SOLUTION OF SIGNAL UNCERTAINTY PROBLEM AT ANALYTICAL DESIGN OF CONSECUTIVE COMPENSATOR IN PIEZO ACTUATOR CONTROL

А -Е Е Е А Ы Е , Е А а–ю ь 2016 16№ 3 ISSN 2226-1494 http://ntv.ifmo.ru/ SCIENTIFIC AND TECHNICAL JOURNAL OF INFORMATION TECHNOLOGIES, MECHANICS AND OPTICS

May–June 2016 Vol. 16 No 3 ISSN 2226-1494 http://ntv.ifmo.ru/en

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a _{, - , 197101,}

: sbystrov@mail.ru

ɂɧɮɨɪɦɚɰɢɹɨɫɬɚɬɶɟ

22.01.16, 16.03.16 doi: 10.17586/2226-1494-2016-16-3-451-459

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//

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Ⱥɧɧɨɬɚɰɢɹ

ɉɪɟɞɦɟɬɢɫɫɥɟɞɨɜɚɧɢɹ. .

, . Ɇɟɬɨɞ.

, 1958 . Э

– .

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. Ɉɫɧɨɜɧɵɟɪɟɡɭɥɶɬɚɬɵ.

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Ʉɥɸɱɟɜɵɟɫɥɨɜɚ

, , ,

,

Ȼɥɚɝɨɞɚɪɧɨɫɬɢ

( 074-U01) ( 14. Z50.31.0031).

SOLUTION OF SIGNAL UNCERTAINTY PROBLEM AT ANALYTICAL DESIGN

OF CONSECUTIVE COMPENSATOR IN PIEZO ACTUATOR CONTROL

S.V. Bystrova, N.A. Vundera, A.V. Ushakova

a_{ITMO University, Saint Petersburg, 197101, Russian Federation}

Corresponding author: sbystrov@mail.ru

Article info

For citation: Bystrov S.V., Vunder N.A., Ushakov A.V. Solution of signal uncertainty problem at analytical design of consecutive compensator in piezo actuator control. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2016, vol. 16, no. 3, pp. 451–459. doi: 10.17586/2226-1494-2016-16-3-451-459

Abstract

Subject of Research. We present research results for the signal uncertainty problem that naturally arises for the developers of servomechanisms, including analytical design of serial compensators, delivering the required quality indexes for servomechanisms. Method. The problem was solved with the use of Besekerskiy engineering approach, formulated in 1958. This gave the possibility to reduce requirements for input signal composition of servomechanisms by using only two of their quantitative characteristics, such as maximum speed and acceleration. Information about input signal maximum speed and acceleration allows entering into consideration the equivalent harmonic input signal with calculated amplitude and frequency. In combination with requirements for maximum tracking error, the amplitude and frequency of the equivalent harmonic effects make it possible to estimate analytically the value of the amplitude characteristics of the system by error and then convert it to amplitude characteristic of open-loop system transfer function. While previously Besekerskiy approach was mainly used in relation to the apparatus of logarithmic characteristics, we use this approach for analytical synthesis of consecutive compensators. Main Results. Proposed technique is used to create analytical representation of "input–output" and "error–output" polynomial dynamic models of the designed system. In turn, the desired model of the designed system in the "error–output" form of analytical representation of transfer functions is the basis for the design of consecutive compensator, that delivers the desired placement of state matrix eigenvalues and, consequently, the necessary set of dynamic indexes for the designed system. The given procedure of consecutive compensator analytical design on the basis of Besekerskiy engineering approach under conditions of signal uncertainty is illustrated by an example. Practical Relevance.

The obtained theoretical results are used in the task of developing precise positioning systems with piezoelectric actuation mechanism. Proposed procedure for analytical synthesis of consecutive compensator is also believed to be usable for design of servo mechanisms of arbitrary application.

Keywords

signal uncertainty, Besekerskiy approach, consecutive compensator, piezoelectric actuator, precise positioning system

Acknowledgements

This work was supported by the Government of the Russian Federation, Grant 074-U01 and the Ministry of Education and Science of the Russian Federation (Project 14. Z50.31.0031)

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g  g g    g g   ;

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1 0 942 c ;



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;

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, 2000 2,56 10 1250 391 10

k W s

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  

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7. ( . . 15– . 16)

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

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2826 2662092

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W s s

W s

W s s s s

  

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0 1

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0 1 , 0 10

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5

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5

10 ,

m

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10 10 0, 01

m gm

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. 1.

. 2.

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1 0,8 0,6

0,4

0,2

0 0,004 0,008 0,012 t, c

g(t)

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10–5

10–7

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5

4

3

2

1

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g(t)

. 3.

( ) ( )

9. . 6

.

Ɂɚɤɥɸɱɟɧɢɟ

,

,

.

[17], .

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10–5 10–7

g(t)

y(t) ₁ (t)

0,5 0

–0,5 –1 –1,5

0 1 2 3 4 t, c 0 1 2 3 4 t, c 1

0,5 0 –0,5

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, polinova_nina@mail.ru

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79214215187@ya.ru

Sergey V. Bystrov – PhD, Associate professor, Associate professor, ITMO University, Saint Petersburg, 197101, Russian Federation, sbystrov@mail.ru

Nina A. Vunder – postgraduate, ITMO University, Saint Petersburg, 197101, Russian

Federation, polinova_nina@mail.ru