Seminars

Coordinate coupling raises serious numerical, analysis, and control design problems that grow with the size of the system. On the other hand, decoupled dynamic equations facilitate numerical computation, analysis, control design since each equation can be treated independently. Unfortunately, most practical, complex systems, are not naturally decoupled so developing accurate enough decoupled approximations is of interest.

  In this talk the issue of building such accurate decoupled approximations for second order systems is addressed by leveraging concepts from robust control theory. For this purpose, first a parameter dependent decoupled approximation model is constructed for an original system that is coupled. System gains (e.g. energy gain, peak to peak gain) are used to characterize the approximation error between time responses of the coupled system and its decoupled approximation. A key advantage of system gains is that they characterize the approximation error in time domain over large classes of physically and theoretically relevant signals (e.g. finite energy/finite peak signals). Then some system parameters (e.g. damping, stiffness coefficients) are selected using stochastic optimization to design the original system such that the approximation error is minimized. Effectively, the physical system is designed to provide a decoupled approximation model that guarantees accurate approximation for an entire class of signals. This is a major advantage for many practical applications when perturbation signals can be described only in terms of limited features.

  Since these ideas originated from a long standing interest of the presenter in research in structural dynamics and control, examples that use tensegrity structures are included. These structures are designed to yield accurate decoupled linear models with respect to all signals of finite energy and finite peak. Further analysis corrects several misconceptions regarding decoupling, system properties, and control design.