Simultaneous frequency and depth adaptation of notch filter for controlling damped vibrations

Manufacturing demands have increased in recent years, requiring a tack time a few tens of milliseconds to assembly machines with vibrational modes of less than a couple of hundreds of Hz. For typical high-frequency range (approximately 800 Hz) vibrations, notch filters with a depth of 1.0 are successfully used for vibration suppression. However, low-frequency range (approximately 200 Hz) vibrations typically result from the viscoelasticity of couplings and cannot be compensated for using a typical notch filter with a depth of 1.0. In addition, the damping levels can change significantly depending on specific application types as well as load and environment conditions, which in turn makes pre-implementation, off-line tests impractical. Therefore, it is desired to identify in real-time the damping conditions and adjust the notch filter depth, as well as the center frequency of the notch filter. Many methods are available for estimating the center frequency and the damping ratio in real-time, but the well-known zero-vibration derivative (ZVD) method to estimate the damping ratio cannot be applied in real-time. This paper develops a new real-time method to adaptively change the notch filter depth, using the methods of random decrement and peak detection. Experiments on an actual industrial servo system are used to demonstrate that damped vibrations are successfully compensated for by the proposed method.