### Abstract

In rollover prevention systems, a traditional rollover index can detect only un-tripped rollovers that happen due to high lateral acceleration from sharp turns. It fails to detect tripped rollovers that happen due to tripping from external inputs such as forces when a vehicle strikes a curb or a road bump. In order to develop a new rollover index that can detect both tripped and un-tripped rollovers, state estimation in the presence of unknown disturbance inputs is required. Therefore, this paper develops a methodology for estimation of unknown inputs in a class of nonlinear systems. The methodology is based on nonlinear observer design and dynamic model inversion to compute the unknown inputs from output measurements. The observer design utilizes the mean value theorem to express the nonlinear estimation error dynamics as a convex combination of known matrices with time varying coefficients. The observer gains are then obtained by solving linear matrix inequalities (LMIs). The developed approach can enable observer design for a large class of bounded Jacobian nonlinear systems with unknown inputs. The developed nonlinear observer is then applied for rollover index estimation. The developed rollover index is evaluated through simulations with an industry standard software, CARSIM, and with experimental tests on a 1/8^{th} scaled vehicle. The simulation and experimental results show that the developed nonlinear observer can reliably estimate vehicle states, unknown normal tire forces, and rollover index for predicting both un-tripped and tripped rollovers.

Original language | English (US) |
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Title of host publication | 2012 American Control Conference, ACC 2012 |

Pages | 2090-2095 |

Number of pages | 6 |

State | Published - Nov 26 2012 |

Event | 2012 American Control Conference, ACC 2012 - Montreal, QC, Canada Duration: Jun 27 2012 → Jun 29 2012 |

### Publication series

Name | Proceedings of the American Control Conference |
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ISSN (Print) | 0743-1619 |

### Other

Other | 2012 American Control Conference, ACC 2012 |
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Country | Canada |

City | Montreal, QC |

Period | 6/27/12 → 6/29/12 |

### Fingerprint

### Cite this

*2012 American Control Conference, ACC 2012*(pp. 2090-2095). [6314784] (Proceedings of the American Control Conference).

**Real-time estimation of rollover index for tripped rollovers with a novel unknown inputs nonlinear observer.** / Phanomchoeng, G.; Rajamani, Rajesh.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2012 American Control Conference, ACC 2012.*, 6314784, Proceedings of the American Control Conference, pp. 2090-2095, 2012 American Control Conference, ACC 2012, Montreal, QC, Canada, 6/27/12.

}

TY - GEN

T1 - Real-time estimation of rollover index for tripped rollovers with a novel unknown inputs nonlinear observer

AU - Phanomchoeng, G.

AU - Rajamani, Rajesh

PY - 2012/11/26

Y1 - 2012/11/26

N2 - In rollover prevention systems, a traditional rollover index can detect only un-tripped rollovers that happen due to high lateral acceleration from sharp turns. It fails to detect tripped rollovers that happen due to tripping from external inputs such as forces when a vehicle strikes a curb or a road bump. In order to develop a new rollover index that can detect both tripped and un-tripped rollovers, state estimation in the presence of unknown disturbance inputs is required. Therefore, this paper develops a methodology for estimation of unknown inputs in a class of nonlinear systems. The methodology is based on nonlinear observer design and dynamic model inversion to compute the unknown inputs from output measurements. The observer design utilizes the mean value theorem to express the nonlinear estimation error dynamics as a convex combination of known matrices with time varying coefficients. The observer gains are then obtained by solving linear matrix inequalities (LMIs). The developed approach can enable observer design for a large class of bounded Jacobian nonlinear systems with unknown inputs. The developed nonlinear observer is then applied for rollover index estimation. The developed rollover index is evaluated through simulations with an industry standard software, CARSIM, and with experimental tests on a 1/8th scaled vehicle. The simulation and experimental results show that the developed nonlinear observer can reliably estimate vehicle states, unknown normal tire forces, and rollover index for predicting both un-tripped and tripped rollovers.

AB - In rollover prevention systems, a traditional rollover index can detect only un-tripped rollovers that happen due to high lateral acceleration from sharp turns. It fails to detect tripped rollovers that happen due to tripping from external inputs such as forces when a vehicle strikes a curb or a road bump. In order to develop a new rollover index that can detect both tripped and un-tripped rollovers, state estimation in the presence of unknown disturbance inputs is required. Therefore, this paper develops a methodology for estimation of unknown inputs in a class of nonlinear systems. The methodology is based on nonlinear observer design and dynamic model inversion to compute the unknown inputs from output measurements. The observer design utilizes the mean value theorem to express the nonlinear estimation error dynamics as a convex combination of known matrices with time varying coefficients. The observer gains are then obtained by solving linear matrix inequalities (LMIs). The developed approach can enable observer design for a large class of bounded Jacobian nonlinear systems with unknown inputs. The developed nonlinear observer is then applied for rollover index estimation. The developed rollover index is evaluated through simulations with an industry standard software, CARSIM, and with experimental tests on a 1/8th scaled vehicle. The simulation and experimental results show that the developed nonlinear observer can reliably estimate vehicle states, unknown normal tire forces, and rollover index for predicting both un-tripped and tripped rollovers.

UR - http://www.scopus.com/inward/record.url?scp=84869455237&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84869455237&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84869455237

SN - 9781457710957

T3 - Proceedings of the American Control Conference

SP - 2090

EP - 2095

BT - 2012 American Control Conference, ACC 2012

ER -