Parameter identification of linear systems based on smoothing
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This final technical report covers a three and one-half year period preceding February 28, 1993 during which support was provided under NASA Grant NAG-1-1065. Following a general description of the system identification problem and a brief survey of methods to attack it, the basic ideas behind the approach taken in this research effort are presented. The results obtained are described with reference to the published work, including the five semiannual progress reports previously submitted and two interim technical reports.
This paper presents two approaches that will improve the accuracy of explicit approximations of frequency responses. They are important components of structural design optimization and system identification. The first is a product form approximation that improves approximated frequency responses near resonant conditions. This approach is applicable to both design optimization and system identification problems. The second is aimed at improving the computed sensitivity coefficients that are used to solve system identification problems.
In identifying the rotordynamic coefficients of a high-Reynolds-number hydrostatic bearing, fluid-flow induced forces present a unique problem, in that they provide an unmeasureable and uncontrollable excitation to the bearing. An analysis method is developed that effectively eliminates the effects of fluid-flow induced excitation on the estimation of the bearing rotordynamic coefficients, by using power spectral densities. In addition to the theoretical development, the method is verified experimentally by single-frequency testing, and repeatability tests. Results obtained for a bearing are the twelve rotordynamic coefficients (stiffness, damping, and inertia coefficients) as functions of eccentricity ratio, speed, and supply pressure.
Virtually all space structure mission requirements include control of vibration, position, and possibly shape. In order to satisfy their requirements it is necessary to know the dynamic characteristics of the structure. Therefore, a means must be developed to continuously determine a dynamic model, or changes in the model, and to appropriately adapt the controls to these changes. The detection and location of physical damage would also be a very beneficial characteristic of such a procedure. A discussion outlining the methods to perform On-Orbit Model Determination is presented.
The method investigated in the current research work is based on the identification of the equations of motion during test flights, followed by the solution of these identified equations to numerically compute the flutter dynamic pressure. The current research work is aimed at overcoming two main difficulties which arise when: (1) A continuous system is truncated into a system with a finite number of degrees of freedom. (2) The desired range of frequencies is wide; in the latter case, numerical difficulties occur that can only partly be overcome by giving relatively more weight to the high frequency modes. Results pertaining to the above first point will be presented under section entitled 'Truncation Effects', and results pertaining to the above second point will be presented under section entitled 'Frequency Range Effects'. The numerical example used herein consists of a continuous simply supported beam. It is further assumed that the object of the identification procedure is to identify the beam's first seven modes.
An amended six degree of freedom helicopter stability and control derivative model was developed in which body acceleration and control rate derivatives were included in the Taylor series expansion. These additional derivatives were derived from consideration of the effects of the higher order rotor flapping dynamics, which are known to be inadequately represented in the conventional six degree of freedom, quasistatic stability derivative model. The amended model was a substantial improvement over the conventional model, effectively doubling the unsable bandwidth and providing a more accurate representation of the short period and cross axis characteristics. Further investigations assessed the applicability of the two stability derivative model structures for flight test parameter identification. Parameters were identified using simulation data generated from a higher order base line model having sixth order rotor tip path plane dynamics. Three lower order models were identified: one using the conventional stability derivative model structure, a second using the amended six degree of freedom model structure, and a third model having eight degrees of freedom that included a simplified rotor tip path plane tilt representation.
An amended six degree of freedom helicopter stability and control derivative model was developed in which body acceleration and control rate derivatives were included in the Taylor series expansion. These additional derivatives were derived from consideration of the effects of the higher order rotor flapping dynamics, which are known to be inadequately represented in the conventional six degree of freedom, quasistatic stability derivative model. The amended model was a substantial improvement over the conventional model, effectively doubling the usable bandwidth and providing a more accurate representation of the short period and cross axis characteristics. Further investigations assessed the applicability of the two stability derivative model structures for flight test parameter identification. Parameters were identified using simulation data generated from a higher order base line model having sixth order rotor tip path plane dynamics. Three lower order models were identified: one using the conventional stability derivative model structure, a second using the amended six degree of freedom model structure, and a third model having eight degrees of freedom that included a simplified rotor tip path plane tilt representation. Previously announced in STAR as N82-32376
An amended six degree of freedom helicopter stability and control derivative model was developed in which body acceleration and control rate derivatives were included in the Taylor series expansion. These additional derivatives were derived from consideration of the effects of the higher order rotor flapping dynamics, which are known to be inadequately represented in the conventional six degree of freedom, quasistatic stability derivative model. The amended model was a substantial improvement over the conventional model, effectively doubling the unstable bandwidth and providing a more accurate representation of the short period and cross axis characteristics. Further investigations assessed the applicability of the two stability derivative model structures for flight test parameter identification. Parameters were identified using simulation data generated from a higher order base line model having sixth order rotor tip path plane dynamics. Three lower order models were identified: one using the conventional stability derivative model structure, a second using the amended six degree of freedom model structure, and a third model having eight degrees of freedom that included a simplified rotor tip path plane tilt representation. Previously announced in STAR as N82-32376
Parameter identification and modeling are key elements of a design and operational flight strategy for control of flexible space structures. The emphasis of the identification program is on on-orbit applications to spacecraft control. High performance robust controllers will result from advanced design synthesis techniques and on-orbit identification/system tuning. Near term goals for the program include development of an integrated on-line processing capability for flexible body parameter identification, and validation with physical structure experiments.
System parameters identification from short-term signal observations, using Bayesian approach
Identification and control of linear dynamic systems with unknown parameters
Parameter indeterminacy in system identification for mathematical model with adjustable parameters matched to system output by feedback
This paper describes the use of a combined model and parameter identification approach, based on modal analysis and artificial intelligence (AI) techniques, for identifying damage or flaws in a rotating truss structure incorporating embedded piezoceramic sensors. This smart structure example is representative of a class of structures commonly found in aerospace systems and next generation space structures. Artificial intelligence techniques of classification, heuristic search, and an object-oriented knowledge base are used in an AI-based model identification approach. A finite model space is classified into a search tree, over which a variant of best-first search is used to identify the model whose stored response most closely matches that of the input. Newly-encountered models can be incorporated into the model space. This adaptativeness demonstrates the potential for learning control. Following this output-error model identification, numerical parameter identification is used to further refine the identified model. Given the rotating truss example in this paper, noisy data corresponding to various damage configurations are input to both this approach and a conventional parameter identification method. The combination of the AI-based model identification with parameter identification is shown to lead to smaller parameter corrections than required by the use of parameter identification alone.
Bayesian identification of system parameters for observable and nonobservable input signals
The problem of the parameter identification of large scale dynamic systems involving a system matrix characterized by approximately 200 elements is addressed. By using phase variable transformations, a mathematical model of an aeroelastic airplane is described in a form that is amenable to partial or piecemeal acceptance of parameters estimated from flight data. A mathematical model of the U.S. Air Force Total In-Flight Simulator was computed using the FLEXSTAB digital computer program. As data became available during the progress of the flight test program, this data was processed and substituted in the mathematical model for parameters analytically obtained from the FLEXSTAB program. The results tend to show a progressive and orderly transition from an analytically defined mathematical model to one obtained from the flight tests of the actual aircraft.
Phase variable transformations are used to construct the mathematical model of an aeroelastic aircraft in a form that is amenable to partial or piecemeal acceptance of parameters estimated from flight data. The problem is one of parameter identification of large scale dynamic systems involving a system matrix characterized by about 200 elements. A mathematical model of the USAF Total In-Flight Simulator was computed using the FLEXSTAB program. As data became available during the progress of the flight test program, it was processed and substituted in the mathematical model for parameters obtained from the FLEXSTAB program. Results tend to show a progressive and orderly transition from an analytically defined mathematical model to one obtained from the flight tests of the actual aircraft.
Orbit parameters identification method based on given tracking data span applied to lunar orbiter tracking using Fourier analysis