SYSTEM DYNAMICS & CONTROL CHAPTER 2 REVIEW DYNAMICS LAGRANGE’S METHOD Dr... 17 Lagrange’s Method 2011 – Vo Tuong Quan Modeling and designing a PID controller for an Inverted m mas
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CHAPTER 2
REVIEW DYNAMICS
LAGRANGE’S METHOD
Dr Vo Tuong Quan
HCMUT - 2011
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1 Calculate the kinetic energy of system (K or T)
Lagrange’s Method
2011 – Vo Tuong Quan
0
2
1 2
2
1 2
Rot
P mgh
1 Calculate the potential energy of the system (P or V or U)
1 Calculate the rotation kinetic energy of system (K or T)
Lagrange equation: L = K – P
Then: Calculate the equation
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Mass Spring system
Lagrange’s Method
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2
2
1 2 1 2
2
d x
dt
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Multi degree of freedom system
Lagrange’s Method
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Simple pendulum
Lagrange’s Method
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We need to transform the coordinate
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Lagrange’s Method
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Simple pendulum
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Double pendulum
Lagrange’s Method
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Lagrange’s Method
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Double pendulum
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Lagrange’s Method
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Double pendulum
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Lagrange’s Method
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Double pendulum
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equation of two-link elbow planar arm
Lagrange’s Method
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Lagrange’s Method
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Modeling and designing a PID controller for an Inverted
(m) mass of the pendulum (b) coefficient of friction for cart (l) length to pendulum center of mass (I) mass moment of inertia of the
pendulum (F) force applied to the cart (x) cart position coordinate
( ) pendulum angle from vertical (down)
Source: http://ctms.engin.umich.edu/CTMS/index.php?example=InvertedPendulum§ion=SystemModeling
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Lagrange’s Method
2011 – Vo Tuong Quan