DSSM – Discrete state space model of a linear system

Block SymbolLicensing group: ADVANCED

Function Description
The DSSM block (Discrete State Space Model) simulates behavior of a linear system

\begin{array}{rcl} x (k + 1) & = & A_{d} x (k) + B_{d} u (k), 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.

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. $⊙$ 0.0	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
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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