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Frequency domain stability criteria for distributed nonlinear sampled-data systems.

Popov-type sufficient conditions are presented for the absolute stability of a class of closed loop sampled-data systems. The closed loop system consists of a linear distributed element, a feedback controller (linear or nonlinear), a sampler, and possibly a zero-order hold circuit. The distributed element is assumed to be finite Hankel transformable, and such that its dynamics can be represented by a transfer function which is the ratio of the multiple (Laplace and finite Hankel) transforms of output and input. The input is assumed to be distributed. The stability criterion presented here parallels the criterion for distributed systems that are finite Fourier transformable. An example is given to illustrate the applications of the stability criterion.

Nagarajan, N.

Analysis of multiloop, multirate sampled-data systems

Based upon new identities between z-transforms at a basis rate, z-transforms at faster rates, and modified z-transforms, the equivalence between the frequency decomposition method and the switch decomposition method is precisely presented so that results of one method are easily obtained from results of the other. Next, a method is developed for determining the closed loop transfer function of multiloop, multirate sampled-data systems with noninteger ratio sampling rates. Previously, this process involved solving a complex system of equations with rational polynomial coefficients. Herein, this is avoided by introducing a systematic decomposition of matrix operators which naturally arise from the switch decomposition method. The matrix operators are simplified by introducing the shifted transforms of signals sampled at one of the faster rates.

Boykin, W. H.

Time and frequency domain analysis of sampled data controllers via mixed operation equations

Specification of the mathematical equations required to define the dynamic response of a linear continuous plant, subject to sampled data control, is complicated by the fact that the digital components of the control system cannot be modeled via linear ordinary differential equations. This complication can be overcome by introducing two new mathematical operations; namely, the operation of zero order hold and digial delay. It is shown that by direct utilization of these operations, a set of linear mixed operation equations can be written and used to define the dynamic response characteristics of the controlled system. It also is shown how these linear mixed operation equations lead, in an automatable manner, directly to a set of finite difference equations which are in a format compatible with follow on time and frequency domain analysis methods.

Frisch, H. P.

Averaging analysis for discrete time and sampled data adaptive systems

Earlier continuous time averaging theorems are extended to the nonlinear discrete time case. Theorems for the study of the convergence analysis of discrete time adaptive identification and control systems are used. Instability theorems are also derived and used for the study of robust stability and instability of adaptive control schemes applied to sampled data systems. As a by product, the effects of sampling on unmodeled dynamics in continuous time systems are also studied.

Fu, Li-Chen

A FORTRAN program for the analysis of linear continuous and sample-data systems

A FORTRAN digital computer program which performs the general analysis of linearized control systems is described. State variable techniques are used to analyze continuous, discrete, and sampled data systems. Analysis options include the calculation of system eigenvalues, transfer functions, root loci, root contours, frequency responses, power spectra, and transient responses for open- and closed-loop systems. A flexible data input format allows the user to define systems in a variety of representations. Data may be entered by inputing explicit data matrices or matrices constructed in user written subroutines, by specifying transfer function block diagrams, or by using a combination of these methods.

Edwards, J. W.

Phase lock acquisition for sampled data PLLs using the sweep technique

Simulation results of the swept-acquisition performance of residual carrier phase-locked loops (PLLs) are reported. The loops investigated are sampled data counterparts of the continuous time type II and III loops currently in use in Deep Space Network receivers. It was found that sweep rates of 0.2 B(sub L)(2) to 0.4 B(sub L)(2) Hz/s can be used, depending on the loop parameters and loop signal-to-noise ratio (SNR), where B(sub L) is the one-sided loop noise bandwidth. Type III loops are shown to be not as reliable as type II loops for acquisition using this technique, especially at low SNRs.

Aguirre, S.

A separation theorem for the stochastic sampled-data LQG problem

This paper considers the control of a continuous linear plant disturbed by white plant noise when the control is constrained to be a piecewise constant function of time; i.e. a stochastic sampled-data system. The cost function is the integral of quadratic error terms in the state and control, thus penalizing errors at every instant of time while the plant noise disturbs the system continuously. The problem is solved by reducing the constrained continuous problem to an unconstrained discrete one. It is shown that the separation principle for estimation and control still holds for this problem when the plant disturbance and measurement noise are Gaussian.

Halyo, N.

Multirate sampled-data systems analysis via vector operators

The primary difficulties of both the time-domain switch decomposition method and the frequency-domain decomposition method are overcome by introducing certain matrix operators and performing spectral factorization of resulting matrices of polynomials in the z-transform variable. Topological operations of the switch-decomposition method are simplified. This new approach eliminates the need to solve a system of equations with rational polynomial coefficients such as arises in the frequency-decomposition method. The determination of a multirate sampled-data system's characteristic polynomial no longer requires the evaluation of a determinant of rational polynomial elements. New results on obtaining modified z-transforms from standard z-transforms at a faster rate and vice versa are presented.

Boykin, W. H.

Digital modelling, ideal state reconstructor, and control for time-delay sampled-data systems

The cascaded discrete-time state-space representation of a cascaded continuous-time system with fractional input delays is established. Based on the time-delay digital modelling, a practically implementable ideal state reconstructor is also established such that system states are exactly reconstructed via the measurement histories of inputs and outputs without a state observer. By utilizing the blockpulse function approximation the digital modelling of cascaded continuous-time systems with fractional input delays can be carried out, and an artificial input design method is proposed to determine the state feedback gain. Thus the practically implementable digital control law can be established for digital control of time-delay sampled-data systems. An illustrative example is shown to demonstrate the effectiveness of the proposed method.

Tsai, J. S. H.

The relationship between orbital, earth-based, and sample data for lunar landing sites

Results are reported of a detailed examination of data available for the Apollo lunar landing sites, including the Apollo orbital measurements of six major elements derived from XRF and gamma-ray instruments and geochemical parameters derived from earth-based spectral reflectivity data. Wherever orbital coverage for Apollo landing sites exist, the remote data were correlated with geochemical data derived from the soil sample averages for major geological units and the major rock components associated with these units. Discrepancies were observed between the remote and the soil-anlysis elemental concentration data, which were apparently due to the differences in the extent of exposure of geological units, and, hence, major rock eomponents, in the area sampled. Differences were observed in signal depths between various orbital experiments, which may provide a mechanism for explaining differences between the XRF and other landing-site data.

Clark, P. E.

Post-fire time series of sensor and geochemistry sample data from surface water, groundwater, precipitation, soil, and vegetation across Oak Creek watershed, Washington

This dataset supports a broader study examining wildfire impacts on hydrologic connectivity across 5 sites within the Oak Creek watershed and the resulting biogeochemical impacts. Stream sites were selected using the Advanced Terrestrial Simulator (ATS) hydrologic model to identify locations with varying groundwater contributions and hydrologic responses across different burn severity scenarios. The Retreat Fire burned from July 23 to August 2 in 2024, affecting the five study sites at varying burn severities. Each site is equipped with YSI EXO2 sondes logging sub-hourly throughout the year, and grab samples are collected approximately every six weeks. YSI sondes are used to measure temporally resolved proxies for groundwater inputs (specific conductivity) and organic matter (fluorescent dissolved organic matter; fDOM) along with basic water quality and depth. Grab samples of surface water, groundwater, and precipitation are analyzed for water stable isotopes and conductivity to understand endmembers for hydrologic mixing Grab samples of surface water, groundwater, soil water, and litter/vegetation/soil leachates are analyzed for organic matter composition measured by Fourier-Transform Ion Cyclotron Resonance Mass Spectrometry (FTICR-MS) to understand organic matter dynamics. Game camera photos are provided in a separate data package available at https://data.ess-dive.lbl.gov/datasets/doi:10.15485/3018598. Future versions of this dataset will include time series data from YSI EXO2 sondes (fDOM, dissolved oxygen, temperature, depth, specific conductance, turbidity, pH), BaroTROLL sensors (air temperature and barometric pressure), rain gauges (precipitation), and data from the soil and vegetation samples. Because this study is ongoing, this data package will be updated regularly to include newly collected data and the additional data types. For details on how to navigate data packages generated by this project, see https://data.ess-dive.lbl.gov/portals/PNNLRiverCorridorSFA/About. In addition to a readme, this data package also includes a file-level metadata (FLMD) file that describes each file and a data dictionary (DD) that describes all column/row headers and variable definitions. This dataset is comprised of (1) a folder of field photos; (2) a folder of surface water sample data; (3) a folder of raw Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS) data; (4) a data checks report; (5) file-level metadata; (6) data dictionary; (7) field metadata; (8) readme; (9) international generic sample number (IGSN) mapping file; and (10) field protocols. The sample data subfolder contains (1) dissolved organic carbon (DOC, measured as non-purgeable organic carbon, NPOC) data and averages; (2) total dissolved nitrogen data and averages; (3) stable water isotopes and averages; (4) methods codes; (5) FTICR-MS methods; and (15) a subfolder of 9.4 Tesla (9.4T) FTICR-MS data. This folder contains the processed data and three subfolders, one containing the .xml files, one containing the water CoreMS output files, and the other containing instructions and scripts for processing the files in CoreMS (https://github.com/EMSL-Computing/CoreMS). All files are .csv, .pdf, .R, .xml, .d, .html, .Rmd, .py, .cal, .json, .jpg, .jpeg, .png, .mov, or .mp4.

Biogeochemistry

High Accuracy Evaluation of the Finite Fourier Transform Using Sampled Data

Many system identification and signal processing procedures can be done advantageously in the frequency domain. A required preliminary step for this approach is the transformation of sampled time domain data into the frequency domain. The analytical tool used for this transformation is the finite Fourier transform. Inaccuracy in the transformation can degrade system identification and signal processing results. This work presents a method for evaluating the finite Fourier transform using cubic interpolation of sampled time domain data for high accuracy, and the chirp Zeta-transform for arbitrary frequency resolution. The accuracy of the technique is demonstrated in example cases where the transformation can be evaluated analytically. Arbitrary frequency resolution is shown to be important for capturing details of the data in the frequency domain. The technique is demonstrated using flight test data from a longitudinal maneuver of the F-18 High Alpha Research Vehicle.

Morelli, Eugene A.