A report proposes the use of waveforms having fractal shapes reminiscent of sawteeth (in contradistinction to conventional regular sawtooth waveforms) as reference signals for pulse-width modulation in control systems for thrusters of spacecraft flying in formation.
Fractal reference signals may also be attractive in some terrestrial control systems — especially those in which pulse-width modulation is used for precise control of electric motors. The report asserts that the use of fractal reference signals would enable the synchronous control of several variables of a spacecraft formation, such that consumption of propellant would be minimized, intervals between thruster firings would be long (as preferred for performing scientific observations), and delays in controlling large-thrust maneuvers for retargeting would be minimized. The report further asserts that whereas different controllers would be needed for different modes of operation if conventional pulsewidth modulation were used, the use of fractal reference signals would enable the same controller to function nearly optimally in all regimes of operation, so that only this one controller would be needed.
This work was done by Boris Lurie of Caltech and Helen Lurie of UCLA for NASA's Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at www.techbriefs.com/tsp under the Electronics/Computers category. NPO-30402
This Brief includes a Technical Support Package (TSP).

Fractal Reference Signals in Pulse-Width Modulation
(reference NPO-30402) is currently available for download from the TSP library.
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Overview
The document is a New Technology Reporting Form from the California Institute of Technology's Jet Propulsion Laboratory (JPL), detailing an innovative approach to pulse-width modulation (PWM) using fractal reference signals. This technology aims to enhance thruster control for formation flying in space interferometry, where precision and minimal propellant consumption are critical during observations.
The motivation behind this innovation stems from the challenges faced in thruster control, particularly during different operational regimes. Traditional PWM methods, which typically use a saw-tooth reference signal, can lead to complications due to varying requirements for target acquisition and observation. The proposed solution involves using a fractal-type reference signal, which allows for synchronous control of multiple variables (up to six) in formation flying. This method not only minimizes propellant consumption but also reduces delay times during the PWM process, making it more efficient for both observation and target acquisition.
The document outlines the novelty of this approach, emphasizing its potential advantages over conventional PWM techniques, particularly in specific applications such as space missions. The technology is still in the developmental phase, with plans for future computer simulations to test its effectiveness in real-world scenarios.
The report also includes information about contributors to the project, funding sources (notably NASA), and the status of the technology regarding patents and publications. It indicates that the technology has not yet been published or presented at conferences but may be disclosed to the public in the future.
In terms of commercialization, the document notes that while the technology is not yet in use outside of JPL, there are plans for its application in space interferometers and formation flying missions. The innovation is positioned as a significant improvement in motion control systems, with potential implications for various aerospace applications.
Overall, this New Technology Reporting Form highlights a promising advancement in PWM technology, leveraging fractal signals to improve control systems in aerospace applications, particularly for NASA's future missions. The document serves as a foundation for further research and development in this area, aiming to enhance the efficiency and effectiveness of space exploration technologies.

