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Martin Vítek
ZCU-nixie-clock
Commits
f4cf941c
Commit
f4cf941c
authored
Sep 17, 2020
by
Martin Vítek
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Plain Diff
Made state variable from Uin
parent
7d734cf0
Changes
2
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Showing
2 changed files
with
111 additions
and
133 deletions
+111
-133
Model/boost_model.tex
Model/boost_model.tex
+65
-95
Model/model_sim.m
Model/model_sim.m
+46
-38
No files found.
Model/boost_model.tex
View file @
f4cf941c
...
...
@@ -69,7 +69,8 @@ U_{in} &= (R_{62} + R_{Q25} + R_{L3})i_l + L_3\derivative{i_l}{t} + R_{Q24}i_l \
\begin{align}
\derivative
{
i
_
l
}{
t
}
&
=
\frac
{
1
}{
L
_
3
}
U
_{
in
}
-
\frac
{
R
_{
62
}
+R
_{
Q25
}
+R
_{
L3
}
+R
_{
Q24
}}{
L
_
3
}
i
_
l
\\
\derivative
{
u
_
c
}{
t
}
&
= -
\frac
{
1
}{
C
_{
out
}
(R
_{
63
}
+R
_{
load
}
)
}
u
_
c
\derivative
{
u
_
c
}{
t
}
&
= -
\frac
{
1
}{
C
_{
out
}
(R
_{
63
}
+R
_{
load
}
)
}
u
_
c
\\
\derivative
{
U
_{
in
}}{
t
}
&
= 0
\end{align}
\vspace
{
1em
}
...
...
@@ -77,16 +78,14 @@ U_{in} &= (R_{62} + R_{Q25} + R_{L3})i_l + L_3\derivative{i_l}{t} + R_{Q24}i_l \
\begin{align}
\derivative
{}{
t
}
\begin{bNiceMatrix}
i
_
l
\\
u
_
c
\end{bNiceMatrix}
\begin{bNiceMatrix}
i
_
l
\\
u
_
c
\\
U
_{
in
}
\end{bNiceMatrix}
&
=
\begin{bNiceMatrix}
-
\frac
{
R
_{
62
}
+R
_{
Q25
}
+R
_{
L3
}
+R
_{
Q24
}}{
L
_
3
}
&
0
\\
0
&
-
\frac
{
1
}{
C
_{
out
}
(R
_{
63
}
+R
_{
load
}
)
}
-
\frac
{
R
_{
62
}
+R
_{
Q25
}
+R
_{
L3
}
+R
_{
Q24
}}{
L
_
3
}
&
0
&
\frac
{
1
}{
L
_
3
}
\\
0
&
-
\frac
{
1
}{
C
_{
out
}
(R
_{
63
}
+R
_{
load
}
)
}
&
0
\\
0
&
0
&
0
\end{bNiceMatrix}
\begin{bNiceMatrix}
i
_
l
\\
u
_
c
\end{bNiceMatrix}
+
\begin{bmatrix}
\frac
{
1
}{
L
_
3
}
\\
0
\end{bmatrix}
U
_{
in
}
\begin{bNiceMatrix}
i
_
l
\\
u
_
c
\\
U
_{
in
}
\end{bNiceMatrix}
\end{align}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
...
...
@@ -107,7 +106,8 @@ C_{out}\derivative{u_c}{t} &= i_l - \frac{u_c}{R_{63}+R_{load}}
\begin{align}
\derivative
{
i
_
l
}{
t
}
&
=
\frac
{
1
}{
L
_
3
}
(U
_{
in
}
-u
_
c)-
\frac
{
R
_{
62
}
+R
_{
Q25
}
+R
_{
L3
}
+R
_{
s
_{
D6
}}}{
L
_
3
}
i
_
l
\\
\derivative
{
u
_
c
}{
t
}
&
=
\frac
{
1
}{
C
_{
out
}}
i
_
l-
\frac
{
1
}{
C
_{
out
}
(R
_{
63
}
+R
_{
load
}
)
}
u
_
c
\derivative
{
u
_
c
}{
t
}
&
=
\frac
{
1
}{
C
_{
out
}}
i
_
l-
\frac
{
1
}{
C
_{
out
}
(R
_{
63
}
+R
_{
load
}
)
}
u
_
c
\\
\derivative
{
U
_{
in
}}{
t
}
&
= 0
\end{align}
\vspace
{
1em
}
...
...
@@ -115,16 +115,14 @@ C_{out}\derivative{u_c}{t} &= i_l - \frac{u_c}{R_{63}+R_{load}}
\begin{align}
\derivative
{}{
t
}
\begin{bmatrix}
i
_
l
\\
u
_
c
\end{bmatrix}
\begin{bmatrix}
i
_
l
\\
u
_
c
\\
U
_{
in
}
\end{bmatrix}
=
\begin{bmatrix}
-
\frac
{
R
_{
62
}
+R
_{
Q25
}
+R
_{
L3
}
+R
_{
s
_{
D6
}}}{
L
_
3
}
&
-
\frac
{
1
}{
L
_
3
}
\\
\frac
{
1
}{
C
_{
out
}}
&
-
\frac
{
1
}{
C
_{
out
}
(R
_{
63
}
+R
_{
load
}
)
}
-
\frac
{
R
_{
62
}
+R
_{
Q25
}
+R
_{
L3
}
+R
_{
s
_{
D6
}}}{
L
_
3
}
&
-
\frac
{
1
}{
L
_
3
}
&
\frac
{
1
}{
L
_
3
}
\\
\frac
{
1
}{
C
_{
out
}}
&
-
\frac
{
1
}{
C
_{
out
}
(R
_{
63
}
+R
_{
load
}
)
}
&
0
\\
0
&
0
&
0
\end{bmatrix}
\begin{bmatrix}
i
_
l
\\
u
_
c
\end{bmatrix}
+
\begin{bmatrix}
\frac
{
1
}{
L
_
3
}
\\
0
\end{bmatrix}
U
_{
in
}
\begin{bmatrix}
i
_
l
\\
u
_
c
\\
U
_{
in
}
\end{bmatrix}
\end{align}
...
...
@@ -143,16 +141,14 @@ $A_1$, $B_1$ - Q24 v uzavřeném stavu, $A_2$, $B_2$ - Q24 v otevřeném stavu.
\begin{align}
\derivative
{}{
t
}
\begin{bmatrix}
i
_
l
\\
u
_
c
\end{bmatrix}
\begin{bmatrix}
i
_
l
\\
u
_
c
\\
U
_{
in
}
\end{bmatrix}
=
\begin{bmatrix}
-
\frac
{
R
_{
62
}
+R
_{
Q25
}
+R
_{
L3
}
+R
_{
s
_{
D6
}}}{
L
_
3
}
&
-
\frac
{
1-d
}{
L
_
3
}
\\
\frac
{
1-d
}{
C
_{
out
}}
&
-
\frac
{
1
}{
C
_{
out
}
(R
_{
63
}
+R
_{
load
}
)
}
-
\frac
{
R
_{
62
}
+R
_{
Q25
}
+R
_{
L3
}
+R
_{
s
_{
D6
}}}{
L
_
3
}
&
-
\frac
{
1
}{
L
_
3
}
(1-d)
&
\frac
{
1
}{
L
_
3
}
\\
\frac
{
1
}{
C
_{
out
}}
(1-d)
&
-
\frac
{
1
}{
C
_{
out
}
(R
_{
63
}
+R
_{
load
}
)
}
&
0
\\
0
&
0
&
0
\end{bmatrix}
\begin{bmatrix}
i
_
l
\\
u
_
c
\end{bmatrix}
+
\begin{bmatrix}
\frac
{
1
}{
L
_
3
}
\\
0
\end{bmatrix}
U
_{
in
}
\begin{bmatrix}
i
_
l
\\
u
_
c
\\
U
_{
in
}
\end{bmatrix}
\end{align}
\subsection
{
Odezva otevřené smyčky pro různé hodnoty střídy
}
...
...
@@ -172,43 +168,42 @@ U_{in}
\begin{align}
\derivative
{}{
t
}
\begin{bmatrix}
i
_
l
\\
u
_
c
\end{bmatrix}
\begin{bmatrix}
i
_
l
\\
u
_
c
\\
U
_{
in
}
\end{bmatrix}
=
\begin{bmatrix}
-
\frac
{
R
_{
in
}}{
L
_
3
}
&
0
\\
0
&
-
\frac
{
1
}{
C
_{
out
}
R
_{
out
}}
-
\frac
{
R
_{
in
}}{
L
_
3
}
&
0
&
\frac
{
1
}{
L
_
3
}
\\
0
&
-
\frac
{
1
}{
C
_{
out
}
R
_{
out
}}
&
0
\\
0
&
0
&
0
\end{bmatrix}
\begin{bmatrix}
i
_
l
\\
u
_
c
\end{bmatrix}
\begin{bmatrix}
i
_
l
\\
u
_
c
\\
U
_{
in
}
\end{bmatrix}
+
\begin{bmatrix}
-
\frac
{
\overline
{
u
_
c
}}{
L
_
3
}
\\
\frac
{
\overline
{
i
_
L
}}{
C
_{
out
}}
\frac
{
\overline
{
i
_
L
}}{
C
_{
out
}}
\\
0
\end{bmatrix}
D
+
\begin{bmatrix}
\frac
{
1
}{
L
_
3
}
\\
0
\end{bmatrix}
U
_{
in
}
\end{align}
\section
{
Diskretizace
}
\begin{align}
\derivative
{}{
t
}
\begin{bmatrix}
i
_
l
\\
u
_
c
\end{bmatrix}
\begin{bmatrix}
i
_
l
\\
u
_
c
\\
U
_{
in
}
\end{bmatrix}
=
\begin{bmatrix}
-
\frac
{
R
_{
in
}}{
L
_
3
}
&
0
\\
0
&
-
\frac
{
1
}{
C
_{
out
}
R
_{
out
}}
-
\frac
{
R
_{
in
}}{
L
_
3
}
&
0
&
\frac
{
1
}{
L
_
3
}
\\
0
&
-
\frac
{
1
}{
C
_{
out
}
R
_{
out
}}
&
0
\\
0
&
0
&
0
\end{bmatrix}
\begin{bmatrix}
i
_
l
\\
u
_
c
\end{bmatrix}
\begin{bmatrix}
i
_
l
\\
u
_
c
\\
U
_{
in
}
\end{bmatrix}
+
\begin{bmatrix}
-
\frac
{
\overline
{
u
_
c
}}{
L
_
3
}
&
\frac
{
1
}{
L
_
3
}
\\
\frac
{
\overline
{
i
_
L
}}{
C
_{
out
}}
&
0
\end{bmatrix}
\begin{bmatrix}
D
\\
U
_{
in
}
-
\frac
{
\overline
{
u
_
c
}}{
L
_
3
}
\\
\frac
{
\overline
{
i
_
L
}}{
C
_{
out
}}
\\
0
\end{bmatrix}
D
\end{align}
\vspace
{
1em
}
...
...
@@ -216,34 +211,13 @@ U_{in}
\begin{align}
\begin{bmatrix}
i
_{
l,t+1
}
\\
u
_{
c,t+1
}
i
_{
l,t+1
}
\\
u
_{
c,t+1
}
\\
U
_{
in,t+1
}
\end{bmatrix}
=
\boldsymbol
{
A
}
\begin{bmatrix}
i
_
l
\\
u
_
c
\end{bmatrix}
\begin{bmatrix}
i
_
{
l,t
}
\\
u
_
{
c,t
}
\\
U
_{
in,t
}
\end{bmatrix}
+
\boldsymbol
{
B
}
\begin{bmatrix}
D
\\
U
_{
in
}
\end{bmatrix}
\end{align}
\begin{align}
\begin{bmatrix}
i
_{
l,t+1
}
\\
u
_{
c,t+1
}
\end{bmatrix}
=
\boldsymbol
{
A
}
\begin{bmatrix}
i
_
l
\\
u
_
c
\end{bmatrix}
+
\begin{bmatrix}
\boldsymbol
{
B
}_{
1,1
}
\\
\boldsymbol
{
B
}_{
2,1
}
\end{bmatrix}
D +
\begin{bmatrix}
\boldsymbol
{
B
}_{
1,2
}
\\
\boldsymbol
{
B
}_{
2,2
}
\end{bmatrix}
U
_{
in
}
\boldsymbol
{
B
}
D
\end{align}
...
...
@@ -256,78 +230,74 @@ U_{in}
\begin{align}
\begin{bmatrix}
i
_{
l,t+1
}
\\
u
_{
c,t+1
}
\\
\Delta
_{
t+1
}
i
_{
l,t+1
}
\\
u
_{
c,t+1
}
\\
U
_{
in,t+1
}
\\
\Delta
_{
t+1
}
\end{bmatrix}
&
=
\begin{bmatrix}
\boldsymbol
{
A
}_{
1,1
}
&
\boldsymbol
{
A
}_{
1,2
}
&
0
\\
\boldsymbol
{
A
}_{
2,1
}
&
\boldsymbol
{
A
}_{
2,2
}
&
0
\\
0
&
\mathrm
{
d
}
t
&
1
\\
\boldsymbol
{
A
}_{
1,1
}
&
\boldsymbol
{
A
}_{
1,2
}
&
\boldsymbol
{
A
}_{
1,3
}
&
0
\\
\boldsymbol
{
A
}_{
2,1
}
&
\boldsymbol
{
A
}_{
2,2
}
&
\boldsymbol
{
A
}_{
2,3
}
&
0
\\
\boldsymbol
{
A
}_{
3,1
}
&
\boldsymbol
{
A
}_{
3,2
}
&
\boldsymbol
{
A
}_{
3,3
}
&
0
\\
0
&
\mathrm
{
d
}
t
&
0
&
1
\\
\end{bmatrix}
\begin{bmatrix}
i
_{
l,t
}
\\
u
_{
c,t
}
\\
\Delta
_
t
i
_{
l,t
}
\\
u
_{
c,t
}
\\
U
_{
in,t
}
\\
\Delta
_
t
\end{bmatrix}
+
\begin{bmatrix}
\boldsymbol
{
B
}_{
1,1
}
\\
\boldsymbol
{
B
}_{
2,1
}
\\
\boldsymbol
{
B
}_{
3,1
}
\\
0
\end{bmatrix}
D +
\begin{bmatrix}
\boldsymbol
{
B
}_{
1,2
}
\\
\boldsymbol
{
B
}_{
2,2
}
\\
0
\\
\end{bmatrix}
U
_{
in
}
+
\begin{bmatrix}
0
\\
0
\\
-
\mathrm
{
d
}
t
0
\\
0
\\
0
\\
-
\mathrm
{
d
}
t
\end{bmatrix}
u
_{
c,t
}^
*
\end{align}
\begin{align}
\begin{bmatrix}
i
_{
l,t+1
}
\\
u
_{
c,t+1
}
\\
\Delta
_{
t+1
}
i
_{
l,t+1
}
\\
u
_{
c,t+1
}
\\
U
_{
in,t+1
}
\\
\Delta
_{
t+1
}
\end{bmatrix}
&
=
\begin{bmatrix}
\boldsymbol
{
A
}_{
1,1
}
&
\boldsymbol
{
A
}_{
1,2
}
&
0
\\
\boldsymbol
{
A
}_{
2,1
}
&
\boldsymbol
{
A
}_{
2,2
}
&
0
\\
0
&
\mathrm
{
d
}
t
&
1
\\
\boldsymbol
{
A
}_{
1,1
}
&
\boldsymbol
{
A
}_{
1,2
}
&
\boldsymbol
{
A
}_{
1,3
}
&
0
\\
\boldsymbol
{
A
}_{
2,1
}
&
\boldsymbol
{
A
}_{
2,2
}
&
\boldsymbol
{
A
}_{
2,3
}
&
0
\\
\boldsymbol
{
A
}_{
3,1
}
&
\boldsymbol
{
A
}_{
3,2
}
&
\boldsymbol
{
A
}_{
3,3
}
&
0
\\
0
&
\mathrm
{
d
}
t
&
0
&
1
\\
\end{bmatrix}
\begin{bmatrix}
i
_{
l,t
}
\\
u
_{
c,t
}
\\
\Delta
_
t
i
_{
l,t
}
\\
u
_{
c,t
}
\\
U
_{
in,t
}
\\
\Delta
_
t
\end{bmatrix}
+
\begin{bmatrix}
\boldsymbol
{
B
}_{
1,1
}
&
\boldsymbol
{
B
}_{
1,2
}
&
0
\\
\boldsymbol
{
B
}_{
2,1
}
&
\boldsymbol
{
B
}_{
2,2
}
&
0
\\
0
&
0
&
-
\mathrm
{
d
}
t
\boldsymbol
{
B
}_{
1,1
}
&
0
&
0
&
0
\\
\boldsymbol
{
B
}_{
2,1
}
&
0
&
0
&
0
\\
\boldsymbol
{
B
}_{
3,1
}
&
0
&
0
&
0
\\
0
&
0
&
0
&
-
\mathrm
{
d
}
t
\end{bmatrix}
\begin{bmatrix}
D
\\
U
_{
in
}
\\
u
_{
c,t
}^
*
D
\\
0
\\
0
\\
u
_{
c,t
}^
*
\end{bmatrix}
\end{align}
\section
{
Regulátor
}
\begin{align}
d
&
= -
\boldsymbol
{
L
}
x
_
t -
\boldsymbol
{
K
}
w
\\
d
&
= -
\boldsymbol
{
L
}
D
&
= -
\boldsymbol
{
L
}
x
_
t -
\boldsymbol
{
K
}
w
\\
D
&
= -
\boldsymbol
{
L
}
\begin{bmatrix}
i
_{
l,t
}
\\
u
_{
c,t
}
\\
\Delta
_{
t
}
i
_{
l,t
}
\\
u
_{
c,t
}
\\
U
_{
in,t
}
\\
\Delta
_{
t
}
\end{bmatrix}
-
\boldsymbol
{
K
}
\begin{bmatrix}
D
\\
U
_{
in
}
\\
u
_{
c,t
}^
*
\end{bmatrix}
\\
-
\boldsymbol
{
K
}
u
_{
c,t
}^
*
\\
\boldsymbol
{
L
}
&
= dlqr(
\boldsymbol
{
A
}
,
\boldsymbol
{
B
}
,
\boldsymbol
{
Q
}
,
\boldsymbol
{
N
}
,
\boldsymbol
{
R
}
)
\\
\boldsymbol
{
K
}
&
=
\{
-
\boldsymbol
{
C
_
w
}
[
\boldsymbol
{
I
}
-(
\boldsymbol
{
A
}
-
\boldsymbol
{
BL
}
)]
^{
-1
}
\boldsymbol
{
B
}
\}
^{
-1
}
\\
\boldsymbol
{
C
}_
w
&
=
\begin{bmatrix}
1
&
0
&
0
\\
0
&
1
&
0
\\
0
&
0
&
1
1
&
0
&
0
&
0
\\
0
&
1
&
0
&
0
\\
0
&
0
&
1
&
0
\\
0
&
0
&
0
&
1
\end{bmatrix}
\end{align}
...
...
Model/model_sim.m
View file @
f4cf941c
...
...
@@ -30,13 +30,15 @@ il_lin = 0.83;
% Continuous time matrixes
cssm
.
A
=
[
-
par
.
Rin
/
par
.
L3
,
0
;
0
,
-
1
/(
par
.
Cout
*
par
.
Rout
)];
cssm
.
A
=
[
-
par
.
Rin
/
par
.
L3
,
0
,
1
/
par
.
L3
;
0
,
-
1
/(
par
.
Cout
*
par
.
Rout
),
0
;
0
,
0
,
0
];
cssm
.
B
=
[
-
uc_lin
/
par
.
L3
,
1
/
par
.
L3
;
il_lin
/
par
.
Cout
,
0
];
cssm
.
B
=
[
-
uc_lin
/
par
.
L3
;
il_lin
/
par
.
Cout
;
0
];
cssm
.
C
=
eye
(
2
);
cssm
.
C
=
eye
(
size
(
cssm
.
B
,
1
)
);
cssm
.
D
=
zeros
(
size
(
cssm
.
B
));
...
...
@@ -44,46 +46,48 @@ cssm.D = zeros(size(cssm.B));
dssm
=
c2d
(
ss
(
cssm
.
A
,
cssm
.
B
,
cssm
.
C
,
cssm
.
D
),
Ts
);
% Add error integration
dsys
.
A
=
[
dssm
.
A
(
1
,
1
),
dssm
.
A
(
1
,
2
),
0
;
dssm
.
A
(
2
,
1
),
dssm
.
A
(
2
,
2
),
0
;
0
,
Ts
,
1
];
dsys
.
B
=
[
dssm
.
B
(
1
,
1
),
dssm
.
B
(
1
,
2
),
0
;
dssm
.
B
(
2
,
1
),
dssm
.
B
(
2
,
2
),
0
;
0
,
0
,
-
Ts
];
dsys
.
C
=
eye
(
3
);
dsys
.
A
=
[
dssm
.
A
(
1
,
1
),
dssm
.
A
(
1
,
2
),
dssm
.
A
(
1
,
3
),
0
;
dssm
.
A
(
2
,
1
),
dssm
.
A
(
2
,
2
),
dssm
.
A
(
2
,
3
),
0
;
dssm
.
A
(
3
,
1
),
dssm
.
A
(
3
,
2
),
dssm
.
A
(
3
,
3
),
0
;
0
,
Ts
,
0
,
1
];
dsys
.
B
=
[
dssm
.
B
(
1
,
1
);
dssm
.
B
(
2
,
1
);
dssm
.
B
(
3
,
1
);
0
];
dsys
.
C
=
eye
(
size
(
dsys
.
B
,
1
));
dsys
.
D
=
zeros
(
size
(
dsys
.
B
));
% Simulate system (open loop)
% i = 1;
% i0 = 0.75;
% u0 = 170;
% delta0 = 0.9;
% tmax = 0.1;
%
% sim.vars(:,1) = [i0, u0, delta0];
% sim.t(i) = 0;
%
% for t=dssm.Ts:dssm.Ts:tmax
% sim.vars(:, i+1) = dsys.A*sim.vars(:, i) + dsys.B*[1-d; Uin; uc_req];
% sim.t(i+1) = t;
%
% i = i+1;
% end
%Simulate system (open loop)
i
=
1
;
i0
=
0.75
;
u0
=
Uin
;
delta0
=
0.9
;
tmax
=
0.1
;
% Plot it
%plot_sim(sim, "Open loop response", 1);
sim
.
vars
(:,
1
)
=
[
i0
,
u0
,
Uin
,
delta0
];
sim
.
t
(
i
)
=
0
;
for
t
=
dssm
.
Ts
:
dssm
.
Ts
:
tmax
sim
.
vars
(:,
i
+
1
)
=
dsys
.
A
*
sim
.
vars
(:,
i
)
+
dsys
.
B
*
(
1
-
d
);
sim
.
t
(
i
+
1
)
=
t
;
i
=
i
+
1
;
end
%Plot it
plot_sim
(
sim
,
"Open loop response"
,
1
);
% Regulator
Q
=
diag
([
0
,
0.01
,
0.5
]);
% Q = diag([0, 0.5, 0, 0.5]);
Q
=
1e-5
*
eye
(
4
);
R
=
1
;
N
=
zeros
(
3
);
N
=
zeros
(
size
(
Q
,
1
),
1
);
L
=
dlqr
(
dsys
.
A
,
dsys
.
B
,
Q
,
R
,
N
);
% Cw = eye(3);
Cw
=
[
1
,
0
,
0
;
0
,
1
,
0
;
0
,
0
,
1
];
p
=
inv
(
eye
(
3
)
-
(
dsys
.
A
-
dsys
.
B
*
L
));
Cw
=
eye
(
4
);
p
=
inv
(
eye
(
4
)
-
(
dsys
.
A
-
dsys
.
B
*
L
));
K
=
inv
(
-
Cw
*
p
*
dsys
.
B
);
...
...
@@ -148,16 +152,20 @@ title("d");
function
plot_sim
(
sim
,
what
,
num
)
figure
(
num
);
sgtitle
(
sprintf
(
"%s"
,
what
));
subplot
(
1
,
3
,
1
);
subplot
(
1
,
4
,
1
);
plot
(
sim
.
t
,
sim
.
vars
(
1
,:));
title
(
"il"
);
subplot
(
1
,
3
,
2
);
subplot
(
1
,
4
,
2
);
plot
(
sim
.
t
,
sim
.
vars
(
2
,:));
title
(
"uc"
);
subplot
(
1
,
3
,
3
);
subplot
(
1
,
4
,
3
);
plot
(
sim
.
t
,
sim
.
vars
(
3
,:));
title
(
"Uin"
);
subplot
(
1
,
4
,
4
);
plot
(
sim
.
t
,
sim
.
vars
(
4
,:));
title
(
"delta"
);
hold
off
end
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