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Course description: One of the important themes of control design is to achieve internally stable closed loop systems while making the influence of certain exogenous disturbance inputs on certain system variables, as small as possible. In the intermediate periods of control history, from 1970 to 1985, much attention was on perfect elimination of the effect of disturbances on system outputs by using geometric or polynomial-algebraic methods. However, recent optimization-based approaches have mainly aimed at minimizing these effects, and within this framework the issue of robustness against modeling uncertainty, expressed in different norms, has been solved by numerically tractable optimization problems. This course provides fundamental concepts of feedback control design for multivariable, finite dimensional linear time invariant systems with a focus on recent methods on H2 and Hinf theories. Topics to be covered consist of:
1. Mathematical preliminaries: Linear spaces and subspaces, singular value decomposition, 2. Internal stability, multivariable poles and zeros, invariant subspaces, disturbance decoupling, 3. Coprime factorization, Controller parameterization, 4. Performance specifications, uncertainty and robustness, 5. Model reduction 6. Optimal Hinf/H2 control and estimation: LMI formulations 7. Miscellaneous topics (if time allows) such as Model validation, Time delay systems
Grading: 1. Homework: 30% 2. Mid-term exam 1: 15% 3. Mid-term exam 2: 15% 4. Final exam: 40%
________________________________________________________________________ References:
1. K. Zhou and J. Doyle, "Essentials of robust control", Prentice Hall, 1998 2. S. Skogestad, “Multivariable feedback control: analysis and design”, Wiley, 2005 (SEE) 3. J. Doyle, Francis, and Tannenbaum, “Feedback Control Theory”, Macmillan in, 1992 (SEE) 4. H. Trentelman, A. Stoorvogel and M. Hautus, “Control theory for linear systems”, Springer, 2001 5. G. Bryant, “Multivariable control system design techniques : dominance and direct methods”, Wiley, 1996 6. Callier, Frank M, “Multivariable feedback systems”, Springer, 1982 7. H. Golub and C. Van Loan, "Matrix computations", John Hopkins University press 8. N. Andrei, Modern control theory: A historical perspective (SEE) |
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Multivariable Control 25-477 Spring 2007
Credits: 3 Level: Graduate, required Prerequisite: Modern Control Hours: Saturday & Monday, 1:30 to 3:00 pm Location:
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