Slide 1Slide 2Slide 3Steady-state tracking & sys. typesSlide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Example of tankSlide 23Slide 24Slide 25exampleSlide 27Slide 28Time domain response specifications0 0.2 0.4 0.6 0.8 1 1.2-0.200.20.40.60.811.2Step ResponseTime (sec)Amplitude0 0.5 1 1.5 2 2.5 3-0.200.20.40.60.811.21.41.6Step ResponseTime (sec)AmplitudeSteady-state tracking & sys. types•Unity feedback control:G(s) C(s)+-r(s)ey(s)plant Go.l.(s)+-r(s)ey(s)ololGGsrsy1)()(T.F. get & open, loop cut i.e. yto e from T.F. loop open the is )()()(..sGsesylos. an cancel can otherwise , need , If but :into factored be always can 00000,0)1()1)(1()1()1)(1(000110111110121....bNbabKanpNaaaNasasasasasbsbsbsTsTsTssTsTsTKGGmNNNNNNNnnnmmpNmbalolopslossslossslololoKsGessrsGssrsseetesrsGsysrsesrsGsGsy----11)(111)()(1)()(lim)()()(11)()()()()(1)()(0..0..0......step to :input step For:tracking state-steady:error tracking:loop-closedfinite )0(r, w.r.t.0" type" called is system the,0 If)K control alproportion with confused be not to p, small use here(11step toThen const.error position static called )0()(lim denote00..P....0abGKNKeGsGKloppsslolosp-. zero input with step acan track higher or 1 typeof systemA 011step to0 )0( ,2 or type ,1 typecalled is systemlarger or ,2or ,1 If. zero-non input with step acan track system 0 type01111000..00sspsslopsspsseKeaabGKNeabKe-higheror 1 for type 00 for type 11then,)(:unitnot is step Ifhigheror 1 for type 00 for type 11:input stepunit For 0000RabesRsrabessssconst errorvelocity static called:denoteramp to :ramp unit is If)(lim1)(1lim)(1lim)(11lim)(1)(lim1)()(0002002ssGKKssGssGssGsssGssressrsrolsvvolsolsolsolsssr(t)tsignal. input ramp a track not can system 0 typeramp to system, 0 type For-vsssnmmsvKeabsasasbsbsbsKbaN10limlim0,0,00000101000. error statesteady zero-non withramp tracks system 1 typefiniteramp to finite, 1: type ForssvssnmmsnmmsveKeabasasbsbsbasasbsbsbsKbaaN-,010limlim!0,0,0,11012101001010010. no withinput ramp a track can system higher or 2 typeramp to higher, or 2 type Forfactor a as s has still ones cancelssvssnmmsnmmsveKesasasbsbsbasasasasbsbsbsKbaaN-01limlim0,0,3,222310100012233010010  1type if :then unit, not is ramp If2type if 1type if 0type if :input ramp unit For-RKesRsrbaKevssvss1)(01201)(121)(1)(:23tttrssr- input onaccelerati unitassssssssKsGssGsssGsssGssree1)(1lim)(1lim)(11lim)(1)(lim20220300acc to r(t)t0-asssnmmsasaKeabsasasbsbsbsKasssGK10limlim0)(lim002001012000acc to den. in of factor no system, 0 type Forconstant. error onaccelerati the is sig. acc. tract tcan' system 1 or 0 typeacc to bu i.e.den. in of factor one i.e.. in of factor one system, 1 type For-asssnnnmmsaKeabsasasasbsbsbsKaassGs10limlim0,0)(11000111012010error. s.s. finite withsig.acc tract can system 2 typeacc to orden. in of factors two or, in of factors two :2 type-01)0(0lim0,0,01,20202022110120210baKebabsasasbsbsbsKaaasGsNassnnnmmsaerror. s.s. nowith sig. acccan tract syst.higher or 3 type01acc to0lim0,03higher or 3 type0331101200210-assnnnmmsaKebsasasbsbsbsKbaaaNstabilize. to difficult are system higher or 2 type but tracting. bettertyper larger like seems :Cautionby A. multiplied be to needs then, :rather acc, unit not If3type if 2type if 0,1type if acc to :input acc. forsummary --ssassettAbaKe)(12101202r(t)=R·1(t)r(s)=R/sr(t)=R·t·1(t)r(s)=R/s2r(t)=R·1/2·t2r(s)=R/s3type 0(N=0 a0≠0)Kp=b0/a0ess=R/(1+Kp)Kv=0ess=∞Ka=0ess=∞type 1(N=1 a0=0 a1≠0 b0≠0 )Kp= ∞ess=0Kv=b0/a1ess=R/KvKa=0ess=∞type 2, N=2a0=a1=0 a2≠0,b0≠0Kp= ∞ess=0Kv= ∞ess=0Kp=b0/a2ess=R/Katype≥3, N ≥ 3a0=a1=a2=0 b0≠0Kp= ∞ess=0Kv= ∞ess=0Ka= ∞ess=0sys.typeref.inputExample of tankassvssppssavppploppKeKeRKKeKKRKGKNRAsRKsHsCsGKsCRAsRsHK1111110,)0(00,1)()()()(,1)(..acc to ramp to step to type :control H+- CassIvsspssaIsvpIpIpIpKeRKKeKeKRKssGKKNsRAssRKsKsHsCsGsKsKsKKsCsH1110110,)(lim,1)1()()()()()(),(0acc to ramp to step to type den, in of factor one but same :control PIthe to loop the following from path the in #T.F. loop open the in #i.e. in # is w.r.t.type sys.type. sys. is tracking statesteady toKey esssGssr11)(1)(+r(s) Kps+KIs+-r(s)e ωn2s(s+2ξ ωn) 1Ts+1)(1srs w.r.t.2 type 2 :path in #count e.g.example1type one is there:default Takespecified. dist. or input No :Noteacc. ramp. step. to error statesteady & constants error type, system find,1)5.0)(5.1()15.3()(sssssKsG G(s)r(s)e(s) y(s)KKeeeKKKssGKKvssssssasvp2.411002.45.05.115.3)(lim0ramp to 1 type for acc to 1 type for step to 1 type for 1 type for12112151215)(lim2002,221)5)(12()1(5)(202asssassssvpKesGsKeeKKssssssGacc to typeramp to step to type type