### Abstract

Original language | English |
---|---|

Pages (from-to) | 475-486 |

Number of pages | 11 |

Journal | Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering |

Volume | 221 |

Issue number | 3 |

DOIs | |

Publication status | Published - Feb 2007 |

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### Keywords

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

### Cite this

*Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering*,

*221*(3), 475-486. https://doi.org/10.1243/09596518JSCE313

}

*Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering*, vol. 221, no. 3, pp. 475-486. https://doi.org/10.1243/09596518JSCE313

**Position control of flexible manipulator using non-linear H∞ with state-dependent Riccati equation.** / Shawky, A.M.; Ordys, A.W.; Petropoulakis, L.; Grimble, M.J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Position control of flexible manipulator using non-linear H∞ with state-dependent Riccati equation

AU - Shawky, A.M.

AU - Ordys, A.W.

AU - Petropoulakis, L.

AU - Grimble, M.J.

PY - 2007/2

Y1 - 2007/2

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.

KW - flexible manipulator

KW - state-dependent Riccati equation

KW - H∞ optimization

U2 - 10.1243/09596518JSCE313

DO - 10.1243/09596518JSCE313

M3 - Article

VL - 221

SP - 475

EP - 486

JO - Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering

JF - Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering

SN - 0959-6518

IS - 3

ER -