### Abstract

The article presents an adaptive fuzzy control approach to the problem of control of electrostatically actuated MEMS, which is based on differential flatness theory and which uses exclusively output feedback. It is shown that the model of the electrostatically actuated MEMS is a differentially flat one and this permits to transform it to the so-called linear canonical form. For the new description of the system's dynamics the transformed control inputs contain unknown terms which depend on the system's parameters. To identify these terms an adaptive fuzzy approximator is used in the control loop. Thus an adaptive fuzzy control scheme is implemented in which the unknown or unmodeled system dynamics is approximated by neurofuzzy networks and next this information is used by a feedback controller that makes the electrostatically activated MEMS converge to the desirable motion setpoints. This adaptive control scheme is exclusively implemented with the use of output feedback, while the state vector elements which are not directly measured are estimated with the use of a state observer that operates in the control loop. The learning rate of the adaptive fuzzy system is suitably computed from Lyapunov analysis, so as to assure that both the learning procedure for the unknown system's parameters, the dynamics of the observer and the dynamics of the control loop will remain stable. The Lyapunov stability analysis depends on two Riccati equations, one associated with the feedback controller and one associated with the state observer. Finally, it is proven that for the control scheme that comprises the feedback controller, the state observer and the neurofuzzy approximator, an H-infinity tracking performance can be achieved. The functioning of the control loop has been evaluated through simulation experiments.

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

Pages (from-to) | 138-157 |

Number of pages | 20 |

Journal | Fuzzy Sets and Systems |

Volume | 290 |

DOIs | |

Publication status | Published - May 1 2016 |

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### Keywords

- Adaptive fuzzy control
- Electrostatically actuated MEMS
- H-infinity tracking performance
- Lyapunov stability
- Neurofuzzy approximation
- Riccati equations
- State observers

### ASJC Scopus subject areas

- Artificial Intelligence
- Logic

### Cite this

*Fuzzy Sets and Systems*,

*290*, 138-157. https://doi.org/10.1016/j.fss.2015.08.027

**Flatness-based adaptive fuzzy control of electrostatically actuated MEMS using output feedback.** / Rigatos, G.; Zhu, G.; Yousef, H.; Boulkroune, A.

Research output: Contribution to journal › Article

*Fuzzy Sets and Systems*, vol. 290, pp. 138-157. https://doi.org/10.1016/j.fss.2015.08.027

}

TY - JOUR

T1 - Flatness-based adaptive fuzzy control of electrostatically actuated MEMS using output feedback

AU - Rigatos, G.

AU - Zhu, G.

AU - Yousef, H.

AU - Boulkroune, A.

PY - 2016/5/1

Y1 - 2016/5/1

N2 - The article presents an adaptive fuzzy control approach to the problem of control of electrostatically actuated MEMS, which is based on differential flatness theory and which uses exclusively output feedback. It is shown that the model of the electrostatically actuated MEMS is a differentially flat one and this permits to transform it to the so-called linear canonical form. For the new description of the system's dynamics the transformed control inputs contain unknown terms which depend on the system's parameters. To identify these terms an adaptive fuzzy approximator is used in the control loop. Thus an adaptive fuzzy control scheme is implemented in which the unknown or unmodeled system dynamics is approximated by neurofuzzy networks and next this information is used by a feedback controller that makes the electrostatically activated MEMS converge to the desirable motion setpoints. This adaptive control scheme is exclusively implemented with the use of output feedback, while the state vector elements which are not directly measured are estimated with the use of a state observer that operates in the control loop. The learning rate of the adaptive fuzzy system is suitably computed from Lyapunov analysis, so as to assure that both the learning procedure for the unknown system's parameters, the dynamics of the observer and the dynamics of the control loop will remain stable. The Lyapunov stability analysis depends on two Riccati equations, one associated with the feedback controller and one associated with the state observer. Finally, it is proven that for the control scheme that comprises the feedback controller, the state observer and the neurofuzzy approximator, an H-infinity tracking performance can be achieved. The functioning of the control loop has been evaluated through simulation experiments.

AB - The article presents an adaptive fuzzy control approach to the problem of control of electrostatically actuated MEMS, which is based on differential flatness theory and which uses exclusively output feedback. It is shown that the model of the electrostatically actuated MEMS is a differentially flat one and this permits to transform it to the so-called linear canonical form. For the new description of the system's dynamics the transformed control inputs contain unknown terms which depend on the system's parameters. To identify these terms an adaptive fuzzy approximator is used in the control loop. Thus an adaptive fuzzy control scheme is implemented in which the unknown or unmodeled system dynamics is approximated by neurofuzzy networks and next this information is used by a feedback controller that makes the electrostatically activated MEMS converge to the desirable motion setpoints. This adaptive control scheme is exclusively implemented with the use of output feedback, while the state vector elements which are not directly measured are estimated with the use of a state observer that operates in the control loop. The learning rate of the adaptive fuzzy system is suitably computed from Lyapunov analysis, so as to assure that both the learning procedure for the unknown system's parameters, the dynamics of the observer and the dynamics of the control loop will remain stable. The Lyapunov stability analysis depends on two Riccati equations, one associated with the feedback controller and one associated with the state observer. Finally, it is proven that for the control scheme that comprises the feedback controller, the state observer and the neurofuzzy approximator, an H-infinity tracking performance can be achieved. The functioning of the control loop has been evaluated through simulation experiments.

KW - Adaptive fuzzy control

KW - Electrostatically actuated MEMS

KW - H-infinity tracking performance

KW - Lyapunov stability

KW - Neurofuzzy approximation

KW - Riccati equations

KW - State observers

UR - http://www.scopus.com/inward/record.url?scp=84959494731&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959494731&partnerID=8YFLogxK

U2 - 10.1016/j.fss.2015.08.027

DO - 10.1016/j.fss.2015.08.027

M3 - Article

VL - 290

SP - 138

EP - 157

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

SN - 0165-0114

ER -