WOLFRAM SYSTEM MODELER
StateSpaceLinear state space system |
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Wolfram Language
In[1]:=
SystemModel["Modelica.Blocks.Continuous.StateSpace"]
Out[1]:=
Information
This information is part of the Modelica Standard Library maintained by the Modelica Association.
The State Space block defines the relation between the input u and the output y in state space form:
der(x) = A * x + B * u
y = C * x + D * u
The input is a vector of length nu, the output is a vector of length ny and nx is the number of states. Accordingly
A has the dimension: A(nx,nx), B has the dimension: B(nx,nu), C has the dimension: C(ny,nx), D has the dimension: D(ny,nu)
Example:
parameter: A = [0.12, 2;3, 1.5]
parameter: B = [2, 7;3, 1]
parameter: C = [0.1, 2]
parameter: D = zeros(ny,nu)
results in the following equations:
[der(x[1])] [0.12 2.00] [x[1]] [2.0 7.0] [u[1]]
[ ] = [ ]*[ ] + [ ]*[ ]
[der(x[2])] [3.00 1.50] [x[2]] [0.1 2.0] [u[2]]
[x[1]] [u[1]]
y[1] = [0.1 2.0] * [ ] + [0 0] * [ ]
[x[2]] [u[2]]
Parameters (9)
| nin |
Value: size(B, 2) Type: Integer Description: Number of inputs |
|---|---|
| nout |
Value: size(C, 1) Type: Integer Description: Number of outputs |
| A |
Value: [1, 0; 0, 1] Type: Real[:,size(A, 1)] Description: Matrix A of state space model (e.g., A=[1, 0; 0, 1]) |
| B |
Value: [1; 1] Type: Real[size(A, 1),:] Description: Matrix B of state space model (e.g., B=[1; 1]) |
| C |
Value: [1, 1] Type: Real[:,size(A, 1)] Description: Matrix C of state space model (e.g., C=[1, 1]) |
| D |
Value: zeros(size(C, 1), size(B, 2)) Type: Real[size(C, 1),size(B, 2)] Description: Matrix D of state space model |
| initType |
Value: Modelica.Blocks.Types.Init.NoInit Type: Init Description: Type of initialization (1: no init, 2: steady state, 3: initial state, 4: initial output) |
| x_start |
Value: zeros(nx) Type: Real[nx] Description: Initial or guess values of states |
| y_start |
Value: zeros(ny) Type: Real[ny] Description: Initial values of outputs (remaining states are in steady state if possible) |
Outputs (1)
| x |
Type: Real[size(A, 1)] Description: State vector |
|---|
Connectors (2)
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u |
Type: RealInput[nin] Description: Connector of Real input signals |
|---|---|---|
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y |
Type: RealOutput[nout] Description: Connector of Real output signals |