Answer Happy

x=5
y=5
[2]. [35 pts] Powered scooter balance control problem is depicted below. The applied force frepresents the net tangential force on the scooter wheels, whereas the angle represents the angular position of the pendulum part. Use the parameter values as M = 5* (x + y) kg, m = 2 * (y+z) kg, L = 1 m. a) Assuming small angular displacements (0 = 0), derive equations that govern the angular position 8 (t) and the applied force f(t). Note that horizontal motion of the lower part and angular motion of the pendulum part must be analyzed first. b) Obtain a transfer function between the angular position (s) and the applied force F(s). c) Design a controller to maintain near zero according to the following specifications: damping ratio of = 0.707 and a 2% settling time of 1 s. Check to make sure that the designed closed-loop controller is stable. m A M L