A robotic arm actuated at the elbow joint is shown in Figure DP7.9(a), and the control system for the actuator is shown in Figure DP7.9(b). Plot the root locus for K ‰¥ 0. Select Gp(s) so that the steady-state error for a step input is equal to zero. Using the Gp(s) selected, plot y(t) for K equal to 1, 1.5, and 2.85. Record the rise time, settling time (with a 2% criterion), and percent overshoot for the three gains. We wish to limit the overshoot to less than 6% while achieving the shortest rise time possible. Select the best system for 1 ‰¤ K ‰¤ 2.85.
Figure DP7.9
(a) A robotic arm actuated at the joint elbow,
(b) Its control system.

Wrist Light weight flexible armm Elbow oint Controlier Elbow actuator ts) Actual position Position s(s + 4) 2s+5