- The Mechanism Of The Ball And Beam System Contains Two Dofs Initially The Euler Lagrange Equation Is Used To Define The 1 (44.31 KiB) Viewed 27 times
The mechanism of the ball and beam system contains two DOFs. Initially the Euler-Lagrange equation is used to define the kinetic energy (1) and potential energy (2) for the system. 1 1 K -m, 1 +-J₁ 2 ^^ ³ ² + = √(√₂ + m₂r¹²¹² ) α²¹² + 12 Jocke (1) 2 R₂ 2 1 P (2) mog sina+mgr sin a 2 BAR
By taking the Laplace transform of the previous equation, now we get the following equation is J d +m₂)R(s)s² = −m₂g₁ -(0(s)) (9) LB 2 R₂ Rearranging the equation (9), we can find the transfer function from the gear angle (0 (s)) to the ball position (R(s)), d J P(S)=-m₂g 2 LB Rb + m₂)/s² (10)