Truss space structures system identification using the multiple boundary condition test method
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The uncertainties inherent in the dynamics of flexible spacecraft make robustness questions very important when designing vibration suppression systems for these vehicles. This often leads to the use of sensors and actuators which are collocated on the structure, so as to avoid the potentially destabilizing problem of unknown modal phase differences between noncollocated sensors and actuators. The closed-loop performance attainable is, of course, reduced if only collocated pairs are considered. The object of the present study is to investigate whether the special properties of the transmission zeros of such structures can be used to quantify these performance limitations. The approach is based on recent results concerning the transmission zeros of flexible structures.
The Finite Element-Transfer Matrix (FETM) method was developed for reducing the computational efforts involved in structural analysis. While being widely used by structural analysts, this method does, however, have certain limitations, particularly when used for the control design of large flexible structures. In this paper, a new formulation based on the FETM method is presented. The new method effectively overcomes the limitations in the original FETM method, and also allows an easy construction of reduced models that are tailored for the control design. Other advantages of this new method include the ability to extract open loop frequencies and mode shapes with less computation, and simplification of the design procedures for output feedback, constrained compensation, and decentralized control. The development of this new method and the procedures for generating reduced models using this method are described in detail and the role of the reduced models in control design is discussed through an illustrative example.
The new pole/zero cancellation technique developed for the problem of sensitivity and robustness in vibration isolation systems for flexible spacecraft requires an analysis of the sensitivity of transmission zeros. This paper analyzes the sensitivity of the transmission zeros of flexible structures with compatible sensors and actuators, in terms of partial derivatives and condition numbers. It is shown that, in both measures, the sensitivities of the zeros of such a system are closely related to those of its poles. It is also shown that the closed-loop poles produced by applying the pole/zero cancellation to the structure have sensitivities approaching those of the zeros, so that these are given by the sensitivities of the open-loop poles. Examples are presented that illustrate these points.
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One of the major problems associated with the control of flexible structures is the estimation of system states. Since the parameters of the structures are not constant under varying loads and conditions, conventional fixed parameter state estimators can not be used to effectively estimate the states of the system. One alternative is to use a state estimator which adapts to the condition of the system. One such estimator is the Kalman filter. This filter is a time varying recursive digital filter which is based upon a model of the system being measured. This filter adapts the model according to the output of the system. Previously, the Kalman filter has only been used in an off-line capacity due to the computational time required for implementation. With recent advances in computer technology, it is becoming a viable tool for use in the on-line environment. A distributed Kalman filter implementation is described for fast estimation of the state of a flexible arm. A key issue, is the sensor structure and initial work on a distributed sensor that could be used with the Kalman filter is presented.
An open loop optimal control algorithm is developed for general flexible structures, based on Laplace transform methods. A distributed parameter model of the structure is first presented, followed by a derivation of the optimal control algorithm. The control inputs are expressed in terms of their Fourier series expansions, so that a numerical solution can be easily obtained. The algorithm deals directly with the transcendental transfer functions from control inputs to outputs of interest, and structural deformation penalties, as well as penalties on control effort, are included in the formulation. The algorithm is applied to several structures of increasing complexity to show its generality.
The results of active control experiments performed for the Mini-Mast truss structure are presented. The primary research objectives were: (1) to develop active structural control concepts and/or techniques; (2) to verify the concept of robust non-minimum-phase compensation for a certain class of non-colocated structural control problems through ground experiments; (3) to verify a 'dipole' concept for persistent disturbance rejection control of flexible structures; and (4) to identify CSI (Control Structure Interaction) issues and areas of emphasis for the next generation of large flexible spacecraft. The classical SISO (Single Input and Single Output) control design approach was employed.
A research program to evaluate telerobotic methods for inspace assembly of large truss structures has been initiated at the NASA Langley Research Center. A commercial robot is mounted on a carriage positioning system and a tetrahedral truss, which is composed of 102 members each 2 m long, is assembled on a rotating motion-base. The facility system is described including details of characterization tests on the truss structure. The current status of the assembly tests is discussed and observations from these tests indicate that no problems have been encountered that would prohibit automated telerobotic assembly from being a viable inspace construction method.
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A special class of nonlinear damping models is investigated in which the damping force is proportional to the product of positive integer or the fractional power of the absolute values of displacement and velocity. For a one-degree-of-freedom system, the classical Krylov-Bogoliubov 'averaging' method is used, whereas for a distributed system, both an ad hoc perturbation technique and the finite difference method are employed to study the effects of nonlinear damping. The results are compared with linear viscous damping models. The amplitude decrement of free vibration for a single mode system with nonlinear models depends not only on the damping ratio but also on the initial amplitude, the time to measure the response, the frequency of the system, and the powers of displacement and velocity. For the distributed system, the action of nonlinear damping is found to reduce the energy of the system and to pass energy to lower modes.
This paper presents the development and experimental results of an automated on-orbit system identification method for large flexible spacecraft that yields estimated quantities to support on-line design and tuning of robust high performance control systems. The procedure consists of applying an input to the plant, obtaining an output, and then conducting nonparametric identification to yield the spectral estimate of the system transfer function. A parametric model is determined by curve fitting the spectral estimate to a rational transfer function. The identification method has been demonstrated experimentally on the Large Spacecraft Control Laboratory in JPL.
A very robust technique for the realization/identification of structural dynamic systems is presented. This methodology combines the eigensystem realization algorithm (ERA) and minimum model error (MME) techniques to develop an extremely robust algorithm able to distinguish modes whose amplitudes are small fractions of the noise amplitude. As the amplitude of the noise grows, the enhanced robustness of the combined ERA/MME algorithm becomes more significant. This is a result of the MME being able to produce simulated measurements of much greater accuracy than the original measurements, for input to the ERA. The new method was able to determine correct model order at noise levels many times higher than the original ERA for the realization problem in which the model order must be derived.