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Research Papers

Servo System Identification Using Relay Feedback: A Time-Domain Approach

[+] Author and Article Information
Jia Liu

e-mail: lamen@sjtu.edu.cn

Jianhua Wu

e-mail: wujh@sjtu.edu.cn

Zhenhua Xiong

e-mail: mexiong@sjtu.edu.cn

Xiangyang Zhu

e-mail: mexyzhu@sjtu.edu.cn
State Key Laboratory of Mechanical
System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received January 18, 2012; final manuscript received August 9, 2012; published online November 12, 2012. Assoc. Editor: Robert Landers.

J. Manuf. Sci. Eng 134(6), 061012 (Nov 12, 2012) (10 pages) doi:10.1115/1.4007715 History: Received January 18, 2012; Revised August 09, 2012

In servo systems, the dynamic characteristics may not only differ between axes but may also vary with moving directions for a single axis. The direction dependent characteristics would result in additional tracking or positioning error and degrade the performance of the system. In this paper, relay feedback tests are successfully applied to identify the dynamic characteristics in servo systems. A time-domain method is used to analyze the relay feedback other than the conventional describing function (DF) method. The time-domain method utilizes the same oscillation parameters (oscillation amplitude and half period) as the DF method for system identification. However, the time-domain method takes several advantages: First, the direction dependent characteristics of the system can be properly revealed; second, no approximation is made in this method, so that the exact expressions of the amplitudes and the periods of the limit cycles under relay feedback can be derived. A feedforward compensator is then designed using the estimated values of the system parameters. Simulation results show that the identification results through the time-domain method are more accurate than the DF method and are more robust under different relay parameters. Real time experiments show that the feedforward compensator designed by the proposed method compensates disturbances related to the direction and hence improves the tracking and positioning performance of the servo system.

Copyright © 2012 by ASME
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References

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Figures

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Fig. 1

Block diagram of relay feedback test with additional dead time

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Fig. 2

Oscillatory waveforms excited by relay feedback

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Fig. 3

Relay signals with μ1 = 0.2 and D = 0.08 s

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Fig. 4

Relay signals with μ2 = 0.3 and D = 0.08 s

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Fig. 5

Identification results of direction dependent system with different relay parameters

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Fig. 6

Identification results of symmetric system with different relay parameters

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Fig. 7

Experimental setup

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Fig. 8

Output of relay with μ1 = 6000 and D = 0.08 s

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Fig. 9

Input of relay with μ1 = 6000 and D = 0.08 s

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Fig. 10

Output of relay with μ2 = 8000 and D = 0.08 s

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Fig. 11

Input of relay with μ2 = 8000 and D = 0.08 s

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Fig. 12

Block diagram of PD controller with feedforward compensator

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Fig. 13

Sinusoidal motion profile

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Fig. 14

Tracking error without compensation

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Fig. 15

Tracking error with compensation using time-domain method

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Fig. 16

Tracking error with compensation using DF method

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Fig. 17

Positioning without compensation

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Fig. 18

Positioning with compensation using DF method

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Fig. 19

Positioning with compensation using time-domain method

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