Tutorial 12

1 Control Engineering CE447 Tutorial 12 Prepared by A/Prof Victor Sreeram School of Electronic and Computer Engineering University of Western Australia School of Electrical, Electronic and Computer Engineering. Control Engineering (CE) 447 Tutorial 12 1. A helicopter near hover can be described by the equations x -0.02 -1.4 9.8 x 9.8 1 1 x = -0.01 -0.4 0.0 x + 6.3 u 2 2 x 0.0 1.0 0.0 x 0.0 3 3 where x = horizontal velocity, x = pitch rate, x = pitch angle, 1 2 3 u = rotor tilt angle. (a) Find the open loop poles (b) Show that a state feedback law to move the poles to s = -2, s = -1– j is k = 0.0628 0.4706 0.9949 [ ] 2. Consider the system defined by x = Ax + Bu where 0 1 0 0 A = 0 0 1 , B = 0 , C = 1 2 3 [ ] -2 -4 -6 1 By using the state feedback control u = - Kx, is desired to have the closed-loop poles at s = - 2 – j4, s = - 6. Determine the state feedback gain matrix K. 3. Consider the system defined by x = Ax + Bu y = Cx where 0 1 0 0 A = 0 0 1 , B = 0 , c = 1 0 0 [ ] -6 -11 -6 1 2 Control Engineering CE447 ...