<![CDATA[This manuscript proposes a Proportional-Integral-Derivative (PID) control algorithm based on Lyapunov stability criteria. To verify the technique, the study is further extended to investigate its feasibility in controlling the liquid level of a coupled-tank system. A comparative study is conducted with the well-established Ziegler-Nichols tuning technique, known for its rapid and aggressive response. While Ziegler-Nichols often achieves quick tuning, it is prone to instability or degraded performance, particularly in systems with slow dynamics, such as the coupled-tank system. The results demonstrate the practical viability of the Lyapunov-based PID approach. The findings show that the Lyapunov-PID controller significantly outperforms the Ziegler-Nichols PID, achieving a 33.63% reduction in overshoot and a 45.14% improvement in settling time. These improvements highlight the advantage of incorporating Lyapunov-based criteria in PID design for systems where stability and performance are critical. However, the proposed approach has limitations such as increased computational complexity and the need for abstract tuning effort, along with difficulty in selecting appropriate Lyapunov functions.]]>
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