The open-loop transfer function of a robot arm drive a.Using the Routh-Hurwitz criterion, it is easy to check that the system is stable for all(positive) values of K. Use the

root-locus technique to arrive at the same conclusion by sketching the root-locus. Mark all point of interest, including centroid, angle of departure etc. b. It is desired to pick the gain K to have an overshoot of 10% or less. Make any required(reasonable) assumptions, and determine the range K< K* for the PO condition to be met. I would prefer if you don't use matlab's rlocus to do this, but if you do use the rlocus and move your cursor to find how large K can be for this criterion, you must still justify your work (for example, this system is third order, so what assumptions did you use to do your"analysis"). c. Simulate your results in Simulink, and show me that for the value of K = K* in(b), the PO is less than10%. You can use matlab if you prefer it to using Simulink. My results (using matlab’s step command) are shown in the figure on the right. \text { might be approximated by } G(s) H(s)=\frac{K(s+21)}{(s+20)\left(s^{2}+4 s+8\right)}, K>0