Driving at Resonance Point of Multi-Degree-of-Freedom System by Decentralized Control

Abstract

A control method has been developed to always excite a multi-degree-of-freedom system efficiently at a resonance frequency. When an excitation point corresponds to a vibration detection point in the multi-degree-of-freedom system, a phase lag at a resonance frequency and a phase lead at an anti-resonance frequency alternately appear in the vibration characteristics, and the phase lag becomes 90° at all the resonance frequencies. Therefore, if a controller that has a phase lag of 90° and a constant gain in a wide frequency range is used, self-excited vibration is generated at all the resonance frequencies. The self-excited vibration controller can be expressed as the sum of the positive velocity feedback control with a high gain in a high frequency domain and the integral control of the displacement with a high gain in a low frequency domain. A local feedback controller for each actuator consists of a self-excited vibration controller, a saturation element that limits excitation force, and a negative velocity feedback controller that provides damping. A driving at a resonance point system using many actuators with local feedback control, that is, decentralized control, is excellent in its adaptability to the environment, in its extendibility, and in its fault tolerance. In addition, the self-excited vibration mode can be freely switched on by changing the frequency of the sine wave that causes the self-excited vibration.