Previous lecture. Lecture 5 Control of DVD reader. TheDVD-reader tracking problem. Can you see the laser spot?

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1 Lecture 5 Control of DVD reader Previou lecture Focu control Radial control (Track following) Lecture 4: Specification in frequency domain Loop haping deign Problem formulation Modeling Specification Focu loop haping Radial control (track following) Thi will be ued in both today cae tudy and in Lab 1. Don t forget to ign up for lab 1 on home page. Experimental verification baed on work by Bo Lincoln TheDVD-reader tracking problem Scaled verion of the control tak in a DVD player You are traveling at half the peed of light, along a line from which you may only deviate 1 m The line i not traight but ocillate up to 4.5 km ideway 23 time per econd Good luck! TheDVD-reader tracking problem Can you ee the laer pot? Track 3.5 m/ peed along track.22 µm tracking tolerance 1 µm deviation at 23 Hz due to aymetric dic.74 µm DVD Digital Veratile Dic, 4.7 Gbyte CD Compact Dic, 65 Mbyte Dik Sledge Pick up head 1

2 Track Radial electromagnet Len Spring Focu electromagnet Light detector Laer Input-output diagram for DVD control Thefourphoto detector vertical force Focu error radial force PUH & Dik Radial error focu error = (AD) (BC) Note: There are no other enor in the pick-up head to help keep the laer in the track. Focu error ignal Radial error by puh-pull Poible to ee track Focu Error Correct focu Len height Too low Too high Look at (AC) (BD) Radial error by phae-difference (DPD) Radial error ignal 1 track f1 f2 Radial Error Correct radial poition DPD PP Radial poition f 1 =AD, f 2 =BC Error ignalre created be time difference Note: Larger linear error region if uing DPD. 2

3 Experimental frequency repone model Idea/Purpoe Matematical model and pecification Analyi Magnitude 1 5 Bode diagram 5 Experiment Synthei Phae (deg) Frequency (rad/ec) Implementation P f ()= What Signal are Relevant for Focu Control? Specification Cancel diturbance due to dic aymmetry C(iω)P f (iω) 1 for ω 23.1 Hz d r e u F Σ C Σ P x Σ n y Reject meaurement noie C(iω)P f (iω) 1 for ω>2khz 1 (Compare to the bit rate, which i in the order of1mhz) Firt Order Lag Compenator Lead and Lag Compenator Ue lag-filter to increae the gain below24 Hz. The break point need to be well below 2 khz in order to avoid additional phae lag at the cut-off frequency:c 1 ()=.4 6 Further compenation i needed for tability. A lead filter to increae the phae near 2 khz;c 2 ()=.4 6 1/5 1/5. Adjut gain The gain need to be adjuted at high frequencie. Now the cloed loop ytem i table with good margin, but the gain at 23.1 Hz i till too low, jut 1 intead of 1; Final controller The gain at 23.1 Hz can be corrected by modifying the break point of the lag filter to get the final controller C()= /5 1/5. Notice that ( thi i very imilar ) to a PID controller of the form C()=K. 1 T i T d 1T d /N 3

4 Radial control Make the laer follow the track by moving "ideway"/radially The Focu control problem i eential to olve firt Rotation center Track poition Eccentricity Tracking via Move len (electromagnet/fat motion) Move ledge (low/large range) Diturbance Track Time Figure: The dic i often a bit eccentric (i.e. not rotating around the track center). The reulting track poition, which the Pick-Up-Head ha to follow, i a inu-like. eccentric (up to 1 track in one rotation) phyical vibration of DVD-player noie (dirt etc) An etimated tranfer function for the radial ervo (from the control ignaluto the radial errorre) DVD pecification (tandard ECMA-267) 1 Bode Diagram Phae (deg) Magnitude (db) Frequency (rad/ec) Sytem identification made by inuoidal excitation. The plot on previou lide i a copy from the DVD pecification, tandard ECMA-267. The plot how the pecified 1G radial C radial, which i the invere of the enitivity function, and the curve correpond roughly to the open-loop tranfer function. In clear text, the pecification require the following: A low-frequency (< 23 Hz) gain of 7 db or more for the open-loop ytem. A cut-off frequency of ω c =2.4 khz=15 krad/. Differentdeign choice There are a number of different deign method to ue Example: Loop-haping Pole-placement LQG ("State feedback" in combination with Kalman filter)... Problemwith outputditurbance How to get rid of ocillation? The eccentricity caue problem (about 1-2 Hz and ocillation of up to 1 track). Can t be exactly modeled due to uncertainty. Ocillation C radial u G radial RE 1 How to proceed? Figure: A model of how the dik ocillation affect the ytem. For example, if the ocillation offet at ome point in time i 6.2 track, the DVD radial ervo ha to be at 6.2 track too to have zerore. 4

5 From lecture 3... Ifw 1 andw 2 i colored noie then re-writew 1 andw 2 a output ignal from linear ytem with white noie inputv 1 andv 2. v 1 H v 2 e w 1 =G 1 (p)v 1, w 2 =G 2 (p)v 2 Make a tate pace realization ofg 1 andg 2 and extend the ytem decription with thee tate ẋ(t)=ax(t)bu(t)nv 1 (t) z(t)=mx(t)d z u(t) y(t)=cx(t)d y u(t)v 2 (t) where the extended tatex conit of the tatexand the tate from the tate-pace realization ofg 1 andg 2. A i the correponding ytem matrix for the extended ytem etc. u G RE Figure: Noie model: There i both white proce noiev 1, and a track-offet which i modeled a the white noiev 2 through a filterh. When deigning a tate etimator, we can give the Kalman filter a hint of what to expect, by modeling the eccentricity a white noie through a filterha hown in the figure above. The filter H hould have a high gain in the frequency range where the ocillation act. Experiment Track Radial electromagnet Len Spring Focu electromagnet Laer Light detector vertical force radial force PUH & Dik Focu error Radial error DEMO Summary Reference Problem formulation Modeling Specification Focu loop haping Track following pec diturbance modelling LQG-deign will follow in Lecture 9-11 Experimental verification See alo handout Lecture note L5 (available from lu.e-domain) "Sening and Control in Optical Drive How to Read Data from a Clear Dic" by Amir H. Chaghajerdi, June 28, IEEE Control Sytem Magazine, pp Next lecture Lecture 6 Controllability and obervability Singular value Multivariable zero - L1-L5 Specification, model and loop-haping by hand L6-L8 Limitation on achievable performance 5

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