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 std::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 std::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>
 
  <SIMULATION>
    <Timing TStart="0" TEnd="11.0"/>
    <Integrator Method="RK45_i" NumCores="1" LogStates="1" UseRSSNorm="0">
      <StepControl StepMax="0.002" StepMin="0.00000001" AbsTol="1e-3" RelTol="1e-3"/>
    </Integrator>
    
  </SIMULATION>
 
<OBSERVERS>
    <FileOutput TOutput="0, 0:1:10, 30" Select="objects:all"/>
  </OBSERVERS>
</Contents>

This SimObject is referred to as Math/LinearSystem