H_{2} Design of Decoupled Control Systems Based on Directional Interpolations

Journal of Electrical Engineering and Technology.
2013.
Nov,
8(6):
1551-1558

- Received : March 14, 2013
- Accepted : June 04, 2013
- Published : November 01, 2013

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1. Introduction

One important characteristic of the multivariable systems is coupling interactions between input and output variables. Efforts to eliminate these interactions lead to finding controllers that make the transfer matrix from the inputs to the outputs diagonal. Once a closed loop system is decoupled, engineers can exploit the well-established design methods of single-input-single-output control system for each channel. The existence condition of a decoupling controller is now well known. For two-degreeof- freedom (2DOF) configuration, Doseor and Gündes
[1]
and Lee and Bongiorno
[2
,
3]
show that a decoupling controller always exists if the plant is internally stabilizable. On the other hand, a decoupling controller of the 1DOF control system does not always exist. For 1DOF configuration, necessary and sufficient conditions for the existence of decoupling controllers are presented by
[4
,
5
,
6]
. While the existence condition of the decoupling controllers has been sufficiently studied, not many papers treat performance issues of decoupled systems. The robust stability problem of decoupling controllers is first addressed by Safonov and Chen
[7]
. They obtain the stabilizing controllers maximizing stability margin in the
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2. Decoupling Problem and its Solution

The model under consideration is shown in
Fig. 1.
The vectors
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3.H2Design of Decoupled Control Systems

In this section, we formulate an
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4. An Illustrative Example

As a brief example to show the procedures to obtain the optimal transfer matrix
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5. Conclusion and Discussion

Decoupling design of lineal multivariable control systems is treated for the generalized plant model within the
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Citing 'H_{2} Design of Decoupled Control Systems Based on Directional Interpolations
'

@article{ E1EEFQ_2013_v8n6_1551}
,title={H_{2} Design of Decoupled Control Systems Based on Directional Interpolations}
,volume={6}
, url={http://dx.doi.org/10.5370/JEET.2013.8.6.1551}, DOI={10.5370/JEET.2013.8.6.1551}
, number= {6}
, journal={Journal of Electrical Engineering and Technology}
, publisher={The Korean Institute of Electrical Engineers}
, author={Park, Kiheon
and
Kim, Jin-Geol}
, year={2013}
, month={Nov}