### Abstract

The sliding mode control algorithm is developed for the coupled modal space control of a flexible structure when the bounds on the system parameters’ errors are known. An explicit method to construct the desired sliding hyperplanes for the coupled model sliding mode control is formulated. A boundary layer is used around each sliding hyperplane to eliminate the chattering phenomenon. Three types of steady state solutions for the closed-loop system inside the boundary layers are found: the zero solution (origin of the state space), the constant nonzero solution, and the limit cycle. The amplitudes, phase angles, and the frequency of the limit cycle have been estimated by the describing function approach. The modal displacements corresponding to the constant nonzero solution have been obtained analytically. The stability of the zero solution has been examined by the linearized system analysis. Using a flexible tetrahedral truss structure, numerical examples are presented to verify the theoretical analyses.

Original language | English (US) |
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Pages | 404-413 |

Number of pages | 10 |

State | Published - Jan 1 1990 |

Event | Guidance, Navigation and Control Conference, 1990 - Portland, United States Duration: Aug 20 1990 → Aug 22 1990 |

### Other

Other | Guidance, Navigation and Control Conference, 1990 |
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Country | United States |

City | Portland |

Period | 8/20/90 → 8/22/90 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Aerospace Engineering

### Cite this

*Coupled modal sliding mode control of vibration in flexible structures*. 404-413. Paper presented at Guidance, Navigation and Control Conference, 1990, Portland, United States.

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**Coupled modal sliding mode control of vibration in flexible structures.** / Kao, C. K.; Sinha, A.

Research output: Contribution to conference › Paper

TY - CONF

T1 - Coupled modal sliding mode control of vibration in flexible structures

AU - Kao, C. K.

AU - Sinha, A.

PY - 1990/1/1

Y1 - 1990/1/1

N2 - The sliding mode control algorithm is developed for the coupled modal space control of a flexible structure when the bounds on the system parameters’ errors are known. An explicit method to construct the desired sliding hyperplanes for the coupled model sliding mode control is formulated. A boundary layer is used around each sliding hyperplane to eliminate the chattering phenomenon. Three types of steady state solutions for the closed-loop system inside the boundary layers are found: the zero solution (origin of the state space), the constant nonzero solution, and the limit cycle. The amplitudes, phase angles, and the frequency of the limit cycle have been estimated by the describing function approach. The modal displacements corresponding to the constant nonzero solution have been obtained analytically. The stability of the zero solution has been examined by the linearized system analysis. Using a flexible tetrahedral truss structure, numerical examples are presented to verify the theoretical analyses.

AB - The sliding mode control algorithm is developed for the coupled modal space control of a flexible structure when the bounds on the system parameters’ errors are known. An explicit method to construct the desired sliding hyperplanes for the coupled model sliding mode control is formulated. A boundary layer is used around each sliding hyperplane to eliminate the chattering phenomenon. Three types of steady state solutions for the closed-loop system inside the boundary layers are found: the zero solution (origin of the state space), the constant nonzero solution, and the limit cycle. The amplitudes, phase angles, and the frequency of the limit cycle have been estimated by the describing function approach. The modal displacements corresponding to the constant nonzero solution have been obtained analytically. The stability of the zero solution has been examined by the linearized system analysis. Using a flexible tetrahedral truss structure, numerical examples are presented to verify the theoretical analyses.

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M3 - Paper

AN - SCOPUS:84998579426

SP - 404

EP - 413

ER -