blockStateSpace
Linear state space system
Extends from Interfaces.MIMO (Multiple Input Multiple Output continuous control block).
Information
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
| Type | Name | Default | Description |
|---|---|---|---|
| Real[:,size(A, 1)] | A | [1, 0; 0, 1] | Matrix A of state space model (e.g., A=[1, 0; 0, 1]) |
| Real[size(A, 1),:] | B | [1; 1] | Matrix B of state space model (e.g., B=[1; 1]) |
| Real[:,size(A, 1)] | C | [1, 1] | Matrix C of state space model (e.g., C=[1, 1]) |
| Real[size(C, 1),size(B, 2)] | D | zeros(size(C, 1), size(B, 2)) | Matrix D of state space model |
| Integer | nin (from MIMO) | 1 | Number of inputs |
| Integer | nout (from MIMO) | 1 | Number of outputs |
| Initialization | |||
| Modelica.Blocks.Types.Init | initType | Modelica.Blocks.Types.Init.NoInit | Type of initialization (1: no init, 2: steady state, 3: initial state, 4: initial output) |
| Real[nx] | x_start | zeros(nx) | Initial or guess values of states |
| Real[ny] | y_start | zeros(ny) | Initial values of outputs (remaining states are in steady state if possible) |
Connectors
| Type | Name | Default | Description |
|---|---|---|---|
| RealInput[nin] | u (from MIMO) | Connector of Real input signals | |
| RealOutput[nout] | y (from MIMO) | Connector of Real output signals |
Components
| Type | Name | Default | Description |
|---|---|---|---|
| Real[size(A, 1)] | x | State vector |