The George W. Woodruff School of Mechanical Engineering Georgia Institute of Technology ME64015 HW SET #5 Due Wednesday 11/6/2019 ME6401Q Due Wednesday 11/13/2019 1. In an appropriate dimensionless unite the equations, the linearized equation of motion of the Segway transportation device shown below is given by = 0 tu, U = u where u is the linear acceleration input, & is the angular displacement output, and v is the linear velocity output. To simultaneously regulate velocity and to keep the rider upright, a state feedback controller of the form u = -kid - kid - ke(v - ve) where ve is the desired (constant ) linear velcity. (a) Find the open loop poles of the system and indicate whether it is stable or not. (b) Find gains ki, An, and be that places the closed loop poles at s = -2 and s = -2 1 2j. (c) Simulate the performance of your controller in (b) for ve = 1. Plot # (t) and v (t) ve. t in each case Figure 1: 2. Consider the dynamics of a helicopter given by: -0.3 10 2: 1 10 -0.4 -0.2 -2 0 + 10 & + -0.2 0 1.0 0 0 where my = horizontal velocity, my = pitch rate, ap = pitch angle, u = rotor tilt angle, w = headwind. (a) Find the open loop poles of the system and indicate whether it is stable or not. (b) Design an integral feedback controller of the formu = -kix -kr Jou()-va()]dr such that the closed loop poles are placed at s = -2 (repeated) and = = v2(-1# j)