Haust 2003 - ’"Héskéli Islands /R 11 - Stofur...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ’"Héskéli Islands /R 11 - Stofur 258 o 261 ’réfstaéur Eintakafjbldi: "’ Skrifle gt préf ‘ C 2 314%, 4 (arm Deild: Verkfraabideild Kennari: Olafur Pétur Pélsson, désent. Sfmar; Hs.: 0 vs.:525-4952 - GSM: 082160-0 Sjélfvirk styrikerfi Nfimer 0g heiti préfgreinar: Préfdagur 0g timi: Miavikudagur 17. desember 2003 kl. 13:30-16:30 Hjélpargfign: D Baekur, greinar Oll Skrifleg hjdlpargbgn leyfileg nemafartc‘ilvur g] Rfiaustrikua préfbék E Reiknitélva D Tb'lva mefj textaminni D Onnur gégn 65a taeki (")nnur fyrirmaeli: Aagangur af) préfverkefni ab loknu préfi [:l Kennari veitir aégang a6 préfverkefni Kennslusvié sendir eintak til Héskélabékasafns Lokafrestur til a6 skila einkunnum: MiaVikudagur 14. janfiar 2004 Héskéli islands Verkfraeaideild 08.21.60 Sjélfvirk styrikerfi (")ll hjélpargiign leyfileg nema fartfilvur 17. des. 2003 kl. 13:30-16:30 Daemi 1 (20%) R1 (S) Y1 (s) R3(s) Kerfié é myndinni hefur brjfi innmerki 0g tvé fitmerki. a) Finnié 611 6 yfirfaarslufél] kerfisins. b) Skrifié upp fistandsh’kan sem lysir sambandinu milli Y2(s) 0g Rl(s). Daemi 2 (20%) Gcfié er eftirfarandi ll’kan é éstandsformi x1 — 5 l x, 1 0 u, = + 5c: — 4 0 x2 1 —l u2 yl _ 1 1 X] y 2 — — l 0 x2 a) Er kerfié stbéugt? b) Finnié yfirfasrsluféllin (bau eru fjégur). c) Leggié til eina aéra éstandsframsetningu sama kerfis. Daemi 4 (30%) Tiénisvérun épekkts yfirfzerslufalls (G(s) é reitamyndinni hér a6 neéan) mé sjé é mynd 1 0g nzikvxmari gildi fttiflu l a) Ritié upp 0g rissié fitmerkié, C(t), begar kerfié er 1' stbéugu éstandi 0g innmerkié er einingarbrep x(t) = l . b) Endurtakié 1i??? 3) fyrir innmerkié x(t) = 25in(t) (s + 0,1) S X(s) C(s) c) Hvaé kallast pessi stirring? been via NL’1 er styn‘ngunni Gr(s) =10 d) Endurtakié liéi a) 0g b) M C (s) H Sty/ring NL’1 er lykkjunni lokaé eins 0g synt er é myndinni hér a6 ofan. e) Endurtakjé a6 lokum a) 0g b) fyrir lokaéa kerfié. Tafla 1 BodeDiagram 5:? E .... w [id -1 a” was 1 0‘ Mynd 1 Frequency (radisec) 2 H3 Haskéli islands Verkfraefiideild 08.21.60 Automatic Control (Sjalfvirk styrikerfi) 011 hjalpargiign leyfileg nema fartiilvur 17. des. 2003 kl. 13:30-16:30 Example 1 (20%) Y1 (s) R3(s) The above system has three inputs and two outputs 3) Find all of the 6 transfer functions. b) Write a state space representation of the relationship between Y2(s) and R1(s). Example 2 (20 %) Given the following state space representation lift: (Slim fillil ltHL slil a) Is the system stable? b) Find the four transfer functions. c) Propose another state space representation for this system. Example 3 (30%) A system is described by following block diagram: It is known that the transfer function of the controller is 013) = K (s +b) (that is PD—controller) but the system it self can have three different transfer functions i) 0(5): 3:61 .- — l 11) GM" S(s+a) pp: 1 ill) GWZW where b = 2a > 0. In the following answers major calculations are not needed. a) Sketch the root locus for these three systems without the control. b) Sketch on the same plot the root locus of the system with the control and describe the effect of the controller on this system. c) Sketch the Bode plot for these three systems without the control. d) Sketch the Bode plot for the system with the controller on the same plot as in c) and show the effect of the controller. e) Sketch the Nyquist plot (polar plot) for the three cases with and without the controller. Example 4 (30 %) Frequency response for an unknown system (with transfer function (6(5)) is shown in figure 1 and table 1 X“) C(s) a) Find the output of this system in steady state when the input is unit step x(t) = l. b) Repeat a) with the input x(t) = 2sin(t) (s + 0,1) . Now the controller Gr. (3) =10 IS added as shown in the figure S c) What is the controller called? (1) Repeat a) and b) Now the loop is closed as shown in the figure above. e) Finally, repeat a) and b) for the closed loop. WW» . —~—q~«-_-—Ww -- 7— «~~—-»-—-w Table 1 0.1000 0.1129 0.1833 —15.6675 0.2976 -25.2282 0.4833 40.1875 0.7848 -63.0046 1.0000 -78.6901 1.2743 -98.8807 2.0691 -158.0950 3.3598 —10 8193 -210.7501 5.4556 —23 8169 -236.6598 8.8587 -36.6818 -250.l780 252.5211 Bode Diagram Magnitude [d3] Phase [deg] Frequency (radisec) Figure 1 ...
View Full Document

Page1 / 8

Haust 2003 - ’"Héskéli Islands /R 11 - Stofur...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online