Feedback - Feedforward

["William H. Cutler" <72734.3452@]

June 3, 1996

To the SD Community,

Feedback. Feedforward. I dont think the words per se are important. The
important issue is to get an accurate representation of the system. Of course,
in talking about that representation, it is important to have commonly
understood terms, which in their precise technical meaning are not misleadingly
different from the common meaning.

My thinking has been on both sides of the argument over the coffee cooling
example -- whether it is or is not an example of a feedback process. Most of
the time Ive been thinking "not" -- its just a simple unidirectional flow
process. But my final conclusion is that it is. In fact there are two circular
causal structures there. I arrived at this conclusion by very carefully
diagramming the system, being sure to make every quantity and relationship
explicitly visible.

My representation of a system is in terms of state variables, parameters,
functional blocks, and interfacing lines between blocks. Each block contains a
function connecting some subset of the state variables and parameters. The
lines represent the transfer of state variable values between pairs of
functional blocks.

The coffee cup cooling system has three functional blocks. They represent the
coffee cup, the room, and the thermal resistance between the two. The state
variables are TsubC, temperature of the coffee cup; TsubR, temperature of the
room; and Q, heat flow rate from coffee to room. Parameters are CsubC, heat
capacity of the coffee cup; CsubR, heat capacity of the room; and R, resistance
of the thermal resistance.

If we set up the system diagram with coffee cup on the left, room on the right,
and resistance in between, then the heat flow when cooling the coffee is left to
right.

At the interfaces between the functional blocks, I put a separate line for each
variable that is transferred. That makes the loops visible. I put an arrow on
the line showing the direction that the information is passed. At the interface
between coffee cup and resistance, there are two lines. The coffee cup passes
the value of TsubC to the resistance. The resistance passes the value of Q to
the coffee cup. That constitutes one of the two circular causal structures.
Likewise between resistance and room, TsubR is passed from room to resistance
and Q is passed from resistance to room. That constitutes the other circular
causal structure. The two loops are linked by the resistance since Q = (TsubC -
TsubR)
.

What would be an analogous system without feedback? To make it concrete, think
of water flowing out of an elevated tank through a pipe into a reservoir. If
the pipe is represented by a linear resistance term (head loss proportional to
flow rate) then the representation of draining the tank is exactly the same as
cooling the coffee. The tank will drain quickly at first, then more slowly as
water level in the tank lowers and reduces the head available to drive water
through the pipe. To make it an open-loop system (no feedback), replace the
pipe resistance with a constant-flow metering device (e. g. a fixed displacement
pump driven at a constant speed by a very large motor that completely overwhelms
the effect of water pressure). Now the tank drains at a rate determined by the
motor speed and there is no feedback.

Whats the point? What we call feedback is present when there is a closed
circular structure or loop in the path formed by passing information (state
variable values) among functional blocks. The "back" in feedback represents our
perception that information is kind of flowing up stream. In open loop causal
thinking (like the constant flow tank draining example), we perceive causality
as flowing from a to b to c (metering device runs at constant speed a, pulls
water out of tank at constant rate b, causes water level c to drop at constant
rate). If we add a controller that causes the value of water level c to control
the speed of pump a, then we call that feedback.

Feedforward is similar, except that we are sending information downstream ahead
of the normal progression of causal steps. I experience an example of this
almost every day near my home. To drive out of my neighborhood I have to cross
a railroad grade crossing. The track is elevated relative to the road so the
roadway goes sharply up to the track, then sharply down on the other side.
Driving over the grade crossing caused my car to pitch uncomfortably, so Ive
learned to compensate. If I let up on the brakes just before my front wheels
hit the rise, the nose of the car starts to come up, reducing the shock of
hitting the bump. This is a feed forward signal that I put into the system in
advance of a disturbance to reduce the magnitude of the response. Of course,
there is feedback at a higher level, because I compare my position with the
position of the bump to know when to insert the correction. At a still higher
level, there is feedback in the process which adjusted my behavior (learning) so
that I do something that makes my life more comfortable in coping with this
minor daily discomfort.

Regards, Bill Cutler
4114 Park Blvd.
Palo Alto, CA 94306, USA
72734.3452@compuserve.com
415-493-8715