cleveland state university mce441: intr. linear control...
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Cleveland State University
MCE441: Intr. Linear Control Systems
Lecture 3: Dynamic Modeling of Engineering Systems
Mechanical Systems
Prof. Richter
Ideal Spring
⊲ Ideal Spring
Viscous LinearDamper
Laws for mechanicalsystems
Simple example:quarter-carsuspension
More difficultexample
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Viscous Linear Damper
Ideal Spring
⊲Viscous LinearDamper
Laws for mechanicalsystems
Simple example:quarter-carsuspension
More difficultexample
3 / 9
Laws for mechanical systems
Ideal Spring
Viscous LinearDamper
⊲
Laws formechanicalsystems
Simple example:quarter-carsuspension
More difficultexample
4 / 9
� Newton’s law, translational: ~F =
d(m~v)dt
� Rotational: ~T =d~L
dt
� Constant mass: ~F = m~a
� Constant moment of inertia, rotation about principal axis:~T = I
d~w
dt= I~α
� Each mass and each d.o.f. contribute a second-order ODE
Simple example: quarter-car suspension
Ideal Spring
Viscous LinearDamper
Laws for mechanicalsystems
⊲
Simple example:quarter-carsuspension
More difficultexample
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Find the I/O differential equation (x, y)
Solution
Ideal Spring
Viscous LinearDamper
Laws for mechanicalsystems
⊲
Simple example:quarter-carsuspension
More difficultexample
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More difficult example
Ideal Spring
Viscous LinearDamper
Laws for mechanicalsystems
Simple example:quarter-carsuspension
⊲More difficultexample
7 / 9
Find the I/O differential equation (F,y)
Solution
Ideal Spring
Viscous LinearDamper
Laws for mechanicalsystems
Simple example:quarter-carsuspension
⊲More difficultexample
8 / 9
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