Fractional System Toolbox for Matlab - mechatronics
Fractional System Toolbox for Matlab - mechatronics
Fractional System Toolbox for Matlab - mechatronics
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A new tool <strong>for</strong> mathematical models<br />
of physical systems<br />
<strong>Fractional</strong> differential equation<br />
n<br />
⎛ d ⎞<br />
a0⎜<br />
⎟<br />
⎝ dt<br />
⎠<br />
a0<br />
y<br />
n<br />
⎛ d ⎞<br />
1⎜<br />
⎟<br />
⎝ dt<br />
⎠<br />
a1<br />
n<br />
⎛ d ⎞<br />
L⎜<br />
⎟<br />
⎝ dt<br />
⎠<br />
aL<br />
n<br />
⎛ d ⎞<br />
0⎜<br />
⎟<br />
⎝ dt<br />
⎠<br />
n<br />
⎛ d ⎞<br />
1⎜<br />
⎟<br />
⎝ dt<br />
⎠<br />
n<br />
⎛ d ⎞<br />
M ⎜ ⎟<br />
⎝ dt<br />
⎠<br />
() t + a y()<br />
t + ... + a y()<br />
t = b u()<br />
t + b u()<br />
t + ... + b u()<br />
t<br />
<strong>Fractional</strong> state space representation<br />
⎧<br />
⎛ ⎞<br />
⎪⎜<br />
⎟<br />
⎨⎝<br />
dt<br />
⎠<br />
⎪<br />
⎩y<br />
d n<br />
x<br />
() t = A x()<br />
t + B u()<br />
t<br />
() t = C x()<br />
t + D u()<br />
t<br />
Mathematical viewpoint<br />
b0<br />
b1<br />
•Modal decomposition<br />
•Output analytical expression<br />
•Stability properties<br />
bM
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