A modified sliding-mode observer design with application to diffusion equation

ABSTRACT

In many physical systems, the system's full state cannot be measured. An observer is designed to reconstruct the state from measurements. Disturbances often contribute to the dynamics of the system, and the designed observer must account for them. In this paper, a modified sliding-mode observer (SMO), a robust observer, is proposed that combines the efficiency of a nonlinear observer with the robustness of an SMO. The estimation error is proven to converge to zero under natural assumptions. This improved observer is compared with an extended Kalman filter and an unscented Kalman filter, as well as a standard SMO for three different versions of heat equation: a linear, a quasi-linear, and a nonlinear heat equation. The comparisons are done with and without an external disturbance. The simulations show improved performance of the modified SMO over other observers.

KEYWORDS:

• Robust observer
• distributed parameter systems
• heat equation
• observer design
• sliding-mode observer
• Kalman filtering

Acknowledgments

The authors would like to acknowledge the financial support of the Ontario Research Fund and Automotive Partnership Canada in this work.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Automotive Partnership Canada (APCPJ395996-09); Ontario Research Fund (ORF-RE File #04-039).