A Multiobjective ℋ∞ Control Problem: Model Matching and Disturbance Rejection

Model Matching Control for Binaural Reproduction over Loudspeakers

“…Note that Problem 1 is an infinite-dimensional optimization to find the solution as a transfer function, and therefore it cannot be solved effectively. In this subsection, the feedforward control problem is equivalently reduced to the synthesis of a feedback H ∞ controller [15], [16], which is solvable in a computationally tractable way [18].…”

“…In this paper, instead of series connection of the model of the desired sound field and the inversion of the reproduced sound field, we design a model matching controller in a lump. The design is reduced to output tracking control in the formulation of H ∞ control [15], [16]. In the method, low gain specification is imposed on the controller, which is important for improving the robustness against the uncertainties in the sound field.…”

Discrete-Time H∞ Model Matching Problem in Two Degrees of Freedom Control Structure

“…Gahinet & Apkarian (1994) re-derived the solution of the standard H ∞ OCP given by DGKF in the framework of LMI. In Gören & Akın (2002), an LMI-based solution of the unilateral H ∞ MMP is presented; also a solution of a multi-objective H ∞ control problem is obtained using the results given in Gahinet & Apkarian (1994). In all these studies on the standard H ∞ MMP, the controller structures that could be used in feedback configuration have not been considered in the formulation of the problem.…”

“…In all these studies on the standard H ∞ MMP, the controller structures that could be used in feedback configuration have not been considered in the formulation of the problem. However, one can say that the controller R(s) with property of stable and causal rational matrix, which is found in the form of a pre-compensator as a solution of the unilateral H ∞ MMP, can generally be established by dynamic state feedback (Kucera, 1992 andGören &Akın, 2002).…”

“…To consider the control structures for the system to be controlled in the formulation of the problem, the H ∞ MMP is defined as find a controller minimizing the H ∞ norm of T m (s)-T cl (s) in the specific control structure, such that the rational matrices T m (s) and T cl (s) are the model and the closed loop system transfer matrices respectively. In Gören (2003), the continuous-time H ∞ MMP in the 2DOF control structure is considered and the LMI-based solvability conditions of the problem are presented using the results given in Apkarian & Gören &Akın 2002. In recent years, there has been a rapid increase in the use of industrial digital controllers. With the complete continuous-time synthesis theory, a natural approach to discrete-time synthesis problem is to transform the continuous-time controller into discrete-time via the bilinear transformation.…”