Position control of flexible manipulator using non-linear H∞ with state-dependent Riccati equation

A.M. Shawky, A.W. Ordys, L. Petropoulakis, M.J. Grimble

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18 Citations (Scopus)

Abstract

The paper is concerned with the control of the tip position of a single-link flexible manipulator. The non-linear model of the manipulator is derived and tested, assuming the number of model shape functions to be two. It is known that the assumed modes method introduces uncertainty to the model by neglecting higher-order dynamics. There are other sources of uncertainty, such as friction. In addition, the model is non-linear. Therefore, for the next task, which is the controller design, the H∞ approach is proposed to deal efficiently with uncertainties, and the non-linear nature of the problem is addressed by the use of the state-dependent Riccati equation (SDRE) technique. Following the SDRE approach, the state-feedback non-linear control law is derived, which minimizes a quadratic cost function. This solution is then mapped into the H∞ optimization problem. The resulting control law has been tested with the simulation model of the flexible manipulator and the results are discussed in the paper.
LanguageEnglish
Pages475-486
Number of pages11
JournalProceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering
Volume221
Issue number3
DOIs
Publication statusPublished - Feb 2007

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Flexible manipulators
Riccati equations
Position control
State feedback
Cost functions
Manipulators
Friction
Controllers
Uncertainty

Keywords

  • flexible manipulator
  • state-dependent Riccati equation
  • H∞ optimization

Cite this

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title = "Position control of flexible manipulator using non-linear H∞ with state-dependent Riccati equation",
abstract = "The paper is concerned with the control of the tip position of a single-link flexible manipulator. The non-linear model of the manipulator is derived and tested, assuming the number of model shape functions to be two. It is known that the assumed modes method introduces uncertainty to the model by neglecting higher-order dynamics. There are other sources of uncertainty, such as friction. In addition, the model is non-linear. Therefore, for the next task, which is the controller design, the H∞ approach is proposed to deal efficiently with uncertainties, and the non-linear nature of the problem is addressed by the use of the state-dependent Riccati equation (SDRE) technique. Following the SDRE approach, the state-feedback non-linear control law is derived, which minimizes a quadratic cost function. This solution is then mapped into the H∞ optimization problem. The resulting control law has been tested with the simulation model of the flexible manipulator and the results are discussed in the paper.",
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AU - Ordys, A.W.

AU - Petropoulakis, L.

AU - Grimble, M.J.

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N2 - The paper is concerned with the control of the tip position of a single-link flexible manipulator. The non-linear model of the manipulator is derived and tested, assuming the number of model shape functions to be two. It is known that the assumed modes method introduces uncertainty to the model by neglecting higher-order dynamics. There are other sources of uncertainty, such as friction. In addition, the model is non-linear. Therefore, for the next task, which is the controller design, the H∞ approach is proposed to deal efficiently with uncertainties, and the non-linear nature of the problem is addressed by the use of the state-dependent Riccati equation (SDRE) technique. Following the SDRE approach, the state-feedback non-linear control law is derived, which minimizes a quadratic cost function. This solution is then mapped into the H∞ optimization problem. The resulting control law has been tested with the simulation model of the flexible manipulator and the results are discussed in the paper.

AB - The paper is concerned with the control of the tip position of a single-link flexible manipulator. The non-linear model of the manipulator is derived and tested, assuming the number of model shape functions to be two. It is known that the assumed modes method introduces uncertainty to the model by neglecting higher-order dynamics. There are other sources of uncertainty, such as friction. In addition, the model is non-linear. Therefore, for the next task, which is the controller design, the H∞ approach is proposed to deal efficiently with uncertainties, and the non-linear nature of the problem is addressed by the use of the state-dependent Riccati equation (SDRE) technique. Following the SDRE approach, the state-feedback non-linear control law is derived, which minimizes a quadratic cost function. This solution is then mapped into the H∞ optimization problem. The resulting control law has been tested with the simulation model of the flexible manipulator and the results are discussed in the paper.

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