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Research Papers

Optimal Dynamic Quantizers for Feedback Control With Discrete-Level Actuators: Unified Solution and Experimental Evaluation

[+] Author and Article Information
Shun-ichi Azuma1

Graduate School of Informatics, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japansazuma@i.kyoto-u.ac.jp

Yuki Minami

Department of Control Engineering, Maizuru National College of Technology, 234 Shiroya, Maizuru 625-8511, Japanminami@maizuru-ct.ac.jp

Toshiharu Sugie

Graduate School of Informatics, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japansugie@i.kyoto-u.ac.jp

Actually, the crane system in Fig. 2 has nonlinear dynamics. In this paper, for simplicity, we employ an approximate linear model around the stable equilibrium. In addition, the effect of the payload’s position and velocity on the cart’s velocity is omitted. Despite this simplification, we have experimentally confirmed that this model captures the behavior.

Note that the value of q[μ] is uniquely determined for every μRm. For example, q[μ]=[00] for μ[d/2d/2] and q[μ]=[0d] for μ[d/2d/2].

1

Corresponding author.

J. Dyn. Sys., Meas., Control 133(2), 021005 (Feb 11, 2011) (10 pages) doi:10.1115/1.4002952 History: Received February 23, 2009; Revised January 12, 2010; Published February 11, 2011; Online February 11, 2011

This paper proposes to use optimal dynamic quantizers for feedback control in mechatronics systems when the actuator signals are constrained to discrete-valued signals. Here, the dynamic quantizer is a device that transforms the continuous-valued signals into the discrete-valued ones depending on the past signal data, as well as the current data. First, a closed form optimal quantizer is presented in a general linear fraction transformation representation setting. The optimal quantizer minimizes the deviation of the output produced by the quantized signals from the corresponding output yielded by the continuous-valued signals before quantization. Then, its experimental evaluation is performed by using a crane positioning system with a discrete-valued input to demonstrate the effectiveness of the proposed quantizers.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Two feedback systems

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Figure 2

Crane positioning system

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Figure 3

Responses of the system in Fig. 1 with a static quantizer (solid lines), and responses of the system in Fig. 1 (dotted lines)

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Figure 4

Responses of the system in Fig. 1 with a dynamic quantizer (solid lines), and responses of the system in Fig. 1 (dotted lines)

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Figure 5

Two general feedback systems

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Figure 6

Error system for Σ and ΣQ

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Figure 7

Responses of the system in Fig. 1 with the optimal dynamic quantizer Q∗ (solid lines) and responses of the system in Fig. 1 (dotted lines)

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Figure 8

Overview of experimental device

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Figure 9

Experimental result: responses of the system in Fig. 1 with the optimal dynamic quantizer Q∗ (solid lines) and responses of the system in Fig. 1 (dotted lines)

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Figure 10

Experimental result: responses of the system in Fig. 1 with the static quantizer (solid lines) and responses of the system in Fig. 1 (dotted lines)

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