<![CDATA[Control systems with time delays introduce system stability problems because time delays cause exponential effects to the system response. Conventional root-locus methods cannot be used directly on systems with delays due to irrational mathematical forms. This study analyzes the shifting effect of time delay on the stability of linear control systems by using the first-order Padé approach to enable the application of the root-locus method. The system model used is a second-order linear system with a transfer function of , and is analyzed under conditions without delay and with delays of 0.5, 1, and 1.5 seconds. Simulations were performed using MATLAB software. The results show that the addition of delay causes a right pole shift of the imaginary axis, reduces the stability margin of the system, and results in a more oscillative response as well as a longer time for the system to stabilize. The first-order Padé approach is shown to be effective in facilitating the visual analysis of stability in time-delayed systems. The findings make a practical contribution in adapting classical analysis techniques to the needs of modern control systems and can be widely applied in the development of network-based control systems, industrial automation, and real-time control.]]>
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