Name | Description |
---|---|
![]() | Example to check controllability of a state space system |
![]() | Example to check controllability of a state space system |
![]() | Example to check controllability of a state space system |
![]() | Example to check controllability of a state space system and print the controllable poles |
![]() | Compute time response of a state space system |
![]() | Initial response example |
![]() | Impulse response example |
![]() | Step response example |
![]() | Compute poles and invariant zeros of a SISO state space system by transformation to a minmal system |
![]() | Example to check controllability of a state space system |
![]() | Compute invariant zeros of transfer function |
![]() | Transform a TransferFunction into a StateSpace description |
![]() | Example to compute a transfer function matrix of a MIMO system from state space representation |
![]() | Example to compute a transfer function from SISO state space representation |
![]() | Example to compute a zeros-and-poles representation of a MIMO system from state space representation |
![]() | Example to compute a zeros and poles representation from SISO state space representation |
![]() | Example for pole placing using Ackermann's method |
![]() | Description |
![]() | Description |
![]() | Description |
![]() | Example for plotting eigenvalues and invariant zeros of a state space system |
![]() | Constructs a transfer function from state space representation and plots the Bode diagram with automatic determination of the frequency range to plot |
![]() | Constructs a transfer function from state space representation and plots the Bode diagram with automatic determination of the frequency range to plot |
![]() | Time response plot example |
![]() | Impulse plot example |
![]() | Initial condition plot example |
![]() | Plot ramp response |
![]() | Step plot example |
![]() | case studies of systems with zeros |
![]() | Example to demonstrate the transformation to Jordan- observabilitiy- and controllability canonical form |
![]() | Example how to extract input/output related subsystems from state space system record |
![]() | Example to compute the minimal state space realization of a given SISO state space realization |
Name | Description |
---|---|
ssi | |
analyseOptions | |
system data definition | |
systemOnFile | true, if state space system is defined on file |
fileName | file where matrix [A, B; C, D] is stored |
matrixName | Name of the state space system matrix |
Name | Description |
---|---|
ok |
Name | Description |
---|---|
ssi | |
system data definition | |
systemOnFile | true, if state space system is defined on file |
fileName | file where matrix [A, B; C, D] is stored |
matrixName | Name of the state space system matrix |
Name | Description |
---|---|
ok |
Name | Description |
---|---|
ssi | |
system data definition | |
systemOnFile | true, if state space system is defined on file |
fileName | file where matrix [A, B; C, D] is stored |
matrixName | Name of the state space system matrix |
Name | Description |
---|---|
ok |
Name | Description |
---|---|
ssi | |
system data definition | |
systemOnFile | true, if state space system is defined on file |
fileName | file where matrix [A, B; C, D] is stored |
matrixName | Name of the state space system matrix |
Name | Description |
---|---|
ok |
Computes the time response of the system StateSpace sc = StateSpace(A=[-1,1;0,-2],B=[1, 0;0, 1],C=[1,0; 0,1],D=[0, 0; 0, 0]), sampled at Ts=0.01 with inititial state x0=[0;0] subject to the system input u = ones(samples,2), (samples is set to 30).
Name | Description |
---|---|
u[:, 2] |
Computes and plots the step response
Name | Description |
---|---|
y[:, size(sc.C, 1), size(sc.B, 2)] | Output response: (number of samples) x (number of outputs) x (number of inuputs) |
Computes and plots the step response
Name | Description |
---|---|
y[:, size(sc.C, 1), size(sc.B, 2)] | Output response: (number of samples) x (number of outputs) x (number of inuputs) |
Computes and plots the step response
Name | Description |
---|---|
y[:, size(sc.C, 1), size(sc.B, 2)] | Output response: (number of samples) x (number of outputs) x (number of inuputs) |
Name | Description |
---|---|
system data definition | |
fileName | file where matrix [A, B; C, D] is stored |
matrixName | Name of the state space system matrix |
system matrices | |
A[:, :] | |
B[:, :] | |
C[:, :] | |
D[:, :] |
Name | Description |
---|---|
ok |
Name | Description |
---|---|
ssi | |
system data definition | |
systemOnFile | true, if state space system is defined on file |
fileName | file where matrix [A, B; C, D] is stored |
matrixName | Name of the state space system matrix |
Name | Description |
---|---|
ok |
Name | Description |
---|---|
z[:] | Zeros (Complex vector of numerator zeros) |
p[:] | Poles (Complex vector of denominator zeros) |
k | Constant multiplied with transfer function |
Name | Description |
---|---|
zp |
Name | Description |
---|---|
ok |
Name | Description |
---|---|
system data definition | |
systemOnFile | true, if state space system is defined on file |
fileName | file where matrix [A, B; C, D] is stored |
matrixName | Name of the state space system matrix |
system matrices | |
A[:, size(A, 1)] | |
B[size(A, 2), :] | |
C[:, size(A, 1)] | |
D[size(C, 1), size(B, 2)] |
Name | Description |
---|---|
ok |
Name | Description |
---|---|
system data definition | |
systemOnFile | true, if state space system is defined on file |
fileName | file where matrix [A, B; C, D] is stored |
matrixName | Name of the state space system matrix |
system matrices | |
A[:, :] | |
B[:, :] | |
C[:, :] | |
D[:, :] |
Name | Description |
---|---|
ok |
Name | Description |
---|---|
system data definition | |
systemOnFile | true, if state space system is defined on file |
fileName | file where matrix [A, B; C, D] is stored |
matrixName | Name of the state space system matrix |
system matrices | |
A[:, size(A, 1)] | |
B[size(A, 2), :] | |
C[:, size(A, 1)] | |
D[size(C, 1), size(B, 2)] |
Name | Description |
---|---|
ok |
Name | Description |
---|---|
system data definition | |
systemOnFile | true, if state space system is defined on file |
fileName | file where matrix [A, B; C, D] is stored |
matrixName | Name of the state space system matrix |
system matrices | |
A[:, :] | |
B[:, :] | |
C[:, :] | |
D[:, :] |
Name | Description |
---|---|
ok |
Computes the gain vector k for the state space system
sc = StateSpace(A=[-1,1;0,-2],B=[0, 1],C=[1,0; 0, 1],D=[0; 0])such that for the state feedback
u = -k*y = -k*xthe closed-loop poles are placed at
p = {-3,-4}.
Extends from Modelica.Icons.Function (Icon for a function).
Name | Description |
---|---|
sc |
Name | Description |
---|---|
k[2] | Gain vector |
Name | Description |
---|---|
ss |
Name | Description |
---|---|
L[:, :] | |
kss |
Name | Description |
---|---|
ssi | |
system data definition | |
systemOnFile | true, if state space system is defined on file |
fileName | file where matrix [A, B; C, D] is stored |
matrixName | Name of the state space system matrix |
Name | Description |
---|---|
ok |
Name | Description |
---|---|
ssi | |
system data definition | |
systemOnFile | true, if state space system is defined on file |
fileName | file where matrix [A, B; C, D] is stored |
matrixName | Name of the state space system matrix |
Name | Description |
---|---|
ok |
Name | Description |
---|---|
ss | Linear system in state space form |
poles | = true, to plot the poles (i.e. the eigenvalues) of ss |
zeros | = true, to plot the (invariant) zeros of ss |
defaultDiagram | Default diagram layout |
device | Properties of device where figure is shown |
Name | Description |
---|---|
system data definition | |
systemOnFile | true, if state space system is defined on file |
fileName | file where matrix [A, B; C, D] is stored |
system matrices | |
A[:, size(A, 1)] | |
B[size(A, 2), :] | |
C[:, size(A, 1)] | |
D[size(C, 1), size(B, 2)] |
Name | Description |
---|---|
ok |
Name | Description |
---|---|
systemOnFile | true, if state space system is defined on file |
fileName | file where matrix [A, B; C, D] is stored |
A[:, size(A, 1)] | |
B[size(A, 2), :] | |
C[:, size(A, 1)] | |
D[size(C, 1), size(B, 2)] | |
iu | index of inout |
iy | index of output |
Name | Description |
---|---|
ok |
Computes the impulse response of the system StateSpace sc = StateSpace(A=[-1,1;0,-2],B=[1, 0;0, 1],C=[1,0; 0,1],D=[0, 0; 0, 0]).
Name | Description |
---|---|
response | type of time response |
ss |
Computes the impulse response of the system StateSpace sc = StateSpace(A=[-1,1;0,-2],B=[1, 0;0, 1],C=[1,0; 0,1],D=[0, 0; 0, 0]).
Name | Description |
---|---|
ss |
Computes the initial condition response of the system StateSpace sc = StateSpace(A=[-1,1;0,-2],B=[1, 0;0, 1],C=[1,0; 0,1],D=[0, 0; 0, 0]) to the initial condition x0=[1;1].
Name | Description |
---|---|
ss |
Computes the ramp response of the system StateSpace sc = StateSpace(A=[-1,1;0,-2],B=[1, 0;0, 1],C=[1,0; 0,1],D=[0, 0; 0, 0]).
Name | Description |
---|---|
ss |
Computes and plots the step response
Name | Description |
---|---|
ss |
Computes the initial condition response of the system StateSpace sc = StateSpace(A=[-1,1;0,-2],B=[1, 0;0, 1],C=[1,0; 0,1],D=[0, 0; 0, 0]) to the initial condition x0=[1;1]. This example plts the output y and the states (x1, x2, x3) of a system with the input
where zk is an invariant zero of the system. Assuming appropriate initial conditions, the output of the system is forced to zero. It is demonstrated that the output can also be forced to zero by applying a transient unstable input. Although the output is zero, the states show transient and unstable behavior. In comparison, the outputs as an reaction of inputs with half or double frequency are not equal to zero.u(t) = uk*exp(zk*t)
Name | Description |
---|---|
system data definition | |
fileName | file where matrix [A, B; C, D] is stored |
matrixName | Name of the state space system matrix |
system matrices | |
A[:, :] | |
B[:, :] | |
C[:, :] | |
D[:, :] |
Name | Description |
---|---|
ok |
Name | Description |
---|---|
A[:, :] | |
B[:, :] | |
C[:, :] | |
D[:, :] | |
system data definition | |
fileName | file where matrix [A, B; C, D] is stored |
matrixName | Name of the state space system matrix |
Name | Description |
---|---|
ok |