Control Systems/System Representations
System Representations[edit | edit source]
This is a table of times when it is appropriate to use each different type of system representation:
|Linear, Time-Invariant, Distributed||no||yes||no|
|Linear, Time-Invariant, Lumped||yes||yes||yes|
General Description[edit | edit source]
These are the general external system descriptions. y is the system output, h is the system response characteristic, and x is the system input. In the time-variant cases, the general description is also known as the convolution description.
State-Space Equations[edit | edit source]
These are the state-space representations for a system. y is the system output, x is the internal system state, and u is the system input. The matrices A, B, C, and D are coefficient matrices.
[Analog State Equations]
These are the digital versions of the equations listed above. All the variables have the same meanings, except that the systems are digital.
[Digital State Equations]
Transfer Functions[edit | edit source]
These are the transfer function descriptions, obtained by using the Laplace Transform or the Z-Transform on the general system descriptions listed above. Y is the system output, H is the system transfer function, and X is the system input.
[Analog Transfer Function]
[Digital Transfer Function]
Transfer Matrix[edit | edit source]
This is the transfer matrix system description. This representation can be obtained by taking the Laplace or Z transforms of the state-space equations. In the SISO case, these equations reduce to the transfer function representations listed above. In the MIMO case, Y is the vector of system outputs, X is the vector of system inputs, and H is the transfer matrix that relates each input X to each output Y.
[Analog Transfer Matrix]
[Digital Transfer Matrix]