$\mathcal{H}_{2}$ -Optimal Blending of Inputs and Outputs for Modal Control

Abstract

For many dynamical systems it is required to actively control individual modes, especially when these are lightly damped or even unstable. In order to achieve a maximum control performance, these systems are often augmented with a large number of control inputs and measurement outputs. To overcome the challenge of choosing an adequate combination of input and output signals for modal control, an H2-optimal isolation of modes via blending of inputs and outputs is proposed in this article. Enforcing an explicit mode decoupling, the approach enables controlling individual modes with simple single-input single-output controllers. A numerically efficient algorithm is derived for the joint computation of the interdependent input and output blending vectors. The effectiveness of the proposed approach is demonstrated by increasing the modal damping of an aeroelastic system.Index Terms-mode decoupling, modal control, over-actuated and over-sensed systems

Design and Optimization of an Aeroservoelastic Wind Tunnel Model

“…In order to damp the first wing bending mode, the modal control approach from [32] was used. The control approach suggests isolating the target mode(s) by blending control inputs and measurement outputs in an H 2 optimal way in order to enable a subsequent single-input single-output (SISO) controller design.…”

“…Here, the control inputs are the command signals for the servos driving the three trailing edge flaps and the measurement outputs are eight vertical accelerations measured at the outer part of the wing, as depicted in Figure 13. The input and output blending vectors k u ∈ R 3 and k y ∈ R 8 with |k u | = k y = 1 were derived for each model separately using the algorithm described in [32]. As SISO controller, a proportional-integral (PI) controller c(s) = λ k i s + k p was chosen.…”

“…To tackle this problem, promising control approaches as presented in [27] or [28] have proposed to blend control inputs or measurement outputs, and thereby reduce the control problem size. Through the combination of blending inputs and outputs with the objective of isolating and damping aeroelastic modes which dominate the structural loads, accordingly, blending-based control approaches have been applied, for example, in [29][30][31], where herein, the approach from [32] is used.…”

Structured Control Design for a Highly Flexible Flutter Demonstrator

“…To efficiently solve the nonlinear optimization problem Equation (4), the findings in [13,14] are applied to the objective function (4) giving…”

“…Hence, the original problem of maximizing the H 2 -norm is turned into a problem of maximizing the magnitude of the complex scalar k T y M(jω n )k u . Computing this magnitude according to [14] and factoring the real-valued blending vectors k y and k u , results in…”