An application of output feedback adaptive control for a flexible wing aircraft illustrates the approaches.

Adaptive Contro↗

NASA NTRS1983

Control techniques to improve Space Shuttle solid rocket booster separation

The present Space Shuttle's control system does not prevent the Orbiter's main engines from being in gimbal positions that are adverse to solid rocket booster separation. By eliminating the attitude error and attitude rate feedback just prior to solid rocket booster separation, the detrimental effects of the Orbiter's main engines can be reduced. In addition, if angular acceleration feedback is applied, the gimbal torques produced by the Orbiter's engines can reduce the detrimental effects of the aerodynamic torques. This paper develops these control techniques and compares the separation capability of the developed control systems. Currently with the worst case initial conditions and each Shuttle system dispersion aligned in the worst direction (which is more conservative than will be experienced in flight), the solid rocket booster has an interference with the Shuttle's external tank of 30 in. Elimination of the attitude error and attitude rate feedback reduces that interference to 19 in. Substitution of angular acceleration feedback reduces the interference to 6 in. The two latter interferences can be eliminated by atess conservative analysis techniques, that is, by using a root sum square of the system dispersions.

Tomlin, D. D.↗

NASA NTRS1993

Six-Degree-Of-Freedom Magnetic Vibration Isolator

Feedback control provides soft mount and damping of vibrations. Active magnetic suspension system centers inner structure in position and orientation with respect to principal Cartesian coordinate axes of base or outer structure, stationary with respect to building or vehicle. System helps to isolate suspended mass from vibrations of building or vehicle. Designed to isolate 500-kg experimental apparatus from vibrations of spacecraft, but also used on Earth, provided that its z axis vertical and system assisted by low-stiffness vertical spring that, in steady state, holds up inner structure at nominal vertical position.

Gerver, Michael J.↗

NASA NTRS1992

Pilot-in-the-loop analysis of propulsive-only flight control systems

Longitudinal control system architectures which directly couple flight stick motions to throttle commands for a multi-engine aircraft are presented. This coupling enables positive attitude control with complete failure of the flight control system. The architectures chosen vary from simple feedback gains to classical lead-lag compensators with and without prefilters. Each architecture is reviewed for its appropriateness for piloted flight. The control systems are then analyzed with pilot-in-the-loop metrics related to bandwidth required for landing. Results indicate that current and proposed bandwidth requirements should be modified for throttles-only flight control. Pilot ratings consistently showed better ratings than predicted by analysis. Recommendations are made for more robust design and implementation. The use of quantitative feedback theory for compensator design is discussed. Although simple and effective augmented control can be achieved in a wide variety of failed configurations, a few configuration characteristics are dominant for pilot-in-the-loop control.

Chou, Hwei-Lan↗

NASA NTRS1996

Pilot-in-the-Loop Analysis of Propulsive-Only Flight Control Systems

Longitudinal control system architectures are presented which directly couple flight stick motions to throttle commands for a multi-engine aircraft. This coupling enables positive attitude control with complete failure of the flight control system. The architectures chosen vary from simple feedback gains to classical lead-lag compensators with and without prefilters. Each architecture is reviewed for its appropriateness for piloted flight. The control systems are then analyzed with pilot-in-the-loop metrics related to bandwidth required for landing. Results indicate that current and proposed bandwidth requirements should be modified for throttles only flight control. Pilot ratings consistently showed better ratings than predicted by analysis. Recommendations are made for more robust design and implementation. The use of Quantitative Feedback Theory for compensator design is discussed. Although simple and effective augmented control can be achieved in a wide variety of failed configurations, a few configuration characteristics are dominant for pilot-in-the-loop control. These characteristics will be tested in a simulator study involving failed flight controls for a multi-engine aircraft.

Chou, Hwei-Lan↗

NASA NTRS2018

Faraday Forcing of High-Temperature Levitated Liquid Metal Drops for the Measurement of Surface Tension

In this work, a method for the measurement of surface tension using continuous periodic forcing is presented. To reduce gravitational effects, samples are electrostatically levitated prior to forcing. The method, called Faraday forcing, is particularly well suited for fluids that require high temperature measurements such as liquid metals where conventional surface tension measurement methods are not possible. It offers distinct advantages over the conventional pulse-decay analysis method when the sample viscosity is high or the levitation feedback control system is noisy. In the current method, levitated drops are continuously translated about a mean position at a small, constant forcing amplitude over a range of frequencies. At a particular frequency in this range, the drop suddenly enters a state of resonance, which is confirmed by large executions of prolate/oblate deformations about the mean spherical shape. The arrival at this resonant condition is a signature that the parametric forcing frequency is equal to the drop’s natural frequency, the latter being a known function of surface tension. A description of the experimental procedure is presented. A proof of concept is given using pure Zr and a Ti(sub 39.5)Zr(sub 39.5)Ni(sub 21) alloy as examples. The results compare favorably with accepted literature values obtained using the pulse-decay method.

Nevin Brosius↗

NASA NTRS2011

Project Management Using Modern Guidance, Navigation and Control Theory

Implementing guidance, navigation, and control (GN&C) theory principles and applying them to the human element of project management and control is not a new concept. As both the literature on the subject and the real-world applications are neither readily available nor comprehensive with regard to how such principles might be applied, this paper has been written to educate the project manager on the "laws of physics" of his or her project (not to teach a GN&C engineer how to become a project manager) and to provide an intuitive, mathematical explanation as to the control and behavior of projects. This paper will also address how the fundamental principles of modern GN&C were applied to the National Aeronautics and Space Administration's (NASA) Constellation Program (CxP) space suit project, ensuring the project was managed within cost, schedule, and budget. A project that is akin to a physical system can be modeled and managed using the same over arching principles of GN&C that would be used if that project were a complex vehicle, a complex system(s), or complex software with time-varying processes (at times nonlinear) containing multiple data inputs of varying accuracy and a range of operating points. The classic GN&C theory approach could thus be applied to small, well-defined projects; yet when working with larger, multiyear projects necessitating multiple organizational structures, numerous external influences, and a multitude of diverse resources, modern GN&C principles are required to model and manage the project. The fundamental principles of a GN&C system incorporate these basic concepts: State, Behavior, Feedback Control, Navigation, Guidance and Planning Logic systems. The State of a system defines the aspects of the system that can change over time; e.g., position, velocity, acceleration, coordinate-based attitude, and temperature, etc. The Behavior of the system focuses more on what changes are possible within the system; this is denoted in the state of the system. The behavior of a system, as captured in the system modeling, when properly done will aid in accurately predicting future system performance. The Feedback Control system understands the state and behavior of the system and uses feedback to adjust control inputs into the system. The feedback, which is the right arm of the Control system, allows change to be affected in the overall system; it therefore is important to not only correctly identify the system feedback inputs, but also the system response to the feedback inputs. The Navigation system takes multiple data inputs and based on a priori knowledge of the inputs, develops a statistically based weighting of the inputs and measurements to determine the system's state. Guidance and Planning Logic of the system, complete with an understanding of where the system is (provided by the Navigation system), will in turn determine where the system needs to be and how to get it there. With any system/project, it is critical that the objective of the system/project be clearly defined -- not only to plan but to measure performance and to aid in guiding the system or the project. The system principles discussed above, which can be and have been applied to the current CxP space suit development project, can also be mapped to real-world constituents, thus allowing project managers to apply systems theories that are well defined in engineering and mathematics to a discipline (i.e., Project Management) that historically has been based in personal experience and intuition. This mapping of GN&C theory to Project Management will, in turn, permit a direct, methodical approach to Project Management, planning and control providing a tool to help predict (and guide) performance and an understanding of the project constraints, how the project can be controlled, and the impacts to external influences and inputs. This approach, to a project manager, flows down to the three bottom-line variables of cost, schedule, and scope ando the needed control of these three variables to successfully perform and complete a project.

Hill, Terry R.↗

NASA NTRS2000

Aspects of body self-calibration

The representation of body orientation and configuration is dependent on multiple sources of afferent and efferent information about ongoing and intended patterns of movement and posture. Under normal terrestrial conditions, we feel virtually weightless and we do not perceive the actual forces associated with movement and support of our body. It is during exposure to unusual forces and patterns of sensory feedback during locomotion that computations and mechanisms underlying the ongoing calibration of our body dimensions and movements are revealed. This review discusses the normal mechanisms of our position sense and calibration of our kinaesthetic, visual and auditory sensory systems, and then explores the adaptations that take place to transient Coriolis forces generated during passive body rotation. The latter are very rapid adaptations that allow body movements to become accurate again, even in the absence of visual feedback. Muscle spindle activity interpreted in relation to motor commands and internally modeled reafference is an important component in permitting this adaptation. During voluntary rotary movements of the body, the central nervous system automatically compensates for the Coriolis forces generated by limb movements. This allows accurate control to be maintained without our perceiving the forces generated.

NASA Discipline Neuroscience↗

NASA NTRS1986

Acoustic Translation of an Acoustically Levitated Sample

Acoustic-levitation apparatus uses only one acoustic mode to move sample from one region of chamber to another. Sample heated and cooled quickly by translation between hot and cold regions of levitation chamber. Levitated sample is raised into furnace region by raising plunger. Frequency of sound produced by transducers adjusted by feedback system to maintain (102) resonant mode, which levitates sample midway between transducers and plunger regardless of plunger position.

Barmatz, M. B.↗

NASA NTRS2010

Project Management Using Modern Guidance, Navigation and Control Theory

The idea of control theory and its application to project management is not new, however literature on the topic and real-world applications is not as readily available and comprehensive in how all the principals of Guidance, Navigation and Control (GN&C) apply. This paper will address how the fundamental principals of modern GN&C Theory have been applied to NASA's Constellation Space Suit project and the results in the ability to manage the project within cost, schedule and budget. A s with physical systems, projects can be modeled and managed with the same guiding principles of GN&C as if it were a complex vehicle, system or software with time-varying processes, at times non-linear responses, multiple data inputs of varying accuracy and a range of operating points. With such systems the classic approach could be applied to small and well-defined projects; however with larger, multi-year projects involving multiple organizational structures, external influences and a multitude of diverse resources, then modern control theory is required to model and control the project. The fundamental principals of G N&C stated that a system is comprised of these basic core concepts: State, Behavior, Control system, Navigation system, Guidance and Planning Logic, Feedback systems. The state of a system is a definition of the aspects of the dynamics of the system that can change, such as position, velocity, acceleration, coordinate-based attitude, temperature, etc. The behavior of the system is more of what changes are possible rather than what can change, which is captured in the state of the system. The behavior of a system is captured in the system modeling and if properly done, will aid in accurate system performance prediction in the future. The Control system understands the state and behavior of the system and feedback systems to adjust the control inputs into the system. The Navigation system takes the multiple data inputs and based upon a priori knowledge of the input, will develop a statistical-based weighting of the input to determine where the system currently is located. Guidance and Planning logic of the system with the understanding of where it is (provided by the navigation system) will in turn determine where it needs to be and how to get there. Lastly, the system Feedback system is the right arm of the control system to allow it to affect change in the overall system and therefore it is critical to not only correctly identify the system feedback inputs but also the system response to the feedback inputs. And with any systems project it is critical that the objective of the system be clearly defined for not only planning but to be used to measure performance and to aid in the guidance of the system or project.

Hill, Terry↗

NASA NTRS2010

Collective Intelligence and Three Aspects of Planning in Organizations: A NASA Example

For many complex sociotechnical systems, planning seems to require explicit coordination; certainly, in executing a plan the activities of different actors must be tightly coupled. However, distributing the needed planning information can be very burdensome and error prone, because different groups need different collections of information, updated or kept current on different time cycles. Further, the information needed to form successful plans is often highly distributed, and while feedback about the success of prior plans may exist, it may not be available to those in a position of using this to improve plans or to detect and resolve other problems in the system (Weick, 1995). Tools to support various aspects of planning have been developed, and can provide a huge benefit to the individuals working on that aspect. To be tractable, most solutions address a quite bounded slice of work, isolating it from the larger context. Prospective planning takes place over multiple, nested cycles of decision making. This builds a plan that specifies activities of different granularity. "Subplans" may specify multiple parallel activities by different groups and individuals, as well as sequential, nested actions by a single actor. Planning produces valuable, sharable, external, representations: in addition to prospective use, plans support retrospective assessment and also action in the present. Viewing planning in a larger context - both temporal and organizational -- enables noticing what one does not know and generating more systemic and effective solutions. Viewing a problem as one of collective intelligence invites thinking about the larger organizational context. Many approaches to supporting collective intelligence do not support execution of highly contingent actions, distributed across many players, and hence provide incomplete support for planning. However, CI technology maybe helpful in managing the processes of gathering information for decision making in planning and of distributing plan information to various actors, needed on various time cycles.

Billman, Dorrit↗

NASA NTRS2004

Second-Generation Six-Limbed Experimental Robot

The figure shows the LEMUR II - the second generation of the Limbed Excursion Mechanical Utility Robot (LEMUR), which was described in "Six-Legged Experimental Robot" (NPO-20897), NASA Tech Briefs, Vol. 25, No. 12 (December 2001), page 58. The LEMUR II incorporates a number of improvements, including new features, that extend its capabilities beyond those of its predecessor, which is now denoted the LEMUR I. To recapitulate: the LEMUR I was a six-limbed robot for demonstrating robotic capabilities for assembly, maintenance, and inspection. The LEMUR I was designed to be capable of walking autonomously along a truss structure toward a mechanical assembly at a prescribed location and to perform other operations. The LEMUR I was equipped with stereoscopic video cameras and image-data-processing circuitry for navigation and mechanical operations. It was also equipped with a wireless modem, through which it could be commanded remotely. Upon arrival at a mechanical assembly, the LEMUR I would perform simple mechanical operations with one or both of its front limbs. It could also transmit images to a host computer. Each of the six limbs of the LEMUR I was operated independently. Each of the four rear limbs had three degrees of freedom (DOFs), while each of the front two limbs had four DOFs. The front two limbs were designed to hold, operate, and/or be integrated with tools. The LEMUR I included an onboard computer equipped with an assortment of digital control circuits, digital input/output circuits, analog-to-digital converters for input, and digital-to-analog (D/A) converters for output. Feedback from optical encoders in the limb actuators was utilized for closed-loop microcomputer control of the positions and velocities of the actuators. The LEMUR II incorporates the following improvements over the LEMUR I: a) The drive trains for the joints of the LEMUR II are more sophisticated, providing greater torque and accuracy. b) The six limbs are arranged symmetrically about a hexagonal body platform instead of in straight lines along the sides. This symmetrical arrangement is more conducive to omnidirectional movement in a plane. c) The number of degrees of freedom of each of the rear four limbs has been increased by one. Now, every limb has four degrees of freedom: three at the hip (or shoulder, depending on one s perspective) and one at the knee (or elbow, depending on one s perspective). d) Now every limb (instead of only the two front limbs) can perform operations. For this purpose, each limb is tipped with an improved quick-release mechanism for swapping of end-effector tools. e) New end-effector tools have been developed. These include an instrumented rotary driver that accepts all tool bits that have 0.125-in. (3.175-mm)-diameter shanks, a charge-coupled-device video camera, a super bright light-emitting diode for illuminating the work area of the robot, and a generic collet tool that can be quickly and inexpensively modified to accept any cylindrical object up to 0.5 in. (12.7 mm) in diameter. f) The stereoscopic cameras are mounted on a carriage that moves along a circular track, thereby providing for omnidirectional machine vision. g) The control software has been augmented with software that implements innovations reported in two prior NASA Tech Briefs articles: the HIPS algorithm ["Hybrid Image-Plane/Stereo Manipulation" (NPO-30492), Vol. 28, No. 7 (July 2004), page 55] and the CAMPOUT architecture ["An Architecture for Controlling Multiple Robots" (NPO-30345), Vol. 28, No. 10 (October 2004), page 65].

Kennedy, Brett↗

NASA NTRS2012

Initial Evaluation of a Conflict Detection Tool in the Terminal Area

Despite the recent economic recession and its adverse impact on air travel, the Federal Aviation Administration (FAA) continues to forecast an increase in air traffic demand that may see traffic double or triple by the year 2025. Increases in air traffic will burden the air traffic management system, and higher levels of safety and efficiency will be required. The air traffic controllers primary task is to ensure separation between aircraft in their airspace and keep the skies safe. As air traffic is forecasted to increase in volume and complexity [1], there is an increased likelihood of conflicts between aircraft, which adds risk and inefficiency to air traffic management and increases controller workload. To attenuate these factors, recent ATM research has shown that air and ground-based automation tools could reduce controller workload, especially if the automation is focused on conflict detection and resolution. Conflict Alert is a short time horizon conflict detection tool deployed in the Terminal Radar Approach Control (TRACON), which has limited utility due to the high number of false alerts generated and its use of dead reckoning to predict loss of separation between aircraft. Terminal Tactical Separation Assurance Flight Environment (T-TSAFE) is a short time horizon conflict detection tool that uses both flight intent and dead reckoning to detect conflicts. Results of a fast time simulation experiment indicated that TTSAFE provided a more effective alert lead-time and generated less false alerts than Conflict Alert [2]. TSAFE was previously tested in a Human-In-The-Loop (HITL) simulation study that focused on the en route phase of flight [3]. The current study tested the T-TSAFE tool in an HITL simulation study, focusing on the terminal environment with current day operations. The study identified procedures, roles, responsibilities, information requirements and usability, with the help of TRACON controllers who participated in the experiment. Metrics such as lead alert time, alert response time, workload, situation awareness and other measures were statistically analyzed. These metrics were examined from an overall perspective and comparisons between conditions (altitude resolutions via keyboard entry vs. ADS-B entry) and controller positions (two final approach sectors and two feeder sectors) were also examined. Results of these analyses and controller feedback provided evidence of T-TSAFE s potential promise as a useful air traffic controller tool. Heuristic analysis also provided information on ways in which the T-TSAFE tool can be improved. Details of analyses results will be presented in the full paper.

Verma Savita Arora↗

NASA NTRS2000

Model Refinement Using Eigensystem Assignment

IA novel approach for the refinement of finite-element-based analytical models of flexible structures is presented. The proposed approach models the possible refinements in the mass, damping, and stiffness matrices of the finite element model in the form of a constant gain feedback with acceleration, velocity, and displacement measurements, respectively. Once the free elements of the structural matrices have been defined, the problem of model refinement reduces to obtaining position, velocity, and acceleration gain matrices with appropriate sparsity that reassign a desired subset of the eigenvalues of the model, along with partial mode shapes, from their baseline values to those obtained from system identification test data. A sequential procedure is used to assign one conjugate pair of eigenvalues at each step using symmetric output feedback gain matrices, and the eigenvectors are partially assigned, while ensuring that the eigenvalues assigned in the previous steps are not disturbed. The procedure can also impose that gain matrices be dissipative to guarantee the stability of the refined model. A numerical example, involving finite element model refinement for a structural testbed at NASA Langley Research Center (Controls-Structures-Interaction Evolutionary model) is presented to demonstrate the feasibility of the proposed approach.

Maghami, Peiman G.↗

NASA NTRS1998

Model Refinement Using Eigensystem Assignment

This paper presented a novel approach for the refinement of finite-element-based analytical models of flexible structures is presented. The proposed approach models the possible refinements in the mass, damping, and stiffness matrices of the finite element model in the form of a constant gain feedback with acceleration, velocity, and displacement measurements, respectively. Once, the free elements of the structural matrices have been defined, the problem of model refinement reduces to obtaining position, velocity, and acceleration gain matrices, which reassign a desired subset of the eigenvalues of the model, along with partial mode shapes, from their baseline values to those obtained from system identification test data. A sequential procedure is used to assign one self-conjugate pair of closed-loop eigenvalues at each step using symmetric output feedback gain matrices, and the closed-loop eigenvectors are partially assigned, while ensuring that the eigenvalues assigned in the previous steps are not disturbed. The procedure can also impose that gain matrices be dissipative in order to guarantee the stability of the refined model. A numerical example, involving finite element model refinement for a structural testbed at NASA Langley (CSI Evolutionary Model) is presented to demonstrate the feasibility of the proposed approach.

Maghami, Pieman G.↗