# 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

NameLabelDescriptionData TypeValid 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
1

mo_initType/choice2

Steady state initialization (derivatives of states are zero)

Number

0
1

mo_initType/choice3

Initialization with initial states

Number

0
1

mo_initType/choice4

Initialization with initial outputs (and steady state of the states if possible)

Number

0
1

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

NameLabelDescriptionData TypeValid Values

mo_u

u

u

Structure

mo_u/fixed

fixed

Cell of vectors

true
false

mo_u/start

start

Cell of vectors

mo_y

y

y

Structure

mo_y/fixed

fixed

Cell of vectors

true
false

mo_y/start

start

Cell of vectors

mo_x

x

x

Structure

mo_x/fixed

fixed

Cell of vectors

true
false

mo_x/start

start

Cell of vectors

## Ports

NameTypeDescriptionIO TypeNumber

u

implicit

Connector of Real input signals

input

1

y

implicit

Connector of Real output signals

output

1