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# Enhancing The Mathematical Interpretation of The Root-Locus Method of Closed-Loop Control System Analysis Using Matlab

A closed-loop control system that has an initial transient response can be stable or unstable depending on what happens after the initial transient response. If the initial transient response continues in the unstable direction, the control system is not usable for the input parameters because it is unstable. On the other hand, if the initial transient response is countered by the control system action, the system becomes stable, and the control system is usable for the input parameters. The basic characteristics of the transient response of a closed-loop control system can be determined based on the location of its poles on its Root-Locus plot. How the poles move and their mathematical interpretation in time domain are predictors of the control system performance. From a design point of view, in certain cases, a gain adjustment will move the poles to desired locations. In other cases, addition of a compensator is necessary. In this article MATLAB is used to determine the required changes and to guide the required actions for obtaining the required changes to the pole locations in order to achieve the system performance specifications. Additionally, MATLAB is used to get the closed-loop control system response in time domain. Studying the system response in time domain enhances the understanding of the Root-Locus technique.