VIBRATION ANALYSIS AND SUPPRESSION CONTROL OF AN ELEVATOR STRING ACTUATED BY A PM SYNCHRONOUS SERVO MOTOR

Abstract This paper presents the vibration analysis and suppression control of a moving elevator string. A dynamic formulation is proposed first for the non-linear vibrations of the string with time-varying length and a weight attached at the lower end. The permanent magnet (PM) synchronous sevo motor is used as the actuator to drive the rotor. A set of non-linear, time-varying differential equations describing this system is derived by Hamilton's principle. Due to the winding of the string either on or off the rotor, the mass and inertia of the rotor are time-dependent. The Galerkin method is used with time-dependent basis functions to determine the approximate solutions. A variable structure control (VSC) scheme is applied to suppress the transient amplitudes of vibrations. The sliding surfaces are determined in terms of the errors between the system states and the ideal states of the string and the rotor. The numerical results show that the motion-induced vibrations of the moving string and the tracking performance of the rotor can be controlled effectively.