OPTIMAL-DESIGN OF SDOF ENVELOPE SYSTEMS FOR THE RESPONSES OF MDOF DYNAMIC-SYSTEMS

The concept of envelope system for a given dynamic system is proposed in this paper which refers to those systems whose module of transfer f unction in the whole range of frequency domain is always bigger than t hat of a given system. This concept opens a new way to study the probl ems of robust design and modelling for dynamic systems. The condition that an envelope system has to satisfy is rendered as the determinatio n of the positiveness of a real polynomial function and Sturm's sequen ce method is used to establish an easily implemented criterion for eva luating the positiveness of the polynomial in terms of its coefficient s. The optimization for the envelope system is expressed as the minimi zation of the 2-norm of its transfer function and simplex method is em ployed to search for the optimal solution. Two dynamic systems are use d to illustrate the optimal design for the envelope systems of some of their responses. (C) 1998 John Wiley & Sons, Ltd.