# Phd Defense by Yonguen Yoon

Event Details
• Date/Time:
• Thursday March 14, 2019
8:30 am - 10:00 am
• Location: Tech Square Research Building (TSRB) Room 523A
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Summary Sentence: Prediction of Limit-Cycle Oscillations in Piecewise Linear Systems

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Ph.D. Thesis Defense by

Yongeun Yoon

Prediction of Limit-Cycle Oscillations in Piecewise Linear Systems

8:30 AM, Thursday, March 14, 2019

Tech Square Research Building (TSRB) Room 523A

ABSTRACT:

The mathematical model of most of mechanical and electrical systems involves the piecewise linear system, which consists of linear part and piecewise nonlinearities (PN) or sector-bounded nonlinearities such as saturation, backlash, dead-zone, etc. Many piecewise linear systems inherently possess periodic orbits called as a limit-cycle oscillation (LCO) as one of its solutions, which can seriously undermine the system performance depending on its amplitude and frequency. Therefore, how to predict LCO and its parameters-the frequency and the amplitude is one of the primary concerns for the control and system engineers.

To cope with the adverse LCO of the system we need to identify and change the LCO parameters. On top of the well-known piecewise linear system analysis we apply Floquet theory to identify LCO parameters. The introduction of Floquet theory to piecewise linear systems is allowed through the transformation of PNs into corresponding equivalent analytic functions. Together with switching functions based on the exact switching order, the Floquet theory leads to the verification of the stability of LCO as well as the identification of LCO parameters. In addition, the basic approach used to identify the LCO parameters also enables us to determine the least upper bound of the system gain that does not cause any LCO.  Furthermore, with the design of appropriate lead compensators we can increase the LCO frequency up to a higher band so that the LCO amplitude would decrease to a desirable level. We take an example of a simple rate saturated feedback system common in aircraft flight control systems to demonstrate the effectiveness of the framework presented above. Also, the following example of YF-12 flight control system illustrates this framework works well even in the control systems with multiple PNs.

COMMITTEE MEMBERS:

Professor   Eric N. Johnson,               School of Aerospace Engineering (Advisor)

Professor   Eric M. Feron,                   School of Aerospace Engineering

Professor   J. V. R. Prasad,                 School of Aerospace Engineering

Professor   Magnus B. Egerstedt,       School of Electrical and Computer Engineering

Professor   Federico Bonetto,             School of Mathematics

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