(588e) Disturbance Decoupled Functional Observers for Simultaneous Fault Detection and Estimation in Nonlinear Systems

In control theory, a functional observer is an auxiliary system that is driven by the available system outputs and mirrors the dynamics of a physical process to estimate one or more functions of the system states. The use of functional observers arises in many applications. For example, functional estimates are useful in feedback control system design because the control signal is often a linear combination of the states, and it is possible to utilize a functional observer to directly estimate the feedback control signal. From a practical point of view, the most common class of applications is related to condition monitoring of dynamic systems, for the purpose of fault detection and/or estimation.

An important issue in the design of functional observers arises from the fact that accurate modeling of a real system is difficult and unknown disturbances/ uncertainties could hamper convergence of the estimate to its true value. This motivates imposing disturbance decoupling requirements in the design of a functional observer.

This present work extends our previous work on functional observers by considering the effect of unknown external disturbances on functional observer design in nonlinear systems. Necessary and sufficient conditions for disturbance decoupling are derived for functional observers designed from the point of view of observer error linearization. Following this, the application of disturbance decoupled functional observers for fault diagnosis is studied. Necessary and sufficient conditions for functional observers to achieve simultaneous disturbance decoupled fault detection and estimation are derived. The disturbance decoupled functional observer design methodology will be illustrated using a non-isothermal CSTR case study

References

• Kravaris, Costas, and Sunjeev Venkateswaran. "Functional observers with linear error dynamics for nonlinear systems." Systems & Control Letters157 (2021): 105021..
• Venkateswaran, Sunjeev, Qiancheng Liu, Benjamin A. Wilhite, and Costas Kravaris. "Design of linear residual generators for fault detection and isolation in nonlinear systems." International Journal of Control95, no. 3 (2022): 804-820..
• Venkateswaran, Sunjeev, Benjamin A. Wilhite, and Costas Kravaris. Functional observers with linear error dynamics for discrete-time nonlinear systems, Automatica, Accepted.
• Venkateswaran, Sunjeev, M. Ziyan Sheriff, Benjamin Wilhite, and Costas Kravaris. "Design of functional observers for fault detection and isolation in nonlinear systems in the presence of noises." Journal of Process Control108 (2021): 68-85.