a) Obtain a state-variable representation of the system. b) Linearize the dynamics and obtain a state-space representation of the system around the equilibrium position 0 = 180 degrees, = 0. Pvor point length c) A constant torque, in counter-clockwise direction, is applied as an input to the pendulum. Angular position is the measured output. Derive the transfer function from the torque to angular position for the linearized pendulum system obtained in part b). Massles rod M, mass

Elements Of Electromagnetics
7th Edition
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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penaulum shown in the figure, the nonlinear equations of motion are given by
where g is gravity, L is the length of the pendulum, m
is the mass attached at the end of the pendulum (we
- 0.
assume the rod is massless), and k is the coefficient of
sin e
friction at the pivot point.
a) Obtain a state-variable representation of the system.
b) Linearize the dynamics and obtain a state-space
representation of the system around the equilibrium position
@ = 180 degrees, ở = 0.
Pvor point
Llength
c) A constant torque, in counter-clockwise direction, is
applied as an input to the pendulum. Angular position is the
measured output. Derive the transfer function from the
torque to angular position for the linearized pendulum
system obtained in part b).
Massles rod
m, mass
Transcribed Image Text:penaulum shown in the figure, the nonlinear equations of motion are given by where g is gravity, L is the length of the pendulum, m is the mass attached at the end of the pendulum (we - 0. assume the rod is massless), and k is the coefficient of sin e friction at the pivot point. a) Obtain a state-variable representation of the system. b) Linearize the dynamics and obtain a state-space representation of the system around the equilibrium position @ = 180 degrees, ở = 0. Pvor point Llength c) A constant torque, in counter-clockwise direction, is applied as an input to the pendulum. Angular position is the measured output. Derive the transfer function from the torque to angular position for the linearized pendulum system obtained in part b). Massles rod m, mass
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