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NASA NTRS1989

On some numerical schemes for transonic flow problems

New second-order-accurate finite-difference approximations for a class of nonlinear PDEs of mixed type, which includes the two-dimensional low-frequency transonic small-disturbance equation (TSD) and full-potential equation (FP), are presented. For the TSD equation, the scheme is implemented via a time-splitting algorithm; the inclusion of flux limiters keeps the total variation nonincreasing and eliminates spurious oscillations near shocks. Global-linear-stability, TVD, and entropy-stability results are proved. Numerical results for the flow over a thin airfoil are presented. Current techniques used to solve the TSD equation may easily be extended to second-order accuracy by this method. For the FP equation, the new scheme requires no subsonic/supersonic switching and no numerical flux biasing. Global linear stability for all values of the Mach number is proved.

Mostrel, Marco Mosche↗

NASA NTRS2003

Autonomous Telemetry Collection for Single-Processor Small Satellites

For the Space Technology 5 mission, which is being developed under NASA's New Millennium Program, a single spacecraft processor will be required to do on-board real-time computations and operations associated with attitude control, up-link and down-link communications, science data processing, solid-state recorder management, power switching and battery charge management, experiment data collection, health and status data collection, etc. Much of the health and status information is in analog form, and each of the analog signals must be routed to the input of an analog-to-digital converter, converted to digital form, and then stored in memory. If the micro-operations of the analog data collection process are implemented in software, the processor may use up a lot of time either waiting for the analog signal to settle, waiting for the analog-to-digital conversion to complete, or servicing a large number of high frequency interrupts. In order to off-load a very busy processor, the collection and digitization of all analog spacecraft health and status data will be done autonomously by a field-programmable gate array that can configure the analog signal chain, control the analog-to-digital converter, and store the converted data in memory.

Speer, Dave↗

NASA NTRS1991

Theory and simulation of a high-frequency magnetic drift wave

The equilibrium of a nonneutral plasma in a toroidal vessel with a toroidal magnetic field is analyzed. In the zero inertia limit it is heuristically shown from force balance considerations that there is an electrostatic hoop force and a force due to diamagnetism along the major radius. The problem of equilibrium is formulated in terms of solutions of a 2D partial difference equation. This equation is solved in the large-aspect-ratio limit and a general expression for the shift of the potential axis is obtained which shows that the shift is approximately epsilon and that it depends solely on the internal capacitance of the cloud. The simulation study is based upon the modified MHD equations and the nonlocal nature of the mode is investigated. Applications to sub-Alfvenic plasma expansions, electromagnetic waves in the earth's magnetosphere, and plasma switches are discussed.

Huba, J. D.↗

NASA NTRS1993

Power attenuation characteristics as switch-over criterion in personal satellite mobile communications

A third generation mobile system intends to support communications in all environments (i.e., outdoors, indoors at home or office and when moving). This system will integrate services that are now available in architectures such as cellular, cordless, mobile data networks, paging, including satellite services to rural areas. One way through which service integration will be made possible is by supporting a hierarchical cellular structure based on umbrella cells, macro cells, micro and pico cells. In this type of structure, satellites are part of the giant umbrella cells allowing continuous global coverage, the other cells belong to cities, neighborhoods, and buildings respectively. This does not necessarily imply that network operation of terrestrial and satellite segments interconnect to enable roaming and spectrum sharing. However, the cell concept does imply hand-off between different cell types, which may involve change of frequency. Within this propsective, the present work uses power attenuation characteristics to determine a dynamic criterion that allows smooth transition from space to terrestrial networks. The analysis includes a hybrid channel that combines Rician, Raleigh and Log Normal fading characteristics.

Castro, Jonathan P.↗

NASA NTRS2001

The Transition from Hydrogen Bonding to Ionization in (HCI)n(NH3)n and (HCI)n(H2O)n Clusters: Consequences for Anharmonic Vibrational Spectroscopy

Anharmonic vibrational frequencies and intensities are calculated for 1:1 and 2:2 (HCl)(sub n)(NH3)(sub n) and (HCl)(sub n)(H2O)(sub n) complexes, employing the correlation-corrected vibrational self-consistent field method with ab initio potential surfaces at the MP2/TZP computational level. In this method, the anharmonic coupling between all vibrational modes is included, which is found to be important for the systems studied. For the 4:4 (HCl)(sub n)(H2O)(sub n) complex, the vibrational spectra are calculated at the harmonic level, and anharmonic effects are estimated. Just as the (HCl)(sub n)(NH3)(sub n) structure switches from hydrogen-bonded to ionic for n=2, the (HCl)(sub n)(H2O)(sub n) switches to ionic structure for n=4. For (HCl)2(H2O)2, the lowest energy structure corresponds to the hydrogen-bonded form. However, configurations of the ionic form are separated from this minimum by a barrier of less than an O-H stretching quantum. This suggests the possibility of experiments on ionization dynamics using infrared excitation of the hydrogen-bonded form. The strong cooperative effects on the hydrogen bonding, and concomitant transition to ionic bonding, makes an accurate estimate of the large anharmonicity crucial for understanding the infrared spectra of these systems. The anharmonicity is typically of the order of several hundred wave numbers for the proton stretching motions involved in hydrogen or ionic bonding, and can also be quite large for the intramolecular modes. In addition, the large cooperative effects in the 2:2 and higher order (HCl(sub n)(H2O)(sub n) complexes may have interesting implications for solvation of hydrogen halides at ice surfaces.

Chaban, Galina M.↗

NASA NTRS1994

A radio telescope for the calibration of radio sources at 32 gigahertz

A 1.5-m-diameter radio telescope has been designed, developed, and assembled to directly measure the flux density of radio sources in the 32-GHz (Ka-band) frequency band. The main goal of the design and development was to provide a system that could yield the greatest absolute accuracy yet possible with such a system. The accuracy of the measurements have a heritage that is traceable to the National Institute of Standards and Technology. At the present time, the absolute accuracy of flux density measurements provided by this telescope system, during Venus observations at nearly closest approach to Earth, is plus or minus 5 percent, with an associated precision of plus or minus 2 percent. Combining a cooled high-electron mobility transistor low-noise amplifier, twin-beam Dicke switching antenna, and accurate positioning system resulted in a state-of-the-art system at 32 GHz. This article describes the design and performance of the system as it was delivered to the Owens Valley Radio Observatory to support direct calibrations of the strongest radio sources at Ka-band.

Gatti, M. S.↗

NASA NTRS2004

Silicon Carbide Diodes Characterization at High Temperature and Comparison With Silicon Devices

Commercially available silicon carbide (SiC) Schottky diodes from different manufacturers rated at 200, 300, 600, and 1200 V, were electrically tested and characterized as a function of temperature up to 300 C. Electrical tests included both steady state and dynamic tests. Steady state tests produced forward and reverse I-V characteristic curves. Transient tests evaluated the switching performance of the diodes in either a hard-switched DC to DC buck converter or a half-bridge boost converter. For evaluation and comparison purposes, the same tests were performed with current state-of-the-art ultra fast silicon (Si) pn-junction diodes of similar ratings and also a Si Schottky diode. The comparisons made were forward voltage drop at rated current, reverse current at rated voltage, and turn-off peak reverse recovery current and reverse recovery time. In addition, efficiency measurements were taken for the buck DC to DC converter using both the SiC Schottky diodes and the Si pn-junction diodes at different temperatures and frequencies. The test results showed that at high temperature, the forward voltage drop for SiC Schottky diodes is higher than the forward drop of the ultra fast Si pn-junction diodes. As the temperature increased, the forward voltage drop of the SiC Schottky increased while for the ultra fast Si pn-junction diodes, the forward voltage drop decreased as temperature increased. For the elevated temperature steady state reverse voltage tests, the SiC Schottky diodes showed low leakage current at their rated voltage. Likewise, for the transient tests, the SiC Schottky diodes displayed low reverse recovery currents over the range of temperatures tested. Conversely, the Si pn-junction diodes showed increasing peak reverse current values and reverse recovery times with increasing temperature. Efficiency measurements in the DC to DC buck converter showed the advantage of the SiC Schottky diodes over the ultra fast Si pn-junction diodes, especially at the higher temperatures and higher frequencies.

Lebron-Velilla, Ramon C.↗

NASA NTRS1987

Modeling and stability analysis for the upper atmosphere research satellite auxiliary array switch component

A feedback control system, called an auxiliary array switch, was designed to connect or disconnect auxiliary solar panel segments from a spacecraft electrical bus to meet fluctuating demand for power. A simulation of the control system was used to carry out a number of design and analysis tasks that could not economically be performed with a breadboard of the hardware. These tasks included: (1) the diagnosis of a stability problem, (2) identification of parameters to which the performance of the control system was particularly sensitive, (3) verification that the response of the control system to anticipated fluctuations in the electrical load of the spacecraft was satisfactory, and (4) specification of limitations on the frequency and amplitude of the load fluctuations.

Wolfgang, R.↗

NASA NTRS2005

Prototype development of a Geostationary Synthetic Thinned Aperture Radiometer (GeoSTAR)

Weather prediction and hurricane tracking would greatly benefit of a continuous imaging capability of a hemisphere at millimeter wave frequencies. We are developing a synthetic thinned aperture radiometer (STAR) prototype operating from 50 to 56 GHz as a ground-based testbed to demonstrate the technologies needed to do full earth disk atmospheric temperature soundings from Geostationary orbit with very high spatial resolution. The prototype consists of a Y-array of 24 MMIC receivers that are compact units implemented with low noise InP MMIC LNAs, second harmonic I-Q mixers, low power IF amplifiers and include internal digital bias control with serial line communication to enable low cost testing and system integration. Furthermore, this prototype STAR includes independent LO and noise calibration signal phase switching circuitry for each arm of the Y-array to verify the operation and calibration of the system.

Millimeter wave low noise amplifiers↗

NASA NTRS1993

INPIStron switched pulsed power for dense plasma pinches

The inverse plasma switch INPIStron was employed for 10kJ/40kV capacitor bank discharge system to produce focused dense plasmas in hypocycloidal-pinch (HCP) devices. A single unit and an array of multiple HCP's were coupled as the load of the pulsed power circuit. The geometry and switching plasma dynamics were found advantageous and convenient for commutating the large current pulse from the low impedance transmission line to the low impedance plasma load. The pulse power system with a single unit HCP, the system A, was used for production of high temperature plasma focus and its diagnostics. The radially running down plasma dynamics, revealed in image converter photographs, could be simulated by a simple snow-plow model with a correction for plasma resistivity. The system B with an array of 8-HCP units which forms a long coaxial discharge chamber was used for pumping a Ti-sapphire laser. The intense UV emission from the plasma was frequency shifted with dye-solution jacket to match the absorption band of the Ti crystal laser near 500 nm. An untuned laser pulse energy of 0.6 J/pulse was obtained for 6.4 kJ/40 kV discharge, or near 103 times of the explosion limit of conventional flash lamps. For both systems the advantages of the INPIStron were well demonstrated: a single unit is sufficient for a large current (greater than 50 kA) without increasing the system impedance, highly reliable and long life operation and implied scalability for the high power ranges above I(sub peak) = 1 MA and V(sub hold) = 100 kV.

Han, Kwang S.↗

NASA NTRS1991

Nonlinear optical properties of organic materials: A theoretical study

Replacement of electronic switching circuits in computing and telecommunication systems with purely optical devices offers the potential for extremely high throughput and compact information processing systems. The potential application of organic materials containing molecules with large nonresonant nonlinear effects in this area have triggered intensive research during the last decade. Interest on this area was due to two facts: (1) that many organic materials show nonlinearities that are orders of magnitude larger than those of conventional inorganic materials such as lithium niobate and potassium dihydrogen phosphate; and (2) that organic materials show much flexibility in terms of molecular designs. Some of the desirable characteristics that these materials should have are that they be transparent to the frequency of the incident laser and its second or third harmonic, that they have a high damage threshold, and, in the case of second-order effects, that their crystal structure or molecular orientation be accentric. Since polymeric assemblages can enhance the nonlinear response of organic molecules severalfold, efforts have been directed toward the synthesis of thin films with interpenetrating lattices of electroactive molecules. The goal of this theoretical investigation is to predict the magnitude of the molecular polarizabilities of organic molecules that could be incorporated into films. These calculations are intended to become a powerful tool to assist material scientists in screening for the best candidates for optical applications. The procedure that was developed for the present calculations is based on the static-field approach, and is a modification to the method developed by Dewar and Stewart, 1984 for calculating molecular linear polarizabilities.

Cardelino, Beatriz H.↗

NASA NTRS2000

The NASA Spacecraft Transponding Modem

A new deep space transponder is being developed by the Jet Propulsion Laboratory for NASA. The Spacecraft Transponding Modem (STM) implements the standard transponder functions and the channel service functions that have previously resided in spacecraft Command/Data Subsystems. The STM uses custom ASICs, MMICs, and MCMs to reduce the active device parts count to 70, mass to I kg, and volume to 524 cc. The first STMs will be flown on missions launching in the 2003 time frame. The STM tracks an X-band uplink signal and provides both X-band and Ka-band downlinks, either coherent or non-coherent with the uplink. A NASA standard Command Detector Unit is integrated into the STM, along with a codeblock processor and a hardware command decoder. The decoded command codeblocks are output to the spacecraft command/data subsystem. Virtual Channel 0 (VC-0) (hardware) commands are processed and output as critical controller (CRC) commands. Downlink telemetry is received from the spacecraft data subsystem as telemetry frames. The STM provides the following downlink coding options: the standard CCSDS (7-1/2) convolutional coding, ReedSolomon coding with interleave depths one and five, (15-1/6) convolutional coding, and Turbo coding with rates 1/3 and 1/6. The downlink symbol rates can be linearly ramped to match the G/T curve of the receiving station, providing up to a 1 dB increase in data return. Data rates range from 5 bits per second (bps) to 24 Mbps, with three modulation modes provided: modulated subcarrier (3 different frequencies provided), biphase-L modulated direct on carrier, and Offset QPSK. Also, the capability to generate one of four non-harmonically related telemetry beacon tones is provided, to allow for a simple spacecraft status monitoring scheme for cruise phases of missions. Three ranging modes are provided: standard turn around ranging, regenerative pseudo-noise (PN) ranging, and Differential One-way Ranging (DOR) tones. The regenerative ranging provides the capability of increasing the ground received ranging SNR by up to 30 dB. Two different avionics interfaces to the command/data subsystem's data bus are provided: a MIL STD 1553B bus or an industry standard PCI interface. Digital interfaces provide the capability to control antenna selection (e.g., switching between high gain and low gain antennas) and antenna pointing (for future steered Ka-band antennas).

Berner, Jeff B.↗

NASA NTRS1999

EXPRESS Rack Technology for Space Station

The EXPRESS rack provides accommodations for standard Mid-deck Locker and ISIS drawer payloads on the International Space Station. A design overview of the basic EXPRESS rack and two derivatives, the Human Research Facility and the Habitat Holding Rack, is given in Part I. In Part II, the design of the Solid State Power Control Module (SSPCM) is reviewed. The SSPCM is a programmable and remotely controllable power switching and voltage conversion unit which distributes and protects up to 3kW of 12OVDC and 28VDC power to payloads and rack subsystem components. Part III details the development and testing of a new data storage device, the BRP EXPRESS Memory Unit (BEMU). The BEMU is a conduction-cooled device which operates on 28VDC and is based on Boeing-modified 9GB commercial disk-drive technology. In Part IV results of a preliminary design effort for a rack Passive Damping System (PDS) are reported. The PDS is intended to isolate ISPR-based experiment racks from on-orbit vibration. System performance predictions based on component developmental testing indicate that such a system can provide effective isolation at frequencies of 1 Hz and above.

Davis, Ted B.↗

NASA NTRS2001

Using Dynamic Interface Modeling and Simulation to Develop a Launch and Recovery Flight Simulation for a UH-60A Blackhawk

Joint Shipboard Helicopter Integration Process (JSHIP) is a Joint Test and Evaluation (JT&E) program sponsored by the Office of the Secretary of Defense (OSD). Under the JSHDP program is a simulation effort referred to as the Dynamic Interface Modeling and Simulation System (DIMSS). The purpose of DIMSS is to develop and test the processes and mechanisms that facilitate ship-helicopter interface testing via man-in-the-loop ground-based flight simulators. Specifically, the DIMSS charter is to develop an accredited process for using a flight simulator to determine the wind-over-the-deck (WOD) launch and recovery flight envelope for the UH-60A ship/helicopter combination. DIMSS is a collaborative effort between the NASA Ames Research Center and OSD. OSD determines the T&E and warfighter training requirements, provides the programmatics and dynamic interface T&E experience, and conducts ship/aircraft interface tests for validating the simulation. NASA provides the research and development element, simulation facility, and simulation technical experience. This paper will highlight the benefits of the NASA/JSHIP collaboration and detail achievements of the project in terms of modeling and simulation. The Vertical Motion Simulator (VMS) at NASA Ames Research Center offers the capability to simulate a wide range of simulation cueing configurations, which include visual, aural, and body-force cueing devices. The system flexibility enables switching configurations io allow back-to-back evaluation and comparison of different levels of cueing fidelity in determining minimum training requirements. The investigation required development and integration of several major simulation system at the VMS. A new UH-60A BlackHawk interchangeable cab that provides an out-the-window (OTW) field-of-view (FOV) of 220 degrees in azimuth and 70 degrees in elevation was built. Modeling efforts involved integrating Computational Fluid Dynamics (CFD) generated data of an LHA ship airwake and integrating a real-time ship motion model developed based on a batch model from Naval Surface Warfare Center. Engineering development and integration of a three degrees-of-freedom (DOF) dynamic seat to simulate high frequency rotor-dynamics dependent motion cues for use in conjunction with the large motion system was accomplished. The development of an LHA visual model in several different levels of resolution and an aural cueing system in which three separate fidelity levels could be selected were developed. VMS also integrated a PC-based E&S simFUSION system to investigate cost effective IG alternatives. The DIMSS project consists of three phases that follow an approved Validation, Verification and accreditation (VV&A) process. The first phase will support the accreditation of the individual subsystems and models. The second will follow the verification and validation of the integrated subsystems and models, and will address fidelity requirements of the integrated models and subsystems. The third and final phase will allow the verification and validation of the full system integration. This VV&A process will address the utility of the simulated WOD launch and recovery envelope. Simulations supporting the first two stages have been completed and the data is currently being reviewed and analyzed.

Sweeney, Christopher↗

NASA NTRS1989

A design procedure for the phase-controlled parallel-loaded resonant inverter

High-frequency-link power conversion and distribution based on a resonant inverter (RI) has been recently proposed. The design of several topologies is reviewed, and a simple approximate design procedure is developed for the phase-controlled parallel-loaded RI. This design procedure seeks to ensure the benefits of resonant conversion and is verified by data from a laboratory 2.5 kVA, 20-kHz converter. A simple phasor analysis is introduced as a useful approximation for design purposes. The load is considered to be a linear impedance (or an ac current sink). The design procedure is verified using a 2.5-kVA 20-kHz RI. Also obtained are predictable worst-case ratings for each component of the resonant tank circuit and the inverter switches. For a given load VA requirement, below-resonance operation is found to result in a significantly lower tank VA requirement. Under transient conditions such as load short-circuit, a reversal of the expected commutation sequence is possible.

King, Roger J.↗

NASA NTRS2002

Time-Accurate Simulations and Acoustic Analysis of Slat Free-Shear-Layer

Unsteady computational simulations of a multi-element, high-lift configuration are performed. Emphasis is placed on accurate spatiotemporal resolution of the free shear layer in the slat-cove region. The excessive dissipative effects of the turbulence model, so prevalent in previous simulations, are circumvented by switching off the turbulence-production term in the slat cove region. The justifications and physical arguments for taking such a step are explained in detail. The removal of this excess damping allows the shear layer to amplify large-scale structures, to achieve a proper non-linear saturation state, and to permit vortex merging. The large-scale disturbances are self-excited, and unlike our prior fully turbulent simulations, no external forcing of the shear layer is required. To obtain the farfield acoustics, the Ffowcs Williams and Hawkings equation is evaluated numerically using the simulated time-accurate flow data. The present comparison between the computed and measured farfield acoustic spectra shows much better agreement for the amplitude and frequency content than past calculations. The effect of the angle-of-attack on the slat's flow features radiated acoustic field are also simulated presented.

Khorrami, Mehdi R.↗

NASA NTRS1999

Spatial Orientation and Balance Control Changes Induced by Altered Gravito-Inertial Force Vectors

Seventeen healthy and eight vestibular deficient subjects were exposed to an interaural centripetal acceleration of 1 G (resultant 45 deg roll tilt of 1.4 G) on a 0.8 meter radius centrifuge for a period of 90 minutes in the dark. The subjects sat with head fixed upright, except every 4 of 10 minutes when instructed to rotate their head so that their nose and eyes pointed towards a visual point switched on every 3 to 5 seconds at random places (within +/- 30 deg) in the Earth horizontal plane. Motion sickness caused some subjects to limit their head movements during significant portions of the 90 minute period, and led three normal subjects to stop the test earlier. Eye movements, including directed saccades for subjective Earth- and head-referenced planes, were recorded before, during, and immediately after centrifugation using electro-oculography. Postural stability measurements were made before and within ten minutes after centrifugation. In normal subjects, postural sway and multisegment body kinematics were gathered during an eyes-closed head movement cadence (sway-referenced support platform), and in response to translational/rotational platform perturbations. A significant increase in postural sway, segmental motion amplitude and hip frequency was observed after centrifugation. This effect was short-lived, with a recovery time of several postural test trials. There were also asymmetries in the direction of post-centrifugation center of sway and head tilt which depended on the subject's orientation during the centrifugation adaptation period (left ear or right ear out). To delineate the effect of the magnitude of the gravito-inertial vector versus its direction during the adaptive centrifugation period, we tilted eight normal subjects in the roll axis at a 45 deg angle in the dark for 90 minutes without rotational motion. Their postural responses did not change following the period of tilt. Based on verbal reports, normal subjects overestimated roll-tilt during 90 minutes of both tilt and centrifugation stimuli. Subjective estimates of head-horizontal, provided by directed saccades, revealed significant errors after approximately 30 minutes that tended to increase only in the group who underwent centrifugation. Immediately after centrifugation, subjects reported feeling tilted on average 10 degrees in the opposite direction, which was in agreement with the direction of their earth-directed saccades. In vestibular deficient (VD) subjects, postural sway was measured using a sway-referenced or earth-fixed support surface, and with or without a head movement sequence. 'Me protocol was selected for each patient during baseline testing, and corresponded to the most challenging condition in which the patient was able to maintain balance with eyes closed. Bilaterally VD subjects showed no postural decrement after centrifugation, while unilateral VD subjects had varying degrees of decrement. Unilateral VD subjects were tested twice; they underwent centrifugation both with right ear out and left ear out. Their post-centrifuation center of sway shifted at right angles depending on the centrifuge GIF orientation. Bilateral VD subjects bad shifts as well, but no consistent directional trend. VD subjects underestimated roll-tilt during centrifugation, These results suggest that orientation of the gravito-inertial vector and its magnitude arc both used by the central nervous system for calibration of multiple orientation systems. A change in the background gravito-inertial force (otolith input) can rapidly initiate postural and perceptual adaptation in several sensorimotor systems, independent of a structured visual surround.

Kaufman, Galen D.↗

NASA NTRS2008

Controller for Driving a Piezoelectric Actuator at Resonance

A digital control system based partly on an extremum-seeking control algorithm tracks the changing resonance frequency of a piezoelectric actuator or an electrically similar electromechanical device that is driven by a sinusoidal excitation signal and is required to be maintained at or near resonance in the presence of uncertain, changing external loads and disturbances. Somewhat more specifically, on the basis of measurements of the performance of the actuator, this system repeatedly estimates the resonance frequency and alters the excitation frequency as needed to keep it at or near the resonance frequency. In the original application for which this controller was developed, the piezoelectric actuator is part of an ultrasonic/sonic drill/corer. Going beyond this application, the underlying principles of design and operation are generally applicable to tracking changing resonance frequencies of heavily perturbed harmonic oscillators. Resonance-frequency-tracking analog electronic circuits are commercially available, but are not adequate for the present purpose for several reasons: The input/output characteristics of analog circuits tend to drift, often necessitating recalibration, especially whenever the same controller is used in driving a different resonator. In the case of an actuator in a system that has multiple modes characterized by different resonance frequencies, an analog controller can tune erroneously to one of the higher-frequency modes. The lack of programmability of analog controllers is problematic when faults occur, and is especially problematic for preventing tuning to a higher-frequency mode. In contrast, a digital controller can be programmed to restrict itself to a specified frequency range and to maintain stability even when the affected resonator is driven at high power and subjected to uncertain disturbances and variable loads. The present digital control system (see figure) is implemented by means of an algorithm that comprises three main subalgorithms: a hill-climbing control algorithm, an estimation-based extremum-seeking control (ESC) algorithm, and a supervisory algorithm. The hill-climbing algorithm is useful for coarse tracking to find and remain within the vicinity of the resonance. The ESC algorithm is not capable of coarse resonance tracking, but is capable of fine resonance tracking once the estimates of parameters generated by the hill-climbing algorithm have converged sufficiently. On the basis of the parameter-estimation errors, the supervisory algorithm switches operation to whichever of the other two algorithms performs best at a given time.

Aldrich, Jack↗