Using Semi-Definite Programming for Multi-Constrained H_2Controller Design in Active Noise and Vibration Control

Authors: Olkin J.A.; Titterton Jr. P.J.

Source: The Journal of VLSI Signal Processing, Volume 14, Number 1, 1996 , pp. 57-66(10)

Publisher: Springer

Buy & download fulltext article:

Price: $47.00 plus tax (Refund Policy)

Abstract:

We consider the practical design of linear controllers to meet a given set of H_2 specifications. The Q-parametrization reduces the problem to a quadratic minimization subject to multiple quadratic constraints, which we solve using semi-definite programming (SDP) methods. Each SDP iteration requires calculating a primal and dual search direction and minimizing the cost function along the plane defined by these search directions. The primal direction requires solving a least squares problem whose normal equation matrix is composed of a block-Toeplitz portion plus other structured matrices. We make use of Kronecker products and FFT's to greatly reduce the calculation. The dual search direction and plane search are accelerated by low-rank representations of the SDP structured matrices.

As an example, we design controllers which explore the optimal tradeoff between in-band residual and out-of-band enhancement of acoustic radiation from a (mathematically modeled) submerged spherical shell, while simultaneously constraining two sensitivity measures. For this example we show that significant reduction in out-of-band enhancement is possible with only minor in-band penalties.

Language: English

Document Type: Regular paper

Affiliations: 1: Applied Control and Signal Processing Group, SRI International, Menlo Park, CA 94025

Publication date: 1996-01-01