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17 Cards in this Set
- Front
- Back
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differential / difference equation to transfer function |
create H(s) using H(s) = Y(s)/U(s) (transform input if required) |
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State Space representation (ABCD) to transfer function |
Fadeev algorithm then using S1s + S2s... in form C x S x B and all / s^n + a1s^(n-1)... |
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Quotient Rule |
f/g - differentiated: f'g - g'f / g^s |
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euler's formula |
e^(iw) = cos(w) + isin(w) |
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integration by parts |
int(v du) = vu - int(u dv) |
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Differential Equation to state update equation (models) |
from q'' = A(n)x + A(n-1)x... A0
to Matrix: with A0, A1, etc. to A(n-2) in the bottom row. I above on the right |
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Species system symbols |
big Epsilon: natural growth sigma: natural cut-off alpha: relationship to others |
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Phase diagram |
dy/dx where the functions dy and dx are known from the growth equations |
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Transfer function to impulse response function |
Partial fraction expansion PFE |
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State-space representation to impulse response function directly (not using Fadeev) |
using formula with exponents |
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networks to transfer function |
use complex formula |
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being observable |
can observe the state through the output |
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being controllable |
can go to any other state from any finite state |
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into controllable or observable canonical form |
just copy the damn coefficients according to the damn formula |
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model classes |
discrete/continuous, linear/non-linear, deterministic/non-d black-box, white-box, grey |
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parsimony principle |
simple model is preferred: lower cost, maintenance etc |
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Model Cycle: |
problem analysis conceptual modelling (relationships, IO) mathematical model class selection (black,white) Conceptual validation (experts) Implementation (program) verification (test) system identification and calibration (using data, best match) Model validation (cross-validation) Model analysis (uncertainty, sensitivity) |
