Static Error EECS240 Spring Settling. Static Error (cont.) Step Response. Dynamic Errors. c 1 FA { V 1. Lecture 13: Settling

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1 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 rngng AD (wtched-ca aler): gan a gnal u by a rece aount wthn T ale Φ 2 Statc Error (cont.) o c c FA { FA relatve error Exale: loed loo gan: c -4, F, 4F, F F /6 ( hurt!) Φ Φ Φ2 Φ2 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 o L o c L + ( F ) () t v o, te tec e 23 deal reone 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 EES240 Lecture 3 7 EES240 Lecture 3 0 Te Doan Ste Reone ae 2: /z not neglgble Frequency doan: ote, z te Te doan: v () Relatve ettlng error: t o, te t tec e 23 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 0.%: t (no eedorward) 6.9 t (wth eedorward) -ln[e-3/(0.67*0.75)]7.3 EES240 Lecture 3 8 EES240 Lecture 3 Te Doan Ste Reone Frequency doan: nut te: te te, outut te: z z ote, te, te Te doan: (nvere Lalace tranor) t v () t ote, tec e 23 { 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 () o c n Le Model or non-donant ole: 0 ( ) Ku unty gan bandwdth o T u ( ) EES240 Lecture 3 9 EES240 Lecture 3 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 wth β 3dB, 3dB z α α wth bandwdth o T () << loed-loo gan (gnore eedorward zero): o c z n Le 3dB wth ( ) 3dB o Le EES240 Lecture 3 4 EES240 Lecture 3 7 Settlng Te Doublet Analy Settlng te : t 3 ( K) or 0, Otu at K3.3 Ste reone () te ( 3 ) db v t c Ae Be o, te wth B β ( β ) 2 A B EES240 Lecture 3 5 EES240 Lecture 3 8

4 Doublet Exale Slewng Tranconductor I v. : α β Model or (nonlnear) lewng aler Pecewe lnear aroxaton: Slewng wth 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. β 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 wthn 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 * o tlew tln o,te te EES240 Lecture 3 2 EES240 Lecture 3 24

5 Slewng Analy (cont.) Slewng erod: L xte, te, wth L x x x, te * o 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 3 25