Active Attenuation of Periodic Vibration in Nonlinear Systems Using an Adaptive Harmonic Controller

Abstract

The article describes a nonlinear adaptive controller for the attenuation of harmonic disturbances in nonlinear systems. The steepest descent algorithm is used to adapt the controller coefficients and synthesize the optimum periodic waveform at the input of the nonlinear system, giving the best attenuation of the disturbance. A simple frequencydomain model of the system is required to implement the steepest descent approach. The scheme is particularly applicable where the secondary actuator used for active vibration control is a nonlinear device such as a magnetostrictive actuator. Simulation studies show that an adaptive scheme of this type is robust to the choice of frequency-domain model when the nonlinearity is hysteretic, but much more sensitive when the nonlinearity is a saturation function. A real-time adaptive harmonic controller has been built and used to control the motion of a magnetostrictive actuator. With dc and 7 harmonics under control the system was able to overcome the inherent nonlinearity of the actuator at fundamental frequencies in excess of 3 kHz.

Modeling active vibration control of a geared rotor system

“…Even though the gear vibration and sound generation phenomenon is quite complex, the highly deterministic, tonal character of the gear signature makes the problem a likely candidate for resolving via active control application. This is evident from recent interest that led to several active gear vibration control studies [3][4][5][6][7][8][9]. 3 Author to whom any correspondence should be addressed.…”

“…Later, Chen and Brennan [5] proposed an alternate active control scheme that used three magnetostrictive actuators mounted directly onto the side of one of the gears in order to generate circumferential forces for suppressing steady-state torsional vibrations. The controller implemented was based on a frequency domain adaptive harmonic controller previously designed for nonlinear systems [6] even though it may be applicable to cases with multiple-harmonic responses. Their experimental results yielded about 7 dB of reduction in gear angular vibrations at the tooth meshing frequencies between 150 and 350 Hz.…”

Active control of nonlinear systems

“…Intuitively such a control system will be stable provided the nonlinear interaction terms are not larger than the linear interaction terms, although this condition cannot be guaranteed even for simple forms of nonlinearity such as the saturation function. 12 When the subsonic compressed air source is used as the secondary actuator in an active control system, it presents an interesting control challenge, which can be understood by referring back to Eq. (1).…”

Adaptive control of tonal disturbance in mechanical systems with nonlinear damping

“…Nonlinear controllers are thus required for the control of a tone in these forms of nonlinearity, because the plant must be driven with a nonsinusoidal input to control the sinusoidal response – see, for example, Sutton and Elliott (1995). The response of a system with cubic damping to a sinusoidal excitation is, however, mainly sinusoidal (Lang et al., 2009; Laalej et al., 2012; Ghandchi Tehrani and Elliott, 2014; Elliott et al., 2015).…”