Consider the extender robot presented in AP6.7. The block diagram of the system is shown in Figure P10.33 [14]. The goal is that the compensated system will have a velocity constant K_v equal to 80, so that the settling time (with a 2% criterion) will be 1.6 seconds, and that the overshoot will be 16%, so that the dominant roots have a ζ of 0.5. Determine a lead-lag compensator using root locus methods.