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Description
The problem of systematically designing a control system continues to remain a subject of intense research. In this thesis, a very powerful control system design environment for Linear Time-Invariant (LTI) Multiple-Input Multiple-Output (MIMO) plants is presented. The environment has been designed to address a broad set of closed loop metrics and constraints; e.g. weighted H-infinity closed loop performance subject to closed loop frequency and/or time domain constraints (e.g. peak frequency response, peak overshoot, peak controls, etc.). The general problem considered - a generalized weighted mixed-sensitivity problem subject to constraints - permits designers to directly address and tradeoff multivariable properties at distinct loop breaking points; e.g. at plant outputs and at plant inputs. As such, the environment is particularly powerful for (poorly conditioned) multivariable plants. The Youla parameterization is used to parameterize the set of all stabilizing LTI proper controllers. This is used to convexify the general problem being addressed. Several bases are used to turn the resulting infinite-dimensional problem into a finite-dimensional problem for which there exist many efficient convex optimization algorithms. A simple cutting plane algorithm is used within the environment. Academic and physical examples are presented to illustrate the utility of the environment.
ContributorsPuttannaiah, Karan (Author) / Rodriguez, Armando A (Thesis advisor) / Tsakalis, Konstantinos S (Committee member) / Si, Jennie (Committee member) / Arizona State University (Publisher)
Created2013
Description
For the last 50 years, oscillator modeling in ranging systems has received considerable
attention. Many components in a navigation system, such as the master oscillator
driving the receiver system, as well the master oscillator in the transmitting system
contribute significantly to timing errors. Algorithms in the navigation processor must
be able to predict and compensate such errors to achieve a specified accuracy. While
much work has been done on the fundamentals of these problems, the thinking on said
problems has not progressed. On the hardware end, the designers of local oscillators
focus on synthesized frequency and loop noise bandwidth. This does nothing to
mitigate, or reduce frequency stability degradation in band. Similarly, there are not
systematic methods to accommodate phase and frequency anomalies such as clock
jumps. Phase locked loops are fundamentally control systems, and while control
theory has had significant advancement over the last 30 years, the design of timekeeping
sources has not advanced beyond classical control. On the software end,
single or two state oscillator models are typically embedded in a Kalman Filter to
alleviate time errors between the transmitter and receiver clock. Such models are
appropriate for short term time accuracy, but insufficient for long term time accuracy.
Additionally, flicker frequency noise may be present in oscillators, and it presents
mathematical modeling complications. This work proposes novel H∞ control methods
to address the shortcomings in the standard design of time-keeping phase locked loops.
Such methods allow the designer to address frequency stability degradation as well
as high phase/frequency dynamics. Additionally, finite-dimensional approximants of
flicker frequency noise that are more representative of the truth system than the
tradition Gauss Markov approach are derived. Last, to maintain timing accuracy in
a wide variety of operating environments, novel Banks of Adaptive Extended Kalman
Filters are used to address both stochastic and dynamic uncertainty.
attention. Many components in a navigation system, such as the master oscillator
driving the receiver system, as well the master oscillator in the transmitting system
contribute significantly to timing errors. Algorithms in the navigation processor must
be able to predict and compensate such errors to achieve a specified accuracy. While
much work has been done on the fundamentals of these problems, the thinking on said
problems has not progressed. On the hardware end, the designers of local oscillators
focus on synthesized frequency and loop noise bandwidth. This does nothing to
mitigate, or reduce frequency stability degradation in band. Similarly, there are not
systematic methods to accommodate phase and frequency anomalies such as clock
jumps. Phase locked loops are fundamentally control systems, and while control
theory has had significant advancement over the last 30 years, the design of timekeeping
sources has not advanced beyond classical control. On the software end,
single or two state oscillator models are typically embedded in a Kalman Filter to
alleviate time errors between the transmitter and receiver clock. Such models are
appropriate for short term time accuracy, but insufficient for long term time accuracy.
Additionally, flicker frequency noise may be present in oscillators, and it presents
mathematical modeling complications. This work proposes novel H∞ control methods
to address the shortcomings in the standard design of time-keeping phase locked loops.
Such methods allow the designer to address frequency stability degradation as well
as high phase/frequency dynamics. Additionally, finite-dimensional approximants of
flicker frequency noise that are more representative of the truth system than the
tradition Gauss Markov approach are derived. Last, to maintain timing accuracy in
a wide variety of operating environments, novel Banks of Adaptive Extended Kalman
Filters are used to address both stochastic and dynamic uncertainty.
ContributorsEchols, Justin A (Author) / Bliss, Daniel W (Thesis advisor) / Tsakalis, Konstantinos S (Committee member) / Berman, Spring (Committee member) / Mittelmann, Hans (Committee member) / Arizona State University (Publisher)
Created2020