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Control of linear parameter varying systems.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Control of linear parameter varying systems./
作者:	Wu, Fen.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 1995,
面頁冊數:	157 p.
附註:	Source: Dissertations Abstracts International, Volume: 57-07, Section: B.
Contained By:	Dissertations Abstracts International57-07B.
標題:	Mechanical engineering. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9602802
ISBN:	9798208778098

Control of linear parameter varying systems.
Wu, Fen.

Control of linear parameter varying systems. - Ann Arbor : ProQuest Dissertations & Theses, 1995 - 157 p.

Source: Dissertations Abstracts International, Volume: 57-07, Section: B.

Thesis (Ph.D.)--University of California, Berkeley, 1995.

This item must not be sold to any third party vendors.

In this thesis we study the control problem of linear parameter varying (LPV) systems using LPV controllers. The LPV plants are finite-dimensional linear systems with known, parameter-dependent state-space data. The parameter is assumed measurable in real-time and varies in a known, bounded set. Our study is motivated by the gain-scheduling design method, and our results constitute a new approach to gain-scheduling. Our design goal is: formulate a performance measure for an LPV system; develop computable bounds for the performance measure; determine conditions for the existence of a parameter-dependent controller so that the closed-loop system has suitable performance, or determine that no suitable controller exists. We aim for theorems that express conditions as the (in)feasibility of linear matrix inequalities (LMIs), which is a convex decision problem. The first problem involves LQG performance for LPV systems, and is analogous to the standard ${\\cal H}\\sb2$ performance for LTI and LTV systems. We give two analysis theorems (as LMIs) to bound the LQG performance of LPV systems. These bounds are less conservative than those in the current literature. For control synthesis, we consider two controllers: a parameter-dependent controller and a parameter-dependent state-feedback controller with optimal (Kalman) filter. We use convex optimization to reduce the performance bound of the closed-loop system. Next, we investigate the induced L$\\sb2$-norm control of LPV systems which have bounded parameter variation rates and real-time measurement of the parameter and its derivative. Previous L$\\sb2$-gain LPV research used a single quadratic Lyapunov function for analysis, leading to conservatism in achievable performance. To remedy this, we employ parameter-dependent Lyapunov functions, and develop an efficient bound on the induced L$\\sb2$-norm by exploiting the known bound on the parameter's rate of variation. We then formulate the necessary and sufficient conditions for the existence of an LPV controller that renders this bound less than 1. The conditions are three LMI constraints on positive definite matrix functions of the parameters, resulting in an infinite dimensional convex feasibility problem. By parameterizing a subspace of the function space with a finite number of basis functions, the solvability condition is (approximately) converted to a finite-dimensional convex problem.

ISBN: 9798208778098Subjects--Topical Terms:

649730
Mechanical engineering.
Subjects--Index Terms:

gain scheduling

Control of linear parameter varying systems.
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245 1 0 $a Control of linear parameter varying systems.
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300 $a 157 p.
500 $a Source: Dissertations Abstracts International, Volume: 57-07, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Packard, Andrew.
502 $a Thesis (Ph.D.)--University of California, Berkeley, 1995.
506 $a This item must not be sold to any third party vendors.
506 $a This item must not be added to any third party search indexes.
520 $a In this thesis we study the control problem of linear parameter varying (LPV) systems using LPV controllers. The LPV plants are finite-dimensional linear systems with known, parameter-dependent state-space data. The parameter is assumed measurable in real-time and varies in a known, bounded set. Our study is motivated by the gain-scheduling design method, and our results constitute a new approach to gain-scheduling. Our design goal is: formulate a performance measure for an LPV system; develop computable bounds for the performance measure; determine conditions for the existence of a parameter-dependent controller so that the closed-loop system has suitable performance, or determine that no suitable controller exists. We aim for theorems that express conditions as the (in)feasibility of linear matrix inequalities (LMIs), which is a convex decision problem. The first problem involves LQG performance for LPV systems, and is analogous to the standard ${\\cal H}\\sb2$ performance for LTI and LTV systems. We give two analysis theorems (as LMIs) to bound the LQG performance of LPV systems. These bounds are less conservative than those in the current literature. For control synthesis, we consider two controllers: a parameter-dependent controller and a parameter-dependent state-feedback controller with optimal (Kalman) filter. We use convex optimization to reduce the performance bound of the closed-loop system. Next, we investigate the induced L$\\sb2$-norm control of LPV systems which have bounded parameter variation rates and real-time measurement of the parameter and its derivative. Previous L$\\sb2$-gain LPV research used a single quadratic Lyapunov function for analysis, leading to conservatism in achievable performance. To remedy this, we employ parameter-dependent Lyapunov functions, and develop an efficient bound on the induced L$\\sb2$-norm by exploiting the known bound on the parameter's rate of variation. We then formulate the necessary and sufficient conditions for the existence of an LPV controller that renders this bound less than 1. The conditions are three LMI constraints on positive definite matrix functions of the parameters, resulting in an infinite dimensional convex feasibility problem. By parameterizing a subspace of the function space with a finite number of basis functions, the solvability condition is (approximately) converted to a finite-dimensional convex problem.
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650 4 $a Aerospace materials. $3 3433227
650 4 $a Aerospace engineering. $3 1002622
650 4 $a Systems science. $3 3168411
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773 0 $t Dissertations Abstracts International $g 57-07B.
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856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9602802