Parameter estimation for uncertain systems based on fault diagnosis using Takagi-Sugeno model

- The T-S model allows reducing the complexity of nonlinear systems and extending tools of linear theory to nonlinear systems.
- The observer estimates state and parameter uncertainty and involves immeasurable premise variables and nonlinear outputs.
- The robustness is based on H∞ techniques and the sensitivity regarding model uncertainties is expressed using the H- index.
- The proposed method is investigated using nonlinear process: the three-tank system.

The paper addresses a systematic procedure to deal with state and parameter uncertainty estimation for nonlinear time-varying systems. A robust observer with respect to states, inputs and perturbations is designed, using a Takagi-Sugeno (T-S) approach with unknown premise variables. Tools of the linear automatic to the nonlinear systems are applied, using the Linear Matrix Inequalities optimization. The observer estimates the uncertainties, the states and minimizes the effect of external disturbances on the estimation error. The uncertainties are modelled in a polynomial way which allows considering the uncertainty estimation as a fault detection problem. The residual sensitivity to faults while maintaining robustness according to a noise signal is handled by H∞/H− approach. The method performance is illustrated using the three-tank system.