Eetu, interesting diagrams
Some more input, this is from A Primer For Programmers, draft, BP, emphasis by me,
BP: Mon Nov 09, 1992
Suggestions for standard terminologyA function is a physical device with an output signal the magnitude of which can be
computed from the state of its input magnitudes. All functions are true mathematical
functions: that is, they may have multiple inputs (arguments) but they produce only one
output (value of the function given those arguments). Thus the term function refers both
to some physical element of the system and to the equivalent mathematical function that
describes the dependence of its output on its input(s) in terms of magnitudes.A generic control system consists of an input function, a comparator, and an output
function. The output of one function generates a variable that is an input to another
function. Such information-carrying variables inside the system are called signals. A
signal not only represents the value of the function, but serves to carry that value to
the input of another function in a different physical location. All signals have a single
measure, magnitude. The name of a signal identifies a pathway; the value of the signal
indicates the momentary magnitude of the signal carried unidirectionally by that pathway.The environment model
In the environment of a control system the variables are called quantities. The output of
the output function is measured in terms of an effect on a physical variable called the
output quantity. The output function in a model of a single control system interacting
with an environment is therefore a transducer: its input is a signal while its output is
a quantity. The output quantity is always defined so that its magnitude depends only on
the output function’s value: it is always a single variable. If it has multiple effects
in the environment, each of those effects must be separately indicated in a model of the
environment.The input to the control system is another physical variable called the input quantity.
The input function senses the state of the input quantity and converts it to a perceptual
signal. The input function is also a transducer in a single system-environment model; its
input is a physical quantity and its output is a signal. An input function may respond to
multiple input quantities.In the environment, there is a feedback link connecting the output quantity to the input
quantity. This link is called the environmental feedback function, or simply the feedback
function.Also in the environment there is a link through which independent environmental variables
called disturbing quantities act on the input quantity concurrently with the action of
the output quantity on the input quantity. Because the number and kind of disturbing
quantities is immaterial, it is customary, when modeling a single control system, to
represent all disturbing quantities and their individual links to the input quantity
as a single equivalent disturbance acting through a single equivalent disturbing function.The control system model
The perceptual signal generated by the input quantity enters a comparator; also entering
the comparator is a reference signal, an independent variable. Where possible, the signs
of various system constants are chosen so that the reference signal has a positive effect
on the comparator while the perceptual signal has a negative effect. The comparator is a
function with two arguments and a single value. The output value is represented by an
error signal, the magnitude of which is equal to the reference signal’s magnitude minus
the perceptual signal’s magnitude. The error signal enters the output function. Often, as
shorthand, we speak of subtracting one signal from another, or adding signals together.
What is meant is that the magnitudes are subtracted or added.
The system-environment diagram
sr
sp +| se
-----------> (fc)----------->
| - | CONTROL
(fi) (fo) SYSTEM
----------- | --------------------------- | -------------
qi <-----------(ff)<--------- qo ENVIRONMENT
^
|
(fd)
^
|
qd
DEFINITIONS:
Signals:
sp = perceptual signal
sr = reference signal
se = error signalFunctions:
fi = input function
fc = comparison function or comparator
fo = output function
ff = feedback function
fd = disturbance functionQuantities:
qi = input quantity
qo = output quantity
qd = disturbing quantityTHE CONTROL EQUATIONS:
System:
sp = fi(qi)
se = sr - spInterface transducers:
qo = fo(se)
sp = fi(qi)Environment:
qi = ff(qo) + fd(qd)Combined equations:
System: qo = fo(sr - fi(qi))
Env: qi = ff(qo) + fd(qd)
AM: I made some changes to the diagram, to make the adding function (fa) in the environment explicitly drawn, and varibles qi, qd and qf written next to “lines”, following the same convention as inside the control system. If the comparator gets a special box, all it does is subtract the sp from sr, so should an adder, as it adds qf and d. All the equations defined by Bill previously still hold, this is just a diagram change. Maybe I’d be happier if names qd and d would switch, though.
sr
sp +| se
----------->(fc )----------->
| - | CONTROL
(fi) (fo) SYSTEM
----------- | --------------------------- | -------------
qi | | ENVIRONMENT
| + |
(fa) <--------(ff)<-------------
^ + qf qo
d |
(fd)
^
qd |
AM: One of the interesting points Bill made is that there could be multiple input quantities entering the input function. We could call them x1, x2, x2, or we could call them qi1, qi2, qi3. If the perceptual signal p or sp is a function of those input quantities, then how do we call the hypothetical controlled variable in the Experimenter, that is a function of the same input quantities? I guess “controlled quantity”, or qc is ok? The general process of TCV is still the same, it is just switching up the names a bit.