February, 1997
Technology Update

Chaos Takes Practical Steps toward Applications

by Edward J. Kompass, Contributing Editor
Sidebar:
Nonlinear Has Advantages Over Standard
.Chaos theory is now being studied aggressively using very practical empirical methods. The results are extremely promising for control applications.

  Five years ago this spring, the first Conference on Chaos in Manufacturing was convened by Dick Morley (R. Morley Inc., Milford, N.H.) in Santa Fe, N.M. Mr. Morley chose this exotic location to attract speakers from the Santa Fe Institute (SFI), who would have to leave their offices for only a few hours to attend.

  SFI is a research haven for Nobelists from many disciplines, and a number of them had been studying the characteristics of complex nonlinear systems for some years when interest in chaos systems and chaos theory arose.

  Early Chaos conferences stemmed originally from Mr. Morley's success with the application of so-called "autonomous control agents" in place of detailed overall system simulations that include all control loop interactions. This latter system design technique is, of course, the current convention: Model the total system as completely as possible, including all dynamics and all cross-couplings, and negative feedback will take care of everything.

  A big problem with this conventional approach to control system design is that it relies on linear mathematics, and real systems always include nonlinearities, which are necessarily neglected. The models are mathematical, and nonlinear differential equations are generally not solvable. Thus, conventional designs work over limited regimes, and then only sometimes.

Never an exact fit

..Besides being extremely difficult and sometimes requiring the writing and testing of hundreds of pages of software code, such total system simulations can never represent the real system exactly.

  Based on studied observations by scientists of real-world complex systems in nature as diverse as plant growth, weather systems, and ant hills, it has become clear that nature's control systems are simplicity itself. They certainly do not depend on any overall invisible model that defines necessary behavior of individual "agents" (variable controllers?) for system direction or stability. Apparently, it is only necessary that individual variable controllers do their own local control, modified by simple rules about their relationships to other controllers' behaviors and the system goal. Thus birds flock, fishes school, and bees swarm.

  In Mr. Morley's original application, more than five years ago, seven truck body painting booths at General Motors became autonomous control agents that individually selected their next tasks by bid from a conveyor line of mixed body styles and color specifications. The result minimized paint changes in the several booths (a very expensive time and materials lost operation). The simple system replaced a simulation that ran to more than 500 pages of computer code with just a few pages and saved GM millions of dollars in time and paint.

  Recognizing this result as natural chaos control applied to manufacturing control, Mr. Morley decided to get the word out through these conferences.

Chaos, April 8-11

..The 5th Chaos Conference in Santa Fe, N.M., is set for April 8-11. It's highly recommended for control engineers who look to the future. Mr. Morley has also instituted East Coast conferences in the fall, and the second of these, late last September in Cambridge, Mass., produced some exciting accounts of practical successes with control of nonlinear systems through use of chaos principles.

In combination

..A summary of recent research results titled "Chaos in Combustion" was presented by Stuart Daw of Oak Ridge National Laboratory. Mr. Daw said that chaos is often observed as bounded, continuously unstable fluctuations resulting from dynamic nonlinearities.

  This random-like behavior presents a lack of clear patterns with traditional analysis tools, causing difficulties in prediction and control. New tools from chaos theory allow observation of nonlinear structure and control of chaotic instabilities. Using these tools, Mr. Daw has shown that pulse combustion can be controlled using very small feedback perturbations.

  Another paper, presented by Paul S. Linsay, described work done at MIT to prove chaos controllability by controlling a double pendulum, in which a free pendulum is hung at the end of a pulse-driven pendulum. When small driving pulses are regularly spaced, there appears to be no pulse frequency that will allow unchaotic behavior. But when the pulse frequency is adjusted dynamically to maintain simple harmonic motion at the driven fulcrum, with no other measurements, the double pendulum behaves as a single pendulum.

Nonlinear Has Advantages Over Standard


..Nonlinear dynamical feedback control has several advantages over standard linear feedback control, according to Paul S. Linsay:

  • The data is the model, there is no need to know the equations of motion for the system.
  • Data from one system variable is sufficient to build the model.
  • Nonlinear control is achieved by applying small perturbations at dynamically chosen times.
  • Control is robust, a 10 to 20 percent error in control parameters still gives good control.
  • It is possible to derive multiple control strategies from the same set of data, because of the underlying structure of chaotic dynamics.

Copyright© 1997 Reed Elsevier, Inc.  Control Engineering Feb 1, 1997

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