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Questions of uniqueness of parameters which were obtained from a system identification algorithm were investigated. The local properties of the surface defined by the error function were used. Static and dynamic numerical experiments on determinate and indeterminate trusses and on shear buildings illustrate the procedure. Examples are given of loading and sensor configurations which produce unique parameters
Information is given in the form of outlines, graphs, tables and charts. Topics include system identification, Bayesian statistical decision theory, Maximum Likelihood Estimation, identification methods, structural mode identification using a stochastic realization algorithm, and identification results regarding membrane simulations and X-29 flutter flight test data.
The problem of designing optimal inputs in the identification of linear systems with unknown random parameters is considered using a Bayesian approach. The information matrix, which is positive definite for the class of systems analyzed, gives a measure of performance for the system inputs. The computation of the optimal closed-loop input mappings is shown to be a nontrivial exercise in adaptive control. Deterministic optimal inputs are shown to be easily computable. Numerical examples are given. A Kalman filter is used to estimate the parameters. A necessary condition for the Kalman filter not to diverge when applying linear feedback is also given.
This paper presents two new techniques for frequency domain identification of linear system parameters. The first technique uses the instrumental variables approach. The frequency domain formulation is shown to give a considerable insight into the selection of efficient and convergent instrumental variables. The new maximum likelihood formulation affords simplier numerical solution and provides a way to select parameter starting values in the gradient based optimization method.
This paper is concerned with the identification of a system in the presence of several error sources. Following some basic definitions, the notion of 'near-equivalence in probability' is introduced using the concept of near-equivalence between a model and process. Necessary and sufficient conditions for the identifiability of system parameters are given. The effect of structural error on the parameter estimates for both deterministic and stochastic cases are considered.
Presented here is an algorithm to compute the Markov parameters of a backward-time observer for a backward-time model from experimental input and output data. The backward-time observer Markov parameters are decomposed to obtain the backward-time system Markov parameters (backward-time pulse response samples) for the backward-time system identification. The identified backward-time system Markov parameters are used in the Eigensystem Realization Algorithm to identify a backward-time state-space model, which can be easily converted to the usual forward-time representation. If one reverses time in the model to be identified, what were damped true system modes become modes with negative damping, growing as the reversed time increases. On the other hand, the noise modes in the identification still maintain the property that they are stable. The shift from positive damping to negative damping of the true system modes allows one to distinguish these modes from noise modes. Experimental results are given to illustrate when and to what extent this concept works.
For the past several years much effort has been given to the development of techniques for designing control systems for large space structures (LSS's). The main objective of these efforts has been to develop a LSS control methodology that produces designs that meet strenuous performance requirements and are robust to model inaccuracies. Unfortunately, performance and robustness are conflicting requirements. Because LSS's can not be fully tested on ground, it has become an accepted fact that the design of LSS control systems to meet performance requirements can not be completed until the LSS is placed on-orbit and tested and an accurate model is extracted from on-orbit test results. Modern MIMO sampled-data frequency response design techniques are viable candidates for designing LSS control systems. First, this paper presents techniques for performing MIMO system identification (ID) from test data. Then, techniques for improving the performance of the system ID process in the presence of noise are presented. Finally, practical utility of the system ID approaches are validated by the presentation of results obtained from application on the LSS Ground Test Facility at Marshall Space Flight Center.
An algorithm for processing flight-test data to provide state estimates and instrument calibrations for aerodynamic or hydrodynamic system identification by the equation error estimation method is developed and demonstrated on synthesized data. The extended-Kalman-filter algorithm employs a locally level, north-pointing frame of reference, accounts for rotating ellipsoidal earth effects, and estimates sensor bias, scale factors, wind components, and process noise levels by maximum-likelihood parameters. The method is found to be most effective with navigation quality inertial input data. The algorithm is applied to data from a six-degree-of-freedom F-4 aircraft simulation and shown to produce state estimates in good agreement with the simulation values.
Future spacecraft include configurations which are too flexible to be adequately tested prior to flight and which will require on-orbit systems identification to ensure safe operation of the flight control system. The structural dynamics model will evolve and its accuracy will improve in stages as ground tests of full-scale components and replica-scale models are performed. State Space Modeling and Conditional Maximum Likelihood Parameter Estimation methodology can provide the formal probability-based framework for the process of upgrading a model as additional test results are obtained. Although the number of unknown parameters can be reduced by the use of canonical forms for the stability matrix, the number of unknown model parameters quickly becomes unmanageable unless advantage is taken of the relationship of a much fewer number of global model parameters. Distributed parameter systems or partial differential equation models are one way to take advantage of such global parameters to reduce the number of unknown model parameters.
Two phase-optimized multisine peak factor minimization algorithms are presented and evaluated. The first algorithm minimizes peak factor by iteratively clipping the peaks of generated multisine signals. The second algorithm optimizes peak factor indirectly through minimization of an approximation of the infinity norm of the multisine. Algorithm performance was evaluated as a function of different signal properties, including the number of harmonics, harmonic spacing, and number of snow harmonics (extra harmonics included for further reduction of the peak factor). The two algorithms are compared against results obtained by minimizing peak factor directly using a simplex algorithm, which has been a common approach when designing phase-optimized multisines for system identification flight tests. Sample results show that the clipping and infinity norm algorithms produced multisine signals with comparable peak factors that were lower than that of the simplex algorithm. However, the clipping algorithm runs an order of magnitude faster than the other two algorithms, which also makes it practical to repeat the algorithm multiple times to achieve even lower peak factors.
Two phase-optimized multisine peak factor minimization algorithms are presented and evaluated. The first algorithm minimizes peak factor by iteratively clipping the peaks of generated multisine signals. The second algorithm optimizes peak factor indirectly through minimization of an approximation of the infinity norm of the multisine. Algorithm performance was evaluated as a function of different signal properties, including the number of harmonics, harmonic spacing, and number of snow harmonics (extra harmonics included for further reduction of the peak factor). The two algorithms are compared against results obtained by minimizing peak factor directly using a simplex algorithm, which has been a common approach when designing phase-optimized multisines for system identification flight tests. Sample results show that the clipping and infinity norm algorithms produced multisine signals with comparable peak factors that were lower than that of the simplex algorithm. However, the clipping algorithm runs an order of magnitude faster than the other two algorithms, which also makes it practical to repeat the algorithm multiple times to achieve even lower peak factors.
The 68th and 69th flights of NASA’s Ingenuity Mars Helicopter marked the first dedicated system identification flights of an aerial vehicle on another planet. Chirp signals were injected into the swashplate cyclic controls for both legs of the two out-and-back flights. Frequency responses were computed from the flight data, using both the Direct Method (DM) and the Joint-Input-Output (JIO) approach, for the identification of stability and control derivatives in forward flight conditions. The resulting identified state-space models were compared against existing flight dynamics simulation models, showing excellent correlation in the higher frequency range. External disturbances were seen to introduce a bias in the identified lower frequency responses, which was partially mitigated using the JIO method. These findings will inform future modeling and flight testing efforts of Mars rotorcraft.
Any High-contrast imaging instrument in a future large ground-based or space-based telescopes will include an integral field spectrograph (IFS) for measuring broadband starlight residuals and characterizing the exoplanet's atmospheric spectrum. In this paper, we report the development of a high-contrast integral field spectrograph (HCIFS) at Princeton University and demonstrate its application in multi-spectral wavefront control. Moreover, we propose and experimentally validate a new reduced-dimensional system identification algorithm for an IFS imaging system, which improves the system's wavefront control speed, contrast and computational and data storage efficiency.
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.
Recent findings from modeling and controller design for the NASA-Marshall Single Structure Control Facility have raised questions regarding the ability of modern control design techniques and modern modeling techniques to deal effectively with the stringent modeling and control design requirements of Large Space Structure Control. A brief and general discussion is presented of the results of studies into the modeling and control issues performed under sponsorship of the NASA/ASEE Summer Faculty Fellowship Program. Several issues are addressed. The first is a study of a modeling technique based on least squares identification of individual transfer functions from measured frequency response data. The second is a study of multiobjective optimization techniques applied to the modeling, or system identification, problem. The third issue is a study into the question of whether multiobjective optimization approaches can be effectively used for control system design using only frequency response data, thereby bypassing the difficult modeling problem. The last issue studied involves the resolution of seeming discrepancies between predicted and measured control computer time delays in the Single Structure Control Facility.
We characterize both nonlinear and high order linear responses of fiber-optic and optoelectronic components using spread spectrum temperature cycling methods. This Thermal Signature Identification System (TheSIS) provides much more detail than conventional narrowband or quasi-static temperature profiling methods. This detail allows us to match components more thoroughly, detect subtle reversible shifts in performance, and investigate the cause of instabilities or irreversible changes. In particular, we create parameterized models of athermal fiber Bragg gratings (FBGs), delay line interferometers (DLIs), and distributed feedback (DFB) lasers, then subject the alternative models to selection via the Akaike Information Criterion (AIC). Detailed pairing of components, e.g. FBGs, is accomplished by means of weighted distance metrics or norms, rather than on the basis of a single parameter, such as center wavelength.
Autonomous Frequency Domain Identification (AU-FREDI) computer program implements system of methods, algorithms, and software developed for identification of parameters of mathematical models of dynamics of flexible structures and characterization, by use of system transfer functions, of such models, dynamics, and structures regarded as systems. Software considered collection of routines modified and reassembled to suit system-identification and control experiments on large flexible structures.
A parameter and state estimation technique for distributed models is demonstrated through the solution of a problem generic to large space antenna system identification. Assuming the position of the reflective surface of the maypole (hoop/column) antenna to be approximated by the static two-dimensional, stretched-membrane partial differential equation with variable-stiffness coefficient functions, a spline-based approximation procedure is described that estimates the shape and stiffness functions from data set observations. For given stiffness functions, the Galerkin projection with linear spline-based functions is applied to project the distributed problem onto a finite-dimensional subspace wherein algebraic equations exist for determining a static shape (state) prediction. The stiffness functions are then parameterized by cubic splines and the parameters estimated by an output error technique. Numerical results are presented for data descriptive of a 100-m-diameter maypole antenna.