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Recent Papers in Reverse Chronological Order | |||||
Mechatronic Systems | Hard Disk Drives | Optical Disk Drives | Phase-Locked Loops | Fuzzy Logic Control | History of Technology |
Patents | Back to the main page ... |
As of April 1, 2000, I have been at Agilent Labs. Thus, the work published since then has been largely done at Agilent Labs. In particular the papers on disk drive history and the tutorial on disk drives were done on my own time while I was at Agilent. They are most likely my swan song for the disk drive work. My new work involves a lot of different aspects of high speed measurement systems. One component of these that involves feedback is a Phase-Locked Loop, so one can expect to see some more PLL work show up here (if I'm lucky). |
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During most of my time at HP Labs, I worked on storage. In particular, I worked on both fixed magnetic disks (often referred to as hard drives) and optical disks (both magneto-optic and DVD+RW). Many of these papers are therefore about hard drives. |
Recent Papers in Reverse Chronological Order
Okay, there's explanation in the rest, but I'll just put these in reverse chronological order, so most recent ones are at the top. |
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Trying to Keep it Real: 25 Years of Trying to Get the Stuff I Learned in Grad School to Work on Mechatronic Systems , by Daniel Y. Abramovitch, was given at the 2015 IEEE Conference on Control Applications (CCA), Part of 2015 IEEE Multi-Conference on Systems and Control September 21-23, 2015. Sydney, Australia, and is in the conference proceedings.
Built-In Stepped-Sine Measurements for Digital Control Systems , by Daniel Y. Abramovitch, was given at the 2015 IEEE Conference on Control Applications (CCA), Part of 2015 IEEE Multi-Conference on Systems and Control September 21-23, 2015. Sydney, Australia, and is in the conference proceedings. This paper describes a way of building a dynamics analyzer into control systems.
A Unified Framework for Analog and Digital PID Controllers , by Daniel Y. Abramovitch, was given at the 2015 IEEE Conference on Control Applications (CCA), Part of 2015 IEEE Multi-Conference on Systems and Control September 21-23, 2015. Sydney, Australia, and is in the conference proceedings. This paper describes a way of thinking about analog and digital PID controllers in a unified way.
Mitigating Rotational Disturbances on a Disk Drive with Mismatched Linear Accelerometers by Daniel Y. Abramovitch and George Hsu was given at the 2015 IEEE Conference on Control Applications (CCA), Part of 2015 IEEE Multi-Conference on Systems and Control September 21-23, 2015. Sydney, Australia, and is in the conference proceedings.
The Multinotch, Part I: A Low Latency, High Numerical Fidelity Filter for Mechatronic Control Systems , by Daniel Y. Abramovitch, was given at the 2015 American Controls Conference, July, 2015, in Chicago, and is in the conference proceedings. This paper describes how to use a specific form of a biquad cascade to get a loop shaping filter that is numerically robust, physically intuitive, and yet still allows minimal computational latency via pre-calculation.
The Multinotch, Part II: Extra Precision Via Δ Coefficients , by Daniel Y. Abramovitch, was given at the 2015 American Controls Conference, July, 2015, in Chicago, and is in the conference proceedings. This paper describes a way of improving the coefficient accuracy in the multinotch, via Δ Coefficients, which exploit the biquad structure to give near floating point resolution with virtually the same speed as fixed point math. Some people confuse this with the δ parameterization, but it is different.
The Discrete Time Biquad State Space Structure: Low Latency with High Numerical Fidelity , by Daniel Y. Abramovitch, was given at the 2015 American Controls Conference, July, 2015, in Chicago, and is in the conference proceedings. This paper maps the great properties of the multinotch into a digital state space structure that I call the discrete time biquad state space (BSS).
The Continuous Time Biquad State Space Structure , by Daniel Y. Abramovitch, was given at the 2015 American Controls Conference, July, 2015, in Chicago, and is in the conference proceedings. This paper creates a continuous time biquad state space (BSS), which is surprisingly useful for modeling when combined with the discrete BSS.
A Tutorial on Laser Interferometry for Precision Measurements , by Russell Loughridge and Daniel Y. Abramovitch, was given at the 2013 American Controls Conference, June, 2013, in Washington, D.C., and is in the conference proceedings. This paper is a tutorial on how laser interferometry is used for precision measurements.
Quintessential Phase: A Method of Mitigating Turbulence Effects in Interferometer Measurements of Precision Motion , by Eric Johnstone and Daniel Y. Abramovitch, was given at the 2013 American Controls Conference, June, 2013, in Washington, D.C., and is in the conference proceedings. This paper describes a way of mitigating the effects of turbulence in interferometer measurments via use of precise estimators. It is the work that necessitated the creation of the Biquad State Space structure.
Keeping It Real Paper
Trying to Keep it Real: 25 Years of Trying to Get the Stuff I Learned in Grad School to Work on Mechatronic Systems , by Daniel Y. Abramovitch, was given at the 2015 IEEE Conference on Control Applications (CCA), Part of 2015 IEEE Multi-Conference on Systems and Control September 21-23, 2015. Sydney, Australia, and is in the conference proceedings.
ID for Mechatronic Systems Papers
Built-In Stepped-Sine Measurements for Digital Control Systems , by Daniel Y. Abramovitch, was given at the 2015 IEEE Conference on Control Applications (CCA), Part of 2015 IEEE Multi-Conference on Systems and Control September 21-23, 2015. Sydney, Australia, and is in the conference proceedings.
This paper describes a way of building a dynamics analyzer into control systems.
PID Control Papers
My work on control for high speed atomic force microscopes (AFMs) led me to delve much deeper into PID (Proportional + Integral + Derivative) control. PIDs, when used in conjuction with mutlinotch filters, can pretty much control most Single Input, Single Output (SISO) mechatronic systems. |
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A Unified Framework for Analog and Digital PID Controllers , by Daniel Y. Abramovitch, was given at the 2015 IEEE Conference on Control Applications (CCA), Part of 2015 IEEE Multi-Conference on Systems and Control September 21-23, 2015. Sydney, Australia, and is in the conference proceedings.
This paper describes a way of thinking about analog and digital PID controllers in a unified way.
Semi-Automatic Tuning of PID Gains for Atomic Force Microscopes , by Daniel Y. Abramovitch, Storrs Hoen, and Richard Workman, was given at the 2008 American Controls Conference, June, 2008, and is in the conference proceedings.
This paper uses the realization that a PID controller can look like a notch filter to design the PID as a notch filter. By that I don't mean a notch that zeros out the response at a frequency, but as an anti-resonance. In particular, when the resonance of an AFM actuator is removed in an inverse dynamics type of control. The key then is how to identify the resonance, and this method uses a frequency domain, and then a severely constrained curve fit. The end result is a PID that really improves the performance of an AFM.
Game of Biquads Papers
The Multinotch, Part I: A Low Latency, High Numerical Fidelity Filter for Mechatronic Control Systems , by Daniel Y. Abramovitch, was given at the 2015 American Controls Conference, July, 2015, in Chicago, and is in the conference proceedings.
This paper describes how to use a specific form of a biquad cascade to get a loop shaping filter that is numerically robust, physically intuitive, and yet still allows minimal computational latency via pre-calculation.
The Multinotch, Part II: Extra Precision Via Δ Coefficients , by Daniel Y. Abramovitch, was given at the 2015 American Controls Conference, July, 2015, in Chicago, and is in the conference proceedings.
This paper describes a way of improving the coefficient accuracy in the multinotch, via Δ Coefficients, which exploit the biquad structure to give near floating point resolution with virtually the same speed as fixed point math. Some people confuse this with the δ parameterization, but it is different.
The Discrete Time Biquad State Space Structure: Low Latency with High Numerical Fidelity , by Daniel Y. Abramovitch, was given at the 2015 American Controls Conference, July, 2015, in Chicago, and is in the conference proceedings.
This paper maps the great properties of the multinotch into a digital state space structure that I call the discrete time biquad state space (BSS).
The Continuous Time Biquad State Space Structure , by Daniel Y. Abramovitch, was given at the 2015 American Controls Conference, July, 2015, in Chicago, and is in the conference proceedings.
This paper creates a continuous time biquad state space (BSS), which is surprisingly useful for modeling when combined with the discrete BSS.
Interferometer Measurement Papers
A pictorial view of displacement measurement with a Michelson Interferometer. Below is a zoomed in view. |
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A Tutorial on Laser Interferometry for Precision Measurements , by Russell Loughridge and Daniel Y. Abramovitch, was given at the 2013 American Controls Conference, June, 2013, in Washington, D.C., and is in the conference proceedings. This paper is a tutorial on how laser interferometry is used for precision measurements.
Quintessential Phase: A Method of Mitigating Turbulence Effects in Interferometer Measurements of Precision Motion , by Eric Johnstone and Daniel Y. Abramovitch, was given at the 2013 American Controls Conference, June, 2013, in Washington, D.C., and is in the conference proceedings. This paper describes a way of mitigating the effects of turbulence in interferometer measurments via use of precise estimators. It is the work that necessitated the creation of the Biquad State Space structure.
AFM Control Papers
Low Latency Demodulation for Atomic Force Microscopes, Part I Efficient Real-Time Integration , by Daniel Y. Abramovitch, was given at the 2011 American Controls Conference, June, 2011, in San Francisco, and is in the conference proceedings.
This paper describes a method of efficient digital demodulation for AC mode signals in an AFM. Part I describes the basic mixing and integration method that rapidly provide demodulated I and Q signals.
Low Latency Demodulation for Atomic Force Microscopes, Part II: Efficient Calculation of Magnitude and Phase , by Daniel Y. Abramovitch, was given at the 2011 IFAC World Congress, August, 2011, in Milan, Italy, and is in the conference proceedings.
This paper describes a method of efficient digital demodulation for AC mode signals in an AFM. Part II describes efficient methods of extracting magnitude and phase from the integrated I and Q signals.
A Tale of Three Actuators: How Mechanics, Business Models and Position Sensing Affect Different Mechatronic Servo Problems , by Daniel Y. Abramovitch, was given at the 2009 American Controls Conference, June, 2009, and is in the conference proceedings.
This paper takes an overview of the control of hard disks, optical disks, and AFMs. It brings in how the different mechanisms and the different business models affect the choices one makes in designing the controller.
Semi-Automatic Tuning of PID Gains for Atomic Force Microscopes , by Daniel Y. Abramovitch, Storrs Hoen, and Richard Workman, was given at the 2008 American Controls Conference, June, 2008, and is in the conference proceedings.
This paper uses the realization that a PID controller can look like a notch filter to design the PID as a notch filter. By that I don't mean a notch that zeros out the response at a frequency, but as an anti-resonance. In particular, when the resonance of an AFM actuator is removed in an inverse dynamics type of control. The key then is how to identify the resonance, and this method uses a frequency domain, and then a severely constrained curve fit. The end result is a PID that really improves the performance of an AFM.
A Tutorial on the Mechanisms, Dynamics, and Control of Atomic Force Microscopes , by Daniel Y. Abramovitch, Sean B. Andersson, Lucy Y. Pao, and George Schitter, was given at the 2007 American Controls Conference, June, 2007, and is in the conference proceedings.
This was a 4 author tutorial paper for an invited tutorial session that we generated. It went over pretty well. It explains from a control perspective, exactly how an AFM works and what might be needed to improve its performance.
A Survey of Non-Raster Scan Methods with Application to Atomic Force Microscopy , by Sean B. Andersson and Daniel Y. Abramovitch, was given at the 2007 American Controls Conference, June, 2007, and is in the conference proceedings.
If we could scan only in areas where there are interesting things to image, that would substantially cut imaging time in an AFM. This paper looks at how non-raster scan methods are used in other areas and how they might be applied to AFMs.
Phase-Locked Loops, Part IV: PLL Simulation Papers
The problem of simulating a PLL is made more difficult by the fact that the system is extremely stiff. These two papers describe how I solved this problem using what I like to refer to as: elegant brute force. These two papers describe some work that I did in 2002 to simulate some high speed communication PLLs. In doing so, I had to teach myself C++ (for about the 4th time) and then use it to build up component class libraries. |
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Efficient and Flexible Simulation of Phase Locked Loops, Part I: Simulator Design , was given at the 2008 American Controls Conference, June, 2008, and is in the conference proceedings. This one describes how the simulator was constructed.
Efficient and Flexible Simulation of Phase Locked Loops, Part II: Post Processing and a Design Example , was given at the 2008 American Controls Conference, June, 2008, and is in the conference proceedings. This one describes the post processing tools that could be hung off of the basic simulation, including a simulated spectrum analyzer, jitter estimation, histograms, etc.
Papers on the History of Control
I have also written a few papers on the history of control. One of these was an interview with Professor Boris Kogan, who was the leader of the team that built the Soviet Union's first analog computer. The other was co-authored with Gene Franklin and was a history of the IEEE Control Systems Society. |
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Analog Computing in the Soviet Union: An Interview with Boris Kogan , appeared in the June 2005 issue of the IEEE Control Systems Magazine.
Fifty Years in Control: The Story of the IEEE Control Systems Society , by Daniel Y. Abramovitch and Gene F. Franklin. appeared in the December 2004 issue of the IEEE Control Systems Magazine.
The Outrigger: A Prehistoric Feedback Mechanism:
This paper was presented at a Special History Plenary Session of the 2003 IEEE Conference on Decision and Control and is in the conference proceedings.
A later version was published in the August, 2005 issue of the IEEE Control Systems Magazine.
The significance of this paper is that it shows that the outrigger is a human built feedback mechanism that predates the water clock by at least a millenium. This means that Chapter 1 of a lot of controls books are going to have to change in the next edition. I did almost all of this in the evenings and at lunch time, but I did get a lot of reference help from the Agilent Labs Library.
Phase-Locked Loops, Part III: Lyapunov Redesign of Classical Digital PLLs
The work on the PLL tutorial paper as well as the time I spent simulating PLLs for our jitter measurement project made me realize that I could use Lyapunov redesign on Classical Digital PLLs as well as analog PLLs. In Roland Best's definition, a Classical Digital PLL is one with a digital phase detector, but with analog loop filters and an analog oscillator. My realization was that once I got to the baseband behavior of the digital phase detector, I was back working with a system well suited to Lyapunov Redesign. |
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Classical Digital PLLs were the first digital PLLs to appear. However, they are still used today especially in frequency ranges that are relatively high compared to the circuit technology. Examples of this include high speed communication and instrumentation systems, which are exactly the systems I was working on between 2000 and 2004. |
The paper itself is part excised tutorial from the PLL tutorial paper and part change of variables from the original Lyapunov Redesign of Analog Phase-Locked Loops paper. |
Disk Drive History:
The following two papers are co-authored with my thesis advisor, general role model, and all around good guy, Gene Franklin. The origin of this paper lies in trying to write the disk drive tutorial. It turns out that in order to understand what is going on in a disk drive control loop, one needs to understand the basic history of the technology. |
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A brief history of the control systems used in hard disk drives appeared in the June 2002 issue IEEE Control Systems Magazine. The version that appeared in the magazine is A Brief History of Disk Drive Control . It was granted the 2003 Control Systems Magazine Outstanding Paper Award.
The original draft had to be substantially reduced to get it into the magazine. Thus, an exerpt from the early portion of the uncut paper provides inisight into the early days of disk drive control. This will be published and presented at the 2002 International Federation of Automatic Control (IFAC) Congress. Disk Drive Control: The Early Days. However, a slightly better version was published the IFAC Annual Reviews in Control (Volume 26, Part 2). Disk Drive Control: The Early Days .
The first published paper emenating from work at Agilent Labs, the following is on phase-locked loops. |
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Phase-Locked Loops, Part II: Control Centric PLL Tutorial
When I started learning about phase-locked loops, they were presented to me as a control system. (Thanks to Dan Witmer.) However, most of the control systems analysis that is done on them is only the simplest kind. This is generally because most folks who work on PLLs are analog circuit designers. There is another set of PLL folks who are in the pure digital area, and a set who only work with software PLLs. However, no matter what form they take, they have the character of a nonlinear feedback loop. In most cases, the nonlinearities are easy to linearize. However, the loops generally have this weird hybrid nature. Some of them have analog and digital pieces (digital logic for the phase detectors coupled with analog filters). Some are purely digital, but are implemented using the analog equations. So, as I was writing a software simulator for some PLLs, I ended up approaching the problem from the control loop perspective once again. This resulted in this tutorial. These are different versions of the public paper. |
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This tutorial, Phase-Locked Loops: A Control Centric Tutorial , was given at the 2002 American 2002 American Controls Conference, May, 2002, and is in the conference proceedings. The paper and talk slides are here.
The ACC tutorial was necessarily limited by the page count. I have allowed more material in an unpublished version of the tutorial, also called: Phase-Locked Loops: A Control Centric Tutorial .
A few years later, I gave an updated version of the talk at Clemson University.
By this time, I was at Agilent Labs, having transferred from HP Labs. However, my publications were still based on the work at HP Labs on storage systems. |
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In 2000, I was asked to participate in a tutorial session on disk drive control at the 2001 American Control Conference. Realizing that there were plenty of good talks coming on the hard disks, I tried to find something I could talk about that would be unique. Having worked on both hard disks and optical disks, I decided to do a talk that compared these two disk drive control systems. |
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High Frequency Wobble Papers :
What is DVD+RW based on? Pretty much the high frequency wobble. At least, that's the key technology that makes it different from other formats and allows DVD+RW disks to be readable by most existing DVD ROMS and players. I had the original idea due to the PES Pareto work and the coherent demodulation work. I wanted a clean reference signal. Dave Towner was the optical engineer how understood how to generate the signals practical. Our patent is the fundamental patent for this format. Here are some papers on the subject. |
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This treatment of the subject focuses more on the servo tricks played to improve the performance of the wobbles. It was presented at the 2000 American Controls Conference, June 29, 2000, and is in the conference proceedings: Turning the Tracking Problem Sideways: Servo Tricks for DVD+RW Clock Generation . The talk slides are also pretty decent.
One version of the paper was presented at the 1999 ODS Conference, July 12, 1999, and is in the conference digest. High Frequency Wobbles: A Write Clock Generation Method for Rewritable DVD That Enables Near Drop-In Compatibility with DVD-ROMs.
A longer version of the paper appeared the conference proceedings and yet another version appeared in the Japanese Journal of Applied Physics. This draft uses the SPIE Proceedings format.
Fuzzy Logic Control, Part II: The Fuzzy versus Conventional Control Debate
At the 1998 IEEE Conference on Decision and Control, there was a debate between Michael Athans and Lotfi Zadeh on merits of fuzzy control versus non-fuzzy control. As part of the IEEE Control Systems Society History Committee, I was involved in the organization and video recording of the event. I wrote some thoughts about this debate into a draft which was later split into two documents by the editor of the IEEE Control Systems Magazine. Furthermore, the section where I critiqued the debate, debunking what I thought were bogus arguments was removed. Finally, the copy editor didn't like my writing style and -- to my mind -- rephrased a bunch of stuff according to his own style. So, here are the original drafts of two documents that eventually appeared in the June 1999 IEEE Control Systems Magazine. |
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The debate report, co-authored with Prof. Linda Bushnell, who is head of the IEEE CSS History Committee and did the bulk of organizing the event. It is basically sections 1-3 of the original draft. Report on the Fuzzy versus Conventional Control Debate . An edited version of this appeared in the June 1999 IEEE Control Systems Magazine.
The opinion piece: basically section 5 of the original draft. Fuzzy Control as a Disruptive Technology . An edited version of this appeared in the June 1999 IEEE Control Systems Magazine.
Customizable Coherent Demodulator Papers :
PES Pareto is a methodology of decomposing baseline noise sources in hard disk drives that Terril Hurst and I invented in 1995 while working at HP Labs. Actually, Dick Henze had a key inspirational piece of the invention, and so is on the papers and the patent. The method allowed us to stack together individual noise sources and see how they contribute to the Position Error Signal (PES) in a hard disk. |
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When HP exited the disk drive business in 1996, we ended up publishing these papers. It turns out that this method became a standard in the disk drive industry. Terril and I were invited to come to Quantum and present the work. Even now, over 10 years later, I can go to a disk drive control session at the American Control Conference and someone will mention doing a Pareto of the system, meaning a decomposition of the noise. |
PES Pareto Papers (ACC): Terril and I presented papers to the 1997 American Control Conference (ACC) on the PES Pareto Method. This is the more complete set.
Fuzzy Logic Control, Part I: Some Crisp Thoughts
At some point in the KittyHawk work, I was looking for methods to deal with the pivot friction and put fuzzy logic as a bullet item on a poster. Hey it was in the trade press, so it was worth a bullet line for a possible method. In the end, my search to try to find out how fuzzy logic actually worked led to a set of notes. Those notes got turned into a paper, entitled Some Crisp Thoughts on Fuzzy Logic . This paper made me very popular with control engineers and very unpopular with fuzzy logic proponents. Apparently, I was burned in effigy on comp.ai.fuzzy, but I have never been able to track down the archived messages. None of these guys ever sent me email explaining why they thought I was wrong. I'm guessing they got distraced by the Kirk-Picard debate. |
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The point that was lost, though, was that I was never against fuzzy logic itself, any more than I would be against a computer chip. What I was opposed to was the way the followers of Lotfi Zadeh overhyped the technology without ever explaining how it worked. When I started to understand how fuzzy logic was solving the problems that it was supposed to be solving, I wrote it down. When I did that, a lot of the magic and mythology disappeared, leaving it a lot closer to what Lotfi had originally invented. |
The KittyHawk drive was HP's attempt at a 1.3" disk drive. The project would later be abandoned and be described in Clayton Christensen's book, The Innovator's Dillema. One of the technical issues was that friction became a much larger issue. Here are 3 papers describing some of the work on that. Also, external shock and vibration were a major issue, so there are some papers on that. |
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Accelerometer Feedforward Disturbance Cancellation in Disk Drives
One of the problems to be solved was that of rejecting rotational disturbances in a mobile drive. While disk drive actuators are balanced so that they are relatively immune to translational shock and vibration, they still need to be able to rotate to get to the data. Thus, they are succeptible to rotational disturbances. |
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As drives shrink, the effect of friction becomes more pronounced. Here is some work that I did (along with Feei Wang) to study the pivot friction in the KittyHawk. |
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A paper entitled Disk Drive Pivot Nonlinearity Modeling Part I: Frequency Domain by Daniel Abramovitch, Feei Wang, and Gene Franklin which was presented at the 1994 American Controls Conference in Baltimore, MD.
Banshee Multivariable Workstation
My first experience with high speed DSP was in generating this testbed system. I got a Banshee board from Atlanta Signal Processing, Inc. and then wrote an interface to it that would allow me to dump filters from Matlab into a running system. I learned a bunch about DSPs, latency, data standards, and how to capture real time data from this system. One patent (with Carl Taussig) came out of this which extended a frequency response function loop unwrapping method used in SISO systems to MIMO systems. |
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Frequency Response Functions Above the Nyquist Rate
When I first arrived at HP Labs, Carl Taussig was extending some work originated by Rick Ehrlich on generating frequency response functions at frequencies beyond the Nyquist Rate. My role was to clear up the presentation of the work. The basic idea is that if we stimulate the sampled-data system with narrow band stimulus (e.g. a pure sine wave) at a frequency above the Nyquist frequency the response will be aliased into the lower bands. However, since the stimulus is narrow band, there is nothing else in the low frequency region for it to interfere with. So, with a little bit (or maybe a lot) of math, one can back out the response of the physical system at the stimulus frequency. This becomes a lot harder when a feedback loop is involved, but Rick and Carl showed how it could be done. |
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Phase-Locked Loops, Part I
An early forray into phase-locked loops. Back in December of 1987, I was working at Ford Aerospace Western Development Labs in Palo Alto. Dan Witmer walked into my cubicle and asked my how I would deal with understanding the nonlinear behavior of a phase-locked loop (PLL). I asked what was a PLL, and he proceeded to describe it in terms of a simple feedback loop. So, I naively said, "I'd use Lyapunov Redesign," a control analysis method. Eventually, I ended up doing just that. |
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This was a second lesson in my maturation as an engineer. Just as I had learned in my thesis work that I didn't like extending theory in the absence of a physical system, I learned here that when I was motivated by the appropriate system, I could find and extend the appropriate theory pretty easily. |
A paper entitled Lyapunov Redesign of Analog Phase-Lock Loops by Daniel Abramovitch which was presented at the 1989 American Controls Conference in Pittsburg, PA and was later published in the IEEE Transactions on Communications (Vol. 38, No. 12, December 1990).
A paper entitled Analysis and Design of a Third Order Phase-Lock Loop by Daniel Y. Abramovitch which was presented at the 1988 IEEE Military Communications Conference in San Diego, CA.
Adaptive Control of Nonlinear Systems
This is the work that eminated from my thesis work. There were two papers that emerged from this, on how the adaptive control algorithms could be still shown to be stable when the actuator saturated. However, I was never overly pleased with this theoretical work. |
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In retrospect, this was a key lesson in my education as an engineer: that I really didn't enjoy sitting in an office trying to extend theory. It would only be after I started working at Ford Aerospace in December of 1987 that I was introduced to phase-locked loops, and learned a lesson about how I could do theory. |
Adaptive Control of Nonlinear Dynamic Systems. , by Daniel Y. Abramovitch. PhD thesis, Stanford University, 1988.
A paper entitled On the Stability of Adaptive Pole-Placement Controllers with a Saturating Actuator , by Daniel Y. Abramovitch and Gene F. Franklin. This appeared in the March 1990 issue of the IEEE Transactions on Automatic Control. An earlier version appeared in the Proceedings of the 26th IEEE Conference on Decision and Control, in December 1987.
A paper entitled Adaptive Control with Saturating Inputs , by Daniel Y. Abramovitch, Robert L. Kosut, and Gene F. Franklin. This appeared in the Proceedings of the 25th IEEE Conference on Decision and Control, in December 1986.