State-space model#

The State-space model block solves the system of equations recorded in the following form (1):

(1)#\[\begin{split} \begin{cases}\dot x=A\cdot x+ B\cdot u \\y=C\cdot x+D\cdot u\\x|_{t=t_o}=x_0 \end{cases} \end{split}\]

where:

x – vector of state variables (dimension n × 1);

\(\dot x\) – vector of derived state variables (dimension n × 1);

u – vector of input values (dimension m × 1);

y – vector of output values (dimension r × 1);

A (dimension n × n), B (dimension n × m), C (dimension r × n), D (dimension r × m) are matrices of factors under vectors.

The following features of input data generation should be taken into account when working with the block:

The number of state variables implemented in the block is determined by the dimension of matrix A and the number of rows of matrix B. Accordingly, the number of rows of matrix B should be equal to the dimension of matrix A;
The number of columns of matrix C should be equal to the number of state variables, i.e. the dimension of matrix A;
The number of input ports is specified in the field Number of input ports. The number of input ports corresponds to the number of input values and determines the length of the vector u. Thus, the number of columns of matrices B and D should be equal to the number of input ports;
Number of output portsis set in the field Number of output ports. The number of output ports corresponds to the number of output values and determines the length of vector y. Thus, the number of rows of matrices C and D should be equal to the number of input ports.

1. Properties#

Property	Default Value	Description	Units of measurement
Matrix A	<1.0;1.0>_<1.0;1.0>	-	-
Matrix B	<1.0>_<1.0>	-	-
Matrix C	<1.0;1.0>	-	-
Matrix D	<1.0>	-	-
Initial values of state variables	1.0; 1.0	-	-
Initial values of inputs	1.0	-	-
Sampling type: Fundamental project frequency decimation; Sample time; Sampling frequency	Fundamental project frequency decimation	-	-
Fundamental project frequency decimation, when selecting `Sampling type` - `Fundamental project frequency decimation`	1	-	-
Sample time, when selecting `Sampling type` - `Sample time`	0.05	-	s
Sampling frequency, when selecting `Sampling type` - `Sampling frequency`	20.0	-	Hz
Number of input ports	1	-	-
Number of output ports	1	-	-

Parameters	Input/Output	Description	Units of measurement	Port type
Input signal	Input	-	-	Automation
Output signal	Output	-	-	Automation

In order to see the connection capabilities of the block, you need to go to page Description of block ports