1. design a control system for 3-link, 3 DOF robot positioning based on PI, PD and PID controllers. Derive torques, linearize it and choose controller gains for three different controllers (PI, PD and PID). What conclusions can be drawn? Controller design could be performed using MATLAB, Mathematica, Maple, LabVIEW or Python. a. Perform simulation experiment with step and sinusoidal function as inputs. b. Perform simulation for trajectory tracking for desired input in form of u=sin(x) between points A and B (chosen by you) with trapezoidal profile of velocity. Data: 1=2m, l2=1m, l3=1m, mass=4kg, mass2=1.5kg, mass3=1kg