Draw the positive and negative gain root-locus of (view attachment to see L equation). Hence find the gain to have a closed loop damping factor (0.7).
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Draw the root locus using matlab or octave. I plotted it from k=-8 to 8. From k=0 the root locus starts at the open loop poles, then with increasing positive gain, the root locus extends into the left-half ...
This solution provides a very detailed explanation on how to solve for this problem. A step-by-step guide is given which act as clear instructions which will lead one to the final answer. Three attachment files are also provided. Two files are saved as ".png" images, showing the partial and full root locus. The third file is the source code data and is saved as a ".m" file.