WOLFRAM SYSTEMMODELER

StateSpace

Linear state space system

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)

u

Type: RealInput[nin]

Description: Connector of Real input signals

y

Type: RealOutput[nout]

Description: Connector of Real output signals