Block Diagram Quick Reference

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Block Diagram Quick Reference
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Full Block Diagram SISO
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1 Quick Reference

Standard Block Diagram

where

  • LaTeX: y is the system output,
  • LaTeX: r is the reference input or desired output,
  • LaTeX: r' is the filtered reference input,
  • LaTeX: e is the error between LaTeX: y and LaTeX: r',
  • LaTeX: P is the plant,
  • LaTeX: H is the feedback sensor,
  • LaTeX: W is the prefilter used shape the reference input, and
  • LaTeX: K is the controller.


LaTeX: OL=PKH


where

Note that LaTeX: W is not part of the OL but is part of the tranfer fuction from LaTeX: y to LaTeX: r. See below.


LaTeX: CL=\frac{OL}{1+OL}=\frac{PKH}{1+PKH}


where


LaTeX: DR=1-CL=\frac{1+OL}{1+OL}-\frac{OL}{1+OL}=\frac{1}{1+OL}=\frac{1}{1+PKH}


where

Note that the LaTeX: DR is from LaTeX: y to LaTeX: d_o.

2 All Transfer Functions

Below is an equation relating every input to the output LaTeX: y

LaTeX: y=\frac{PKH}{1+PKH}Wr+\frac{P}{1+PKH}d_i+\frac{1}{1+PKH}d_o+\frac{-PKH}{1+PKH}n



The transfer function from r to y is

LaTeX: T_{ry}=\frac{PKH}{1+PKH}W


The transfer function from d_i to y is

LaTeX: T_{d_iy}=\frac{P}{1+PKH}


The transfer function from d_o to y is

LaTeX: T_{d_oy}=\frac{1}{1+PKH}


The transfer function from n to y is

LaTeX: T_{ny}=\frac{-PKH}{1+PKH}



For the system to be stable all transfer functions must be stable.