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

x(k + 1) = Adx(k) + Bdu(k d),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. Number of steps of the delay d is the largest integer such that d.T 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 real-time simulation, single simulation step of the above discrete state space model is computed in each execution time instant.



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).



Simulation output holds its value if HLD=on.



Simulated system inputs. First m simulation inputs are used where m is the number of columns of the matrix Bd.  0.0

Double (F64)



Block error code


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


Simulated system outputs. First p simulation outputs are used where p is the number of rows of the matrix Cd.

Double (F64)



Matrix Dd usage flag. If UD=offthen the Dd matrix is not used for simulation (simulation behaves as if the Dd matrix is zero).



Model time delay [s].   0.0 0.0

Double (F64)


Matrix (n × n) of the discrete linear system dynamics.

Double (F64)


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

Double (F64)


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

Double (F64)


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 (F64)


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

Double (F64)

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