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Technical Brief

# Fixed-Order Decoupling of Interval Plant Families

[+] Author and Article Information
Mostafa Negim

Department of Electrical Engineering,
Sharif University of Technology,
Tehran 11365-9363, Iran
e-mail: negim@ee.sharif.edu

Amin Nobakhti

Department of Electrical Engineering,
Sharif University of Technology,
Tehran 11365-9363, Iran
e-mail: nobakhti@sharif.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 14, 2015; final manuscript received August 27, 2016; published online October 17, 2016. Assoc. Editor: Ryozo Nagamune.

J. Dyn. Sys., Meas., Control 139(1), 014502 (Oct 17, 2016) (6 pages) Paper No: DS-15-1270; doi: 10.1115/1.4034747 History: Received June 14, 2015; Revised August 27, 2016

## Abstract

A method for the reduction of interactions in linear time invariant (LTI) multivariable uncertain systems is proposed. An $H∞$-norm metric is proposed for the assessment of interactions in interval uncertain multiple-input multiple-output (MIMO) plants. Based on this, a procedure for the design of fixed-order dynamic decoupling precompensators for MIMO plants with interval uncertainty is outlined which can be solved using efficient solvers such as cvx. The proposed methodology is used to develop a low-order robust multivariable controller for voltage and frequency control of an islanded distributed generation (DG) unit.

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## Figures

Fig. 1

RCDDR for uncompensated DG-R = [76, 760] Ω

Fig. 2

RCDDR for compensated DG-R = [76, 760] Ω. QP designed for R = 760 (col1 = V and col2 = f).

Fig. 3

RCDDR for R = [76, 760] Ω and ω for first column (DG system)

Fig. 4

RCDDR for R = [76, 760] Ω and ω for second column (DG system)

Fig. 5

Independent step response for DG compensated system in nominal resistance R = 76 Ω. QP is designed for R = 76 Ω.

Fig. 6

Dependent step response for DG compensated system in nominal resistance R = 76 Ω. QP is designed for R = 760 Ω.

Fig. 7

Independent step response for DG compensated system in nominal resistance R = 76 Ω. QP is designed for R = 760 Ω.

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