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
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
- In this: publication
- By this: publisher
- In this Subject: Computer Science
- By this author: Olkin J.A. ; Titterton Jr. P.J.

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