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Technical Briefs

Design of H Loop-Shaping Controller for LTI System With Input Saturation: Polytopic Gain Scheduled Approach

[+] Author and Article Information
S. Patra

Department of Electrical Engineering, Indian Institute of Technology, Kharagpur 721302, Indiasouravpat@gmail.com

S. Sen

Department of Electrical Engineering, Indian Institute of Technology, Kharagpur 721302, Indiassen@ee.iitkgp.ernet.in

G. Ray1

Department of Electrical Engineering, Indian Institute of Technology, Kharagpur 721302, Indiagray@ee.iitkgp.ernet.in

1

Corresponding author.

J. Dyn. Sys., Meas., Control 133(1), 014506 (Dec 02, 2010) (6 pages) doi:10.1115/1.4001328 History: Received January 22, 2008; Revised February 14, 2010; Published December 02, 2010; Online December 02, 2010

This paper demonstrates the design of H loop-shaping controller for a linear time invariant (LTI) system with input saturation constraint. The design problem has been formulated in the four-block H synthesis framework, which is equivalent to normalized coprime factor robust stabilization problem. The shaped plant is represented as a polytopic linear parameter varying (LPV) system while saturation nonlinearity is considered. For a polytopic model, the LTI H loop-shaping controllers have been designed at each vertex of the polytope using linear matrix inequalities, and subsequently controllers are scheduled by adopting a certain interpolation procedure. The proposed controller ensures the stability and robust L2-performance of the closed-loop system due to vertex property of the polytopic LPV shaped plant. The effectiveness of the design method has been illustrated through a numerical example.

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Figures

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Figure 1

The block diagram for the H∞ loop-shaping control with input saturation

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Figure 2

Singular values of the nominal and shaped plants

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Figure 3

Output response of the plant at channel 1 when reference input is 10

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Figure 4

Output response of the plant at channel 2 when reference input is 10

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Figure 5

Control input at channel 1

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Figure 6

Control input at channel 2

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Figure 7

Time-varying scheduling parameters

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