### Abstract

This work deals with the design of robust fixed-structure controllers for uncertain systems based on a finite set of measured data. This set of measurements is given in the frequency domain. In the current control design approaches, controllers are usually designed based on plant models obtained on the basis of measured data. However, due to various forms of uncertainties such as: plant parameter variations, external disturbances, measurement noise, etc, such models are unable to perfectly describe the behavior of the physical system. Hence, degradation in the controller performance is expected due to such uncertainties and errors associated with the identification process. For that, we propose a new control technique that uses the uncertain measurements to directly design robust controllers, for a class of uncertainties, without going through the use of identification process. In such a proposed design method, interval techniques are introduced to bound plant uncertainties. Its main principle is to find the set of admissible values of the controller parameters so that the family of all possible frequency responses of the closed-loop system lies between an upper and lower bounds of a desired frequency response. This problem is formulated as a nonlinear programming problem which can easily be solved to characterize the solution set of the controller parameters. The main feature of our proposed approach is that it enables to design robust fixed-structure controllers by taking into account the plant uncertainties. Moreover, since no mathematical model is needed in the controller synthesis, the design process does not depend on the increasing order and complexity of the system. A simulation example is presented to illustrate and validate the efficacy of the proposed method.

Original language | English |
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Title of host publication | 2013 American Control Conference, ACC 2013 |

Pages | 4325-4330 |

Number of pages | 6 |

Publication status | Published - 2013 |

Event | 2013 1st American Control Conference, ACC 2013 - Washington, DC, United States Duration: 17 Jun 2013 → 19 Jun 2013 |

### Other

Other | 2013 1st American Control Conference, ACC 2013 |
---|---|

Country | United States |

City | Washington, DC |

Period | 17/6/13 → 19/6/13 |

### Fingerprint

### Keywords

- Data-based control
- Frequency response template
- Interval analysis
- Nonlinear programming problem
- Plant uncertainty
- Robust controller

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*2013 American Control Conference, ACC 2013*(pp. 4325-4330). [6580505]

**Robust control design method for uncertain system using a set of measurements.** / Khadraoui, S.; Nounou, Hazem; Nounou, Mohamed; Datta, A.; Bhattacharyya, S. P.

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

*2013 American Control Conference, ACC 2013.*, 6580505, pp. 4325-4330, 2013 1st American Control Conference, ACC 2013, Washington, DC, United States, 17/6/13.

}

TY - GEN

T1 - Robust control design method for uncertain system using a set of measurements

AU - Khadraoui, S.

AU - Nounou, Hazem

AU - Nounou, Mohamed

AU - Datta, A.

AU - Bhattacharyya, S. P.

PY - 2013

Y1 - 2013

N2 - This work deals with the design of robust fixed-structure controllers for uncertain systems based on a finite set of measured data. This set of measurements is given in the frequency domain. In the current control design approaches, controllers are usually designed based on plant models obtained on the basis of measured data. However, due to various forms of uncertainties such as: plant parameter variations, external disturbances, measurement noise, etc, such models are unable to perfectly describe the behavior of the physical system. Hence, degradation in the controller performance is expected due to such uncertainties and errors associated with the identification process. For that, we propose a new control technique that uses the uncertain measurements to directly design robust controllers, for a class of uncertainties, without going through the use of identification process. In such a proposed design method, interval techniques are introduced to bound plant uncertainties. Its main principle is to find the set of admissible values of the controller parameters so that the family of all possible frequency responses of the closed-loop system lies between an upper and lower bounds of a desired frequency response. This problem is formulated as a nonlinear programming problem which can easily be solved to characterize the solution set of the controller parameters. The main feature of our proposed approach is that it enables to design robust fixed-structure controllers by taking into account the plant uncertainties. Moreover, since no mathematical model is needed in the controller synthesis, the design process does not depend on the increasing order and complexity of the system. A simulation example is presented to illustrate and validate the efficacy of the proposed method.

AB - This work deals with the design of robust fixed-structure controllers for uncertain systems based on a finite set of measured data. This set of measurements is given in the frequency domain. In the current control design approaches, controllers are usually designed based on plant models obtained on the basis of measured data. However, due to various forms of uncertainties such as: plant parameter variations, external disturbances, measurement noise, etc, such models are unable to perfectly describe the behavior of the physical system. Hence, degradation in the controller performance is expected due to such uncertainties and errors associated with the identification process. For that, we propose a new control technique that uses the uncertain measurements to directly design robust controllers, for a class of uncertainties, without going through the use of identification process. In such a proposed design method, interval techniques are introduced to bound plant uncertainties. Its main principle is to find the set of admissible values of the controller parameters so that the family of all possible frequency responses of the closed-loop system lies between an upper and lower bounds of a desired frequency response. This problem is formulated as a nonlinear programming problem which can easily be solved to characterize the solution set of the controller parameters. The main feature of our proposed approach is that it enables to design robust fixed-structure controllers by taking into account the plant uncertainties. Moreover, since no mathematical model is needed in the controller synthesis, the design process does not depend on the increasing order and complexity of the system. A simulation example is presented to illustrate and validate the efficacy of the proposed method.

KW - Data-based control

KW - Frequency response template

KW - Interval analysis

KW - Nonlinear programming problem

KW - Plant uncertainty

KW - Robust controller

UR - http://www.scopus.com/inward/record.url?scp=84883538588&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883538588&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84883538588

SN - 9781479901777

SP - 4325

EP - 4330

BT - 2013 American Control Conference, ACC 2013

ER -