Iterative design for active control of fluid flow

This paper considers iterative controller design for planar Poiseuille flow by model unfalsification and controller redesign. The main contribution is to show that model-unfalsification-based iterative design can be useful in flow control problems. The a priori knowledge of the dynamics of the sampled system is obtained from the analytic approximation of the Navier-Stokes equations by a Galerkin method. Pole-positions, expected model orders and feasible dynamic variations are valuable prior knowledge which can be taken into account in the uncertainty-model unfalsification-based iterative design scheme developed

H/sub /spl infin// control of nonperiodic two-dimensional channel flow

This paper deals with finite-dimensional boundary control of the two-dimensional (2-D) flow between two infinite parallel planes. Surface transpiration along a few regularly spaced sections of the bottom wall is used to control the flow. Measurements from several discrete, suitably placed shear-stress sensors provide the feedback. Unlike other studies in this area, the flow is not assumed to be periodic, and spatially growing flows are considered. Using spatial discretization in the streamwise direction, frequency responses for a relevant part of the channel are obtained. A low-order model is fitted to these data and the modeling uncertainty is estimated. An H-infinity controller is designed to guarantee stability for the model set and to reduce the wall-shear stress at the channel wall. A nonlinear Navier-Stokes PDE solver was used to test the designs in the loop. The only assumption made in these simulations is that the flow is two dimensional. The results showed that, although the problem was linearized when designing the controller, the controller could significantly reduce fundamental 2-D disturbances in practice

(J,J⁰)-dissipative matrices and singular H^∞control

This paper deals with solving a class of H∞ control problems where the transfer matrix from the external input to the measured output is invertible at infinity while there is no assumption about the infinite and/or imaginary-axis zeros of the transfer matrix from the control input to the penalized output. Our approach is based on the chain-scattering representation and a newly proposed (J,J0)-dissipative factorization extending thus the well-known approach of H.~Kimura, while preserving its simplicity. We provide also a characterization of the set of controllers solving the given problem

Solutions to a class of nonstandard nonlinear H∞H_\infty control problems

This paper presents new solutions to certain nonstandard nonlinear $H_\infty$ control problems. We consider nonlinear affine plants whose measurement output is of dimension larger than the dimension of the external input. This problem is, under proper assumptions, transformed to the problem of stabilization by means of output injection, and solving a Hamilton-Jacobi partial differential inequality arising in singular $H_\infty$ state-feedback control. General sufficient solvability conditions are given. Explicit solutions are available in the local and semilocal cases. The former concerns a certain neighborhood of the origin in the closed loop state-space, while the latter assumes that the trajectories are restricted to a neighborhood of an invariant manifold. The issue of the controller order is addressed and a reduced order controller is obtained in the local case. A new generalization of the chain-scattering formalism provides a very useful framework for solving this problem

Nonstandard H_∞ control based on (J,J⁰)-dissipative factorization

This paper proposes a new approach to solving a class of nonstandard H∞ control problems. It deals with cases where the transfer matrix from the external input to the measurement output is assumed to be invertible at infinity and to have no zero on the imaginary axis. However, there is no assumption about the transfer matrix from the control input to the penalized output. Our approach is based on the chain-scattering representation and a newly proposed (J,J0)-dissipative factorization. It extends the well-known approach to the standard H∞ control based on the (J,J')-lossless factorization while preserving its simplicity. We provide also a parametrization of the set of controllers solving the given problem

Nonlinear coprime factorizations and parameterization of a class of stabilizing controllers

New definitions for right,left and doubly coprime factorizations for nonlinear, input-affine state-space systems are introduced. These definitions are based on the state-to-output stability introduced by Baramov and Kimura (1996) and the chain-scattering formalism. Sufficient conditions for the existence of these factorizations as well as local state-space formulas for factors are given. Finally, these results are applied to obtain a parameterized set of stabilizing controllers to a fairly broad class of plants, for transforming the original feedback control configuration into the open-loop model matching configuration and for thus extending the classical Youla-Kucera parametrization to nonlinear (local) cases