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Preliminary results on the design of decentralized controllers for the COFS I Mast are reported. A nine mode finite element model is used along with second order model of the actuators. It is shown that without actuator dynamics, the system is stable with collocated rate feedback and has acceptable performace. However, when actuator dynamics are included, the system is unstable.
Physical and transform space filtering has been applied to the Fourier spectral collocation solution of the constant coefficient scalar wave equation with a discontinuous initial condition. High order accuracy can be extracted from the unfiltered solution. Smooth, high order Fourier space filtering gives expected polynomial order solutions away from the discontinuity. Spectral accuracy is observed with the physical space filter of Gottlieb and Tadmor.
This paper describes the structural dynamic characteristics of a NASA reference space station configuration as defined in the November 1987 Space Station Program - Systems Engineering and Integration Engineering Data Book. The modes and frequencies of the station below 2.0 Hz were obtained and selected results along with rigid body properties are presented. A three-axis attitude control system using control moment gyros responding to attitude and attitude rate signals is used to regulate the orientation of the station. The stability of the control system with non-collocated sensors is investigated for both compensated and uncompensated control signals. Results from a closed-loop simulation of a commanded attitude change about three axes, and from a closed-loop simulation of the response of the station to an externally applied unit force impulse at the docking port are presented. These simulation results are used to evaluate the possible degree of control/structures interaction which could occur during normal operation of the station.
New three-dimensional spectral multigrid algorithms are analyzed and implemented to solve the variable coefficient Helmholtz equation. Periodicity is assumed in all three directions which leads to a Fourier collocation representation. Convergence rates are theoretically predicted and confirmed through numerical tests. Residual averaging results in a spectral radius of 0.2 for the variable coefficient Poisson equation. In general, non-stationary Richardson must be used for the Helmholtz equation. The algorithms developed are applied to the large-eddy simulation of incompressible isotropic turbulence.
A hybrid bispectral threshold method (HBTM) is presently used to compare cloud amounts derived from Landsat digital data over 22 regions having various cloud types with cloudiness information obtained from collocated, nearly-simultaneous 4 x 8-km GOES visible and IR data. A sensitivity analysis indicates that an rms underestimation of about 0.01 in clear sky reflectance by the HBTM increased the GOES cloud amount by 0.06, which is more than twice the decrese in cloud amount obtained by an equivalent increase in clear-sky reflectance. Landsat imagery and cloud properties derived from the Landsat data are used to explain how the partially cloud-filled GOES pixels were treated by the HBTM. It is found that the HBTM accounts for the effects of partially cloud-filled FOVs in most cases of the present study.
Results of the ratio of stress intensity factor to crack-mouth displacement as a function of crack length are presented for the wedge-loaded compact specimen. Comparisons are made between experimental compliance results, numerical results from collocation methods, and deep-crack limit-solution results. Applications are for crack-arrest and stress-corrosion-cracking tests for metals and other materials under predominantly linear elastic conditions.
Although considerable effort has been put into the study of steady state vibration control, there are few methods applicable to transient vibration control of rotorbearing systems. In this paper optimal control theory has been adopted to minimize rotor vibration due to sudden imbalance, e.g., blade loss. The system gain matrix is obtained by choosing the weighting matrices and solving the Riccati equation. Control forces are applied to the system via a feedback loop. A seven mass rotor system is simulated for illustration. A relationship between the number of sensors and the number of modes used in the optimal control model is investigated. Comparisons of responses are made for various configurations of modes, sensors, and actuators. Furthermore, spillover effect is examined by comparing results from collocated and noncollocated sensor configurations. Results show that shaft vibration is significantly attenuated in the closed loop system.
A decentralized model reference adaptive control (DMRAC) method is developed for large flexible structures (LFS). The development follows that of a centralized model reference adaptive control for LFS that have been shown to be feasible. The proposed method is illustrated using a simply supported beam with collocated actuators and sensors. Results show that the DMRAC can achieve either output regulation or output tracking with adequate convergence, provided the reference model inputs and their time derivatives are integrable, bounded, and approach zero as t approaches infinity.
The coupling of hyperbolic and parabolic systems is discussed in a domain Omega divided into two distinct subdomains omega(+) and omega(-). The main concern is to find the proper interface conditions to be fulfilled at the surface separating the two domains. Next, they are used in the numerical approximation of the problem. The justification of the interface conditions is based on a singular perturbation analysis, i.e., the hyperbolic system is rendered parabolic by adding a small artifical viscosity. As this goes to zero, the coupled parabolic-parabolic problem degenerates into the original one, yielding some conditions at the interface. These are taken as interface conditions for the hyperbolic-parabolic problem. Actually, two alternative sets of interface conditions are discussed according to whether the regularization procedure is variational or nonvariational. It is shown how these conditions can be used in the frame of a numerical approximation to the given problem. Furthermore, a method of resolution is discussed which alternates the resolution of the hyperbolic problem within omega(-) and of the parabolic one within omega(+). The spectral collocation method is proposed, as an example of space discretization (different methods could be used as well); both explicit and implicit time-advancing schemes are considered. The present study is a preliminary step toward the analysis of the coupling between Euler and Navier-Stokes equations for compressible flows.
Data from the TOMS instrument has been used to follow the course of development of the Antarctic ozone springtime minimum since 1979. Addressed is the question of possible north polar region changes which might be deduced from the nine years of TOMS measurements of total ozone. Total ozone is a much more variable quantity in the Northern Hemisphere than in the Southern Hemisphere. This makes the search for trends more difficult and the interpretation of results more uncertain. The 9-yr time series of TOMS data at high latitudes in the Northern Hemisphere is examined. Because the TOMS measurements have drifted by 3 to 4 percent with respect to closely collocated Dobson measurements, it was chosen in this study to adopt the Dobson normalization and adjust the TOMS measurements accordingly. The difference between the last two years (1986 and 1987) of the TOMS record, and the first two years of the record (1979 and 1980) are shown. The difference in percent is given as a function of latitude and time of year. The Antarctic springtime decrease is clearly seen as well as a smaller change which extends to about 50 degrees south latitude at all seasons. Changes in the Northern Hemisphere are less dramatic and are concentrated near the polar night where solar zenith angles are very large. These data are now being examined in more detail and updated results will be presented at the Workshop.
A method for computing the skin-stiffener interface stresses in stiffened composite panels is developed. Both geometrically linear and nonlinear analyses are considered. Particular attention is given to the flange termination region where stresses are expected to exhibit unbounded characteristics. The method is based on a finite-element analysis and an elasticity solution. The finite-element analysis is standard, while the elasticity solution is based on an eigenvalue expansion of the stress functions. The eigenvalue expansion is assumed to be valid in the local flange termination region and is coupled with the finite-element analysis using collocation of stresses on the local region boundaries. Accuracy and convergence of the local elasticity solution are assessed using a geometrically linear analysis. Using this analysis procedure, the influence of geometric nonlinearities and stiffener parameters on the skin-stiffener interface stresses is evaluated.
The nonlinear time evolution of a second mode instability in a Mach 4.5 wall-bounded flow is computed by solving the full compressible, time-dependent Navier-Stokes equations. High accuracy is achieved by using a Fourier-Chebyshev collocation algorithm. Primarily inviscid in nature, second modes are characterized by high frequency and high growth rates compared to first modes. Time evolution of growth rate as a function of distance from the plate suggests this problem is amenable to the Stuart-Watson perturbation theory as generalized by Herbert.
The geometrical structure of the boundary shape for a two-dimensional boundary value problem is identified. The output least square identification method is considered for estimating partially unknown boundary shapes. A numerical parameter estimation technique using the spline collocation method is proposed.
The objective of this study is the simultaneous design of the structural and control system for space structures. This study is focused on considering the effect of the number and the location of the actuators on the minimum weight of the structure, and the total work done by the actuators for specified constraints and disturbance. The controls approach used is the linear quadratic regulator theory with constant feedback. At the beginning collocated actuators and sensors are provided in all the elements. The actuator doing the least work is removed one at a time, and the structure is optimized for the specified constraints on the closed-loop eigenvalues and the damping parameters. The procedure of eliminating an actuator is continued until an acceptable design satisfying the constraints is obtained. The study draws some conclusions on the trade between the total work done by the actuators, and the optimum weight and the number of actuators.
The Chebyshev matrix collocation method is applied to obtain the spatial modes of the Orr-Sommerfeld equation for Poiseuille flow and the Blausius boundary layer. The problem is linearized by the companion matrix technique for semi-infinite domain using a mapping transformation. The method can be easily adapted to problems with different boundary conditions requiring different transformations.
A nonlinear extension of model reference adaptive control (MRAC) technique is used to guide a double arm nonlinearizable robot manipulator with flexible links, driven by actuators collocated with joints subject to uncertain payload and inertia. The objective is to track a given simple linear and rigid but compatible dynamical model in real, possible stipulated time and within stipulated degree of accuracy of convergence while avoiding collision of the arms. The objective is attained by a specified signal adaptive feedback controller and by adaptive laws, both given in closed form. A case of 4 DOF manipulator illustrates the technique.
Techniques for determination of very precise orbits for satellites of the Global Positioning System (GPS) are currently being studied and demonstrated. These techniques can be used to make cm-accurate measurements of station locations relative to the geocenter, monitor earth orientation over timescales of hours, and provide tropospheric and clock delay calibrations during observations made with deep space radio antennas at sites where the GPS receivers have been collocated. For high-earth orbiters, meter-level knowledge of position will be available from GPS, while at low altitudes, sub-decimeter accuracy will be possible. Estimation of satellite orbits and other parameters such as ground station positions is carried out with a multi-satellite batch sequential pseudo-epoch state process noise filter. Both square-root information filtering (SRIF) and UD-factorized covariance filtering formulations are implemented in the software.
The Earth Radiation Budget Experiment (ERBE) data studied at present are as follows: (1) Solar Data from ERBS, NOAA-9, and NOAA-10. The solar total irradiance data obtained by the ERBE solar monitors serve as a calibration check on the earth viewing radiometers, as well as provide the experimental value of the solar constant needed in the net radiation computations. (2) The collocated satellite altitude irradiances from ERBS and Nimbus-7 Earth Radiation Budget Measurements are investigated. The sun-synchronous, near-local-noon Nimbus-7 satellite has coincident orbital intersections with the non-sun-synchronous ERBS spacecraft. The objective here is to compare the WFOV and MFOV (wide and medium field-of-view) observations of the ERBS/ERBE, and the Nimbus-7 ERB data sets at the points of their orbital intersections. (3) Globally and zonally averaged ERBE/ERBS data are examined. Investigations of the globally and zonally averaged ERB obtained from the ERBS SCANNER, MFOV and WFOV and the Nimbus-7 WFOV is being carried out to assess the sensor performance.