A single link of a robot arm is shown in Figure. The arm mass is m and its center of mass is located a distance L from the joint, which is driven by a motor torque Tm through spur gears. Suppose that the equivalent inertia felt at the motor shaft is 0.215 kg.m2. As the arm rotates, the effect of the arm weight generates an opposing torque that depends on the arm angle, and is therefore nonlinear. The effect of the opposing torque at the motor shaft is 4.2 sin θ N.m. Neglect damping in the system. It is desired to have the motor shaft rotate through 3π/4 rad in a total time of 2 s, using a trapezoidal speed profile with t1 = 0.3 s and t2 = 1.7 s.
The given motor parameters are Ra = 4 Ω, La = 3 x 10-3 H, and KT = 0.3 N.m/A. Use MATLAB to obtain of plot of the response of the motor current and the motor speed.

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