Microsoft Word - kr-syn-nest-nabl07.DOC

1. Introduction During recent years the speed-gradient algorithms developed in control engineering area [1,2] have been applied intensively to control of oscillatory motion and particularly to control of vibration units. Among problems solved by speed-gradient approach are control of vibration units in start-up modes (swing-up and passage through resonance) [ 3-5], synchronization [6-8], etc. One of the main arising problems is keeping stable synchronous working mode in order to achieve maximum working amplitude of the platform vibrations. Additional opportunities for development of vibration equipment, especially for vibrational transportation of materials can be provided by using multiple synchronous modes. It keeps constant the ratio of average velocities and/or phases of vibroactuators. Unlike simple synchronization modes which can arise spontaneously , stable multiple synchronous mode can only be achieved by means of advanced control systems. In this paper an algorithm of multiple synchronization of two-rotor vibration unit with time-varying payload is proposed. The performance of the proposed system is analyzed by computer simulation for model of the 2-rotor vibration setup consisting of two rotors driven by DC motors and a rigid platform mounted on an unmovable base. A time-varying payload attached to a platform allows one to study dynamics of material processing. Additional problem arises owing to in-completeness of measurements: only rotor phases are available for measurement. To solve this problem an observer (state estimator) is introduced into the system structure.