Continuous State Space - MapleSim Help

Continuous State Space

Linear state space system

 Description The Continuous State Space (or State Space) block defines the relation between the input $u$ and the output $y$ in state space form: $\stackrel{.}{x}=Ax+Bu$ $y=Cx+\mathrm{D}u$ The input is a vector of length $\mathrm{\nu }$, the output is a vector of the length $\mathrm{ny}$, and $\mathrm{nx}$ is the number of states. Accordingly, $A$ has the dimension: $A\left(\mathrm{nx},\mathrm{nx}\right)$, $B$ has the dimension: $B\left(\mathrm{nx},\mathrm{\nu }\right)$, $C$ has the dimension: $C\left(\mathrm{ny},\mathrm{nx}\right)$, $\mathrm{D}$ has the dimension: $\mathrm{D}\left(\mathrm{ny},\mathrm{\nu }\right)$ The dimensions of the state-space matrices specified in parameters $A$, $B$, $C$, and $\mathrm{D}$ need to be adjusted according to the number of inputs that you provide. To change the dimensions of a matrix in a parameter field, right-click (Control-click for Mac) the parameter field and select Edit Matrix Dimensions. You can then specify the number of rows and columns to include in the matrix. Note: The context menu operation for setting the matrix dimension is not available if the parameter field is blank. In this case, you must enter a matrix as a list of lists, for example, [[1,2],[3,4]].
 Equations $\stackrel{.}{x}=Ax+Bu$ $y=Cx+\mathrm{D}u$

Connections

 Name Description Modelica ID $u$ Real input signals u $y$ Real output signals y

Parameters

General Parameters

 Name Default Units Description Modelica ID A $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ Matrix A of state space model A B $\left[\begin{array}{c}1\\ 1\end{array}\right]$ Matrix B of state space model B C $\left[\begin{array}{cc}1& 1\end{array}\right]$ Matrix C of state space model C D * Matrix D of state space model D Initial Values No initialization Type of initialization initType ${x}_{0}$ $\mathrm{zeros}\left(\mathrm{nx}\right)$ Initial or guess values of states x_start ${y}_{0}$ $\mathrm{zeros}\left(\mathrm{ny}\right)$ Initial values of outputs (remaining states are in steady state if possible) y_start

* $\mathrm{zeros}\left(\mathrm{size}\left(C,1\right),\mathrm{size}\left(B,2\right)\right)$

 Modelica Standard Library The component described in this topic is from the Modelica Standard Library. To view the original documentation, which includes author and copyright information, click here.