Physical Laws for Mechanical

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Physical Laws for Mechanical
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Example car suspension
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Car suspension simplified

• Ignore tire deformation.
• Suppose y1(t) is measured
• from equilibrium position
• when gravity has set in.
• So gravity is canceled by
• spring force at eq. pos.
• ?There are two forces on m

y1(t)
x(t)
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• Newtons Law
• or
• num
• den
• T.F.H(s)
• or

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State Space Model

• For linear motion
• Define two state variables for each mass
• x1position, x2 velocity x1-dot x2
• x2-dot is acc and solve for it from Newtons
• For angular motion
• Define two state variables for each rotating
  inertia
• x1 angle, x2 angular velocity x1-dot x2
• x2-dot is angular acc and solve for it from
  Eulers law

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Quarter car suspension
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u
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For field control with constant armature current
For armature control with constant field current
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Armature controlled motor in feedback
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Get TF from wd to w and Td to w.
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