DSSM – Discrete state space model of a linear system

Block SymbolLicensing group: ADVANCED
PIC

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

x(k + 1) = Adx(k) + Bdu(k),x(0) = x0 y(k) = Cdx(k) + Ddu(k),

where k is the simulation step, x(k) n is the state vector, x0 n is the initial value of the state vector, u(k) m is the input vector, y(k) p is the output vector. The matrix Ad n×n is the system dynamics matrix, Bd n×m is the input matrix, Cd p×n is the output matrix and Dd p×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 x0 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 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

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

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 × n) of the discrete linear system dynamics.

double

Bd

Input matrix (n × m) of the discrete linear system.

double

Cd

Output matrix (p × n) of the discrete linear system.

double

Dd

Direct transmission (feedthrough) matrix (p × 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

x0

Initial value of the state vector (of dimension n) of the discrete linear system.

double

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