Draw the root locus of the systems with open-loop transfer functions given by2(2)()(10)(22)KsGss sss+=++ +Points will be removed for sloppily drawn plots, and omissions of identification of angles, starting and ending coordinate locations, crossover and breakaway locations, and general shape of the loci curves. (b)Utilize MATLAB to draw the root locus plot. Include the plot and printout of your coding

The root locus is a powerful tool for designing and analyzing feedback control system, it is a graphical method by determining the locus of roots in the s-plane as one system parameter is changed. Root Locus plots are a method of evaluating the behavior of a control system. The creation of a root locus plot begins by determining the poles of the control system for a given set of control parameters. These poles are then plotted on a complex coordinate system as seen in the previous section and analyzed to determine the behavior of the system. In addition to determining the stability of the system, the root locus can be used to design the damping ratio and natural frequency of a feedback system. Root locus plots show the roots of the systems characteristic equation as a function of the control variables. In this paper we consider a unity feedback control system with transfer function and then determine the value of k at different damping ratio values. Damping ratio represents the locus of poles.

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