Experiment 6: STUDY OF A POSITION CONTROL SERVOMECHANISM

Transcription

1 Expermen 6: STUDY OF A POSITION CONTROL SERVOMECHANISM 1. Objecves Ths expermen prvdes he suden wh hands-n experence f he peran f a small servmechansm. Ths sysem wll be used fr mre cmplex wrk laer n he curse. The parameers f he sysem wll be evaluaed by a seres f ess. The sepn fllwng peran f he serv wll be suded qualavely fr dfferen values f frward-pah gan, and quanavely fr ne value f gan. Therecal predcns wll be cmpared wh measured respnses.. Inrducn The hardware f a basc psn cnrl servmechansm s prvded. I cnsss essenally f a penmeer-par errr deecr, a preamplfer, a crcu capable f cnnecn as a seres cmpensar, a vlage--vlage pwer amplfer, a DC mr wh negral achgenerar, a gearbx, and a lad. The acual arrangemen s mre cmplcaed han he frn panel pcure (Fg. 1) wuld sugges. In he arrangemen prvded fr hs expermen he effecs f mr armaure nducance and nn-lnear frcn have been masked ver he wrkng range f he basc sysem. Ths has been acheved by he use f hgh gan echnques n asscan wh nernal feedback. The resulan sysem has been 'slwed dwn' elecrncally s ha s perfrmance ver he range f he gven expermenal wrk s essenally lnear and secnd rder when swched Sysem 1 and hrd rder when swched Sysem. Ousde he range f hs wrk (e.g. when he frward pah gan s ncreased well beynd he values requred) he sysem des begn exhb behavur ha cann be explaned n he bass f secnd rder ransfer funcns. Ths need n cncern he sudens perfrmng hs expermen, bu hese effecs wll be suded n laer expermens. Wh reference Fg. 1, he psn f a raable mass (als called he upu psn θ ) s be cnrlled n accrdance wh he psn f a cmmand handwheel (als 1

2 called he npu psn θ ). The upu s ransduced frm a vlage V and he npu s ransduced frm a vlage V. These are subraced elecrncally usng peranal amplfers frm an errr vlage Ve = P Er where E r s he mechancal errr gven by Er = θ θ. The sysem may be slaed frm mechancal cmmands by means f swch S 1. There s an auxlary npu V x fr drec elecrcal cmmands ha can be used fr ceran ess. The sgnal V e wll nrmally be fed va swch S frm V '. The ne e cnrl sgnal V ' s hen passed hrugh an adjusable penmeer f seng A and a e pre-amplfer befre applcan he seres cmpensar. Wh swches 3 and 4 clsed hs cmpensar s a smple amplfer wh gan 3. The ermnals prvded acrss hese swches allw passve cmpnens (.e. ressrs and capacrs) be cnneced n such a way as prduce phase-lead cmpensan, phase-lag cmpensan, prprnal plus negral cnrl P+I, r P+I+ phase lead cmpensan. The upu f he cmpensar s hen cmbned wh he lcal velcy feedback sgnal befre beng pwer-amplfed and fed he mr. The shaf f he mr s cupled va a 5:1 sep dwn gearbx (emplyng a hed bel fr queness) he raable mass whse psn s be cnrlled. The majr lp may be pened by means f swch S 6 and he auxlary velcy feedback lp may be pened by means f swch S 5. The achgenerar s muned n he mr shaf. Is vlage s amplfed and sme f he cmmuar rpple s flered befre feedng he ermnal as V. The prprn f V fedback can be cnrlled by he en-urn penmeer f ceffcen B. An analyss f he lnearsed sysem reveals ha when swched Sysem 1, he sysem can be represened by he ransfer funcn mdel llusraed by he blck dagram shwn n Fg.. Useful equans are develped n Appendx 1.

3 3. Deermnan f sysem parameers Swch Sysem 1, and leave swches S 3 and S 4 clsed fr hs expermen. 3.1 Penmeer Respnsvy P (V/rad) Clse swch S 1, and pen S, S 5, S 6. Then Ve( vls) = Pθ. Recrd hs vlage n AVO n 10 V range wh θ se (say) 0, ± 45, ± 90, ± 135. Pl a graph and hence evaluae P (wh expeced lerance). Cnfrm by recrdng V e wh θ se 1 rad = Tachmeer respnsvy G (V/rad s -1 ) Clse swch S. Se penmeer A 0.40, vary θ and recrd V and me fr n revluns f he upu shaf. Hence evaluae agans W deermne G. W (n rad/s) and pl a graph f V HINT. Tabulae V, n, me fr n revs, W. Thnk abu he accuracy f yur readngs. In he fuure, V wll be used deermne shaf speed. 3.3 Amplfer/Mr/Lad Parameers M (rad s -1 / V), T (s) The seady sae relanshp beween V and θ s gven by: V = P3AM Gθ Recrd suable values, pl a graph and hence evaluae M. 3

4 The ransen respnse f V changes n V x s f he frm: V V e / T () = 0(1 ) where V 0 s he seady sae value and T s he me cnsan. Yu wll carry u a sep es usng VISSIM recrd he pen lp ransen respnse. Duble clck n he cn labeled Exp06, whch sars VISSIM and lads a suable cnfguran fr hs expermen. Usng he muse, cnnec he cn labeled Sep 0 4 he cn labeled V x. Cnnec he cn labeled Sep 0 4 he pl wndw and cnnec he cn labeled V he pl wndw. Then, carry u he physcal cnnecns shwn n Table 1. Termnal n serv Sgnal Number n bx V x 0 V 0 36 V 37 Earh 11 Earh 18 Earh Table 1: Physcal cnnecns 4

5 Ensure ha he daa acqusn channels are assgned n VISSIM accrdng Table. Type f cnversn Sgnal name Channel D/A V x 0 A/D V 0 1 A/D V 0 Table : Daa acqusn channels Use VISSIM (afer an explanan by he demnsrar) ban a suable ransen respnse, and hence deermne he me cnsan T. A sep change n V x frm 0 4 V wh a value f A = 0.40 shuld be suable. If me s shr, yu may assume T = 0. s. 4. Clsed-lp ess n Psnal Serv 4.1 Respnse wh adjusable gan Se A = 0.30, clse swches S 1 and S 6, pen S 5, and examne hw θ fllws manual varans f θ. Reduce A wards zer (e.g. se A 0.10, 0.05, 0.01 ), and hen ncrease wards 1.00 (e.g. se A 0.50, 0.70, 1.00). A each seng f A, bserve he fllwng-acn f he serv and cmmen n he effec f alerng he frward-pah gan n he serv perfrmance. 5

6 4. Sep Respnse wh gven parameers Se A = 1.00 and pen S 1. Use VISSIM ban recrdngs f V and hen V fr sep changes f npu vlage V x frm Deermne he percenage versh, and me peak, and cmpare wh values predced frm he equans fr he serv. (see Appendx 1). Cnfrm ha V s a maxmum when V crsses zer. Appendx 1 Wh reference Fg., when S 5 s pen and all hers are clsed (NOTE. Wh swch S 5 OPEN, he value f B s effecvely zer). The ransfer funcn frm θ θ s gven by: M 1 P3A θ () s (1 + st ) s = θ () s M A P (1 st ) + s Ths ransfer funcn can be re-wren as fllws: θ() s = θ () s s 3AMP T 1 3AMP + s+ T T (A1) Nw cnsder he sandard secnd rder ransfer funcn: Gs () = s ω n + ζωns+ ωn (A) 6

7 Cmparng equans (A1) wh (A) s easy shw ha he undamped naural frequency s gven by: 3AMP ω n = (A3) T whle he dampng ceffcen ζ s gven by: 1 1 T 1 ζ = = = (A4) Tω T 3AMP 3AMPT n Cmpue he values f he dampng ceffcen and undamped naural frequency fr he serv sysem by usng Eqns. (A3) and (A4). The values f he percen versh M p and me peak p fr a secnd rder sysem lke (A) are gven by: M p MaxValue FnalValue ζπ = 100 = exp 100 FnalValue 1 ζ (A5) p = ω n π 1 ζ (A6) Calculae he predced values f M p and p usng Eqns. (A5) and (A6). Revsed by V. Becerra, Sepember

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