<![CDATA[This study presents a comprehensive, simulation-based validation of a Luenberger Observer (LO) specifically designed for fault detection in storage tank systems. It commences with the development of a nonlinear storage tank model, which is subsequently linearized to streamline the observer design process. The LO estimates critical system states and produces residual signals that enable reliable fault detection. The observer gain is meticulously chosen using pole placement techniques to ensure rapid convergence of estimates and overall stability. To evaluate the effectiveness of this approach, three distinct fault scenarios—ramp, square pulse, and inverted ramp signals—are introduced to simulate various types of abnormal conditions that could occur in real-world operations. Simulation results demonstrate that the LO accurately estimates the liquid level states with a mean absolute error of approximately 0.02 meters, equivalent to about 2.6%. Furthermore, the observer detects faults with an average delay between 5 and 9 seconds following fault injection, indicating its prompt response capability. Notably, even with sensor noise levels reaching 6%, the observer maintains stable tracking performance, demonstrating strong robustness against disturbances. Across all tested scenarios, the residual signals show rapid increases during fault conditions and swiftly return near zero once the system reverts to normal operation, with no false alarms observed. Collectively, these results suggest that the Luenberger Observer provides an accurate, rapid, and disturbance-tolerant method for fault detection in storage tank systems. Such an approach offers a practical alternative to data-driven fault detection methodologies, as it relies less on extensive training datasets and can be more readily implemented for real-time industrial monitoring applications.]]>
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