Chng 5: Cht lng h thng iu khin5.1) Cc ch tiu cht lng5.1.1) Sai s xc lp (steady-state error)

Sai s: Sai s xc lp:

Sai s xc lp ca h thng i vi tn hiu vo l hm bc thang n v R(s) = 1/s

trong gi l h s v tr.Nhn xt:a. Kp cng ln th cng nh.b. (Kp = ) nu c cha t nht 1 khu tch phn l tng.

Sai s xc lp ca h thng i vi tn hiu vo l hm dc n v R(s) = 1/s2

trong gi l h s vn tc.Nhn xt: Kv cng ln th cng nh. (Kv = ) nu c cha t nht 2 khu tch phn l tng. (Kv = 0) nu khng cha khu tch phn l tng.

5.1.2) p ng qu (transient response)Kho st: p ng ca h thng i vi ng vo hm bc thang n v. S lin quan gia v tr cc v p ng qu .p ng qu c nh gi da trn cc ch tiu cht lng sau y: vt l:

Thi gian qu tq: thi gian cn sai lch gia p ng v gi tr xc lp khng vt qu ( = 2% hoc 5%).

Thi gian ln tr: thi gian cn p ng tng t 10% n 90% gi tr xc lp.

Yu cu i vi mt mt h thng iu khin: Sai s xc lp nh (chnh xc cao), vt l nh (chnh xc cao), Thi gian xc lp nh (p ng nhanh), Thi gian ln nh (p ng nhanh), Tn hiu iu khin khng qu ln (trnh bo ha khu chp hnh).a) p ng qu h bc 1:

Cc: -1/T (thc) p ng i vi ng vo l hm bc thang n v:

p ng khng vt l. Thi gian qu : trong : = 0.02 (tiu chun 2%) hoc = 0.05 (tiu chun 5%)

Nhn xt: Cc cng xa trc o (T cng nh) p ng cng nhanh.

b) p ng qu h bc 2:

Cc: (phc). p ng qu :

vt l: Thi gian qu : Tiu chun = 5%: Tiu chun = 2%: Nhn xt: Vt l (PO) ch ph thuc . H bc 2 c cng ln th PO cng nh.

Thi gian qu () ph thuc tch (phn thc ca 2 cc). H bc 2 c cc cng nm xa trc o ( cng ln) th cng nh, p ng cng nhanh.VD: Cho h thng c s :

Trong , , , .(a) Xc nh p ng i vi ng vo bc thang n v.(b) Xc nh vt l (PO), tn s giao ng, thi gian xc lp theo tiu chun 2% v 5%.(c) Xc nh sai s xc lp vi ng vo l hm dc n v.Gii

c) H bc cao:H thng thc thng c bc > 2.V tr cc ca h thng quyt nh p ng qu . Cc cng gn trc o ( cng nh) th n c nh hng cng ln n p ng qu . Ni cch khc, p ng qu quyt nh bi nhng cc nm gn trc o. Nhng cc ny gi l cc quyt nh (hay cc tri).Trong trng hp h bc cao c 2 cc nm gn trc o (cc tri), cc cc cn li xa trc o hn cc tri t nht 510 ln, ta c th xp x h bc cao ny bng h bc 2 c cc l 2 cc tri.Vic xp x lm gim bc h thng nhm n gin ha bi ton thit k h thng iu khin (s hc trong chng 6).

5.2) Cc tiu chun ti u ha p ng qu 5.2.1) nh ngha cc tiu chun cht lngTiu chun IAE (Integral of Absolute Error):

Tiu chun ISE (Integral of Squared Error):

Tiu chun ITAE (Integral of Time multiply Absolute Error):

5.2.2) Ti u ha p ng qu h bc 2

p ng qu h bc 2

5.2.3) Ti u ha p ng qu theo chun ITAE p ng qu ca h thng bc n ti u theo tiu chun ITAE th mu s ca hm truyn h kn phi c dng theo bng sau y:BcMu s hm truyn

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Nu mu s hm truyn h kn c dng nh bng trn v t s hm truyn h kn h bc n l th p ng qu ca h thng l ti u v sai s xc lp bng 0.p ng ti u theo chun ITAE

5.3) Quan h gia c tnh tn s v cht lng trong min thi gian5.3.1) Quan h gia c tnh tn s v sai s xc lp

Nhn xt: Sai s xc lp ca h kn ch ph thuc vo bin min tn s thp ca h h, khng ph thuc vo bin tn s cao. H h c bin min tn s thp cng cao th h kn c sai s xc lp cng nh. Trng hp c bit: Nu h h c bin tn s thp v cng ln, th h kn c sai s xc lp bng 0 i vi tn hiu vo hm bc thang.5.3.2) Quan h gia c tnh tn s v cht lng qu

Gi s h h c c tnh tn s nh hnh:

c tnh tn s h kn:

Nhn xt: Bng thng ca h kn xp x tn s ct bin ca h h. H h c tn s ct bin cng cao th h kn c bng thng cng rng H thng p ng cng nhanh, thi gian qu cng nh. H h c d tr pha cng cao th h kn c vt l cng thp. Cc nghin cu thc nghim cho thy d tr pha ca h thng h > 60, th vt l ca h kn < 10%.

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