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 $del$
where $k$ is the simulation step, $x\left(k\right)\in {\mathbb{R}}^{n}$ is the state vector, $x0\in {\mathbb{R}}^{n}$ is the initial value of the state vector, $u\left(k\right)\in {\mathbb{R}}^{m}$ is the input vector, $y\left(k\right)\in {\mathbb{R}}^{p}$ is the output vector. The matrix ${A}_{d}\in {\mathbb{R}}^{n\times n}$ is the system dynamics matrix, ${B}_{d}\in {\mathbb{R}}^{n\times m}$ is the input matrix, ${C}_{d}\in {\mathbb{R}}^{p\times n}$ is the output matrix and ${D}_{d}\in {\mathbb{R}}^{p\times m}$ is the direct transmission (feedthrough) matrix. Number of steps of the delay $d$ is the largest integer such that $d.T\le del$, 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 $x0$ vector is a column, therefore the elements are separated by semicolons (each element is in a separate row).
During the realtime simulation, single simulation step of the above discrete state space model is computed in each execution time instant.
Inputs
R1  Reset signal. When $\mathtt{\text{R1}}=\mathtt{\text{on}}$, 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. $\odot $0.0  Double (F64) 
Outputs
iE  Block error code  Error 



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]. $\downarrow $0.0 $\odot $0.0  Double (F64) 
Ad  Matrix ($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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