DDELSSM – Discrete state space model of a linear system with time delay

Block SymbolLicensing group: ADVANCED

Function Description
The DDELSSM block (Discrete State Space Model with time DELay) simulates behavior of a linear system with time delay $d e l$

$\begin{array}{rcl} x (k + 1) & = & A_{d} x (k) + B_{d} u (k - d), x (0) = x 0 \\ y (k) & = & C_{d} x (k) + D_{d} u (k), \end{array}$

where $k$ is the simulation step, $x (k) \in ℝ^{n}$ is the state vector, $x 0 \in ℝ^{n}$ is the initial value of the state vector, $u (k) \in ℝ^{m}$ is the input vector, $y (k) \in ℝ^{p}$ is the output vector. The matrix $A_{d} \in ℝ^{n \times n}$ is the system dynamics matrix, $B_{d} \in ℝ^{n \times m}$ is the input matrix, $C_{d} \in ℝ^{p \times n}$ is the output matrix and $D_{d} \in ℝ^{p \times m}$ is the direct transmission (feedthrough) matrix. Number of steps of the delay $d$ is the largest integer such that $d . T \leq d e l$ , where $T$ is the block execution period.

All matrices are specified in the same format as in Matlab, i.e. the whole matrix is placed in brackets, elements are entered by rows, elements of a row are separated by spaces (blanks), rows are separated by semicolons. The $x 0$ vector is a column, therefore the elements are separated by semicolons (each element is in a separate row).

During the real-time simulation, single simulation step of the above discrete state space model is computed in each execution time instant.

Inputs

R1	Reset signal. When $R1 = on$ , the state vector x is set to its initial value x0. The simulation continues on the falling edge of R1 (on $\to$ off).	Bool
HLD	Simulation output holds its value if HLD=on.	Bool
u1..u16	Simulated system inputs. First $m$ simulation inputs are used where $m$ is the number of columns of the matrix Bd.	Double (F64)

Outputs

iE	Block error code	Error
	0 .... O.K., the simulation runs correctly -213 . incompatibility of the state space model matrices dimensions xxx .. error code xxx of REXYGEN, see appendix C for details
y1..y16	Simulated system outputs. First $p$ simulation outputs are used where $p$ is the number of rows of the matrix Cd.	Double (F64)

Parameters

UD	Matrix Dd usage flag. If UD=offthen the Dd matrix is not used for simulation (simulation behaves as if the Dd matrix is zero).	Bool
del	Model time delay [s]. $↓$ 0.0	Double (F64)
Ad	Matrix ( $n \times n$ ) of the discrete linear system dynamics.	Double (F64)
Bd	Input matrix ( $n \times m$ ) of the discrete linear system.	Double (F64)
Cd	Output matrix ( $p \times n$ ) of the discrete linear system.	Double (F64)
Dd	Direct transmission (feedthrough) matrix ( $p \times m$ ) of the discrete linear system. The matrix is used only if the parameter UD=on. If UD=off, the dimensions of the Dd matrix are not checked.	Double (F64)
x0	Initial value of the state vector (of dimension $n$ ) of the discrete linear system.	Double (F64)

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