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Dissertation
Computational issues in the design of robust nonlinear controllers
Doctor of Philosophy (Ph.D.), Drexel University
Jul 1998
DOI:
https://doi.org/10.17918/00001472
Abstract
Just like the algebraic Riccati equations (AREs) or inequalities (ARIs) in the linear H[infinity] control theory, the Hamilton-Jacobi equations (HJEs) or inequalities (HJIs) play an essential role in the nonlinear H[infinity] control theory. In this thesis, a successive algorithm for finding an approximate solution of HJE is proposed. Using the existing nonlinear H[infinity] controller formulas, a numerical difficulty could be encountered when a critical assumption is not satisfied. We propose modified nonlinear H[infinity] controller formulas to eliminate the numerical difficulty. The proposed nonlinear H[infinity] controller is identical to the existing nonlinear H[infinity] controller if the assumption is satisfied, and its linear version will be the same as that designed by conventional linear H[infinity] approaches. An important application of the modified nonlinear H[infinity] controller formulas is the H[infinity] approximate input/output (I/O) linearization problem, which essentially is a nonlinear H[infinity] control problem without satisfying the critical assumption. Like the feedback I/O linearization, the H[infinity] approximate I/O linearization modifies a nonlinear system so that its I/O relationship resembles that of a linear system. However, the H[infinity] approximate I/O linearization can handle more general problem since it does not require minimum phase plant or full state feedback. The linearization technique together with [mu]-synthesis is used to design a robust nonlinear controller. An inverted pendulum control problem and a nonminimum phase longitudinal flight control problem are employed to illustrate the design of robust nonlinear controllers.
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Details
- Title
- Computational issues in the design of robust nonlinear controllers
- Creators
- Shr-Shiung Hu
- Contributors
- Bor-Chin Chang (Advisor)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- xii, 141 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Engineering (1970-2026); Mechanical Engineering (and Mechanics) [Historical]; Drexel University
- Other Identifier
- 991014970213004721