Problem #8 Consider a single axis robot control system with an optical shaft encoder measuringboth position and velocity of the joint axis. The open loop transfer function from input armaturevoltage u to the joint angle θ is given byG(s) = (θ(s))/(u(s)) = (1)/(s(a1s a2))Where a1 = 0.16 and a2 = 0.53a. (5 points) Derive the closed loop transfer functionGCL(s) = (θ(s))/((s))b. (5 points) Select kp and kv so that the closed loop joint control is stable with naturalfrequency = 3 and damping ratio
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