Mason's rule

From Wikipedia, the free encyclopedia

You have new messages (last change).

Mason's rule, or the Gain formula is a method of solving for the transfer function of a given control output. It is used frequently in Control theory. It can be determined by looking at a Signal-flow graph, or a Block diagram. The gain formula is as follows:

M = \frac{y_{out}}{y_{in}} = \sum_{k=1}^N \frac{M_k \Delta\ _k}{ \Delta\ }

where:

  • yin = input-node variable.
  • yout = output-node variable
  • M = gain between yin and yout
  • N = total number of forward paths between yin and yout
  • Mk = gain of the kth forward path between yin and yout
  • Δ = 1 - (the sum of the gains of every individual loop) + (the sum of the products of the gains of all possible combinations of two non-touching loops) - (the sum of the products of the gains of all possible combinations of three non-touching loops) + ... and so on and so forth.
  • Pmr = the gain product of the mth possible combination of r non-touching loops (1 ≤ r ≤ N ) (Two parts of a signal-flow graph are non-touching if they do not share a common node)
This article or section is in need of attention from an expert on the subject.
Please help recruit one or improve this article yourself. See the talk page for details.
Please consider using {{Expert-subject}} to associate this request with a WikiProject
Retrieved from "http://en.wikipedia.org../../../m/a/s/Mason%27s_rule.html"