1 Quick Reference
- is the system output,
- is the reference input or desired output,
- is the filtered reference input,
- is the error between and ,
- is the plant,
- is the feedback sensor,
- is the prefilter used shape the reference input, and
- is the controller.
- is the open loop transfer function
Note that is not part of the OL but is part of the tranfer fuction from to . See below.
- is the closed loop transfer function
- is the disturbance rejection transfer function
Note that the is from to .
2 All Transfer Functions
Below is an equation relating every input to the output
The transfer function from r to y is
The transfer function from d_i to y is
The transfer function from d_o to y is
The transfer function from n to y is
For the system to be stable all transfer functions must be stable.