ba8ec92c-4528-4792-af18-968ddf9cfa46 73 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

TurboGen regulation

p 1 0.2 s * + (1 0.5 s * + (* 0.8 10 s * + (1 0.2 s * + (* 1 0.5 s * + (* 1 0.05 / + / :

s F p parfrac s convert maple : 55 s + (* 2 s + (* 286533 s * + (* 177 s 2^* + 25 s 3^* + (* /

s F 55 s + (* 2 s + (* 286533 s * + (* s 2^17725 s * + (* + (* / :

t sol s F s t invlaplace allvalues maple :

allvalues expands the Maple kernel RootOf ≡

Maple stacks 3 solutions t sol 1 el t sol 2 el t sol 3 el 31 mat ≡

collect the complete solution

t Sol t sol 1 el t sol 2 el + t sol 3 el + :

The imaginary terms cancel each other, the solution is finally Re[Sol(t)]

12273221381717300000000000002839502998 sqrt * + 3 nthroot (2^* 2839502998 sqrt * + 3 nthroot * 6.8444 1030^*

a 0.01105573 :

f 0.06180166 :

b 5.88632 :

d 0.59684 :

Mathcad 11

c 0.0889443 :

ω 1.782526 :

x peak 0.1 :

t Hz a b t * - exp * c d t * - exp * ω t * cos * + f d t * - exp * ω t * sin * + :

t 1281613 nthroot 2839502998 sqrt * + 3 nthroot * 118 - 613 nthroot 2839502998 sqrt * + 3 nthroot * + (* + i 3 sqrt * 12816123 /^2839502998 sqrt * + (23 /^* - (* + (* 50613 nthroot * 2839502998 sqrt * + 3 nthroot * / exp 12273221381717300000000000002839502998 sqrt * + 3 nthroot (2^* 2839502998 sqrt * + 3 nthroot (* /

Conclude the Smath project

x Sol Re x Hz ≡ Mathcad equates Smath ≡

0 x ≤ x Sol Re if 0 x ≤ x Sol Im if 0 x ≤ x Hz if 31 sys

Response to load change

0 x ≤ x Sol Re if 0 x ≤ x Sol Im if 0 x ≤ x Hz if 3 1 sys

jmG: 2015/10/23

0 x ≤ x sol 1 el Re if 0 x ≤ x sol 2 el Re if 0 x ≤ x sol 3 el Re if

s p 1 0.2 s * + (1 0.5 s * + (* 0.8 10 s * + (1 0.2 s * + (* 1 0.5 s * + (* 1 0.05 / + / :

t sol s p s t invlaplace allvalues maple :

t F t sol 2 el :

x damped 0 x ≤ x F Re Undefined if :

x enveloppe 0 x ≤ x F abs Undefined if :

x damped x enveloppe x enveloppe - 3 1 sys

D 0.8 : τg 0.2 : H 5 : τT 0.5 : R 1 : 51 mat

s xfr 1 R / 12 H * s * D + (1 τg s * + (* 1 τT s * + (* / * :

t XFR s xfr t 0 > assume s t invlaplace maple :

Transfer function XFR(x)

0 x ≤ x XFR N/A if