Static Error EECS240 Spring Static Error (cont.) Settling. Step Response. Dynamic Errors V 1. c 1 FA. Lecture 13: Settling
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1 Statc Error EES240 Srng 202 Lecture 3: Settlng KL o c FA T o Elad Alon Det. o EES - o /A v tatc error te F c EES240 Lecture 3 4 Settlng Why ntereted n ettlng? Ocllocoe: track nut waveor out rngng AD (wtched-ca aler): gan a gnal u by a rece aount n T ale 2 Statc Error (cont.) c c FA FA relatve error Exale: loed loo gan: c = -4, = F, = 4F, = F F = /6 ( hurt!) 2 o Error eccaton: <0.% FA > 000 A > 6000 over outut range EES240 Lecture 3 2 EES240 Lecture 3 5 Ste Reone Two tye o ettlng error : Statc Fnte gan, caactor atch Dynac Take te to reach nal value - o /A v Dynac Error Many oble dynac eect that act ettlng error: Fnte bandwdth Feedorward zero Non-donant ole Doublet Slewng Aroxate analy aroach: Decooe each error ource, olate nteracton Add all error together te EES240 Lecture 3 3 EES240 Lecture 3 6
2 Sngle Te ontant Lnear Settlng ae : /z << For dynac ettlng (and or T 0 >> ), can generally gnore r o x G L G c L F t v o, te tec e deal reone t Relatve ettlng error: t t t e t t ln Eaet nuber to reeber: 2.3 er decade Exale: % ettlng, 4.6n clock cycle: = n L,e uually et by noe ue ettlng to deterne requred g t EES240 Lecture 3 7 EES240 Lecture 3 0 Te Doan Ste Reone ae 2: /z not neglgble Frequency doan: ote, z c te Note: Te doan: For =z the error zero and the crcut ha nnte bandwdth. Alcaton? t v Relatve ettlng error: o, te t tec e z deal reone t t t e t z t ln F Le Exale: c = 0.25, = F, = 250F, = 250F, L = F F = 0.67, L,e =.33F ε = 0.%: t (no eedorward) = 6.9 t ( eedorward) = -ln[e-3/(+0.67*0.75)]=7.3 t EES240 Lecture 3 8 EES240 Lecture 3 Te Doan Ste Reone Frequency doan: nut te: te te, outut te: z c z c ote, te, te Te doan: (nvere Lalace tranor) t v t ote, tec e z deal reone ntal error (eedorward) exonentally decayng error Non-Donant Pole Ignore eed-orward zero or lcty (Jut ncreae nal wng by +F / L,e ) H c n Le Model or non-donant ole: G0 G 2 2 Ku unty gan bandwdth o T u EES240 Lecture 3 9 EES240 Lecture 3 2 2
3 Ste Reone Non-Donant Pole v. Otu K actually deend on requred accuracy Stll, alway want to ad K<~2 EES240 Lecture 3 3 EES240 Lecture 3 6 Non-Donant Pole (cont.) Doublet Relatve error : - v ( t, K) Aler odel: G () G o z z 3dB, 3dB bandwdth o T loed-loo gan (gnore eedorward zero): c z c n Le 3dB 3dB o Le EES240 Lecture 3 4 EES240 Lecture 3 7 Settlng Te Doublet Analy Settlng te : t 3 K or 0, Otu at K=3.3 Ste reone te t 3 t db v t c Ae Be o, te B 2 A B EES240 Lecture 3 5 EES240 Lecture 3 8 3
4 Doublet Exale Slewng Tranconductor I v. : =.5 =0.3 Model or (nonlnear) lewng aler Pecewe lnear aroxaton: Slewng contant current, ollowed by Lnear ettlng exonental t = t lew + t,ln EES240 Lecture 3 9 EES240 Lecture 3 22 Doublet oncluon ae A: 2.e. Doublet ettle ater than aler Ha no act on overall ettlng te Slewng Analy rcut odel durng lewng: ae B: 2 Doublet ettle ore lowly than aler Deterne overall ettlng te (unle n ettlng accuracy requreent) x I SS L o Ad low doublet! EES240 Lecture 3 20 EES240 Lecture 3 23 Fnal Note on Doublet Slewng Analy (cont.),te x x,te * tlew tln,te te EES240 Lecture 3 2 EES240 Lecture
5 Slewng Analy (cont.) Slewng erod: L xte, te, 2 2 L x x x, te * F o x Le tlew SR FI SS Lnear ettlng durng nal * o wng at x : Ste durng lnear ettlng: * F t, ln cte, F Lnear ettlng te: ln * EES240 Lecture
Static Error EECS240 Spring Settling. Static Error (cont.) Step Response. Dynamic Errors. c 1 FA { V 1. Lecture 13: Settling
Statc Error EES240 Srng 200 Lecture 3: Settlng KL o c FA { T o Elad Alon Det. o EES - o /A v tatc error te wth F + + c EES240 Lecture 3 4 Settlng Why ntereted n ettlng? Ocllocoe: track nut waveor wthout
EECS240 Spring Lecture 13: Settling. Lingkai Kong Dept. of EECS
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