WE WANT TO GET STATE SPACE EQUATION FROM LANGRANGE EQ. AND TRANSFER FUNCTION OF THE SYSTEM. WE WANT TO GET STATE SPACE E
Posted: Tue Jun 07, 2022 3:03 pm
WE WANT TO GET STATE SPACE EQUATION FROM LANGRANGE EQ. AND TRANSFER FUNCTION OF THE SYSTEM.
WE WANT TO GET STATE SPACE EQUATION FROM LANGRANGE EQ. AND TRANSFER FUNCTION OF THE SYSTEM.
WE WANT TO GET STATE SPACE EQUATION FROM LANGRANGE EQ. AND TRANSFER FUNCTION OF THE SYSTEM.
These are kinetical and potential energy's of our system. We need to get Langrange Function from this equations.
These are the dynamic equations we need to learn STATE SPACE EQUATIONS.
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
The Lagrange function is the dissimilarity between kinetic energy and potential energy, which is defined by L equation, L = K - P (3)
The dynamic equation (4) representing the variation effect of system variable. Equation (4), equation (5) and (6) show the dynamic equation for two DOF's of the ball and beam system. J 0= ·+m₂)r," + m₂g sina-mora¹² (4) R₂ ƏL d L dt dq Q (5) Əq J + m₂)r"=-mga (6) 2 R₂² where t is the torque produced by the motor applied on the end of the beam. d α Ө (7) L d 1 (0) (8) +m₂)r" = −m₂g LB R₂ b
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)
WE WANT TO GET STATE SPACE EQUATION FROM LANGRANGE EQ. AND TRANSFER FUNCTION OF THE SYSTEM.
WE WANT TO GET STATE SPACE EQUATION FROM LANGRANGE EQ. AND TRANSFER FUNCTION OF THE SYSTEM.
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The Lagrange function is the dissimilarity between kinetic energy and potential energy, which is defined by L equation, L = K - P (3)
The dynamic equation (4) representing the variation effect of system variable. Equation (4), equation (5) and (6) show the dynamic equation for two DOF's of the ball and beam system. J 0= ·+m₂)r," + m₂g sina-mora¹² (4) R₂ ƏL d L dt dq Q (5) Əq J + m₂)r"=-mga (6) 2 R₂² where t is the torque produced by the motor applied on the end of the beam. d α Ө (7) L d 1 (0) (8) +m₂)r" = −m₂g LB R₂ b
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)