THE ERROR-CONTROLLED REGULATOR 



12/5 



and the information available for regulatory purposes is whatever 

 survives the coding imposed by its passage through T (S.8/5). 



Sometimes the information available to R is forced to take an even 

 longer route, so that R is affected only by the actual effect at E. 

 The diagram of immediate effects is then 



and we have the basic form of the simple "error-controlled servo- 

 mechanism" or "closed loop regulator", with its well-known 

 feedback from E to R. The reader should appreciate that this form 

 differs from that of the basic formulation (S.11/4) only in that the 

 information about D gets to R by the longer route 



Again, the information available to R is only such as survives the 

 transmission through T and E. 



This form is of the greatest importance and widest applicability. 

 The remainder of the book will be devoted to it. (The other cases 

 are essentially simpler and do not need so much consideration.) 



12/5. A fundamental property of the error-controlled regulator is 

 that it cannot be perfect in the sense of S.l 1/3. 



Suppose we attempt to formulate the error-controlled system by 

 the method used in S.l 1/3 and 4. We take a table of double entry, 

 with D and R determining an outcome in E. Each column 

 has a variety equal to that of D. What is new is that the rules must 

 be modified. Whereas previously D made a selection (a particular 

 disturbance), then R, and thus E was determined, the play now is 

 that after Z)'s initial selection, R must take a value that is a deter- 

 minate function of the outcome E (for R is er/w-controlled). It 

 is easily shown that with these conditions E's variety will be as large 

 as D's — i.e. R can achieve no regulation, no matter how R is con- 

 structed (i.e. no matter what transformation is used to turn £"s value to 

 an i?-value). 



If the formal proof is not required, a simpler line of reasoning can 

 show why this must be so. As we saw, R gets its information 



223 



