## Feedback

### Definitions

- Process lag
- time for the comparison to take place (slows down the control).
- Control lag
- time to actually make an adjustment.
- Dead time
- time for the control to first start changing something.

The following a is general discussion of feedback in the context of collecting images in SPM. Feedback in SPM is an example of control. Other examples include thermostats or the cruise control in your car.

A process control loop regulates some dynamic (changing in time) variable in a process.

Basically the way this works is that we input some set point and then the “controller” compares the value to the set point and tries to adjust it back to the set point. There are lots of ways to make the comparisons and lots of ways to make the adjustment. Only adjust one parameter.

To measure the 'error' we can simply measure the actual value (b) and the compare it to the set point (r)

e = r - b

where e is the error.

More often the error is expressed as a percent of the possible measurement range (the span):

Where | Is the |
---|---|

c_{p} |
measured value as a percent of the measurement range |

c | actual measured value |

c_{min} |
maximum measured value |

c_{max} |
minimum measured value |

**SO** to get the error expressed as a percent of the possible measurement range (the span):

Where | Is the |
---|---|

e_{p} |
error as a percent of the span |

r | set point |

b | actual measured value |

b_{max} |
maximum measured value |

b_{min} |
minimum measured value |

**OR**: More often the error is expressed as a percent of the possible control range which might be less than the full measurement range (the span):

Where | Is the |
---|---|

p | controller output as % of full scale |

u | value of the output |

_{umin} |
maximum value of controlling parameter |

_{umax} |
minimum value of controlling parameter |