Frequency domain iterative tuning for active noise
and vibration control.
University of Southampton, School of Engineering Sciences,
In this thesis a new adaptive control method, called Iterative Tuning in the Frequency Domain
(FD-IT), is proposed for Active Noise and Vibration Control (ANVC). This approach is a gradient
based self-tuning method which completely relies on analysis of the frequency response of
system dynamics and the spectrum of signals.
The new method is based on a new gradient estimation theory in the frequency domain. In this
theory the gradient of the output spectrum with respect to controller parameters is expressed with
the frequency response of dynamics and the spectrum of signals. When the performance gradient
with respect to controller parameters can be expressed as some function of the signals’ spectrum,
it can be computed out completely in the frequency domain. Similar to audio compression, when
the system’s signals contain few frequencies, the computation of performance gradient can be
greatly simplified by making ”partial modelling” with respect to those frequencies.
According to the proposed theory, the new iterative tuning method, i.e., FD-IT, is developed
for ANVC problems with periodic disturbances. It can tune the feedback/feed-forward controllers
simultaneously with one experiment per iteration except some extra experiments for
initial tuning. It covers both Single Input Single Output (SISO) and Multiple Input Multiple
Output (MIMO) systems. Furthermore, it can be extended to nonlinear systems as well. Some
issues about the implementation of the iterative method are discussed. Through the comparison
with some other popular active control methods in ANVC, the advantages of the new method,
including: the flexibility in selecting controllers, the simplicity in control structure, and the
convenience in implementation, are emphasized.
The effectiveness and robustness of the proposed iterative tuning method are tested through
simulated SISO and MIMO Linear Time Invariant (LTI) systems. Two simulated nonlinearities
are used to illustrate the usefulness of the methods in nonlinear system as well. To show the
practicability, the linear and nonlinear FD-ITs are implemented in an air-duct system with a
PC-DSP based agent-architecture. All the results illustrate that FD-IT is an easy and effective
approach to solve ANVC problems with periodic disturbances.
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