stability5

# stability5 - solve for the poles. QUICK TEST : Hurwitz...

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Slide 1 ME 475 Session 5: Stability Galen King Purdue University Stability A system is asymptotically stable provided that its free response decays to zero.

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Slide 2 ME 475 Session 5: Stability Galen King Purdue University Example 1 pendulum R L m
Slide 3 ME 475 Session 5: Stability Galen King Purdue University Example 2 inverted pendulum R L m

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Slide 4 ME 475 Session 5: Stability Galen King Purdue University Systems with Real Poles Y(s) = y(t) =
Slide 5 ME 475 Session 5: Stability Galen King Purdue University Systems with Complex Poles Y(s) = y(t) =

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Slide 6 ME 475 Session 5: Stability Galen King Purdue University Asymptotic Stability For asymptotic stability, the system transfer function must have poles with exclusively negative real parts. NOTE: poles determine stability; zeros only determine relative contribution of each pole
Slide 7 ME 475 Session 5: Stability Galen King Purdue University Routh-Hurwitz Stability Criterion Allows checking for stability without having to

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Unformatted text preview: solve for the poles. QUICK TEST : Hurwitz Necessary Condition Given the char. eq. a stable system must have: (i) (ii) Slide 8 ME 475 Session 5: Stability Galen King Purdue University Hurwitz Necessary Condition Ex: D(s) = s 2 3s + 2 = 0 stable? Ex: D(s) = s 3 + s 2 + 2s + 8 = 0 stable? We need a sufficient condition. Slide 9 ME 475 Session 5: Stability Galen King Purdue University Routh Array For Slide 10 ME 475 Session 5: Stability Galen King Purdue University Routh Sufficient Condition The number of roots of D(s) having positive real parts (in the RHP) equals the number of sign changes in the 1st column of the Routh array. Ex: D(s) = s 3 + s 2 + 2s + 8 Slide 11 ME 475 Session 5: Stability Galen King Purdue University Routh-Hurwitz Example Find K for a stable system. Actuator Piston K R(s) Y(s) + Slide 12 ME 475 Session 5: Stability Galen King Purdue University Example (cont.)...
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## stability5 - solve for the poles. QUICK TEST : Hurwitz...

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