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Progress in the areas of eddy current computations, modelling and analysis, design optimization methods, wind tunnel Magnetic Suspension and Balance Systems (MSBS), payload pointing and vibration isolation systems, and system identification is reported. Research accomplishments facilitated the demonstration of several new developments in the field of magnetic suspension technology.

An algorithm is presented for identifying a state-space model of linear stochastic systems operating under known feedback controller. In this algorithm, only the reference input and output of closed-loop data are required. No feedback signal needs to be recorded. The overall closed-loop system dynamics is first identified. Then a recursive formulation is derived to compute the open-loop plant dynamics from the identified closed-loop system dynamics and known feedback controller dynamics. The controller can be a dynamic or constant-gain full-state feedback controller. Numerical simulations and test data of a highly unstable large-gap magnetic suspension system are presented to demonstrate the feasibility of this indirect identification method.

Good progress is being made in several major areas. These include eddy current modelling and analysis, design optimization methods, wind tunnel Magnetic Suspension and Balance Systems (MSBS), payload pointing and vibration isolation systems, and system identification. In addition, another successful International Symposium has been completed, with the Proceedings being printed at the time of writing. These activities continue current work under this Grant and extend previous work on magnetic suspension systems and devices in the Guidance and Control Branch and will permit the demonstration of several new developments in the field of magnetic suspension technology.

This paper presents the results of modeling and system identification efforts on the NASA Large-Angle Magnetic Suspension Test Fixture (LAMSTF). The LAMSTF consists of a cylindrical permanent magnet which is levitated above a planar array of five electromagnets mounted in a circular configuration. The analytical model is first developed and open-loop characteristics are described. The system is shown to be highly unstable and requires feedback control in order to apply system identification. Limitations on modeling accuracy due to the effect of eddy-currents on the system are discussed. An algorithm is derived to identify a state-space model for the system from input/output data acquired during closed-loop operation. The algorithm is tested on both the baseline system and a perturbed system which has an increased presence of eddy currents. It is found that for the baseline system the analytic model adequately captures the dynamics, although the identified model improves the simulation accuracy. For the system perturbed by additional unmodeled eddy-currents the analytic model is no longer adequate and a higher-order model, determined through system identification, is required to accurately predict the system's time response.

The High Speed Civil Transport (HSCT) will have to be designed to withstand high aerodynamic load at supersonic speeds (panel flutter) and high acoustic load (acoustic or sonic fatigue) due to fluctuating boundary layer or jet engine acoustic pressure. The thermal deflection of the skin panels will also alter the vehicle's configuration, thus it may affect the aerodynamic characteristics of the vehicle and lead to poor performance. Shape memory alloys (SMA) have an unique ability to recover large strains completely when the alloy is heated above the characteristic transformation (austenite finish T(sub f)) temperature. The recovery stress and elastic modulus are both temperature dependent, and the recovery stress also depends on the initial strain. An innovative concept is to utilize the recovery stress by embedding the initially strained SMA wire in a graphite/epoxy composite laminated panel. The SMA wires are thus restrained and large inplane forces are induced in the panel at elevated temeperatures. By embedding SMA in composite panel, the panel becomes much stiffer at elevated temperatures. That is because the large tensile inplane forces induced in the panel from the SMA recovery stress. A stiffer panel would certainly yield smaller dynamic responses.

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.

A continuum model for the SCOLE configuration has been derived using transfer matrices. Controller designs for distributed parameter systems have been analyzed. Pole-assignment controller design is considered easy to implement but stability is not guaranteed. An explicit transfer function of dynamic controllers has been obtained and no model reduction is required before the controller is realized. One specific LQG controller for continuum models had been derived, but other optimal controllers for more general performances need to be studied.

The Large-Angle Magnetic Suspension Test Facility (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 system consists of a planar array of five copper electromagnets which actively suspend a small cylindrical permanent magnet. The cylinder is a rigid body and can be controlled to move in five independent degrees of freedom. Five position variables are sensed indirectly by using infra-red 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 plans an essential role in controller design. The analytical model of the LAMSTF system includes highly unstable real poles (about 10 Hz) and low-frequency flexible modes (about 0.16 Hz). Projection filters are proposed to identify the state space model from closed-loop test data in time domain. 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. The rate information is obtained by calculating the back difference of the sensed position signals. The reference inputs contain five uncorrelated random signals. This control input and the system reponse are recorded as input/output data to identify the system directly from the projection filters. The sampling time is 4 ms and the model is fairly accurate in predicting the step responses for different controllers while the analytical model has a deficiency in the pitch axis.

In this paper a distributed parameter model for the estimation of modal characteristics of NASA Mini-Mast truss is proposed. A closed-form solution of the Timoshenko beam equation, for a uniform cantilevered beam with two concentrated masses, is derived so that the procedure and the computational effort for the estimation of modal characteristics are improved. A maximum likelihood estimator for the Timoshenko beam model is also developed. The resulting estimates from test data by using Timoshenko beam model are found to be comparable to those derived from other approaches.

Application of expert system concepts to a breadboard Mars oxygen processor unit have been studied and tested. The research was directed toward developing the methodology required to enable autonomous operation and control of these simple chemical processors at Mars. Failure detection and isolation was the key area of concern, and schemes using forward chaining, backward chaining, knowledge-based expert systems, and rule-based expert systems were examined. Tests and simulations were conducted that investigated self-health checkout, emergency shutdown, and fault detection, in addition to normal control activities. A dynamic system model was developed using the Bond-Graph technique. The dynamic model agreed well with tests involving sudden reductions in throughput. However, nonlinear effects were observed during tests that incorporated step function increases in flow variables. Computer simulations and experiments have demonstrated the feasibility of expert systems utilizing rule-based diagnosis and decision-making algorithms.

A novel method is presented for identifying a state-space model and a state estimator for linear stochastic systems from input and output data. The method is primarily based on the relationship between the state-space model and the finite-difference model of linear stochastic systems derived through projection filters. It is proved that least-squares identification of a finite difference model converges to the model derived from the projection filters. System pulse response samples are computed from the coefficients of the finite difference model.

A novel method is presented of identifying a state space model and a state estimator for linear stochastic systems from input and output data. The method is primarily based on the relations between the state space model and the finite difference model for linear stochastic systems derived through projection filters. It is proven that least squares identification of a finite difference model converges to the model derived from the projection filters. System pulse response samples are computed from the coefficients of the finite difference model. In estimating the corresponding state estimator gain, a z-domain method is used. First the deterministic component of the output is subtracted out, and then the state estimator gain is obtained by whitening the remaining signal. Experimental example is used to illustrate the feasibility of the method.

A maximum likelihood estimation for distributed parameter models of large flexible structures was formulated. Distributed parameter models involve far fewer unknown parameters than independent modal characteristics or finite element models. The closed form solutions for the partial differential equations with corresponding boundary conditions were derived. The closed-form expressions of sensitivity functions led to highly efficient algorithms for analyzing ground or on-orbit test results. For an illustration of this approach, experimental data of the NASA Mini-MAST truss was used. The estimations of modal properties involve lateral bending modes and torsional modes. The results show that distributed parameter models are promising in the parameter estimation of large flexible structures.

Most methods of system identification of large flexible structures by far are based on the lumped parameter approach. Because of the considerable computational burden due to the large number of unknown parameters, distributed parameter approach, which greatly decreases the number of unknowns, has being investigated. In this paper a distributed parameter model for the estimation of modal characteristics of NASA Mini-Mast truss has been formulated. Both Bernoulli-Euler beam and Timoshenko beam equations are used to characterize the lateral bending vibrations of the truss. The measurement of the lateral displacement at the tip of the truss is provided to the maximum likelihood estimator. Closed-form solutions of the partial differential equations and closed-form expressions of the sensitivity functions are derived so that the estimation algorithm is highly efficient. The resulting estimates from test data by using Timoshenko beam model are found to be comparable to those derived from finite element analysis.

This paper presents a novel method of estimating the optimal steady state Kalman filter gain of a linear discrete time-invariant system from a non-optimal Kalman filter residual sequence. The relation between the optimal residual sequence and a signal derived from the non-optimal residual sequence is described by a Moving Average (MA) model whose coefficients are expressed in terms of the state space parameters and the optimal steady state Kalman filter gain. In order to identify the MA model, a whitening filter of the derived signal, which corresponds to an AutoRegressive (AR) model of the signal, is first identified using the least-squares method. Then the inverse filter of the whitening filter, which corresponds to the MA model, is calculated. From the coefficients of the identified MA model, the optimal steady state Kalman filter gain can be obtained. Numerical example is provided to illustrate the feasibility of this approach.

A more accurate Timoshenko beam model is used to characterize the bending behavior of the truss. A maximum likelihood estimator for the Timoshenko beam model has been formulated. A closed-form solution of the Timoshenko beam equation, for a uniform cantilevered beam with two concentrated masses, is derived so that the procedure for the estimation of modal characteristics is much improved. The updated model to the NASA Mini-Mast test data is demonstrated.

The objective is to develop a control system design method that (1) recognizes the time dependence of the thermal distortion due to orbital motion and (2) controls variables that are directly related to far field performance for earth pointing space antennas. The first objective is accomplished by expanding the distortion into principal components that are orthogonal in space and time. The approach for the second objective is to expand the far zone electric field in a Zernike-Bessel series. The method accommodates tapered feeds and arbitrary polarizations. Simulations are performed for a geosynchronous radiometer to determine the effectiveness of the control system under variations in solar geometry, structure materials and thermal properties.

A novel approach of integrated system identification and modal state estimation is proposed for control of linear dynamical systems including flexible space structures. There are four steps involved in this approach. First, the relation between a stochastic state space model of a dynamical system and the coefficients of its autoregressive model with exogenous input is derived. Second, an adaptive least-squares transversal predictor is used to estimate the coefficients of the model. Third, a state space model and a steady state Kalman filter gain of the dynamical system are then identified from the coefficients of the model by using the eigensystem realization algorithm. Fourth, a modal state estimator is constructed using the modal parameters of the identified model. On-line implementation of this algorithm can continually improve the modal parameters and the filter gain. It can also gradually update the system model when the system characteristics are slowly changing. A numerical example is used to illustrate the feasibility of the new approach.

In this paper, maximum likelihood estimation for distributed parameter models of large flexible structures has been formulated. Distributed parameter models involve far fewer unknown parameters than independent modal characteristics of finite element models. The closed-form solutions for the partial differential equations with general forced inputs have been derived. The closed-form expressions of the sensitivity functions lead to highly efficient algorithms for analyzing ground or on-orbit test results. Numerical simulations with impulse and step inputs to the NASA Mini-MAST trust have been demonstrated. The estimations of modal properties involve its longitudinal elongation modes, lateral bending modes and torsional modes. The results show that distributed parameter models are promising in the parameter estimation of large flexible structures.

This paper proposes a new approach of obtaining adaptive state estimation of a system in the presence of unknown system disturbances and measurement noise. In the beginning, a non-optimal Kalman filter with arbitrary initial guess for the process and measurement noises is implemented. At the same time, an adaptive transversal predictor (ATP) based on the recursive least-squares (RLS) algorithm is used to yield optimal one- to p- step-ahead output predictions using the previous input/output data. Referring to these optimal predictions the Kalman filter gain is updated and the performance of the state estimation is thus improved. If forgetting factor is implemented in the recursive least-squares algorithm, this method is also capable of dealing with the situation when the noise statistics are slowly time-varying. This feature makes this new approach especially suitable for the control of flexible structures. A numerical example demonstrates the feasibility of this real time adaptive state estimation method.

A prototype expert system was developed for maintaining autonomous operation of a Mars oxygen production system. Normal operation conditions and failure modes according to certain desired criteria are tested and identified. Several schemes for failure detection and isolation using forward chaining, backward chaining, knowledge-based and rule-based are devised to perform several housekeeping functions. These functions include self-health checkout, an emergency shut down program, fault detection and conventional control activities. An effort was made to derive the dynamic model of the system using Bond-Graph technique in order to develop the model-based failure detection and isolation scheme by estimation method. Finally, computer simulations and experimental results demonstrated the feasibility of the expert system and a preliminary reliability analysis for the oxygen production system is also provided.

Single-mode projection filters are developed for eigensystem parameter identification from both analytical results and test data. Explicit formulations of these projection filters are derived using the orthogonal matrices of the controllability and observability matrices in the general sense. A global minimum optimization algorithm is applied to update the filter parameters by using the interval analysis method. The updated modal parameters represent the characteristics of the test data. For illustration of this new approach, a numerical simulation for the MAST beam structure is shown by using a one-dimensional global optimization algorithm to identify modal frequencies and damping. The projection filters are practical for parallel processing implementation.

A feedback controller for the stabilization of closed-loop systems is proposed which is based on the Liapunov stability criterion. A feedback control law is first generated for the linear portion of the system equation using linear control theory. A feedback control is then designed for the nonlinear portion of the system equation by making negative the time derivative of a positive definite Liapunov function.

An articulated flexible manipulator carried on a translational cart is maneuvered by an active controller to perform certain position control tasks. The nonlinear dynamics of the articulated flexible manipulator are derived and a transformation matrix is formulated to localize the nonlinearities within the inertia matrix. Then a feedback linearization scheme is introduced to linearize the dynamic equations for controller design. Through a pole placement technique, a robust controller design is obtained by properly assigning a set of closed-loop desired eigenvalues to meet performance requirements. Numerical simulations for the articulated flexible manipulators are given to demonstrate the feasibility and effectiveness of the proposed position control algorithms.

Single-mode projection filters are developed for eigensystem parameter identification from both analytical results and test data. Explicit formulations of these projection filters are derived using the orthogonal matrices of the controllability and observability matrices in the general sense. A global minimum optimization algorithm is applied to update the filter parameters by using the interval analysis method. The updated modal parameters represent the characteristics of the test data. For illustration of this new approach, a numerical simulation for the MAST beam structure is shown by using a one-dimensional global optimization algorithm to identify modal frequencies and damping. Another numerical simulation of a ten-mode structure is also presented by using a two-dimensional global optimization algorithm to illustrate the feasibility of the new method. The projection filters are practical for parallel processing implementation.

The Single-Mode Projection Filter (SPF) is a newly developed algorithm for eigensystem parameter identification from both analytical results and test data. The SPF is formulated with a single mode only and practical for parallel processing implementation. Explicit formulations of SPF are derived for the multi-input multi-output (MIMO) system by using the orthogonal matrices of the controllability and observability matrices in the general sense. The modal parameters of SPF are initially obtained from an analytical model in modal space. The experimental data are then processed through SPF to update its modal parameters and to minimize a cost function defined by the norm of an error matrix. The updated modal parameters represent the characteristics of the test data. A two-dimensional global minimum optimization algorithm is developed and applied for the filter update by using the interval analysis method. The SPF is developed based on a single-mode subsystem and identifies only one modal frequency and one modal damping within a specified region. For an n-modes structure, n SPF can be implemented for parallel processing to reduce the computational burden. The SPF is applied to analyze the simulated data for the MAST beam structure. The estimated modal parameters are comparable to those from the Eigensystem Realization Algorithm (ERA) and repeated modal frequencies are identified. The modal analysis of the Spacecraft Control Laboratory Experiment (SCOLE) data is also performed by using the ERA and the Maximum Likelihood Estimate (MLE). The result shows that the first five modal frequencies are very close from ERA and MLE. However, there are slight disparities in the damping rates and the computational burdens are quite different among these two algorithms.

Single-mode projection filters are developed for eigensystem parameter estimates from both analytical results and test data. Explicit formulations of these projection filters are derived using the pseudoinverse matrices of the controllability and observability matrices in general use. A global minimum optimization algorithm is developed to update the filter parameters by using interval analysis method. Modal parameters can be attracted and updated in the global sense within a specific region by passing the experimental data through the projection filters. For illustration of this method, a numerical example is shown by using a one-dimensional global optimization algorithm to estimate model frequencies and dampings.

Single-mode projection filters are developed for eigensystem parameter identification and state estimation from both analytical results and test data. Explicit formulations of these projection filters are derived using the pseudoinverse matrices of the controllabilty and observability matrices in the general sense. A global minimum optimization algorithm is developed to update the filter parameters by using the interval analysis method. Modal parameters can be identified and updated in the global sense within a specified region of parameters by passing the experimental data through the projection filters. For illustration of this new approach, a numerical example is shown by using a one-dimensional global optimization algorithm to estimate modal frequencies and damping.