Frequency domain iterative tuning for the control of nonlinear vibrations

A general gradient estimation method is proposed that relies on the computation of system dynamics and signals in the frequency domain. With the theory presented the computation of the gradient of an average linear quadratic (LQ) performance criterion can be simplified using only `partial-modelling¿ with respect a finite signals spectrum. Using gradient estimate a new iterative tuning (IT) method is presented for nonlinear active noise and vibration control (ANVC) problems. The most important novelty of the method is that it performs one experiment per iteration that makes it suitable for implementation as a self-tuning and adaptive controller. Apart from the reduced number of experiments, relative to time domain IFT methods, the new method has the added advantage of its suitability for enhanced disturbance rejection tuning in the frequency domain. The effectiveness of the method is demonstrated on physical laboratory hardware.