The Gestation and Birth of Bond
Graphs
by Prof. H.M. Paytner (c. 2000)
Bond graphs were born in their present form on April 24, 1959.
They were the direct outgrowth of my academic and professional experience during
two previous decades.
My MIT undergraduate and graduate training was centered on
hydroelectric engineering, as was my work at Puget Power and my 8 years teaching
in the Civil Engineering Department at MIT. This involved all aspects of the
typical power plant indicated below.
This training and experience in hydroelectric power actually
forced certain insights upon me, most particularly an awareness of the strong
analogies existing between:
TRANSMISSION (fluid pipes
& electric lines);
TRANSDUCTION (turbines &
generators);
CONTROL
(speed
governors & voltage regulators).
When these analogous devices were
reduced to equations for computer simulation, distinctions became completely
blurred.
Even before 1957 it was obvious that the above hydro+electric
plant necessarily involved two energy-converting transduction multiports: the
hydraulic turbine
converting fluid power
to rotary shaft power
and the electrical generator converting this shaft
power into polyphase AC
power. Moreover, the strict analogy between these two
devices holds right down to the local field- continuum level. Thus the
fluid vorticity
corresponds precisely to the current
density and the fluid
circulation to the magnetizing current, so that even the turbine blades correspond to the
generator pole pieces!
In dynamic consequence, both these highly-efficient components become 2-port
gyrators, [-GY-],with
parasitic losses. Common sense dictated that such compelling analogies implied
some underlying common generalization from which other beneficial
specializations might ensue.
My efforts were also strongly motivated by a preoccupation
with the logical philosophy underlying analogies in general. Such concerns were
much earlier formalized by the mathematician, Eliakim Hastings Moore, in the
following dictum:
"We lay down a fundamental
principle of
generalization by abstraction:
The existence of analogies between
central
features
of various theories implies the
existence
of
a general theory which underlies the
particular
theories and unifies them
with
respect
to those central features... "
In 1954, I moved over to the MIT ME department to establish
the first systems engineering subjects at MIT. It was this specific task which 5
years later produced bond graphs, drawing naturally upon all the attitudes and
experience indicated above. So it was on April 24, 1959, when I was to deliver
the lecture as posted below, I awoke that morning with the idea of the
0,1-junctions somehow planted in my head overnight ! Moreover the very symbols (
0,1 ) for KCL and KVL, respectively, made direct the correspondence between
circuit duality and logical duality. (The limited use of these 3-ports in the
hydro plant BG above hardly does justice to their role in rendering BGs a
complete and formal discipline.)
The Birth of 0 & 1
As mentioned above, it
was at this same Case lecture that the two ideal energy junctions were presented
publicly for the first time. Shown below were 3 sketch sheets prepared on that
morning of April 24, 1959, which were then dittoed and handed out to the
audience as well as transcribed to the blackboard during the
presentation.
Several things should
be noted from these pages. First both noncausal and causal forms of the
0-junction and the 1-junction were given. While the concept is acausal, the
causal forms are radical generalizations of KCL & KVL both within and
without electrical circuitry. It is the causal stroke (invented even before 0
& 1) which yields the new view of state determinism and Hamiltonian
dominance. Few EEs had ever made use of H(p,q).
I can't really remember
why the curious word "chemergetics" was coined but remember that "bond graphs"
would have been equally strange.
But also note the
iconography used to express unfamiliar causality in terms of gender
!
Besides promptly teaching this new system to my 2.751 and
2.752 students, it was first published in 1960 via an evolving series of folio
signatures made available to students and others. This material was then
re-gathered into the 1961 MIT Press book Analysis and Design of Engineering Systems.
However, it took nearly 20 more years before BGs became widely
known and employed. A few individuals were primarily responsible for this
promotion, most notably among others, Dean
Karnopp, Ronald Rosenberg, Jean Thoma and the late
Jan van Dixhoorn.
Jan made BGs familiar to
all parts of Europe while Jean has carried the Gospel to all parts of the Globe.As a result of this
effort many BG books and papers have been published and numerous groups are
actively involved with BGs throughout the world. All these can be located via
the links below.