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Research Papers

Increasing Robustness of Input Shaping Method to Parametric Uncertainties and Time-Delays

[+] Author and Article Information
M. C. Pai

Department of Automation Engineering, Nan Kai University of Technology, Tsa-Tun, Nantou, Taiwan 54210, R.O.Cpmc@nkut.edu.tw

A. Sinha

Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, PA 16802axs22@psu.edu

J. Dyn. Sys., Meas., Control 133(2), 021001 (Feb 11, 2011) (8 pages) doi:10.1115/1.4003090 History: Received November 13, 2007; Revised July 30, 2010; Published February 11, 2011; Online February 11, 2011

The input shaping technique has proven to be highly effective in reducing or eliminating residual vibration of flexible structures. The exact elimination of the residual vibration via input shaping depends on the amplitudes and instants of utilized impulses. However, systems always have parametric uncertainties, which can lead to performance degradation. Furthermore, input shaping method does not deal with vibration excited by external disturbances and time-delays. In this paper, a closed-loop input shaping control scheme is developed for uncertain flexible structure and uncertain time-delay flexible structure systems. The algorithm is based on the sliding mode control and H/μ techniques. This scheme guarantees closed-loop system stability, and yields good performance and robustness in the presence of parametric uncertainties, time-delays and external disturbances as well. Also, it is shown that increasing the robustness to parametric uncertainties and time-delays does not lengthen the duration of the impulse sequence. Numerical examples are presented to verify the theoretical analysis.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Proposed control scheme

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Figure 2

(a) The N−Δs−Ks plot and (b) the V−Δs plot

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Figure 3

Results for example 4.1 using the method in Ref. 10: (a) step response of the model to the shaped input and (b) impulse response of the model to the shaped input

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Figure 4

Results for example 4.1 using the method developed in this paper: (a) ideal response with exact cancellation, (b) response with parameter variations and external disturbance, and (c) output error

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Figure 5

Results for example 4.2: (a) ideal response with exact cancellation, (b) closed-loop response (11), (c) closed-loop response: the proposed method, and (d) output error

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Figure 6

Results for example 4.2: (a) closed-loop response: LQR design, (b) open-loop preshaped response, (c) closed-loop response: the proposed method, and (d) output error

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Figure 7

Results for example 4.3: (a) open-loop preshaped response, (b) closed-loop response: the proposed method, and (c) output error

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