USING SEMIDEFINITE PROGRAMMING FOR MULTI-CONSTRAINED H-2 CONTROLLER-DESIGN IN ACTIVE NOISE AND VIBRATION CONTROL

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 SD P iteration requires calculating a primal and dual search direction an d minimizing the cost function along the plane defined by these search directions. The primal direction requires solving a least squares pro blem whose normal equation matrix is composed of a block-Toeplitz port ion 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 S DP structured matrices. As an example, we design controllers which exp lore the optimal tradeoff between in-band residual and out-of-band enh ancement of acoustic radiation from a (mathematically modeled) submerg ed spherical shell, while simultaneously constraining two sensitivity measures. For this example we show that significant reduction in out-o f-band enhancement is possible with only minor in-band penalties.