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Reduction of order technique pertaining to plant and reference model in controller design for linear plants transfer functions with zeros and slowly varying parameters
An effective computational strategy is presented for the large-rotation, nonlinear axisymmetric analysis of shells of revolution. The three key elements of the computational strategy are: (1) use of mixed finite-element models with discontinuous stress resultants at the element interfaces; (2) substantial reduction in the total number of degrees of freedom through the use of a multiple-parameter reduction technique; and (3) reduction in the size of the analysis model through the decomposition of asymmetric loads into symmetric and antisymmetric components coupled with the use of the multiple-parameter reduction technique. The potential of the proposed computational strategy is discussed. Numerical results are presented to demonstrate the high accuracy of the mixed models developed and to show the potential of using the proposed computational strategy for the analysis of tires.
The measurement resolution of noise directivity patterns from acoustic flight tests was investigated. Directivity angle resolution is affected by the data reduction parameters, the aircraft velocity and flyover altitude, and by deviations of the aircraft from the desired flight path. Equations are developed which determine bounds for the lateral and longitudinal directivity angle resolution as a function of the nominal directivity angle. The equations are applied to a flight test data base and the effects of several flight conditions and data reduction parameters on the directivity angle resolution are presented. The maximum directivity angle resolution typically occurs when the aircraft is at or near the overhead position. In general, directivity angle resolution improves with decreasing velocity, increasing altitude, increasing sampling rate, decreasing block size, and decreasing block averages. Deviations from the desired ideal flight path will increase the resolution. For the flight experiment considered in this study, an average of two flyovers were required at each test condition to obtain an acceptable flight path. The ability of the pilot to maintain the flight track improved with decreasing altitude, decreasing velocity, and practice. Due to the prevailing wind conditions, yaw angles of as much as 20 deg were required to maintain the desired flight path.
The problem of noise suppression of turbojet engines has shown a need for turbulence data within the flow field of various types of nozzles used in ad hoc investigations of the sound power. The result of turbulence studies in a nozzle configuration of four parallel rectangular slots is presented in this report with special attention to the effect of the spacing of the nozzles on the intensity of turbulence, scale of turbulence, spectrum of turbulence, and the mean stream velocity. Taylor's hypothesis, which describes the convection of the turbulence eddies, was tested and found correct within experimental error and certain experimental and theoretical limitations. The convection of the pressure patterns was also investigated, and the value of the convection velocity was found to be about 0.43 times the central core velocity of the jets. The effect of the spacing-to-width ratio of the nozzles upon the turbulence intensity, the scale of turbulence, and the spectral distribution of the noise was found in general to produce a maximum change for spacing-to-width ratios of 1.5 to 2.0. These changes may be the cause of the reduction in sound power reported for similar full-scale nozzles and test conditions under actual (static) engine operation. A noise reduction parameter is defined from Lighthill's theory which gives qualitative agreement with experiments which show the noise reduction is greatest for spacing-to-width ratios of 1.5 to 2.0.
A parallel-processing algorithm and a hardware architecture to implement the algorithm have been devised for timeslot synchronization in the reception of pulse-position-modulated (PPM) optical or radio signals. As in the cases of some prior algorithms and architectures for parallel, discrete-time, digital processing of signals other than PPM, an incoming broadband signal is divided into multiple parallel narrower-band signals by means of sub-sampling and filtering. The number of parallel streams is chosen so that the frequency content of the narrower-band signals is low enough to enable processing by relatively-low speed complementary metal oxide semiconductor (CMOS) electronic circuitry. The algorithm and architecture are intended to satisfy requirements for time-varying time-slot synchronization and post-detection filtering, with correction of timing errors independent of estimation of timing errors. They are also intended to afford flexibility for dynamic reconfiguration and upgrading. The architecture is implemented in a reconfigurable CMOS processor in the form of a field-programmable gate array. The algorithm and its hardware implementation incorporate three separate time-varying filter banks for three distinct functions: correction of sub-sample timing errors, post-detection filtering, and post-detection estimation of timing errors. The design of the filter bank for correction of timing errors, the method of estimating timing errors, and the design of a feedback-loop filter are governed by a host of parameters, the most critical one, with regard to processing very broadband signals with CMOS hardware, being the number of parallel streams (equivalently, the rate-reduction parameter).
A study is made of the thermomechanical buckling and postbuckling responses of flat unstiffened composite panels. The panels are subjected to combined temperature change and applied edge displacement. The analysis is based on a first-order shear deformation, von Karman type nonlinear plate theory. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the plate. An efficient multiple-parameter reduction method is used in conjunction with mixed finite element models, for determining the stability boundary and postbuckling response. The reduction method is also used for evaluating the sensitivity coefficients which measure the sensitivity of the buckling and postbuckling responses to variations in the different lamination and material parameters of the panel. Numerical results are presented showing the effects of variations in the laminate stacking sequence, fiber orientation, number of layers and aspect ratio of the panels on their thermomechanical buckling and postbuckling responses and their sensitivity coefficients.
The Barnes PRT-5 infrared radiometer and L-band channel of the multifrequency microwave radiometer are used to survey the distribution of surface water temperature and salinity. These remote sensors were flown repetitively in November 1971 over the outflow of the Mississippi River into the Gulf of Mexico. Data reduction parameters were determined through the use of flight data obtained over a known water area. With these parameters, the measured infrared and microwave radiances were analyzed in terms of the surface temperature and salinity.
Ground-based photometric measurements of spectral sky radiation have been made using a simple filter instrument. Sky radiation intensities measured in the solar vertical at 3200 and 3600 A are compared to infer total ozone. A model of a multiple scattering Rayleigh atmosphere serves as a primary reduction parameter. Spectral measurements of all-sky radiance distribution are used to study the effects of haze and clouds on the inference of total ozone. The brightness distribution of clear and overcast sky in ultraviolet is also described.
Three ecological optimality hypotheses which have utility in parameter reduction and estimation in a climate-soil-vegetation water balance model are reviewed and tested. The first hypothesis involves short term optimization of vegetative canopy density through equilibrium soil moisture maximization. The second hypothesis involves vegetation type selection again through soil moisture maximization, and the third involves soil genesis through plant induced modification of soil hydraulic properties to values which result in a maximum rate of biomass productivity.
Hydrologic models use relatively simple mathematical equations to conceptualize and aggregate the complex, spatially distributed, and highly interrelated water, energy, and vegetation processes in a watershed. A consequence of process aggregation is that the model parameters often do not represent directly measurable entities and must, therefore, be estimated using measurements of the system inputs and outputs. During this process, known as model calibration, the parameters are adjusted so that the behavior of the model approximates, as closely and consistently as possible, the observed response of the hydrologic system over some historical period of time. This Chapter reviews the current state-of-the-art of model calibration in watershed hydrology with special emphasis on our own contributions in the last few decades. We discuss the historical background that has led to current perspectives, and review different approaches for manual and automatic single- and multi-objective parameter estimation. In particular, we highlight the recent developments in the calibration of distributed hydrologic models using parameter dimensionality reduction sampling, parameter regularization and parallel computing.
The X-56A Multi-Utility Technology Testbed (MUTT) is a subscale airplane that was de-signed as an experimental flight research platform for improving aeroelastic modeling and control technologies. The Phase 1 flight tests, conducted from 2017 to 2019 at the NASA Arm-strong Flight Research Center (AFRC), included 39 flights and approximately 1000 research maneuvers, some of which demonstrated stable closed-loop flight beyond the open-loop flutter speed. This paper summarizes the system identification effort to extract nondimensional stability and control derivatives from the flight test data for constructing aeroelastic models of the flight dynamics. Topics discussed include instrumentation, experiment design, model postulation and reduction, parameter estimation, and others. Throughout the paper, unique challenges for the identification of flexible aircraft, practical aspects of the analysis, and lessons learned are presented.
A method called the eigensystem realization algorithm is developed for modal parameter identification and model reduction of dynamic systems from test data. A new approach is introduced in conjunction with the singular-value decomposition technique to derive the basic formulation of minimum order realization which is an extended version of the Ho-Kalman algorithm. The basic formulation is then transformed into modal space for modal parameter identification. Two accuracy indicators are developed to quantitatively identify the system and noise modes. For illustration of the algorithm, an example is shown using experimental data from the Galileo spacecraft.
A method, called the Eigensystem Realization Algorithm (ERA), is developed for modal parameter identification and model reduction of dynamic systems from test data. A new approach is introduced in conjunction with the singular value decomposition technique to derive the basic formulation of minimum order realization which is an extended version of the Ho-Kalman algorithm. The basic formulation is then transformed into modal space for modal parameter identification. Two accuracy indicators are developed to quantitatively identify the system modes and noise modes. For illustration of the algorithm, examples are shown using simulation data and experimental data for a rectangular grid structure.
The Single-Particle Model (SPM) of Li ion cell is a computationally efficient model for simulating Li ion cell for weak to moderate currents. The model depends n a number of parameters describing the geometry and material properties of a cell components. In order to apply the model to simulating a cell, the best-fit parametric values have to be inferred from a constant discharge data. We report our efforts to determine the best-fit set for 18650 LP batteries. We found that rather than being best-fit by a particular point in the parametric space the data is fit equally well by an ensemble of points clustering about an effective multidimensional manifold in the parametric space. This property of the SPM is known to be shared by a multitude of the so-called "sloppy models" of complex systems, characterized by a few stiff directions in the parametric space, in which the predicted behavior varies significantly, and a number of sloppy directions in which the behavior doesn't change appreciably. Only the stiff parameters combinations are identifiable. Geometrical features of the BFM give insights to possible reduction of the SPM to a model having fewer sloppy parameters. We have constructed a hierarchy of such models. The fully reduced model depends on only stiff effective parameters which are identifiable and can be used for characterization of the battery's state of health.
The problem of synthesizing reduced-order linear models of vibrating structures for the design of fixed-order dynamic feedback control is investigated. The present technique builds on a recently developed procedure for constructing an objective set of mass and stiffness matrices from measured modal parameters that are akin to the Craig-Bampton synthesized ones obtained from finite element models. The constructed mass and stiffness matrices are determined directly from the identification of experimental data, however, rather than through correlation or reconciliation of a finite element model. A model truncation criterion is then applied to the identified minimum-order mass and stiffness model to satisfy certain observability/controllability requirements for the reduced model. Numerical examples illustrate the effectiveness of the proposed technique for synthesizing reduced-order controllers from system realizations of experimental data. The dynamic performance of the resulting closed-loop models is assessed using the known full-order structural dynamics and compared with existing model reduction techniques.
Power spectral analysis feasibility for data reduction for medical interpretation of changes in pulmonary impedance pneumograph in remote monitoring
Data-reduction procedures for determining free stream and post-normal shock kinetic and thermodynamic quantities are derived. These procedures are applicable to imperfect real air flows in thermochemical equilibrium for temperatures to 15 000 K and a range of pressures from 0.25 N/sq m to 1 GN/sq m. Although derived primarily to meet the immediate needs of the 6-inch expansion tube, these procedures are applicable to any supersonic or hypersonic test facility where combinations of three of the following flow parameters are measured in the test section: (1) Stagnation pressure behind normal shock; (2) freestream static pressure; (3) stagnation point heat transfer rate; (4) free stream velocity; (5) stagnation density behind normal shock; and (6) free stream density. Limitations of the nine procedures and uncertainties in calculated flow quantities corresponding to uncertainties in measured input data are discussed. A listing of the computer program is presented, along with a description of the inputs required and a sample of the data printout.
The design procedure of feedback controllers was described and the considerations for the selection of the design parameters were given. The frequency domain properties of single-input single-output systems using state feedback controllers are analyzed, and desirable phase and gain margin properties are demonstrated. Special consideration is given to the design of controllers for tracking systems, especially those designed to track polynomial commands. As an example, a controller was designed for a tracking telescope with a polynomial tracking requirement and some special features such as actuator saturation and multiple measurements, one of which is sampled. The resulting system has a tracking performance comparing favorably with a much more complicated digital aided tracker. The parameter sensitivity reduction was treated by considering the variable parameters as random variables. A performance index is defined as a weighted sum of the state and control convariances that sum from both the random system disturbances and the parameter uncertainties, and is minimized numerically by adjusting a set of free parameters.