H∞ multiple objective robust controllers for infinite-horizon single measurement single control input problems

Y. Theodor; U. Shaked

doi:10.1109/9.328813

H_∞ multiple objective robust controllers for infinite-horizon single measurement single control input problems

Y. Theodor, U. Shaked

School of Electrical Engineering

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

A graphical method is introduced that solves the robust infinite horizon H_∞multiple-objective control problem for single measurement, single control input systems. The solution is obtained by describing boundaries on the Nichols chart. Each boundary defines the set of all admissible gain and phase values for the loop transmission at a given frequency. These boundaries are obtained by using the well-known parameterization of all the solutions for a single objective H_∞control problem [1]. The new method links between the theories of H_∞ and Quantitative Feedback Theory (QFT) [2]. It can be used to design robust H_∞controllers with almost no overdesign, and it provides a convenient solution of H_∞multiple-objective problems that are difficult to solve by the standard four-block setting. It also extends the methods of SISO QFT to deal with a vector of disturbances. The latter may affect the controlled plant through any input coupling matrix and not necessarily through the controller input or the measurement output.

Original language	English
Pages (from-to)	2130-2134
Number of pages	5
Journal	IEEE Transactions on Automatic Control
Volume	39
Issue number	10
DOIs	https://doi.org/10.1109/9.328813
State	Published - Oct 1994

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Tel-Aviv University

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title = "H∞ multiple objective robust controllers for infinite-horizon single measurement single control input problems",

abstract = "A graphical method is introduced that solves the robust infinite horizon H∞multiple-objective control problem for single measurement, single control input systems. The solution is obtained by describing boundaries on the Nichols chart. Each boundary defines the set of all admissible gain and phase values for the loop transmission at a given frequency. These boundaries are obtained by using the well-known parameterization of all the solutions for a single objective H∞control problem [1]. The new method links between the theories of H∞ and Quantitative Feedback Theory (QFT) [2]. It can be used to design robust H∞controllers with almost no overdesign, and it provides a convenient solution of H∞multiple-objective problems that are difficult to solve by the standard four-block setting. It also extends the methods of SISO QFT to deal with a vector of disturbances. The latter may affect the controlled plant through any input coupling matrix and not necessarily through the controller input or the measurement output.",

author = "Y. Theodor and U. Shaked",

note = "Funding Information: The disadvantage of dealing with one global cost is that there is no apparent way of determining the summation weights in advance. These weights control the trade-offs that are made between conflicting objectives, and their choice involves a judicious intuition in a “cut Manuscript received March 29, 1993; revised July 27, 1993 and November 29, 1993. This work was supported by the C. S: M. Maus Chair of Computer Systems Engineering at Tel-Aviv University, Israel. The authors are with the Faculty of Engineering, Department of Electrical Engineering Systems, Tel-Aviv University, Tel-Aviv 69978, Israel. IEEE Log Number 9403952.",

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AB - A graphical method is introduced that solves the robust infinite horizon H∞multiple-objective control problem for single measurement, single control input systems. The solution is obtained by describing boundaries on the Nichols chart. Each boundary defines the set of all admissible gain and phase values for the loop transmission at a given frequency. These boundaries are obtained by using the well-known parameterization of all the solutions for a single objective H∞control problem [1]. The new method links between the theories of H∞ and Quantitative Feedback Theory (QFT) [2]. It can be used to design robust H∞controllers with almost no overdesign, and it provides a convenient solution of H∞multiple-objective problems that are difficult to solve by the standard four-block setting. It also extends the methods of SISO QFT to deal with a vector of disturbances. The latter may affect the controlled plant through any input coupling matrix and not necessarily through the controller input or the measurement output.

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H_∞ multiple objective robust controllers for infinite-horizon single measurement single control input problems

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