[8] K. Ogata, Modern Control Engineering. Prentice-Hall Instrumentation and Controls Series,

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1 [8] K. Ogata, Modern ontrol Engineering. Prentice-Hall Instrumentation and ontrols Series, Englewood lis, New Jersey: Prentice-Hall, [9] G. F. Franklin, J. D. Powell, and M. L. Workman, Digital ontrol of Dynamic Systems. Menlo Park, alifornia: Addison-Wesley, second ed., [10] E. Levy, \omplex-curve tting," IRE Transactions on Automatic ontrol, vol. A-4, pp. 37{ 43, [11] J. L. Adcock, \urve tter for pole-zero analysis," Hewlett-Packard Journal, vol. 38, pp. 33{37, January [12] Hewlett-Packard, urve Fitting in te HP 3562A, product note p 3562a-3 ed., [13] Hewlett-Packard, z-domain urve Fitting in te HP 3563A Analyzer, p 3563a-1 product note ed., [14] R. L. Dailey and M. S. Lukic, \MIMO transfer function curve tting using cebysev polynomials." Presented at te SIAM 35 t Anniversary Meeting, Denver, O, October [15] H. Vold and A. Mel, \Pase errors in complex mode structural modication," Sound and Vibration, vol. 26, pp. 32{34, June [16] M. D. Sidman, F. E. DeAngelis, and G.. Vergese, \Parametric system identication on logaritmic frequency response data," IEEE Transactions on Automatic ontrol, vol. 36, pp. 1065{ 1070, September [17] Bruel & Kjr, Multicannel Analysis System Type 3550, [18]. Moler, J. Little, S. Bangert, and S. Kleiman, P-MATLAB User's Guide. Te MatWorks, Inc., Serborn, MA, Nov Version 2.0. [19] G. Bouwuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, and K. S. Immink, Principles of Optical Disc Systems. Bristol and Boston: Adam Hilger, Ltd., [20] A. B. Marcant, Optical Recording: A Tecnical Overview. Menlo Park, alifornia: Addison- Wesley,

2 Wile tey may seem like simple, intuitive concepts, tey are not easy to maintain wen trying to actually make someting work. However, olding true to tese ideas as allowed te BMW to do tings far beyond te sum of its individual components. As tis paper as attempted to sow, it allows a researcer working on disk drive servos to try some novel designs wit a minimum amount of pain. 7 Acknowledgements Te autor would like to tank arl Taussig and Lennie Kiyama, bot from HP Labs, for teir contributions to te BMW. arl created te interface between te BMW and te HP 3563A. Lennie designed te new A/D board used on te BMW. Muc of te current usefulness of te BMW is due to teir eorts. References [1] L. Ljung, System Identication: Teory for te User. Prentice-Hall Information and System Sciences Series, Englewood lis, New Jersey 07632: Prentice-Hall, [2] L. Ljung and T. Soderstrom, Teory and Practice of Recursive Identication. MIT Press Series in Signal Processing, Optimization, and ontrol, ambridge, Mass 02142: MIT Press, [3] G.. Goodwin and K. S. Sin, Adaptive Filtering Prediction and ontrol. Information and Systems Science Series, Englewood lis, N.J : Prentice-Hall, [4] Hewlett-Packard, ontrol System Development Using Dynamic Signal Analyzers: Application Note 243-2, [5] Hewlett-Packard, HP 3563A ontrol Systems Analyzer, [6] J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurement Procedures. New York, NY: Jon Wiley & Sons, second ed., [7] G. F. Franklin, J. D. Powell, and A. Emami-Naeini, Feedback ontrol of Dynamic Systems. Menlo Park, alifornia: Addison-Wesley, second ed.,

3 6 - A/D - BMW DSP - D/A - m - A/D - Drive DSP - D/A o o - PA/ VM - Arm Mec. Figure 11: Te Bansee DSP can be tougt of as being \clipped" into an existing drive's servo loop as sown. 5 Future Improvements Tere are a few improvements tat could greatly upgrade te convenience of te system. First, a migration from running out of MS-DOS to MS-Windows would greatly improve te data andling capabilities. Tis depends upon a Windows version of Matlab being available (it is now) and porting te Interface Program to MS-Windows. Secondly, te Bansee code can be augmented to include state-space implementation. Tis sould be fairly straigtforward. Finally, porting more of te SA functionality to Matlab m-les and increasing te exibility of te Matlab code would elp. Tese improvements could also be considered as te steps to turning te BMW into a product, rater tan simply being a researc tool. If based on an \open systems" approac, it could be extended to use next generation measurement instruments, oter DSP arcitectures, oter AD programs, and even run on dierent computer arcitectures. 6 Summary Te BMW is built on some very simple yet powerful concepts, namely: run te DSP board from Matlab, leverage existing ardware and software, and blur distinctions between instrumentation, implementation, and analysis. 18

4 50 Plant 00 (s) 50 Plant 01 (s) Mag (db) 0-50 Mag (db) Frequency (Hz) Frequency (Hz) 100 Plant 10 (s) 100 Plant 11 (s) Mag (db) Mag (db) Frequency (Hz) Frequency (Hz) Figure 10: Plant magnitude response for MO servo system. 4 Using te BMW for Magnetic Servo Work An example of ow te BMW could be used in magnetic disk drive researc is sown in Figure 11. onceptually, tis is accomplised by clipping te output lead of te drive's D/A converter it is possible for te Drive DSP to continue to do all te non servo loop specic tings tat it normally does (e.g. spindle motor control, andsaking wit te microcontroller). In practice, tere is a little more tat as to be done to allow te drive DSP to and o te actuator control to te Bansee. Furtermore, functions suc as seek algoritms, reading te track number, and position error signal (PES) decoding may ave to be recoded in te Bansee. However, te large memory space and fast oating point calculations of te Bansee causes tese functions to ave less of an eect on te Bansee DSP tan on a typical drive DSP. By recoding only tose functions tat are necessary, te Bansee DSP is left predominantly free to concentrate on servo algoritms. It sould be fairly clear tat te rapid prototyping, system modeling, and data collection capabilities of te BMW discussed earlier are just as applicable for tis problem. 17

5 20 L Resp. 00 (s) -20 L Resp. 01 (s) Mag (db) Mag (db) Frequency (Hz) Frequency (Hz) 20 L Resp. 10 (s) 10 L Resp. 11 (s) Mag (db) Mag (db) Frequency (Hz) Frequency (Hz) Figure 9: losed-loop magnitude response for MO servo system. reference to focus output, te 10 loop is from focus reference to track output and te 11 loop is from track reference to track output. A key dierence between SISO and MIMO measurements is apparent from tese gures. Note tat even toug te open-loop plant frequency response function from tracking actuator input to focus actuator output (loop 01) is te same order of magnitude as te open-loop plant focus input to focus output frequency response function (loop 00), te closedloop responses are considerably dierent. Tese measurements were made digitally by te SA working wit te BMW. Eac input/output pair was done individually, te results were saved to.mat les, and tese were uploaded to Matlab. Furtermore te compensators were measured openloop and tese measurements were also uploaded to Matlab. By applying Equation 5 in Matlab, te MIMO closed-loop frequency response function, T, can be unwrapped and te MIMO compensator frequency response function,, can be factored out, yielding te MIMO plant frequency response function, P. Te magnitude response of te MIMO plant is sown in Figure 10. urve tting can be done up in Matlab, or eac of te individual frequency response functions can be downloaded into te SA to use its curve tter. Finally, te zero, poles, and gain (ZPK data) can be uploaded back into Matlab. 16

6 Reference (R) m Error (E) ontrol Inputs (U) P Plant Outputs (Y ) Figure 8: MIMO analysis is simplied by using vector signals and matrix transfer functions. As stated earlier many systems can only be measured wile in a feedback control loop. Tus, closed-loop measurements are made using some nominal compensator. Te measurement is ten opened to get at te open-loop frequency response function, P and nally to P. From ere, a iger performance compensator can be designed. On an optical drive, tese are te tings we can measure (eiter continuous or discrete time): T = (I + P ) 1 P = P (I + P ) 1 Transfer function from R to Y S = (I + P ) 1 Transfer function from R to E By direct measurement or computation (3) were T, S,, and P are transfer function matrices and R, E, U, and Y are signal vectors. To get at P we unwrap tese using matrix waveform mat: P = S 1 I or (4) P = T (I T ) 1 = (I T ) 1 T : (5) and factor out. Note tat altoug te compensator was syntesised in Matlab and terefore sould be known, a measurement of provides a ceck tat te DSP is in fact implementing te design properly. If te frequency response function of is not measured, ten it must be syntesised wit te same frequency axis as te measurements of T or S. Tis ensures tat te matrix waveform mat can be done correctly. An example of tis can be seen in Figures 9 and 10. Figure 9 sows te four closed-loop frequency response function measurement of an optical actuator. Te compensator is implemented as a pair of tird order IIR lters in a diagonal conguration ( 01 = 0 and 10 = 0) wic are sampling data at 25 khz. As above, te 00 loop is from focus reference to focus output, te 01 loop is from track 15

7 6 6 H 10 - P 01 r 0 - m - e 0 u m P00 - m Focus Loop y 0 H 01 - P 10 r e 1 u m m P11 - m Tracking Loop y 1 Figure 7: SISO control loops wit cross coupling added. Figure 5 and discussed below. By proper alignment of te detector wit te grooves we can form a focus error signal (FES) and a tracking error signal (TES) tat are ortogonal to eac oter. FES = TES = A + D - k(b + ) A + B + + D A + B - ( + D) A + B + + D (1) (2) Te normal way of looking at focus and tracking is tat tey are completely decoupled as sown in Figure 6. Here P 00 is te focus portion of te actuator, 00 is te focus compensator, P 11 is te tracking portion of te actuator, and 11 is te tracking compensator. Rotary actuation canges te skew angle, making it impossible to decouple te system by simple optical alignment. Wen te coupling is modeled as in Figure 7, te problem can seem intractable. Here te P ij ; i 6= j; can be tougt of as mecanical coupling. Te H ij ; i 6= j; can be tougt of as sensor or optical coupling. A major conceptual simplication is seen in Figure 8. Te key ere is switcing from tin lines to tick lines { also known as going from a scalar to a vector representation. and P represent transfer function or frequency response function matrices. Note tat te sensor module, H, as been lumped wit P ere. 14

8 6 6 T T T 3 Using te BMW for Magneto Optic Drive Servo Researc Tracking () Optical Disk Focus m Wat lens is looking at: ' $ & % A D Detector B Figure 5: Te magneto-optic drive servo problem ontrol Plant Reference 0 - Error 0 m - Input Output 0 P00 Focus Loop ontrol Plant Reference 1 - Error 1 m - Input Output 1 P11 Tracking Loop Figure 6: Focus and tracking as separate 2 Single-Input, Single-Output (SISO) systems Figure 5 sows te optical drive servo problem. An optical drive operates in te far eld of te lens, so it must bot focus and track (as opposed to only tracking for magnetic drives { wic are near eld devices). Te optical disk is grooved, wic forms a diraction pattern on a segmented detector. Tere are many possible servo detection scemes [19, 20], but most (on grooved media) depend upon detector alignment wit te grooves. An example of a detection metod is sown in 13

9 Host. Te Host in turn can save te data into.m or.mat les for use in Matlab. Furtermore,.mat les tat contain te appropriate elements can be downloaded to te SA so tat te waveform processing routines on te SA can be used. ommunication between te Host and te SA are done over te HP-IB. Te measurements can be analog or digital. Bot measurement traces and zero-pole-gain (ZPK) tables (obtained from curve ts) can be uploaded to te ost. Te traces contain binary oating point data wic must be converted to te IEEE format wen tey are uploaded. Likewise, wen a.mat le version of a trace is downloaded, its oating point format must be converted back. Special data structures ave been created tat contain all te information in a trace or in a ZPK table. In order to do digital measurements, te digital pods of te SA are interfaced to te Bansee. Furtermore te Bansee is programmed to inject and extract signals into te appropriate servo loops. Te Interface Program coordinates te Bansee wit te SA. Wen analog measurements are being done, te Bansee is not involved. Te Interface Program disconnects te Bansee and signals are brougt in and out troug te front panel BN connectors of te SA. Wen making digital measurements, te timing of signals becomes quite important. In digital measurement mode, te SA expects a time delay of at least one sample between te signal it puts on te digital bus and te return signal tat it receives. Tus, in te clocking sceme used ere, te signal tat te Bansee writes to te SA is paired wit te signal tat was read from te SA on te previous clock cycle. Furtermore, te Bansee can output a control signal to te D/As wit eiter a full or fractional sample delay between it and te previous A/D read. Wile it is possible to measure a frequency response wen te compensator as a fractional sample delay, tis delay must be removed before doing a curve t. Te sample delay must be correctly known in order to get a reasonable curve t [13]. In te fractional sample delay case, te delay may cange wit dierent compensators or from one loop to anoter, so te delay as to be measured for eac input-output pair. A simpler solution, from te measurement perspective, is to use a full sample delay in te compensators wic will be used in te measurement. Altoug, tis would not be used in a nal compensator, due to te loss in pase margin, it does make te loop unwrapping and curve t muc simpler for te MIMO case. Tis is wat as been used in Figures 9 and

10 amount of memory free for oter operations suc as loading.svo les or interfacing wit te HP 3563A. Finally, te data gatered on any run can be saved into a.m or.mat le for Matlab's use. Data collection works as follows. A record is set up wic tells te Bansee wic variables to store at eac time step. At te start of data collection, control of communication goes from te Host to te Bansee, wic continues to run te control loop and stores te data record for tat time step in te Bansee's Dual Ported RAM. Tis signals te Host, wic unloads te data into a buer in system (DOS) RAM and sends a andsake back to te Bansee. At a sample rate of 25 khz, tere as been no discernible performance eect of storing 10 variables per time step. 2.5.svo MIMO Servo Files Te mecanism for aving Matlab download MIMO servos to te Bansee is also quite exible. Te data transfer is done troug a special le format, called a.svo le. Te key to te.svo le is tat it allows a dynamic data structure olding te entire servo to be allocated as it is being read. Wile tis may seem a minor issue at rst glance, it is quite important given tat Matlab can design servos in eiter transfer function (IIR lter) form or state space form. Eac of tese forms may be implemented in eiter form on te DSP. Any useful le format must allow te Interface Program to create te needed data structure as it reads te le. Furtermore, te structure sould be exible as te number of plant inputs and outputs may vary for any given problem. urrently, bot transfer function forms and state space forms ave been specied for.svo les. Tis le structure leaves open te possibility for many oter servo structures. Te key is tat all can be written easily by Matlab and read quickly by te Interface Program. Te dynamic allocation is essential to te exibility of tis le structure since it allows controllers of dierent orders to be constructed. 2.6 Interface to Dynamics Analyzer Te BMW expands te capability of te SA to Multi-Input, Multi-Output systems. Tis is accomplised by transferring data up to Matlab and performing matrix waveform matematics tere. Data can ten be transferred back to te SA to make use of te signal processing capabilities tere. Of course, te signal processing algoritms in te SA can be ported to Matlab tereby eliminating te need for transferring te data back. Te Interface Program sets up te SA measurements and collects measurement data at te 11

11 2.3 Te Host/Matlab Interface Te interface between Matlab and te Interface Program can be done eiter by memory partition swapping (using P-Matlab) or by issuing a sell escape from eiter AT or 386 Matlab. In bot cases, all transfer of data between te two is troug special le types:.m,.mat, and.svo. Te.m and.mat les are standard le types for Matlab. Te.svo format was especially created to allow Matlab to pass MIMO servos down to te Bansee troug te Interface Program. Te Interface Program is designed to be able to pause its operation wile Matlab runs and resume its operation wit anoter sell escape from Matlab. To do tis te Interface Program keeps a set of variables tat contain te state of te Bansee. Tese are saved into a set of disk les, as well as any oter dynamic data structures tat are currently in memory. Wen te Interface Program resumes, it scans te directory for tese les. If tey exist, ten teir contents are restored into memory and te program continues. 6 If tey are not present, ten te Bansee is assumed to be reset and data variables are initialized. Wit tis sceme, te Interface Program can be considered simply a routine run from Matlab. Te data analysis and servo design is all done in Matlab, and a few key strokes lead to te implementation of a design at te Bansee. 2.4 Real-Time Data ollection Real-time data collection is very exible. Te user as te ability to specify bot te names of te variables to be monitored and te number of samples for wic data collection will be done. Any memory location (and ence any variable) may be monitored by declaring a pointer to tis datum and making it global. Tis second level of indirection allows monitoring of variables for wic te pysical location may cange during te data collection. Te Interface Program produces a table of all te variables available for monitoring wic te user can coose from in a menu fasion. Te only oter information tat te user need specify is weter a particular variable is a 30 oating point or a long integer. In te former case, te variable will ave to be converted to IEEE oating point. Te total size of a data run can not exceed te amount of free RAM wic can be dynamically allocated 7. urrently, tis does not include any memory above 640K. Tis limits te number of records of a given size tat can be taken. Doing tis dynamically leaves te maximum 6 Tis essentially uses te computer disk as a stack, were te Bansee state is \pused" upon exit and \popped" upon re-entry. 7 Known as te eap. 10

12 As mentioned earlier, te SA is a dynamics analyzer for making measurements of bot analog and digital control systems. Quite a few signal processing features are included in te instrument and it can be connected to oter computers via an HP-IB port [5]. 2.1 MIMO Servos at te Bansee In order to preserve muc of Matlab's exibility, a decision was made to implement compensators in one of several general structures, e.g. polynomial form IIR or state space, were te size and parameters of te structures could be easily modied during operation by te Interface Program. Tese few general structure could ten be coded eciently in te DSP assembly language so as to minimize te overead of te general structure's exibility. Tis combination of exibility and speed was made considerably easier to implement by te oating point nature of te TMS32030, wic eliminates most of te need for scaling. urrently compensators at te Bansee are implemented as IIR digital lters. Unlike lters in xed point DSPs, tere are far fewer scaling problems in oating point. Tus, typical scaling tecniques, suc as factoring numerator and denominator polynomials into biquad sections, can be eliminated. Tis allows direct implementation of te transfer function form of compensators designed by Matlab. State space compensator designs may also be implemented by converting tem to polynomial form lters before downloading tem. Te BMW as m-le scripts wic create polynomial form IIR.svo les from Matlab state space design. (Direct implementation of MIMO state space compensators is possible but as not been coded yet.) 2.2 Te Interface Program Te Bansee runs asyncronously from te Host and only needs to interface wit it wen tere is a message passed down from te Interface Program. Te Host runs two programs, Matlab and te Interface Program as sown in Figure 4. Te Interface Program coordinates te interaction of te Bansee and te SA, runs te SA, directs te Bansee's real-time data collection, transfers complete MIMO servo les (.svo les) to te Bansee, and controls te interaction wit Matlab. Te next few sections will discuss tese. 9

13 H researc. Section 5 will discuss possible future enancements to tis system and Section 6 will give a sort summary. 2 How te BMW works.svo les servo parameters Matlab Interface Program Real-Time Data Traces, ZPK.mat &.m les Floating point DSP allows easy implementation of servos designed in Matlab. Servo Parameters 4 A/Ds 4 D/As Bansee H H Testbed Hardware A A Real-Time Traces, ZPK Data 12 Bit Data for Digital Measurements A A Analog Measurements SA (3563A).svo le: an ASII le tat contains an entire MIMO servo. Written by Matlab, read by Interface Program. Key feature of Interface Program: all data structures are dynamic =) exible. Figure 4: Te Bansee Multivariable Workstation: a functional block diagram. A functional block diagram of te BMW is sown in Figure 4. Te ASPI Bansee System (made by Atlanta Signal Processing, Inc.) is a digital signal processing (DSP) board tat is based on te TI TMS32030 oating point DSP cip. It ts into any IBM AT compatible bus. Te ost AT-class macine tat is used ere is an HP Vectra, but any AT class macine could be used. We will use te terms ost and Vectra intercangeably from tis point on. Tere are several metods to communicate between te ost and te Bansee. Matlab is one of a class of interactive, programmable software environments in wic te fundamental data structure is a complex valued matrix [18]. (Oter examples include Matrix-X and ontrol-.) A key dierentiator between Matlab and te oter programs is tat Matlab is compact enoug to run eectively on DOS computers, wile te oters tend to be cumbersome on anyting less tan a class macine. 8

14 Te processing capabilities of measurement devices, suc as dynamics analyzers can be expanded by transferring measurements up to Matlab and processing tem tere. Also, nite word lengt eects are minimized since te operations in Matlab are done in oating point. Te tool, pictured in Figure 3 and called te Bansee Multivariable Workstation, makes use of a Bansee oating point DSP board interfaced to Matlab. Te DSP board resides in 386/486 based MS-DOS macine (in tis case an HP Vectra). Tis was cosen due to te fact tat bot Matlab and a wide variety of DSP boards were available for tis platform. Te oating point DSP eliminates many of te scaling problems faced in SISO control loops on xed point DSPs. Tese problems would only be compounded in a MIMO control system. Matlab as analysis and design capabilities for MIMO control. In between lies a menu driven interface program tat allows te DSP board to be run out of Matlab. Tis combination makes practical te implementation of sopisticated MIMO servo designs wit relatively few keystrokes. Finally, tis is coupled wit an interface 4 to te SA to allow for non-parametric identication of MIMO systems. Tis interface allows for direct digital measurements of feedback control loops implemented wit te Bansee by te SA. Furtermore te interface wit Matlab allows te SA to be used to make closed-loop measurements of Multi-Input, Multi-Output (MIMO) loops wic can ten be opened (using matrix waveform mat). Finally, te interface allows te SA to be essentially run from Matlab by means of a menu-driven interface program. Te interface to Matlab greatly enances te data collection and analysis capabilities of te SA. Pysically, te Bansee is a DSP board made by Atlanta Signal Processors, Inc. (ASPI) based on a single TI TMS32030 oating point DSP cip running at MHz (a 60 nsec instruction cycle). It as been augmented by te addition of a custom analog IO board wic as 4 A/D cannels and 4 D/A cannels 5, so it can implement te compensator,, portion of te MIMO servo loop. It is connected directly to te digital pods of te HP 3563A for making digital measurements. It communicates to an interface program running on te Vectra via a data excange register and dual ported RAM. Te menu driven interface program communicates to te HP 3563A via HP-IB and can be run out of Matlab. Te remainder of tis paper will be as follows: Section 2 will give a general description of ow te Bansee Multivariable Workstation (BMW) works. Section 3 will discuss its use in servo researc for magneto optic drives. Section 4 will discuss ow we propose to use te BMW in magnetic drive 4 Designed by arl Taussig of HP Labs. 5 Designed by Lennie Kiyama of HP Labs. 7

15 it can be connected to oter computers via an HP-IB 3 port. Tus, te possibility of programming te instrument remotely exists and in fact examples in BASI are given in te SA documentation. urrently, te SA can only andle Single-Input, Single-Output control systems. A dramatic improvement in te time it takes to go from measurement to analysis to design to implementation and back to measurement can be acieved by fusing te best features of te above tools. Te pieces of a solution currently exist. Tose pieces are listed below: Tere are good standard AD software packages for MIMO analysis and design e.g. Matlab, Matrix-X, ontrol-. Tere are good oating point DSP cips on te market e.g. DSP32, Motorolla's TI's TMS32030, AT&T's Tere are good instruments for measuring frequency response functions e.g. HP 3563A. Tere is one more realization tat motivates a solution: for complicated control problems, a servo designer wants to spend all teir mental energy working witin te framework of te AD program wit wic tey do teir system modeling and control design. Te solution presented ere can be summed up in one prase: run te DSP board from inside of Matlab. Te advantages of tis pilosopy sould become apparent trougout te paper, but among tem are: Extremely rapid prototyping of designs. It is literally a few keystrokes from te point were Matlab gives you a particular servo design to te point were tat design is running on te drive ardware. Te system intelligence is were it sould be, namely in te AD software. All tat is asked of te DSP is rapid implementation of general ltering scemes. Tis expands te ability of te workstation wit eac improvement of Matlab or new Matlab script tat is created. As tere is a continual stream of new scripts (called m-les) being produced bot by te creators of Matlab (Te Matworks) and by tird party developers (including quite a few academic researcers), tis feature makes te workstation extensible. 3 Also known as te IEEE 488 Standard Interface Bus. Tis is a commonly used bus for connecting instruments and computers. 6

16 between wat is typically te academic and typically te industrial perspective is reenforced in te implementation area. Anoter major issue is exactly ow non-parametric measurements of dynamic systems are made. Instruments wic perform dynamics measurements, called dynamics analyzers, yield frequency response functions [4, 5, 17]. Tese instruments are essentially spectrum analyzers wic are designed to work well in te mecanical frequency ranges (0 Hz{200 khz). Many systems, including disk drives, cannot be measured in open-loop. Tey must ave some nominal control loop around tem so measurements are made from tis closed-loop system. Te analyzers used in tis paper ave a source cannel and two input cannels. Typically, two types of measurements are made: \two wire" measurements of a closed-loop response and \tree wire" measurements of an \open-loop" response. In te case of a two wire measurement, te analyzer source is injected at a junction point of te system and fed into te rst analyzer cannel. A second signal is measured from a cosen spot in te control loop and tis is fed into te second analyzer cannel. In a tree wire measurement, te input to te rst cannel is not te analyzer source, but some dierent measured signal. Te advantage of a tree wire measurement is tat open loop measurements can be made of a closed-loop system. Te disadvantage is tat any noise sources in te loop between te rst analyzer cannel and te second analyzer cannel will bias te measured frequency response function. In te two wire case, te closed-loop measurements must be \opened" by performing loop matematics on te measured frequency response function. Tis operation is subject to nite word lengt eects, since tese instruments usually perform matematics wit xed point DSP cips. Tis can be a problem in places were te closed-loop response is close to 1 (typically at low frequency). Te instruments tat can make and unwrap closed-loop measurements are all single-input, single-output (SISO) devices. Examples of tis type of device are te HP 3562A Dynamic Signal Analyzer (for analog measurements) or te HP 3563A ontrol Systems Analyzer (for digital, analog, or mixed measurements), sown in Figure 2. Since te HP 3563A as a superset of te oter's functionality, it will be te device referred to in te sequel. 2 Measurements wit te HP 3563A ontrol Systems Analyzer (SA) are done as follows. Analog control systems are measured via BN connectors on te front panel of te instrument wile digital measurements can be made by connecting a series of digital pods directly to registers or buses of te digital system under test. Quite a few signal processing features are included in te instrument and 2 Te HP 3563A is referred to as a ontrol Systems Analyzer rater tan a dynamics analyzer because its digital capabilities are motivated by te desire to make measurements of digital control loops. 5

17 E E E Bansee Running MIMO Servo Loops E E ` ` `` a a a a E E E E X X X HP-IB m P MIMO System Q Q Q 386 Vectra Running Matlab HP 3563A e e b b b Figure 3: Bansee Multivariable Workstation From te implementation point of view, it is dicult to try a variety of new control designs wen eac design involves recoding assembly language. Tis works against te ig sampling rates required by ig performance magnetic and optical drives wic mandate tigt assembly language loops on fast DSP cips. In contrast, many low performance magnetic drives are controlled by moderate performance microcontrollers. Wile te lower performance specications of te drives allow for slower sampling rates, te lower performance of te microcontroller PU typically means tat tere is even less PU bandwidt available per sample. Furtermore, te performance of bot DSP cips and microcontrollers improves considerably wen tey use on cip memory exclusively. Tis severely limits te size of te binary code tat can be loaded. Te speed and space requirements mandate tat code be written in tigt assembly language loops. From te perspective of experimenting wit new controller designs or even new controller structures, tis makes tings quite dicult. Even wen some analysis is done in Matlab, te designs tend to be kept simple so tat tey can be easily coded in DSP or microcontroller assembly language. Tis also limits entry of tose researcers wo are quite familiar wit sopisticated algoritms, but wo do not wis to spend time on assembly language programming. Tus, te gap tat exists in te modeling problem 4

18 e e e e Analog Loops (SISO) - m - - P 6 HP 3562A b b b Digital Loops (SISO) - m - - D=A - P - A=D 6 HP 3563A b b b Figure 2: Dynamics Measurements: An example of ow te HP 3562A can be used for making analog meausrements and ow te HP 3563A can be used for making digital measurements. its performance requirements or time and cost constraints dictate tat te system as met its performance and cost requirements. A key dierence wit te textbook problem is tat te measurements are not necessarily (or even often) te parametric, time-domain measurements so prevalent in te on line identication literature [1, 2, 3]. More often, nonparametric frequency domain metods are used to obtain a frequency response function (FRF) from a given system input to a given system output [4, 5, 6]. Often, control design is done strictly in te frequency domain witout reducing te measurement to a parametric model [7, 8, 9]. However, in order to use te sopisticated control algoritms and AD programs now available, or in order to deal wit multivariable 1 problems in a graceful way, a parametric model is essential. Tis can be obtained by curve tting a transfer function to te frequency response function [10, 11, 12, 13, 14]. Tis process itself is imperfect and is one of te main diculties in obtaining good parametric models of industrial control problems [15, 16]. 1 Te term multivariable is synonymous wit MIMO (Multi-Input, Multi-Output) in control and signal processing. 3

19 b Q Q Tis capability as stirred interest in researcers from bot academic and industrial backgrounds. Examples of ow tis as been applied to disk drive researc at HP Labs will be presented. 1 Introduction Analysis ` ` `` a a a a X X X Q Q Q Matlab (P,Workstation) Matrix-X (VAX,Workstation) ontrol- (VAX,Workstation) + b 5 Implementation P Figure 1: A conceptual view of control analysis and implementation tools. Note tat tere is little connection betwen all of tese areas. Tere is typically a very large gap between te academic and industrial control problems. In a textbook control problem one starts wit a parametric model were some features of te problem i.e. some parameters may not be known. In addition tere may be a nonlinearity of known caracter and certain noise properties are assumed. Te objective from tis point is to design a controller to give \good" performance along some metric. For te industrial control problem te starting point is a set of electrical and mecanical parts tat are accompanied by some nominal parametric models. Tese are used to create a nominal controller. From tis point te system can be measured and an improved controller can be generated. Tis process is iterated until eiter te system meets 2

20 Te Bansee Multivariable Workstation: A Tool for Disk Drive Servo Researc y Daniel Y. Abramovitc Hewlett-Packard Laboratories 1501 Page Mill Rd., MS: 2U Palo Alto, A Abstract Te servo design problems for bot magnetic and optical drives ave become more complicated as performance requirements for tese drives get pused iger. In order to easily try sopisticated control algoritms on tese problems, a tool tat makes te pat between design and implementation an easy one would be useful. Te Bansee Multivariable Workstation (BMW) is suc a tool. Te Bansee Multivariable Workstation is a Vectra/DSP based tool for doing Multi-Input, Multi-Output (MIMO) servo work. Te ardware consists of a oating point DSP board (TMS32030 based Bansee) residing in a 386/486 based MS-DOS macine (an HP Vectra). Tese are bot interfaced to an HP3563A ontrol Systems Analyzer, an instrument designed to make measurements of bot analog and digital control loops. Te key feature of tis package is tat te DSP board is cleanly coupled to Matlab, a AD program for servo/signal processing work tat runs on a wide variety of platforms. Tis structure allows instruments designed for Single-Input, Single-Output (SISO) systems, suc as te HP3563A to be used for MIMO systems. Furtermore, tis allows for \running servo experiments from Matlab" and makes it easy to try out sopisticated controller designs wit a few keystrokes. Presented at te 1992 ASME Winter Annual Meeting yto be publised in Advances in Information Storage Systems, ASME Press 1