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Discrete State Space

Discrete state space

Description

The Discrete State Space component defines the relation between the input signal, $u$, and the output signal, $y$, in the state space form

 $x=A\stackrel{^}{x}+Bu$ $y=C\stackrel{^}{x}+\mathrm{D}u$

where $\mathrm{pre}\left(x\right)$ is the value of the discrete state, $x,$at the previous sample time instant. The input is a vector of the length $\mathrm{ν}$, the output is a vector of length $\mathrm{ny}$, and $\mathrm{nx}$ is the number of states. Accordingly, the dimensions are as follows:

A($\mathrm{nx}$,$\mathrm{nx}$),

B($\mathrm{nx}$,$\mathrm{ν}$),

C($\mathrm{ny}$,$\mathrm{nx}$),

D($\mathrm{ny}$,$\mathrm{ν}$)

The Signal Size parameter allows the block to operate on a vector of signals rather than a single signal.

Connections

 Name Description $u$ Continuous input signal connection $y$ Continuous output signal connection

Parameters

 Symbol Default Units Description Modelica ID $A$ - - Matrix A of the state space model A $B$ - - Matrix B of the state space model B $C$ - - Matrix C of the state space model C $\mathrm{D}$ - - Matrix D of the state space model D Sample Period $0.1$ $s$ Sample period of the component samplePeriod ${T}_{0}$ $0$ $s$ First sample time instant startTime ${n}_{\mathbf{in}}$ - - Number of inputs n_in ${n}_{\mathrm{out}}$ - - Number of outputs n_out Signal Size $1$ - Dimension of input and output signals signalSize

Initial Conditions

 Symbol Units Description Modelica ID ${x}_{0}$ - State vector x(0)