Results for “hardware complexity” — Page 13

NASA NTRSDate not supplied

Evolution of the Next Exploration Toilet Through Human-in-the-Loop (HITL) Testing

Human waste collection in space is a unique and necessary function that all crewmembers must perform. The variability in how each crewmember uses the toilet to urinate and defecate introduces complexities and challenges with regards to overall hardware design. Because of this variability, it is important to consider crew inputs in all aspects of a toilet design especially with regards to crew interfaces that could impact overall waste collection. Access to crew feedback is essential to the design process and should be considered early and often through the various design phases. In 2020, NASA started a project for the Human Landing System (HLS) program to develop a Government Furnished Equipment (GFE) toilet option. The project is known as the Lavatory On-Orbit (LOO). During the early development of the LOO, the project team conducted several crew evaluations to collect and summarize valuable crew feedback on system design, function, and overall usability to influence the next design iteration. Because every person could use the system differently in space, it was extremely important to collect and analyze the data in a very methodical manner to appropriately influence the design based on the evaluation results. Establishing a standard process ensures consistent data collection from one evaluation to another, helps to maintain privacy for each test subject’s inputs and removes any potential bias from test subject to test subject. To date, the team has completed four rounds of crew evaluations with multiple crewmembers on prototypes for the different LOO subsystems. This paper will summarize the methodology used to conduct the evaluations as well as how data was collected and analyzed. The paper will also provide details on each of the evaluations and how the design was updated based on the results.

toilet↗

NASA NTRSDate not supplied

Hybrid-Electric Aero-Propulsion Controls Testbed Results with Energy Storage

Electrified aircraft propulsion (EAP) research is a priority of the National Aeronautics and Space Administration (NASA) for its potential to increase propulsion system efficiency, performance, and operability at the subsystem and vehicle levels while decreasing emissions. These EAP systems demand more advanced control algorithms due to increased complexity. NASA has developed a reconfigurable, hardware-in-the-loop rig to verify control algorithm performance using a sub-scale electro-mechanical system. A novel capability of this rig is the ability to test full scale EAP control algorithms on a sub-scale representation of the electro-mechanical system without turbomachinery/rotors. A novel feature is the use of a physical energy storage device within the electro-mechanical system. A dual spool, parallel hybrid-electric turbofan architecture and energy management control system is tested with the goal of verifying the ability to obtain turbomachinery model operability benefits while controlling sub-scale electro-mechanical hardware. Pre-test predictions of the turbofan model, control, and rig performance were obtained through simulation using a software model of the rig. Theoretical results showing the true performance of the turbofan model were obtained through a software simulation using full-scale mechanical shaft models. The paper compares theoretical, predicted, and actual test results from the turbofan model, energy management control and rig perspectives. The results show that the presence of sub-scale electro-mechanical hardware did not inhibit the energy management algorithm from achieving turbomachinery operability benefits.

hybrid↗

NASA NTRSDate not supplied

Hybrid-Electric Aero-Propulsion Controls Testbed Results with Energy Storage

Electrified aircraft propulsion (EAP) research is a priority of the National Aeronautics and Space Administration (NASA) for its potential to increase propulsion system efficiency, performance, and operability at the subsystem and vehicle levels while decreasing emissions. These EAP systems demand more advanced control algorithms due to increased complexity. NASA has developed a reconfigurable, hardware-in-the-loop rig to verify control algorithm performance using a sub-scale electro-mechanical system. A novel capability of this rig is the ability to test full scale EAP control algorithms on a sub-scale representation of the electro-mechanical system without turbomachinery/rotors. A novel feature is the use of a physical energy storage device within the electro-mechanical system. A dual spool, parallel hybrid-electric turbofan architecture and energy management control system is tested with the goal of verifying the ability to obtain turbomachinery model operability benefits while controlling sub-scale electro-mechanical hardware. Pre-test predictions of the turbofan model, control, and rig performance were obtained through simulation using a software model of the rig. Theoretical results showing the true performance of the turbofan model were obtained through a software simulation using full-scale mechanical shaft models. The paper compares theoretical, predicted, and actual test results from the turbofan model, energy management control and rig perspectives. The results show that the presence of sub-scale electro-mechanical hardware did not inhibit the energy management algorithm from achieving turbomachinery operability benefits.

hybrid↗

NASA NTRSDate not supplied

Evolution of the Next Exploration Toilet Through Human-in-the-Loop (HITL) Testing

Human waste collection in space is a unique and necessary function that all crewmembers must perform. The variability in how each crewmember uses the toilet to urinate and defecate introduces complexities and challenges with regards to overall hardware design. Because of this variability, it is important to consider crew inputs in all aspects of a toilet design especially with regards to crew interfaces that could impact overall waste collection. Access to crew feedback is essential to the design process and should be considered early and often through the various design phases. In 2020, NASA started a project for the Human Landing System (HLS) program to develop a Government Furnished Equipment (GFE) toilet option. The project is known as the Lavatory On-Orbit (LOO). During the early development of the LOO, the project team conducted several crew evaluations to collect and summarize valuable crew feedback on system design, function, and overall usability to influence the next design iteration. Because every person could use the system differently in space, it was extremely important to collect and analyze the data in a very methodical manner to appropriately influence the design based on the evaluation results. Establishing a standard process ensures consistent data collection from one evaluation to another, helps to maintain privacy for each test subject’s inputs and removes any potential bias from test subject to test subject. To date, the team has completed four rounds of crew evaluations with multiple crewmembers on prototypes for the different LOO subsystems. This paper will summarize the methodology used to conduct the evaluations as well as how data was collected and analyzed. The paper will also provide details on each of the evaluations and how the design was updated based on the results.

toilet↗

NASA NTRS2003

Increasing software testability with standard access and control interfaces

We describe an approach to improving the testability of complex software systems with software constructs modeled after the hardware JTAG bus, used to provide visibility and controlability in testing digital circuits.

software reliability engineering↗

NASA NTRS2017

Anthropometry and Biomechanics Facility Presentation to Open EVA Research Forum

NASA is required to accommodate individuals who fall within a 1st to 99th percentile range on a variety of critical dimensions. The hardware the crew interacts with must therefore be designed and verified to allow these selected individuals to complete critical mission tasks safely and at an optimal performance level. Until now, designers have been provided simpler univariate critical dimensional analyses. The multivariate characteristics of intra-individual and inter-individual size variation must be accounted for, since an individual who is 1st percentile in one body dimension will not be 1st percentile in all other dimensions. A more simplistic approach, assuming every measurement of an individual will fall within the same percentile range, can lead to a model that does not represent realistic members of the population. In other words, there is no '1st percentile female' or '99th percentile male', and designing for these unrealistic body types can lead to hardware issues down the road. Furthermore, due to budget considerations, designers are normally limited to providing only 1 size of a prototype suit, thus requiring other possible means to ensure that a given suit architecture would yield the necessary suit sizes to accommodate the entire user population. Fortunately, modeling tools can be used to more accurately model the types of human body sizes and shapes that will be encountered in a population. Anthropometry toolkits have been designed with a variety of capabilities, including grouping the population into clusters based on critical dimensions, providing percentile information given test subject measurements, and listing measurement ranges for critical dimensions in the 1st-99th percentile range. These toolkits can be combined with full body laser scans to allow designers to build human models that better represent the astronaut population. More recently, some rescaling and reposing capabilities have been developed, to allow reshaping of these static laser scans in more representative postures, such as an abducted shoulder. All of the hardware designed for use with the crew must be sized to accommodate the user population, but the interaction between subject size and hardware fit is complicated with multi-component, complex systems like a space suit. Again, prototype suits are normally only provided in a limited size range, and suited testing is an expensive endeavor; both of these factors limit the number and size of people who can be used to benchmark a spacesuit. However, modeling tools for assessing suit-human interaction can allow potential issues to be modeled and visualized. These types of modeling tools can be used for analysis of a larger combination of anthropometries and hardware types than could feasibly be done with actual human subjects and physical mockups.

Rajulu, Sudhakar↗

NASA NTRS2014

Developing an Integration Infrastructure for Distributed Engine Control Technologies

Turbine engine control technology is poised to make the first revolutionary leap forward since the advent of full authority digital engine control in the mid-1980s. This change aims squarely at overcoming the physical constraints that have historically limited control system hardware on aero-engines to a federated architecture. Distributed control architecture allows complex analog interfaces existing between system elements and the control unit to be replaced by standardized digital interfaces. Embedded processing, enabled by high temperature electronics, provides for digitization of signals at the source and network communications resulting in a modular system at the hardware level. While this scheme simplifies the physical integration of the system, its complexity appears in other ways. In fact, integration now becomes a shared responsibility among suppliers and system integrators. While these are the most obvious changes, there are additional concerns about performance, reliability, and failure modes due to distributed architecture that warrant detailed study. This paper describes the development of a new facility intended to address the many challenges of the underlying technologies of distributed control. The facility is capable of performing both simulation and hardware studies ranging from component to system level complexity. Its modular and hierarchical structure allows the user to focus their interaction on specific areas of interest.

distributed control↗

NASA NTRS2005

Environmental Conditions for Space Flight Hardware: A Survey

Interest in generalization of the physical environment experienced by NASA hardware from the natural Earth environment (on the launch pad), man-made environment on Earth (storage acceptance an d qualification testing), the launch environment, and the space environment, is ed to find commonality among our hardware in an effort to reduce cost and complexity. NASA is entering a period of increase in its number of planetary missions and it is important to understand how our qualification requirements will evolve with and track these new environments. Environmental conditions are described for NASA projects in several ways for the different periods of the mission life cycle. At the beginning, the mission manager defines survivability requirements based on the mission length, orbit, launch date, launch vehicle, and other factors . such as the use of reactor engines. Margins are then applied to these values (temperature extremes, vibration extremes, radiation tolerances, etc,) and a new set of conditions is generalized for design requirements. Mission assurance documents will then assign an additional margin for reliability, and a third set of values is provided for during testing. A fourth set of environmental condition values may evolve intermittently from heritage hardware that has been tested to a level beyond the actual mission requirement. These various sets of environment figures can make it quite confusing and difficult to capture common hardware environmental requirements. Environmental requirement information can be found in a wide variety of places. The most obvious is with the individual projects. We can easily get answers to questions about temperature extremes being used and radiation tolerance goals, but it is more difficult to map the answers to the process that created these requirements: for design, for qualification, and for actual environment with no margin applied. Not everyone assigned to a NASA project may have that kind of insight, as many have only the environmental requirement numbers needed to do their jobs but do not necessarily have a programmatic-level understanding of how all of the environmental requirements fit together.

Plante, Jeannette↗

NASA NTRSDate not supplied

Lessons Learned from Astrobee Operations on the International Space Station

Since its launch in 2019, NASA has been operating three Astrobee free-flying robots providing an autonomous and adaptable research platform aboard the International Space Station (ISS). These robots have not only facilitated a myriad of national and international research endeavors in microgravity but have also served as a STEM outreach platform for student competitions aboard the ISS. Amidst its extensive operational tenure, spanning over five years and exceeding 1200 hours of cumulative free-flyer operation as of April 2024, the Astrobee robots have encountered software and hardware anomalies. Despite its inherent design for on-orbit repair or replacement, certain anomalies have proven to be complex, necessitating remote resolution via software and firmware updates or, in extreme cases, hardware replacements or the return of faulty units to NASA's ground facilities for repair. Such challenges underscore the delicate balance between the autonomous functionality of Astrobee and the occasional need for human intervention to maintain optimal performance. One recurring point of failure identified during Astrobee's operational lifespan has been the SD card, a critical component utilized by the different Astrobee processors and the Dock Station. The occurrence of SD card anomalies, both on orbit and within ground units, has provided invaluable insights into the improvement of Astrobee's systems and mitigation to future faults. This presentation will focus on four key areas: 1. Overview of Faults and Anomalies: A comprehensive examination of the diverse array of faults and anomalies encountered by Astrobee and its associated systems both in orbit and on the ground. From software glitches to hardware malfunctions, this section provides insights into the challenges faced during Astrobee's operational tenure. 2. Resolution Processes and Procedures: An in-depth discussion of the methodologies and procedures implemented to resolve the encountered anomalies. This includes remote troubleshooting, software patches, firmware updates, and, when necessary, the logistics involved in hardware replacements or down-massing for repair. 3. Implementation of Software Updates and Hardware Upgrades: A detailed exploration of the strategies employed to mitigate the risk of recurring anomalies through the implementation of software updates and hardware upgrades. This section highlights the iterative nature of Astrobee's development, emphasizing the continuous pursuit of robustness and reliability. 4. Lessons Learned and Future Directions: Reflecting on the insights gained from addressing anomalies, this section examines the lessons learned and outlines future directions for enhancing Astrobee's robustness and resilience. It underscores the iterative nature of space exploration and the importance of adaptability and continuous improvement in the pursuit of scientific discovery. Through a nuanced examination of Astrobee's operational challenges and the strategies employed to overcome them, this presentation sheds light on the complexities of operating autonomous robotic systems in the ISS environment. It underscores NASA's commitment to pushing the boundaries of exploration and innovation while navigating the inherent challenges of space exploration.

Astrobee↗

NASA NTRSDate not supplied

Lessons Learned from Astrobee Operations on the International Space Station

Since its launch in 2019, NASA has been operating three Astrobee free-flying robots providing an autonomous and adaptable research platform aboard the International Space Station (ISS). These robots have not only facilitated a myriad of national and international research endeavors in microgravity but have also served as a STEM outreach platform for student competitions aboard the ISS. Amidst its extensive operational tenure, spanning over five years and exceeding 1200 hours of cumulative free-flyer operation as of April 2024, the Astrobee robots have encountered software and hardware anomalies. Despite its inherent design for on-orbit repair or replacement, certain anomalies have proven to be complex, necessitating remote resolution via software and firmware updates or, in extreme cases, hardware replacements or the return of faulty units to NASA's ground facilities for repair. Such challenges underscore the delicate balance between the autonomous functionality of Astrobee and the occasional need for human intervention to maintain optimal performance. One recurring point of failure identified during Astrobee's operational lifespan has been the SD card, a critical component utilized by the different Astrobee processors and the Dock Station. The occurrence of SD card anomalies, both on orbit and within ground units, has provided invaluable insights into the improvement of Astrobee's systems and mitigation to future faults. This presentation will focus on four key areas: 1. Overview of Faults and Anomalies: A comprehensive examination of the diverse array of faults and anomalies encountered by Astrobee and its associated systems both in orbit and on the ground. From software glitches to hardware malfunctions, this section provides insights into the challenges faced during Astrobee's operational tenure. 2. Resolution Processes and Procedures: An in-depth discussion of the methodologies and procedures implemented to resolve the encountered anomalies. This includes remote troubleshooting, software patches, firmware updates, and, when necessary, the logistics involved in hardware replacements or down-massing for repair. 3. Implementation of Software Updates and Hardware Upgrades: A detailed exploration of the strategies employed to mitigate the risk of recurring anomalies through the implementation of software updates and hardware upgrades. This section highlights the iterative nature of Astrobee's development, emphasizing the continuous pursuit of robustness and reliability. 4. Lessons Learned and Future Directions: Reflecting on the insights gained from addressing anomalies, this section examines the lessons learned and outlines future directions for enhancing Astrobee's robustness and resilience. It underscores the iterative nature of space exploration and the importance of adaptability and continuous improvement in the pursuit of scientific discovery. Through a nuanced examination of Astrobee's operational challenges and the strategies employed to overcome them, this presentation sheds light on the complexities of operating autonomous robotic systems in the ISS environment. It underscores NASA's commitment to pushing the boundaries of exploration and innovation while navigating the inherent challenges of space exploration.

Astrobee↗

NASA NTRS2006

Sequencing System Building Blocks: Using a Component Architecture for Sequencing Software

Over the last few years software engineering has made significant strides in making more flexible architectures and designs possible. However, at the same time, spacecraft have become more complex and flight software has become more sophisticated. Typically spacecraft are often one-of-a-kind entities that have different hardware designs, different capabilities, different instruments, etc. Ground software has become more complex and operations teams have had to learn a myriad of tools that all have different user interfaces and represent data in different ways. At Jet Propulsion Laboratory (JPL) these themes have collided to require a new approach to producing ground system software. Two different groups have been looking at tackling this particular problem. One group is working for the JPL Mars Technology Program in the Mars Science Laboratory (MSL) Focused Technology area. The other group is the JPL Multi-Mission Planning and Sequencing Group. The major concept driving these two approaches on a similar path is to provide software that can be a more cohesive flexible system that provides a set of planning and sequencing system of services. This paper describes the efforts that have been made to date to create a unified approach from these disparate groups.

multi mission planning↗

NASA NTRS2005

Sequence System Building Blocks: Using a Component Architecture for Sequencing Software

Over the last few years software engineering has made significant strides in making more flexible architectures and designs possible. However, at the same time, spacecraft have become more complex and flight software has become more sophisticated. Typically spacecraft are often one-of-a-kind entities that have different hardware designs, different capabilities, different instruments, etc. Ground software has become more complex and operations teams have had to learn a myriad of tools that all have different user interfaces and represent data in different ways. At Jet Propulsion Laboratory (JPL) these themes have collided to require an new approach to producing ground system software. Two different groups have been looking at tackling this particular problem. One group is working for the JPL Mars Technology Program in the Mars Science Laboratory (MSL) Focused Technology area. The other group is the JPL Multi-Mission Planning and Sequencing Group . The major concept driving these two approaches on a similar path is to provide software that can be a more cohesive flexible system that provides a act of planning and sequencing system of services. This paper describes the efforts that have been made to date to create a unified approach from these disparate groups.

flexible architectures↗

NASA NTRS1993

KSC ground operations planning for Space Station

At the Kennedy Space Center (KSC) in Florida, processing facilities are being built and activated to support the processing, checkout, and launch of Space Station elements. The generic capability of these facilities will be utilized to support resupply missions for payloads, life support services, and propellants for the 30-year life of the program. Special Ground Support Equipment (GSE) is being designed for Space Station hardware special handling requirements, and a Test, Checkout, and Monitoring System (TCMS) is under development to verify that the flight elements are ready for launch. The facilities and equipment used at KSC, along with the testing required to accomplish the mission, are described in detail to provide an understanding of the complexity of operations at the launch site. Assessments of hardware processing flows through KSC are being conducted to minimize the processing flow times for each hardware element. Baseline operations plans and the changes made to improve operations and reduce costs are described, recognizing that efficient ground operations are a major key to success of the Space Station.

Lyon, J. R.↗

NASA NTRS2003

Reconfigurable Hardware Adapts to Changing Mission Demands

A new class of computing architectures and processing systems, which use reconfigurable hardware, is creating a revolutionary approach to implementing future spacecraft systems. With the increasing complexity of electronic components, engineers must design next-generation spacecraft systems with new technologies in both hardware and software. Derivation Systems, Inc., of Carlsbad, California, has been working through NASA s Small Business Innovation Research (SBIR) program to develop key technologies in reconfigurable computing and Intellectual Property (IP) soft cores. Founded in 1993, Derivation Systems has received several SBIR contracts from NASA s Langley Research Center and the U.S. Department of Defense Air Force Research Laboratories in support of its mission to develop hardware and software for high-assurance systems. Through these contracts, Derivation Systems began developing leading-edge technology in formal verification, embedded Java, and reconfigurable computing for its PF3100, Derivational Reasoning System (DRS ), FormalCORE IP, FormalCORE PCI/32, FormalCORE DES, and LavaCORE Configurable Java Processor, which are designed for greater flexibility and security on all space missions.

Source record↗

NASA NTRS2003

Increasing software testability with standard access and control interfaces

Testing is the most common method of determining whether a software system satisfies its requirements. Traditionally, testing starts with the detailed examination of individual functions or methods, progresses through the integration of functions or methods into subsystems, and ends with testing the functionality and behavior of the completely integrated system. At each stage of testing, the amount of functionality and behavior of the artifact being tested is increasingly limited. One reason for this is that it becomes impossible to test all paths through the system within a reasonable amount of time. However, another reason for this progressive decrease of test coverage has to do with increasingly limited control of and visibility into the state of the artifact being tested. During unit test, it is rather simple to control the inputs of individual functions or methods or view their internal state - modem development environments provide adequate facilities for doing so. However, these facilities do not scale up to the testing of partially or completely integrated systems. Control of and visibility into the system's state is then limited to the input and output facilities provided by the software itself as well as the hardware on which the software is hosted during the test. These facilities are usually insufficient to precisely control the state of individual components or sets of components of the system; they are also inadequate to the task of displaying on demand the state of specific components. We describe an approach to improving the testability of complex software systems with software constructs modeled after the hardware JTAG bus, used to provide visibility and controllability in testing digital circuits.

Tamir, Yuval↗

NASA NTRS2004

A Survey of Formal Methods for Intelligent Swarms

Swarms of intelligent autonomous spacecraft, involving complex behaviors and interactions, are being proposed for future space exploration missions. Such missions provide greater flexibility and offer the possibility of gathering more science data than traditional single spacecraft missions. The emergent properties of swarms make these missions powerful, but simultaneously far more difficult to design, and to assure that the proper behaviors will emerge. These missions are also considerably more complex than previous types of missions, and NASA, like other organizations, has little experience in developing or in verifying and validating these types of missions. A significant challenge when verifying and validating swarms of intelligent interacting agents is how to determine that the possible exponential interactions and emergent behaviors are producing the desired results. Assuring correct behavior and interactions of swarms will be critical to mission success. The Autonomous Nano Technology Swarm (ANTS) mission is an example of one of the swarm types of missions NASA is considering. The ANTS mission will use a swarm of picospacecraft that will fly from Earth orbit to the Asteroid Belt. Using an insect colony analogy, ANTS will be composed of specialized workers for asteroid exploration. Exploration would consist of cataloguing the mass, density, morphology, and chemical composition of the asteroids, including any anomalous concentrations of specific minerals. To perform this task, ANTS would carry miniaturized instruments, such as imagers, spectrometers, and detectors. Since ANTS and other similar missions are going to consist of autonomous spacecraft that may be out of contact with the earth for extended periods of time, and have low bandwidths due to weight constraints, it will be difficult to observe improper behavior and to correct any errors after launch. Providing V&V (verification and validation) for this type of mission is new to NASA, and represents the cutting edge in system correctness, and requires higher levels of assurance than other (traditional) missions that use a single or small number of spacecraft that are deterministic in nature and have near continuous communication access. One of the highest possible levels of assurance comes from the application of formal methods. Formal methods are mathematics-based tools and techniques for specifying and verifying (software and hardware) systems. They are particularly useful for specifying complex parallel systems, such as exemplified by the ANTS mission, where the entire system is difficult for a single person to fully understand, a problem that is multiplied with multiple developers. Once written, a formal specification can be used to prove properties of a system (e.g., the underlying system will go from one state to another or not into a specific state) and check for particular types of errors (e.g., race or livelock conditions). A formal specification can also be used as input to a model checker for further validation. This report gives the results of a survey of formal methods techniques for verification and validation of space missions that use swarm technology. Multiple formal methods were evaluated to determine their effectiveness in modeling and assuring the behavior of swarms of spacecraft using the ANTS mission as an example system. This report is the first result of the project to determine formal approaches that are promising for formally specifying swarm-based systems. From this survey, the most promising approaches were selected and are discussed relative to their possible application to the ANTS mission. Future work will include the application of an integrated approach, based on the selected approaches identified in this report, to the formal specification of the ANTS mission.

Truszkowski, Walt↗

NASA NTRS2009

Hardware Implementation of Lossless Adaptive and Scalable Hyperspectral Data Compression for Space

On-board lossless hyperspectral data compression reduces data volume in order to meet NASA and DoD limited downlink capabilities. The technique also improves signature extraction, object recognition and feature classification capabilities by providing exact reconstructed data on constrained downlink resources. At JPL a novel, adaptive and predictive technique for lossless compression of hyperspectral data was recently developed. This technique uses an adaptive filtering method and achieves a combination of low complexity and compression effectiveness that far exceeds state-of-the-art techniques currently in use. The JPL-developed 'Fast Lossless' algorithm requires no training data or other specific information about the nature of the spectral bands for a fixed instrument dynamic range. It is of low computational complexity and thus well-suited for implementation in hardware. A modified form of the algorithm that is better suited for data from pushbroom instruments is generally appropriate for flight implementation. A scalable field programmable gate array (FPGA) hardware implementation was developed. The FPGA implementation achieves a throughput performance of 58 Msamples/sec, which can be increased to over 100 Msamples/sec in a parallel implementation that uses twice the hardware resources This paper describes the hardware implementation of the 'Modified Fast Lossless' compression algorithm on an FPGA. The FPGA implementation targets the current state-of-the-art FPGAs (Xilinx Virtex IV and V families) and compresses one sample every clock cycle to provide a fast and practical real-time solution for space applications.

FPGA implementation↗

NASA NTRS1972

Control system optimization studies. Volume 2: High frequency cutoff filter analysis

The problem of digital implementation of a cutoff filter is approached with consideration to word length, sampling rate, accuracy requirements, computing time and hardware restrictions. Computing time and hardware requirements for four possible programming forms for the linear portions of the filter are determined. Upper bounds for the steady state system output error due to quantization for digital control systems containing a digital network programmed both in the direct form and in the canonical form are derived. This is accomplished by defining a set of error equations in the z domain and then applying the final value theorem to the solution. Quantization error was found to depend upon the digital word length, sampling rate, and system time constants. The error bound developed may be used to estimate the digital word length and sampling rate required to achieve a given system specification. From the quantization error accumulation, computing time and hardware point of view, and the fact that complex poles and zeros must be realized, the canonical form of programming seems preferable.

Fong, M. H.↗