An optimal H 2 decoupling design for non-square plant systems based on the two-degree-of-freedom standard model

Abstract

We obtain an optimal 2 H decoupling controller for rectangular plants in a standard twodegree-of-freedom controller configuration model. The class of all stabilizing and decoupling loop controllers is parameterized in terms of free diagonal parameter matrices. We determined the optimal decoupling controller from these free parameters. Inner-outer factorization and the Khatri-Rao product expression for the vector operation to a diagonal matrix are the key steps in obtaining the 2 H optimal solution. We provide a compact set of assumptions to assure the existence of the optimal solution.

Decoupling Controller Design for H∞Performance Condition

“…Second, since is a diagonal matrix, controller becomes from (1). If we denote the -th column vector of as , we can simplify as (9) .…”

“…It is shown in [15] (9). The next section provides an example for the design of a decoupling controller that satisfies performance conditions.…”

“…The current study provides a systematic approach for the design of decoupling controllers. Papers [7][8][9] were conducted to study the design of decoupling controllers in the generalized plant model. Park and Choi [10] recently proposed a set of necessary and sufficient conditions for the existence of decoupling controllers in the generalized plant model.…”

Online Tuning of Two Degrees of Freedom Fractional Order Control Loops

“…Araki and Taguchi have presented important results about 2DOF structure with proportional-integral-derivative (PID) controller for tutorial purpose, including equivalent transformations and various explanations [4]. Many design studies of 2DOF control loop with PID (2DOF-PID) were already studied in the literature [5][6][7].…”