= 2. [15pt] Consider a constant speed control with the desired trajectory specified by od [t,...

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= 2. [15pt] Consider a constant speed control with the desired trajectory specified by od [t, 0]; = [1,0], and = 0. Assume that the center of mass for each link (considered as a point mass) is located at the distal tip of the link, and there is no friction. In this case, the dynamic model of this robot can be calculated as V t = M(8) +v(,i) + G(8) [L2m2 + 2L1L2m2 cos 0 + L (m + m) L m + LLm cos Lmz + L-Lzm2 cos 02 where M(0) = [1 m L2m cos My v () = | 2 sin 0,0,0] [mLL2 sin 020 2mL sin 020 m2L1 L2 sin 020 G(0) = [mL29 cos(0 + 0) + (m + m2)L19 cos 0] given m m = 1kg, and g = 9.8m/s. m2L2g cos(01 +0) a) Design the feedforward plus PID feedback controller with torque input using kp 10, ka 5, and ki = 0.2 for both joints. = b) Using MATLAB (or Python), plot the torque and 2 obtained from the controller for t = 0:0.1:5[sec]. Use different colors or line types for and 2 and provide a legend on the graph. Save this as Figure 3. = 1 and 2 (0) = 1 by c) Using MATLAB (or Python), plot 01(t) and 02 (t) for where 01(0) numerically integrating the acceleration resulted from the PID controller. Save this as Figure 4. = 2. [15pt] Consider a constant speed control with the desired trajectory specified by od [t, 0]; = [1,0], and = 0. Assume that the center of mass for each link (considered as a point mass) is located at the distal tip of the link, and there is no friction. In this case, the dynamic model of this robot can be calculated as V t = M(8) +v(,i) + G(8) [L2m2 + 2L1L2m2 cos 0 + L (m + m) L m + LLm cos Lmz + L-Lzm2 cos 02 where M(0) = [1 m L2m cos My v () = | 2 sin 0,0,0] [mLL2 sin 020 2mL sin 020 m2L1 L2 sin 020 G(0) = [mL29 cos(0 + 0) + (m + m2)L19 cos 0] given m m = 1kg, and g = 9.8m/s. m2L2g cos(01 +0) a) Design the feedforward plus PID feedback controller with torque input using kp 10, ka 5, and ki = 0.2 for both joints. = b) Using MATLAB (or Python), plot the torque and 2 obtained from the controller for t = 0:0.1:5[sec]. Use different colors or line types for and 2 and provide a legend on the graph. Save this as Figure 3. = 1 and 2 (0) = 1 by c) Using MATLAB (or Python), plot 01(t) and 02 (t) for where 01(0) numerically integrating the acceleration resulted from the PID controller. Save this as Figure 4.