Position Control 1

POSITION CONTROLI. M hnh ha ng c DCTrong bi bo co v iu khin tc ng c DC, chng ta m t ton hc ng c DC bng hm truyn bc 1 m t quan h gia tc gc (rad/sec) v in p u vo (V) l:

(1)

Vi l thi hng ca h thng, K l h s khuch i xc lp.T , v tr gc ca th xc nh bi tch phn tc gc. Hm truyn vng h gia v tr gc (rad) v in p u vo (V) :

(2)II. c tnh qu ca h bc 2H thng lu tr nng lng khng th p ng mt cch tc thi, v vy h thng s th hin p ng qu khi b tc ng bi u vo hoc nhiu. c tnh p ng qu l mt trong nhng yu t qun trng ca thit k h thng iu khin.Hm truyn ca h bc hai, vi input l u(t) v output l y(t).

(3)p ng ca h bc hai vi cc c tnh qu c th hin trn hnh H.1. Thi gian ln (tr): thi gian cn thit p ng ca h thng tng t 10% n 90%. nh vt l (Mp): gi tr ln nht p ng ca h thng so vi p ng mong mun. Thi gian qu (ts): thi im p ng ra t sau tr i khng vt ra khi min gii hn sai s quanh gi tr xc lp. Thi gian tr (td): Thi gian cn thit p ng ca h t 50% p ng mong mun trong ln u tin. Thi gian ln nh (tp): thi gian p ng ra t gi tr Mp. Sai s xc lp (ess): sai s gia p ng ra v p ng mong mun khi thi gian tin v v cng.

H.1c t cc thng s ca h thng:Thng sK hiuCng thc

Thi gian lntr

Vi

nh vt lMp

Thi gian trtd

Thi gian qu ts (tiu chun 2%)

(tiu chun 5%)

Thi gian ln nhtp

Sai s xc lpess

Da vo cc thng s ny, chng ta c th thit k h thng vi yu cu cht lng t ra.III. H thng iu khin vng kn dng gii thut PID.H thng iu khin vng kn s dng hi tip m n v v b iu khin PID. S khi ca h thng nh hnh H.2.

H.2Hm truyn ca h:

Vi hm truyn trn, ta s chn cc thng s Kp,Kd v Ki thit k h thng c cht lng nh mong mun.IV. B iu khin PDTrong thc t, khng phi lc no chng ta cng dng PID v vic tm ba thng s ph hp vi cht lng h thng cng kh phc tp. Tuy nhin, nu ta lc b i mt thng s trong PID, tc l dng b iu khin PI hoc PD, vn c th cho h thng cht lng tng i chnh xc, v th s gim nh phn tnh ton.

Hm truyn ca b iu khin PD c dng : . Khi , hm truyn kn ca h thng c dng:

Da vo hm truyn trn, ta c th thit k h thng t yu cu nh mong mun. V d ta mun thit k h thng c cp cc quyt nh no , t cc nghim ny ta s c cc thng s l v . Ta c:

(4)(5)T cc cng thc (4) v (5) ta s suy ra c cc thng s Kp v Kd.V. Thit k b iu khin PID bng phng php Zeigler-Nichols :

V hm truyn v tr ca ng c c khu tch phn l tng, ta chn thng s b PID da vo p ng qu ca h kn nh hnh H.3. Tng dn h s khuch i K ca h kn hnh H.3 n gi tr , khi p ng ra ca h kn trng thi xc lp l dao ng n nh vi chu k .

H.3Ta tng K n khi K = 10, ta thy h dao ng vi chu k T = 0.04s (hnh H.4).

H.4

Vy, ta c = 10 v = 0.04. V b iu khin ta chn l b PID nn thng s b iu khin c chn l : = 6; = 0.02 v =0.005.Sau y l p ng ca h thng vi b PID iu chnh theo Zeigler-Nichols. (Hnh H.5).

H.5Sau y l p ng ca h thng vi cc b PID cn chnh quanh gi tr b PID chn theo Zeigler-Nichols.

H.6. = 5, = 0.03, = 0.01

H.7. = 5, = 0.04, = 0.02