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1 7AD-A =FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OH FI 9/5 PRINCIPLE OF THE CONSTRUCTION OF SELF-TUNING LOOPS FOR SERVO Sy-_ETCCU) " EEEEEomhhEEEE JAN 82 B V NOVOSELOV UNCLASSIFIED FTO-ID(RS)T EEEEEET

2 FTD-ID(RS )T FOREIGN TECHNOLOGY DIVISION FE PRINCIPLE OF THE CONSTRUCTION OF SELF-TUNING LOOPS FOR SERVO SYSTEMS OF COMBINED CONTROL by B.V. Novoselov Accroved fcr p.:v.2z release; P20?

3 FTD- ID(RS)T UNEDITED MACHINE TRANSLATION FTD-ID(RS)T January 1982 MICROFICHE NR: FTD-82-C PRINCIPLE OF THE CONSTRUCTION OF SELF-TUNING LOOPS FOR SERVO SYSTEMS OF COMBINED CONTROL By: B.V. Novoselov English pages: 15 Source: Izvestiya Vysshikh Uchebnykh Zavedeniy Elektromekhanika, Nr. 12, December 1969, pp Accesin For Country of origin: USSR This document is a machine translation. Requester: USAMICOM DLiC T Approved for public release; distribution unlimited. U By... Av - 1 ist THIS TRANSLATION IS A RENDITION OF THE ORIGI- NAL FOREIGN TEXT WITHOUT ANY ANALYTICAL OR EDITORIAL COMMENT, STATEMENTS OR THEORIES PREPARED BY: ADVOCATED OR IMPLIED ARE THOSE OF THE SOURCE ANDDO NOT NECESSARILY REFLECT THE POSITION TRANSLATION DIVISION OR OPINION OF THE FOREIGN TECHNOLOGY DI. FOREIGN TECHNOLOGY DIVISION VISION. WP.AFB, OHIO. F T1- ID(RS )T Date 26 Jan L

4 .CARD ON GEOGRAPHIC NAMES TRANSLITERATION SYSTEM ;alic Transliteration Block :talic Transliterai.. - A a A, a Pp p p R r S 6 B, b C S s B * V, v T T T m T t F - *, Y y y y U u e a Ye, ye; e* x X x Kh, kh -' w Zh, zi Ts, ts 3j Z A v Ch, ch F,f jlu LY i Sh, sh - R a, y - - A IIl w Shch, snci. 17 A- Ma..,nm= b & H N.;,n 3 E,e a Yu, yu 7,, -= 2 a Ya, ya ;L:;fe-i, and after ; e, esewnere. as -2 in -.,ussan,:ranzliterate as y- 3r.?UJ3:AN AU D ',L3SH TRiGCNC'METRIC FNC TNS English Russian English Russian E. sn sh slnh arc sn :_ "h cosh arc ch, -1, a r.ta th tanh arc th c-t oth coth arc c* th sec sch sech arc sch e- :sc csch csch arc csch 3s-h Russian rot lg Eng1zish curl lcg

5 DOC PAGE 1 Page PRINCIPLE OF THE CONSTRUCTION OF SELF-TUNING LOOPS FOR SERVO SYSTEMS OF COMBINED CONTROL. B. V. Novoselov. I. Formulation of the problem. The use/application of servo systems of the combined control (SSKR) allows during the final adjustment of the specific type of input effects (VV) to theoretically ensure the complete compensation for the steady errors. However, the transiency of the parameters and the nonlinearity of the characteristics of elements/cells of SSKR cause the disturbance of the conditions for the compensation for the components of errors and, therefore, an increase in the error, frequently up to the inadmissible values. Let SSKR be carried out on the diagram in Fig. la, where A~!=pi -r Tip (I T? Expressions of kinetic N,, dynamic -, of errors and condition for

6 DOC PAGE 2 their complete compensation = K.. k l---""k12) With the disturbance of condition = (change in the factor of amplification of SSKR K or changek5.' takes AhA I - (ha K K 4 ACAK - ' ~_1_,.3) = ' where * - value 1 in the absence of KS. From analysis (1.3) it follows that in the series/row of practical tasks it is necessary to introduce the automatic tuning of the parameters of SSKR as a function of the variable parameter. It is expedient to produce tuning of KS, since in this case there is no need for solving compromise problem during the guarantee of high accuracy and stability. II. Theory of SSKR with KSN of KS. Fig. lb depicts the block diagram of SSKR, in which the parts of KS, developed by differentiators (Dif 1), (Dif 2), are multiplied in the blocks of product (BPI) (BP2) by the output signals of integrators (11), (12) actual error of SSKR by which is realized the Now

7 DOC = PAGE 3 required change of KS with the disturbance of the conditions for error compensation. Page In this diagram is realized actually the integral control with the variable coefficients of integration, which are functions of VV. This control provides during the final adjustment of VV the elimination of the steady errors regardless of the fact the fact that was the reason for their appearance, and does not affect the quality of free transient processes. Work of SSKR with KSN is described by nonlinear equation with the variable coefficients T'. T. - d -,- I -TY dt 2 - dt - K K#. - t dt - AJ " 0 '(t) W 1 '-dt Klt at d- Kt'- t J Let us assume that o,(t), o,'(t), o(t), o"(t) - the slowly changing functions, i.e., a change in them is unessential for the time of the effective duration of transient response of SSKR. Then the formulation of the problem will be the following. At the moment of time t-0 are disrupted the conditions for compensation -,.-

8 DOC = PAGE 4., - =?' 't -- K Self-tuning loops must ensure the elimination of the steady errors. We introduce designations, t tt- r 3 : V -" WI tr,-j-.- " 2.:

9 1 -, DOC PAGE 5 Fig. 1. Block diagrams of SSKR. Page After dividing left and right side of (2.1) by a,(t)+a 2 (t) (sum a 1 (t)+a,(t)#0 except when t=0) and differentiating with respect to t, we will obtain d'" I da, t 1 d 3,M da. t d" a', +, odit_ L a ht I K tit b t, 1)=9., t ) ) r dr" dt, where

10 DOC = PAGE 6 * t 14: "I a,,t: 1 F KI 2, 1). t ; b T +T. T,-: b, = -- t - Equation (2.3) - equation with variable coefficients. General solution it to obtain complicatedly. But according to the form of equation itself (2.3) it is easy to establish/install the conditions for the compensation for separate components of error. When 4,,t -Ci-O.if db:,t d [ -- dt dit d, W2.4) V IWi dt 1 When 0dt) =, 04,=,if - h. e, '.(.' In the case ",( t ="t, -- _, b: -consequently While dt t ),i.e. KSN always provide ",=o. In the case consequently, consequ it dy

11 DOC = PAGE 7 Jb:(t - "Wdb i.e. KSN with t-. The sufficiently effective method of the study of SSKR with KSN of KS is L. A. Zade's method, which uses a parametric transfer function of system [1) - [4]. If VV of SSKR with the variable parameters satisfies the proper conditions, then it it is possible to present with the aid of the integral of Fourier and the error of SSKR in this case can be determined on the following dependences: 0 Pt e'p, t'134p)edp. Page 1334.

12 DOC = PAGE 8 In (2.6)-(2.8),, - the composite relative amplitude of the spectrum of function -. '. T the weighing function of error of SSKR; 'X,p, t) - parametric transfer function of error of SSKR. If equation (2.1) is represented in the form.4 p. t 4 (t "- p. t M(t then for case :'-, : e t the parametric transfer function of error of SSKR will be expressed [4] P, T, t P. V t I where W,(p, t - approximation/approach Cikp, Bt = t * ' 1 *' f d!,;; Aip ; I t. dp ' '.' J), : In the slowly changing parameters of SSKR for the preliminary evaluation/estimate of quality of SSKR with KSN it is possible to uze the zero approximation W,(p, t). For SSKR being investigated with KSN with p.=l, o.'=l. ; 1I, 0,!, p.- t 1 j "T = A ';,' p J - I A *:. p - With 0 ti = r, 7p, -- T.-,-Kp -A t - v do, d-. k -_ it -....

13 DOC = PAGE 9 7,T:1>'-i/i'j- T,- ';'.;,1- i- p (. With 90 t = h #1 t, T' -p-. r,0 K P." TT,pT -T:-A'" p - -- " (2 12, W',tP, t'o T, 1.p' l P-P ip- -A:,t-KW,'- From analysis (2.12'), (2.12") it follows that during the introduction/input of KSN: t-. 1, * -: when -. and with 2. Stability of SSKR during final adjustment of VV is determined by parameters of SSKR, parameters and sign of VV, which requires switching integral signs of error in function of sign of VV.., )-( in any cases except t-n if we utilize tuning on first derivative of VV according to the law (Fig. 1c) " +0 Rdt. For the transient evaluation, using W(p, t)., it is possible to construct the series of dependences w-:) for fixed values k, t Each of the dependences H t will have only one point, which satisfies

14 DOC = PAGE 10 unknown. Connecting the obtained points of smooth curve, let us determine t.t 41. Page III. Results of the experimental investigation of SSKR with KSN of KS. Powering unit of servo system is carried out on the following elements/cells: amplidyne EMU-25Az, direct-current motor Pl2M. Were investigated SSKR with KSN of KS on first-order derivative and SSKR with two KSN of KS on the first and second derivative of VV. As a result of investigations it is established/installed: 1. With the work of SSKR with one KSN: with any p(t), if the frequency of change o(t) lies/rests at the frequency region, passed by KSN; b).=. when. _ after certain small time interval t; c) rms error '. when o,'ti=@,,3inut decreases 5-20 times in comparison with SSKR without KSN; -IJ A

15 DOC = PAGE 11 d) free transient processes KSN does not affect; e) for the stable operation of SSKR with KSN it is necessary during the final adjustment of VV to ensure switching sign otdt in the function of sign of VV. Dead zone h of BR must be not more i (5-7)o/o(2 (Fig. 2a); f) the selection of factor of amplification 12 must be selected, on the basis of the minimum of transit time r during the final adjustment of the velocity discontinuity and minimum "4., or "4.s during the final adjustment of VV *, -), (Fig. 2b). Fig. 2c presents dependences f 7,. where T, - time constant of differentiator, included in the target of the error signal of SSKR.

16 DOC = PAGE "7.. Fig. 2. Graphs/curves of the parameters of SSKR with one KSN. K.ey: (1). lang. min.] (2). s. Page With work of SSKR with two XSN. a) in modes/condit ions, =-t,,( --,t b) during the introduction/input of KSN requirements on the quality for Dif 2 are weakened/attenuated. The denominator of

17 DOC PAGE 13 transfer function Dif 2 can contain time constants sufficiently high in terms of their values; c) are optimum values of factors of amplification W,, W,' integrators, evaluated in minimum t. or. when t)-., 1 sinut and minimum of transit time t, during the final adjustment of velocity discontinuity n,. Moreover the optimum values W,, W.' during the P7aluation/estimate according to minimum H or different (Fig. 3a, b); d) error of SSKR during the disturbances/perturbations X(t) on the performing axis it decreases 5-10 times, if n, in this case is not equal to zero, but the frequency of disturbance/perturbation lies/rests at the frequency region, passed by KSN (Fig. 3c); e) the value of the time constant T. of the real DIF2 for the quality of work of SSKR with KSN practically does not affect (Fig. 3d).

18 DOC = PAGE 14,,~~W ii W" W1.1, ~ 4 6 N,/ 0 2 ' w, -is,' , Fig. 3. Graphs/curves of the parameters of SSKR with two KSN. Key: (1). s. Conclusion/output. 1. Introduction/input of KSN of KS is effective means of increase in accuracy of SSKR. 2. KSN of KS can be used in new developments and in modernized SSKR, since their use/application does not require treatment/processing main circuit of SSKR, but is provided for only

19 DOC a PAGE 15 introduction/input of series/row of supplementary simple devices/equipment. REFERENCES i. Z j J e h L \. *2;rcuit anilv i- )f linear varying par3meter networks. Journ. App Ph..()I Z a J e h L. k. Frequency analv.6l of varlable networks. PIRE. vol. 38. March. I9:'.5 Za d e h L. A.. Un itablity A' line.r varying parameter slstems. Journ. App. ft. ol. 2. Arr!i. 195,5]. o, o A B.,..1HHeH- e ct:ic-et abtoath4ecoro ynpaa.7ehhn c nepexeim.iwi Firpt ecei.." 0ii-mi, 9 II First received 19 VII 1967; revised 22 XI i. ~~~~-mum..-q......