State-Space
Creates a linear dynamic object defined in the state space.
blockType: StateSpace
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Path in the library: |
Description
The block State-Space implements a system whose behaviour is defined as:
,
,
,
where
-
- is the state vector, the elements of which are called the states of the system;
-
- control vector;
-
- output vector;
-
- initial condition of the state vector.
The matrices , , and can be specified as either sparse matrices or dense matrices. The matrix coefficients should have the following characteristics:
-
- the system matrix to , where is the number of states;
-
- control matrix to , where is the number of inputs;
-
- output matrix to , where is the number of output data;
-
- direct communication matrix to .
The block has one input port and one output port. The number of rows in the matrix or is the same as the width of the output port. The number of columns in the matrix or matches the width of the input port. If you want to model an autonomous linear system without input data, set the matrices or to empty. In this case, the block acts as a block with no input port and one output port and realises the following system:
,
,
.
Ports
Output
#
OUT_1
—
output signal
scalar | vector
Details
A real output vector whose width is equal to the number of rows in the matrices or .
| Data types |
|
| Complex numbers support |
No |
Input
#
IN_1
—
input signal
scalar | vector
Details
A real input vector where the width is equal to the number of columns in the matrices or .
| Data types |
|
| Complex numbers support |
No |
Parameters
Main
# A — system matrix, A
Details
Specify a matrix of dimension to , where is the number of states.
| Default value |
|
| Program usage name |
|
| Tunable |
Yes |
| Evaluatable |
Yes |
# B — control matrix, B
Details
Specify a matrix of dimension by , where is the number of states and is the number of inputs.
| Default value |
|
| Program usage name |
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| Tunable |
Yes |
| Evaluatable |
Yes |
# C — output matrix, C
Details
Specify a matrix of dimension by , where is the number of outputs and is the number of states.
| Default value |
|
| Program usage name |
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| Tunable |
Yes |
| Evaluatable |
Yes |
# D — direct coupling matrix, D
Details
Specify a matrix of dimension by , where is the number of output data and is the number of input data.
| Default value |
|
| Program usage name |
|
| Tunable |
Yes |
| Evaluatable |
Yes |
# Initial conditions — initial state vector
Details
Initial state vector.
| Default value |
|
| Program usage name |
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| Tunable |
Yes |
| Evaluatable |
Yes |