StateSpace
Linear state space system
Library
Modelica/Blocks/Continuous
Description
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
| Name | Label | Description | Data Type | Valid Values |
|---|---|---|---|---|
mo_A | A | Matrix A of state space model (e.g., A=[1, 0; 0, 1]) | Matrix | |
mo_B | B | Matrix B of state space model (e.g., B=[1; 1]) | Matrix | |
mo_C | C | Matrix C of state space model (e.g., C=[1, 1]) | Matrix | |
mo_D | D | Matrix D of state space model | Matrix | |
mo_initType | initType | Type of initialization (1: no init, 2: steady state, 3: initial state, 4: initial output) | Structure | |
mo_initType/choice1 | No initialization (start values are used as guess values with fixed=false) | Number | 0 | |
mo_initType/choice2 | Steady state initialization (derivatives of states are zero) | Number | 0 | |
mo_initType/choice3 | Initialization with initial states | Number | 0 | |
mo_initType/choice4 | Initialization with initial outputs (and steady state of the states if possible) | Number | 0 | |
mo_x_start | x_start | Initial or guess values of states | Vector | |
mo_y_start | y_start | Initial values of outputs (remaining states are in steady state if possible) | Vector | |
mo_nin | nin | Number of inputs | Scalar | |
mo_nout | nout | Number of outputs | Scalar | |
mo_nx | nx | number of states | Scalar | |
mo_ny | ny | number of outputs | Scalar |
| Name | Label | Description | Data Type | Valid Values |
|---|---|---|---|---|
mo_u | u | u | Structure | |
mo_u/fixed | fixed | Cell of vectors | true | |
mo_u/start | start | Cell of vectors | ||
mo_y | y | y | Structure | |
mo_y/fixed | fixed | Cell of vectors | true | |
mo_y/start | start | Cell of vectors | ||
mo_x | x | x | Structure | |
mo_x/fixed | fixed | Cell of vectors | true | |
mo_x/start | start | Cell of vectors |
Ports
| Name | Type | Description | IO Type | Number |
|---|---|---|---|---|
u | implicit | Connector of Real input signals | input | 1 |
y | implicit | Connector of Real output signals | output | 1 |