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43 Cards in this Set
- Front
- Back
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to find tau from plot sensor failure (saturating exponential) |
dystep/dt = yss/tau
where dystep/dt = initial slope yss = steady state y-value |
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to find tau from poor sensor failure (decaying exponential) |
dyic/dt = -y0/tau
where dyic/dt = initial slope y0 = initial y value |
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initial state of capacitor |
wire |
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initial state of inductor |
gap |
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final state of capacitor |
gap |
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final state of inductor |
wire |
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voltage divider equation --> |
Vout(s) = z2 / (z1+z2) * Vin(s) |
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z2 = |
elements after node (in impedances) |
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z1 = |
elements before node (in impedances) |
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impedance of R |
R |
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impedance of C |
1/Cs |
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impedance of L |
Ls |
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when t-->0, s |
approaches infinity |
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when t-->infinity, s |
approaches zero |
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for parallel elements in voltage divider, z = |
1/((impedance a)^-1 + (impedance b)^-1)) |
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%OS = |
100 * e^ (zeta*pi/sqrt(1-zeta^2)) |
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wnTp = |
pi/(sqrt(1-zeta^2)) |
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wn in terms of mechanical units |
sqrt K/M |
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zeta in terms of mechanical units |
1/2 * B/(sqrt K/M) |
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to find %OS from a plot |
(y-value of peak - yss)/yss |
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to find Tp from a plot |
time value of highest y-value |
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find zeta from reference curves |
find corresponding zeta from %OS value |
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find frequency of oscillation from reference curves |
given %OS or zeta, find corresponding wnTp value and solve for wn |
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settle time is ... |
the time at which the curve settles completely within the 5% envelope |
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system poles: |
sigma = -zeta * wn w = wn * sqrt(1-zeta^2) |
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transfer function = |
H(s) = X(s)/F(s) |
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when e^-1 |
=0.37 after 1 time constant, dropped 37% of initial value and is within 63% of steady state value |
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when e^-3 |
=0.05 within 5% of steady state after 3 time constants |
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when e^5 |
= 0.006 within 1% of steady state value after 5 time constants |
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t' = |
t/tau |
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zeta is the.. |
damping coefficient tells how much %OS there is controls how high the resonance peak is |
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wn is the ... |
undamped natural frequency |
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peak time is ... |
how long it takes to get to the steady state |
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Tp goes to infinity as ... |
zeta approaces 1 |
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as zeta approaches 1 .... |
Tp goes to infinity and %OS vanishes |
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small zeta values gives %OS |
that approaches 100% |
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5% settle time criteria |
wnTs = 3/zeta |
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phase leads come from... |
high frequency |
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the phase of a product is |
the sum of the phases |
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the phase of a quotient is |
the difference of the phases |
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the phase of any complex function is |
the imaginary part |
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if zeta is small, resonance frequency... |
approaches wn |
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phase = |
tan^-1(imaginary/real) |
