On the synthesis of low order stabilizing controllers /
This dissertation deals with the synthesis of a fixed-order proper, rational stabilizing controller for any finite-dimensional, Single-Input Single-Output Linear Time Invariant plant. A fixed-order stabilization problem arises when simplicity, hardware limitations or reliability in the implementatio...
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
2003.
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| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=765867111&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | This dissertation deals with the synthesis of a fixed-order proper, rational stabilizing controller for any finite-dimensional, Single-Input Single-Output Linear Time Invariant plant. A fixed-order stabilization problem arises when simplicity, hardware limitations or reliability in the implementation of a controller dictates the order of stabilization or when structural limitations on the controller, such as those encountered in the decentralized control of multi-vehicle systems, are present. Verifiable necessary and sufficient conditions for the existence of a fixed-order stabilizing controller are still lacking. In this dissertation, two novel approaches are presented to address this problem. The first approach is based on the Hermite-Biehler theorem and the results of Laguerre to arrive at an approximation of the set of fixed-order stabilizing controllers in terms of the feasibility sets of linear programs. The Hermite-Biehler theorem converts the stability requirement of a closed loop system into a condition that two polynomials have all real and interlacing roots in (0,1). The coefficients of the two polynomials are linear in controller parameters. The results of Laguerre are used to relate the conditions on the two polynomials to the number of sign changes in their coefficients. The second approach is based on the following result: If the set of fixed-order stabilizing controllers is not empty, then there is a stabilizing controller, where the Mikhailov plot of the characteristic polynomial just touches an "extremal" disk - a disk whose radius decreases when the controller is perturbed. An application of the Karush-Kuhn-Tucker's conditions for the problem of determining "extremal" disks results in a set of polynomial equations in controller parameters; at least one solution of the polynomial equation must be stabilizing for a controller of fixed order to exist. A recursive algorithm for reducing the order of a stabilizing controller is also roposed in this dissertation. Any achievable closed loop transfer function is a linear function of the Youla parameter. The controller order reduction is accomplished by the choice of a specific Youla parameter that reduces the order of the closed loop transfer function by pole-zero cancellation. |
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| Item Description: | Vita. "Major Subject: Mechanical Engineering". |
| Physical Description: | xi, 94 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilm Inc. |
| Bibliography: | Includes bibliographical references (leaves 83-86). |