James C. Akers

Modeling, identification, and feedback control of noise in an acoustic duct

Although active noise control has been a subject of interest for over 50 years, it has become feasible only with recent technological advances. This paper formulates the problem of noise control in a one-dimensional acoustic duct in a form that lends itself to the application of feedback control theory. In contrast to most of the literature on the subject which uses feedforward techniques, a feedback approach is used. Inconsistencies that appear in previous feedback control models are rectified, controllers are designed using precompensated linear quadratic Gaussian (LQG) synthesis, and experimental verification of the control designs is presented. The experimental results show a reduction of about 5-12 dB over a frequency range from 150-350 Hz.

Time-domain identification using ARMARKOV/Toeplitz models

Recursive time-domain identification techniques using a recursive least-squares algorithm with an ARMA representation have been used to identify the transfer function coefficients of SISO systems. In this paper we derive an alternative recursive time-domain identification technique that is based upon recursive identification of the Markov parameters of a system. We introduce the recursive ARMARKOV/Toeplitz identification algorithm which estimates the Markov parameters recursively from time-domain input-output data. This identification technique is based upon linear time-invariant finite-dimensional systems having an ARMARKOV representation that relates the current output of a system to past outputs as well as current and past inputs.

Modeling, identification and feedback control of noise in an acoustic duct

We consider a single-input, single-output plant involving one control actuator (speaker) and one control sensor (microphone). Additional speakers and microphones are used to provide disturbances and to assess closed-loop performance. To simplify matters, we confine our consideration in this paper to the case of a collocated sensor and actuator, that is, the control speaker and control microphone located at the same position along the duct. This configuration has been studied in the noise control literature under the name of tightly coupled monopole. In designing feedback controllers for the acoustic duct, we apply modern state space control techniques. The use of such techniques is necessitated by the high order of the identified model, which, for a 400 Hz modeling bandwidth in our experiment, involves 30 states. Feedback controllers designed for noise suppression were obtained by applying LQG synthesis with suitable precompensation to assure robustness to high frequency uncertainty.

An adaptive Toeplitz/ERA time-domain identification algorithm

Two recursive Toeplitz algorithms are used to estimate the Markov parameters of an LTI system from measurements of the inputs and outputs of a system and in turn use ERA to construct a minimal realization. The algorithms can be used either on-line or in an off-line batch mode. The recursive Toeplitz algorithms are shown to be stable and under the assumption of a persistent excitation the estimated Markov parameters converge to the actual Markov parameters. A numerical example of a second-order single-input single-output lightly damped system illustrates the stability and convergence properties of both algorithms. Finally, the algorithms are used to obtain a 20th-order realization of the dynamics of an acoustic duct.