Tradeoffs and Triangles

The activity of optimization involves trade off analysis.  The goal is to improve performance or cost effectiveness, or both if possible.  Nowadays, we have some really sophisticated software tools that allow us to simulate the behavior of complex systems. Computational fluid dynamics, magnetic field simulations, thermal imaging, finite element analysis are a few of the amazing technologies that can now be engaged on desktop computers to conduct sophisticated analysis of performance at the click of a mouse button.

Simulation work that used to require mainframe computing power is now generally available as an add on module to 3D engineering graphics products.  Most of the major 3D engineering design products include animation features that allow the user to build and move the parts in space exactly as they will do when built.  This gives the designer enormous capacity to focus on issues in the design where several alternative solutions may exist.  There are even some intelligent software products that help guide the selection of components to help the designer facilitate the examination of alternative methods of solving certain mechanical problems.

Pretty cool.

But some of the stuff that’s really difficult to ‘automate’ is the stuff that requires human insight.  It kind of begs the question “what it is intelligence”. The area I am concerned with is tradeoff analysis.  And this area of engineering is one for which the world of computer software and ‘artifical intelligence’ has not been of much help.

Tradeoff analyses are normally calculations done  that attempt to examine how, in a given system, performance changes as the values of two competing attributes are altered.   So we look at two variables and assign the minimum and maximum values and look at how less of one and more of the other changes the outcomes in a particular system under examination.

But implicit within this system is the fact that only two variables can be examined at a time.  And, of course, the systems we deal with are much more complex.  The optimization of an electric motor consists of 22 variables, some simple values such as the diameter and length, some more complex having to do with magnetic materials and the many variable needed to describe the electromagnetic field of stator, for example.

So to get more out of the situation we need some different metaphors for looking at motion control and mechatronics applications.  Enter: the triangle.  We go from 2 variables to 3.  But we have a simplifying assumption that any one variable may be temporarily held constant in order to explore the other two.

I came up with a tradeoff analysis for Time, Torque and Inertia.  Published a few years ago in another magazine and briefly mentioned in one of my Design World articles a few months ago.  Basically, Time, Torque and Inertia all interact in very straightforward ways, but the point was to examine the hidden assumption that Inertia was fixed.  This is usually not strictly true, but instead we assume it to be true.  And this assumption prevents finding alternative solutions that may be very attractive.

So by using a triangle, we can create an analytical tool that actually helps us to think about and to find solutions, challenge hidden assumptions and produce better motion control.