Linear system

Linear time-invariant system.

Collaboration diagram for Linear system:

Implements a linear system with constant coefficients. The system is formulated as from the input \(u\) to the output \(y\) with the internal state \(x\).

\[\dot{x}=Ax+Bu,\\ y=Cx+Du\]

The size of the system state vector \(x\), the input \(u\) and the output \(y\) is derived from the sizes of the input matrices which define the system. The matrices are defined as a list of comma separated row vectors, which are in turn separated by the column separator ";".

Example configuration excerpt

<Lib
  LibName   = "fhsim_base"
  SimObject = "Math/LinearSystem"
  Name      = "SystemOne"
  A         = "0,1;-0.5,-2"
  B         = "0;1"
  C         = "1,0"
/>
...
<Connection
  SystemOne.In = "1"
/>
...
<InitialCondition
  SystemOne.State="10,5"
/>

The number of internal system states is N, the number of inputs M and the number of outputs K.

Input Ports

Name	Width	Description
In	M	The input signal \(u\)

Output Ports

Name	Width	Description
Out	K	\(y=Cx+Du\)

Configuration parameters

Name	Width	Description
A	NxN	System matrix
B	NxM	Gain matrix
C	KxN	Output matrix
D	KxM	Feedthrough matrix (Default: zero-matrix)

Initial conditions

Name	Width	Description
State	N	State vector initial conditions

Full example file

<Contents>
  <OBJECTS>
    <Lib
        LibName="base"
        SimObject="Math/LinearSystem" 
        Name="LinSys"
        A="2"
        B="1" 
        C="1"
    />
  </OBJECTS>
  
  <INTERCONNECTIONS>
    <Connection
        LinSys.In="5"
    />
  </INTERCONNECTIONS>
 
  <INITIALIZATION>
    <InitialCondition
    LinSys.State="0"
    />
  </INITIALIZATION>
 
  <INTEGRATION>
    <Engine
    IntegratorMethod="2"
    NumCores="1"
    TOutput="0, 0:1:10, 30"
    LogStates ="1"  
    stepsize ="0"
    HMax="0.002"
    HMin="0.00000001"
    AbsTol="1e-3" RelTol="1e-3"
    UseRSSNormInsteadOfInfNorm="0"
    FileOutput="objects:all"
    />
  </INTEGRATION>
</Contents>

This SimObject is referred to as Math/LinearSystem