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Research Papers

# $H∞$ Closed-Loop Control for Uncertain Discrete Input-Shaped Systems

[+] Author and Article Information
John Stergiopoulos

Department of Electrical and Computer Engineering, University of Patras, Rio Achaia 26500, Greecestergiopoulos@ece.upatras.gr

Anthony Tzes1

Department of Electrical and Computer Engineering, University of Patras, Rio Achaia 26500, Greecetzes@ece.upatras.gr

1

Corresponding author.

J. Dyn. Sys., Meas., Control 132(4), 041007 (Jun 17, 2010) (8 pages) doi:10.1115/1.4001704 History: Received September 27, 2007; Revised March 30, 2010; Published June 17, 2010; Online June 17, 2010

## Abstract

The article addresses the problem of stabilization for uncertain discrete input-shaped systems. The uncertainty affects the autoregressive portion of the transfer function of the system. A discrete input shaper compensator is designed in order to reduce the oscillations of the plant’s response. The input-shaped system’s dynamics are appropriately reformulated for robust controller synthesis, and a robust $H∞$-controller is used in an outer-loop, in order to guarantee stability of the uncertain input-shaped plant. Simulation results confirm the efficacy of the proposed combined scheme in comparison with open-loop input shaping and closed-loop linear quadratic control.

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## Figures

Figure 3

Interconnection of blocks considering parametric uncertainty for the underdamped plant under consideration

Figure 4

Generalized block-form of an uncertain system under control

Figure 7

Impulse response of the nominal single-mode plant

Figure 8

Impulse response of the nominal ZV (a) and EI (b) input-shaped single-mode plant in open-loop (solid), with LQ closed-loop control (dotted), and with H∞ closed-loop control (dashed-dotted)

Figure 9

Impulse response of the perturbed ZV (a) and EI (b) input-shaped single-mode plant in open-loop (solid), with LQ closed-loop control (dotted), and with H∞ closed-loop control (dashed-dotted)

Figure 1

Admissible workspace of the parameters α1,i,α2,i and variations of ωi,ζi for stable underdamped plants

Figure 2

Implementation of an n-modes shaper via convolution of independent ones

Figure 5

Analytic form of interconnection matrix P for the uncertain system under consideration

Figure 6

Packed state-space realization of interconnection matrix P

Figure 10

Impulse response of the nominal dual-mode plant

Figure 11

Impulse response of the nominal ZV input-shaped dual-mode plant in open-loop (solid), with LQ closed-loop control (dotted), with H∞ closed-loop control (dashed-dotted)

Figure 12

Zero-pole locations of the designed H∞-controller for the dual-mode plant

Figure 13

Impulse response of the perturbed ZV input-shaped dual-mode plant in open-loop (solid), with LQ closed-loop control (dotted), and with H∞ closed-loop control (dashed-dotted)

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