WOLFRAM SYSTEM MODELER

# StateSpace

Discrete-time State Space block

# Wolfram Language

In[1]:=
`SystemModel["Modelica.Clocked.RealSignals.Periodic.StateSpace"]`
Out[1]:=

# Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

This block defines the state space representation of a discrete-time block with input vector u, output vector y and state vector x:

```x = A * previous(x) + B * u
y = C * previous(x) + D * u
```

where previous(x) is the value of the clocked state x at the previous clock tick. 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:
[x[1]]   [0.12  2.00] [previous(x[1])]   [2.0  7.0] [u[1]]
[    ] = [          ]*[              ] + [        ]*[    ]
[x[2]]   [3.00  1.50] [previous(x[2])]   [0.1  2.0] [u[2]]

[previous(x[1])]            [u[1]]
y[1]   = [0.1  2.0] * [              ] + [0  0] * [    ]
[previous(x[2])]            [u[2]]
```

# Parameters (6)

nin Value: size(B, 2) Type: Integer Description: Number of inputs Value: size(C, 1) Type: Integer Description: Number of outputs Value: Type: Real[:,size(A, 1)] Description: Matrix A of state space model Value: Type: Real[size(A, 1),:] Description: Matrix B of state space model Value: Type: Real[:,size(A, 1)] Description: Matrix C of state space model Value: zeros(size(C, 1), size(B, 2)) Type: Real[size(C, 1),size(B, 2)] Description: Matrix D of state space model

# Outputs (1)

x Type: Real[size(A, 1)] Description: State vector

# Connectors (2)

u Type: RealInput[nin] Description: Connector of clocked, Real input signals Type: RealOutput[nout] Description: Connector of clocked, Real output signals

# Revisions

Release Notes:

• August 13, 2012 by Bernhard Thiele:
Used the code from Blocks.Discrete.StateSpace and converted it into the Modelica 3.3 clocked equation style.