## Abstract

In this chapter, the problems of state estimation and parameter identification for the pendulum-cart system are addressed. Different high-order sliding-modes techniques are applied for such a mechanical system. The mathematical model is studied and a couple of high-order sliding-modes observers are proposed to estimate the state, in spite of disturbances; exactly and in a finite or fixed time, respectively. Then, using the exact state estimation, two parameter identification algorithms based on sliding-modes techniques are introduced to identify the unknown parameters of the system, i.e. the friction coefficients. Some experiments and comparisons are presented to illustrate the effectiveness of the presented algorithms. Finally, some concluding remarks are given at the end of the chapter.

Original language | English |
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Title of host publication | The Inverted Pendulum in Control Theory and Robotics |

Publisher | Institution of Engineering and Technology |

Pages | 43-70 |

Number of pages | 28 |

ISBN (Electronic) | 9781785613203 |

DOIs | |

State | Published - 1 Jan 2018 |

### Bibliographical note

Publisher Copyright:© The Institution of Engineering and Technology 2018.

## Keywords

- High-order sliding-modes observers
- Mechanical system
- Modelling and identification
- Multivariable control systems
- Observers
- Parameter estimation
- Parameter identification algorithms
- Pendulum-cart system
- Pendulums
- Simulation
- State estimation
- Variable structure systems