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ICS
ICS Public
Lecture Files
Commits
5494e58c
Commit
5494e58c
authored
Aug 05, 2021
by
Patrick Göttsch
Browse files
Gitlab Runner Update from atc-aux-files/master:Merge branch 'ExerciseChapter12' into 'master'
parent
2c5b3461
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ATC/exercise-files/LPV/Exercise1_1/exercise_Hidden_Coupling.m
...exercise-files/LPV/Exercise1_1/exercise_Hidden_Coupling.m
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ATC/exercise-files/LPV/Exercise1_1/model_Hidden_Coupling.slx
ATC/exercise-files/LPV/Exercise1_1/model_Hidden_Coupling.slx
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ATC/exercise-files/LPV/Exercise1_1/model_Hidden_Coupling.slx.r2013a
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ATC/exercise-files/LPV/Exercise1_1/model_Hidden_Coupling.slx.r2014a
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ATC/exercise-files/LPV/Exercise1_1/model_Hidden_Coupling_mod.slx
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ATC/exercise-files/LPV/Exercise1_2/exercise_LTI_LTV_Stability.m
...ercise-files/LPV/Exercise1_2/exercise_LTI_LTV_Stability.m
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ATC/exercise-files/LPV/Exercise1_2/model_LTI_LTV_Stability.slx
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ATC/exercise-files/LPV/Exercise1_2/model_LTI_LTV_Stability.slx.r2013a
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ATC/exercise-files/LPV/Exercise1_1/exercise_Hidden_Coupling.m
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5494e58c
%% Hidden Coupling - Instability of the linearized closed loop
% -------------------------------------------------------------------------
% script : exercise_Hidden_Coupling
% -------------------------------------------------------------------------
% Author : Christian Hoffmann
% Version : May, 28th 2021
% Copyright: CH, 2013
% Update : PG, 2021
% -------------------------------------------------------------------------
%
% 1. Construct linearized closed loop
% 2. Plot eigenvalues for different parameter values
%
% -------------------------------------------------------------------------
%% 1.
rho
=
-
0.9
:
0.01
:
0.9
;
xKe
=
atanh
(
rho
);
urho
=
ureal
(
'urho'
,
0
,
'Range'
,
[
-
1
,
1
]);
uxKe
=
ureal
(
'uxKe'
,
atanh
(
0
),
'Range'
,
[
min
(
xKe
),
max
(
xKe
)]);
uAcl
=
[
-
1
+
(
-
1
/
3
+
2
*
urho
*
uxKe
)/(
1
-
urho
^
2
)
,
1
/(
1
-
urho
^
2
)
;
...
-
(
1
-
urho
^
2
)
,
0
];
for
ii
=
1
:
length
(
rho
)
Aclsubs
=
usubs
(
uAcl
,
'uxKe'
,
xKe
(
ii
));
Aclsubs
=
usubs
(
Aclsubs
,
'urho'
,
rho
(
ii
));
eigVals
(:,
ii
)
=
eig
(
Aclsubs
);
end
%% 2.
ReEig
=
real
(
eigVals
);
plot
(
rho
,
ReEig
(
1
,
:));
hold
on
plot
(
rho
,
ReEig
(
2
,
:),
'r'
);
hold
on
ATC/exercise-files/LPV/Exercise1_1/model_Hidden_Coupling.slx
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5494e58c
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ATC/exercise-files/LPV/Exercise1_1/model_Hidden_Coupling.slx.r2013a
0 → 100644
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5494e58c
File added
ATC/exercise-files/LPV/Exercise1_1/model_Hidden_Coupling.slx.r2014a
0 → 100644
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5494e58c
File added
ATC/exercise-files/LPV/Exercise1_1/model_Hidden_Coupling_mod.slx
0 → 100644
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5494e58c
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ATC/exercise-files/LPV/Exercise1_2/exercise_LTI_LTV_Stability.m
0 → 100644
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5494e58c
%% Investigate the Fact that a LTV Stability Cannot be Inferred from LTI
% Stability
% -------------------------------------------------------------------------
% script : exercise_LTI_LTV_Stability
% -------------------------------------------------------------------------
% Author : Christian Hoffmann
% Version : October, 27th 2015
% Copyright: CH, 2013
% Update : PC, 2015
% -------------------------------------------------------------------------
%
% 1. Define plant
% 2. Plot phase diagrams for various scenarios
%
% -------------------------------------------------------------------------
%% Initialization
clc
;
clear
all
;
close
all
;
warning
off
;
s
=
tf
(
's'
);
% Add subdirectories to path
addpath
(
genpath
(
'.'
))
thisdate
=
datestr
(
now
,
'yyyy-mm-dd_HH-MM'
);
%% 1. Plant Definition
% Parameterized plant definition
A
=
@
(
k
,
b
,
m
)
[
0
1
;
...
-
k
-
b
];
x0
=
[
0
;
1
];
k1
=
3
;
k2
=
1
/
3
;
b1
=
0.5
;
b2
=
0
;
[
V1
,
D1
]
=
eig
(
A
(
k1
,
b2
,
1
))
[
V2
,
D2
]
=
eig
(
A
(
k2
,
b2
,
1
))
% Draw phase portraits
x10_grid
=
-
1
:
2
:
1
;
x20_grid
=
-
1
:
2
:
1
;
x0_grid
=
combvec
(
x10_grid
,
x20_grid
);
% x0_grid = x0_grid(:, 8);
time
=
0
:
0.01
:
100
;
colors
=
{
'k'
,
'b'
,
'r'
};
sys
{
1
}
=
ss
(
A
(
k1
,
b2
,
1
),
zeros
(
2
,
1
),
eye
(
2
),
zeros
(
2
,
1
));
sys
{
2
}
=
ss
(
A
(
k2
,
b2
,
1
),
zeros
(
2
,
1
),
eye
(
2
),
zeros
(
2
,
1
));
% sys{3} = ss(A(k1, b2, 1), zeros(2, 1), eye(2), zeros(2, 1));
figure
(
1
);
hold
on
% phasePlotCompute(sys, x0_grid, time, colors)
[
~
,
~
,
x1
]
=
initial
(
sys
{
1
},
x0
,
10
);
[
~
,
~
,
x2
]
=
initial
(
sys
{
2
},
x0
,
20
);
plot
(
x1
(:,
1
),
x1
(:,
2
),
'r'
,
x2
(:,
1
),
x2
(:,
2
),
'k'
)
xlabel
(
'$y$'
,
'Interpreter'
,
'Latex'
)
ylabel
(
'$\dot{y}$'
,
'Interpreter'
,
'Latex'
)
axis
([
-
2
2
-
2
2
])
grid
on
%%
boolSwitchingLaw
=
0
;
boolSmoothKFunction
=
0
;
sim
(
'model_LTI_LTV_Stability'
)
x_sys
{
1
,
1
}
=
x
.
signals
.
values
;
figure
(
1
);
hold
on
phasePlot
(
x_sys
,
{
'k'
},
2
)
\ No newline at end of file
ATC/exercise-files/LPV/Exercise1_2/model_LTI_LTV_Stability.slx
0 → 100644
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5494e58c
File added
ATC/exercise-files/LPV/Exercise1_2/model_LTI_LTV_Stability.slx.r2013a
0 → 100644
View file @
5494e58c
File added
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