Control and operation of reel-to-reel tape driveswithout tension transducer

S. P. Panda, A. P. Engelmann

Abstract This paper presents the control and operation ofreel-to-reel tape drives without any tension transducer.First, the tape drive model is validated while operating in theread/write or the velocity mode. Utilizing the coupled natureof the velocity-tension loop and the fact that the system iscompletely observable, the tension errors are estimatedbased on the validated model using state estimation tech-niques. The tension error estimates do not correlate wellwith the actual tension errors primarily due to the periodicdisturbances caused by reel eccentricities during steadyrunning and are not used for feedback purposes. In thispaper, the controller design for such transports for thevelocity and the position loops are presented. Due to lack offorced air in the tape path in such drives, there is consid-erable stiction/friction during start-up when the positionloop is used. Feed forward currents which are functions ofdesired tension at the head and tape velocity are used forproper friction compensation. For systems using twotachometers, one for each reel, a linear velocity differencetechnique is presented which shuts down the drive in case ofexcessive or low tape tension and thus preserves tapeintegrity. Finally, test results are presented to illustrate theeffectiveness of the design techniques.

List of symbolsUnless otherwise mentioned, the subscript 1 specifies theFile side reel and the subscript 2 designates the Machineside reel variables

J1, J2 inertia of motor hub plus tape (Kg-m2/rad)b1, b2 viscous damping (Kg-m2/rad-s)r1, r2 radius of reel (m)x1, x2 angular velocity of reel (rad/s)h1, h2 angular position of reel (rad)d1, d2 linear displacement of tape from reel (m)

v1, v2 linear velocity of reel (m/s)v linear velocity of tape at read/write head (m/s)i1, i2 motor current (amps)K1, K2 motor torque constants (N-m/A)T tape tension (N)KT stiffness of tape (N/m)KFT full-tachs in one revolutionTs sampling period (s)ky KFT Ts/2p ¼ full tachs in sample period to linear

velocity gain at 1-m reel radius(full-tach s/radian)

1IntroductionTape units are vital components in data measurement andcomputer systems and will continue to be so for the fore-seeable future [7]. They are used in numerous backupdrives and instrument recorders. Earlier papers on mod-eling and control of reel-to-reel tape drives assumedavailabilty of a tension transducer [1–6, 8]. However, mostmodern commercial tape drives do not have tensiontransducer for reasons of reducing costs. Also the desire toreduce the size of the drive precludes, in many instances,enough space for providing a tension transducer. Theprimary purpose of this paper is to carry out the modelingand control of such drives in the absence of a sensor,namely the tension transducer.

A typical simplified version of a tape drive without thetension transducer is shown in Fig. 1. The drive consists of aSupply reel, a Take-up reel, tape guidance system and theRead/Write head along with the associated electronics. Thistape path is considerably different from earlier tape pathswhich have forced air in the tape path and are provided withguides which are complaint [10]. In this paper we shalldesignate the Supply reel as the File reel and the Take-up reelas the Machine reel. Each reel is controlled through its ownDC brushless motor and current to the reels make up thesystem inputs. Each reel is also provided with its own ta-chometer for position measurement. The tape drive oper-ates in two modes. During read/write operation, it isrequired that the tape drive operates at constant nominalread/write velocity while maintaining a constant nominaltension. Thus, during the velocity-tension mode, the ob-jective of the control system is to maintain a constant ve-locity with constant tension. The velocity variations need tobe within a small percentage, usually within �1%, of thenominal read/write velocity so that effective read/write op-eration is possible. On the other hand, a little more latitude ispossible with tension variation as long as there is no

Microsystem Technologies 10 (2003) 53–59 � Springer-Verlag 2003

DOI 10.1007/s00542-002-0287-2

Received: 26 August 2002/Accepted: 1 November 2002

S. P. Panda (&)Inst. Control Systems Design, Inc.,6485 S. Ivy Court,Englewood, CO 80111-4311, USAe-mail: shibappanda@msn.com

A. P. EngelmannStorage Technology Corporation,Louisville, CO 80028-4274, USA

Paper presented at the 13th Annual Symposium on InformationStorage and Processing Systems, Santa Clara, CA, USA, 17–18June, 2002

53

excessive tension to cause permanent tape distortion andexcessive edge wear. Also, tape tension need to be adequateto provide a proper wrap angle over the head at theincreasingly high read/write speeds being used in currentdrives. While the drive is stopped or is accelerating to orfrom the read/write velocity, the objective is to follow theposition profile with as constant a tension as possible. Allthese goals need to be met in a high performance drive inspite of non-availabilty of a tension transducer and a simplertape path without any pneumatics and air bearings.

Earlier works on control of reel-to-reel type tape drivesare available in [1–6, 8]. These papers assume the avail-ability of tension transducers. The control system modelfor a tape drive system is a Multiple Input Multiple Output(MIMO), specifically a two-input, two-output system. Theforegoing references consider two types of design tech-niques. In one of the techniques, known as the decoupledtransfer function (DTF) method [3, 6, 8], the MIMO 2� 2system is decoupled into two Single Input, Single Output(SISO) systems, and each of systems, i.e., the tension,velocity, or the position loop is designed separately usingstandard SISO design techniques. Additionally, a distur-bance observer is used in [3] to minimize the tensionfluctuations due to disturbances generated by reel eccen-tricities. The use of disturbance observer presumes theavailability of a tension transducer that we assume not tobe present in the current development. The other designtechnique uses the state space methods and preserves thecoupled nature of the system. When state space methodsare used for the controller design in [1–6], it is not clearthat these techniques can be extended to drives withouttension feedback. Also, when decoupling is used in [2, 3,6], it is not general enough to cover all the situations. In[8], however, the decoupling scheme in the transferfunction design and the choice of state variables in thestate-space design have been such that these are readilyextendable to the case when no tension feedback is avail-able. This paper extends the state-space technique of [8] tothe control of tape drives without tension transducers.

The paper is organized as follows. Section 2 of the paperdescribes the validation of the mathematical model of thesystem in the velocity-tension mode. In Sect. 3, tensionerror estimation based on velocity measurement and ob-servability property of the system is carried out. The ten-sion error estimates do not correlate well with the actualtension errors primarily due to the periodic disturbances

caused by reel eccentricities during steady running (oncearounds) and are not used for feedback purposes. Section 4develops the controller design for the system using Dis-crete Linear Quadratic Regulator (DLQR) techniques. InSect. 5, tape path friction compensation for speeds varyingfrom zero to full speed is described. Section 6 develops thelinear velocity difference technique for protection of thetape in case of high or low tension. Section 7 discusses testresults and conclusions are presented in Sect. 8.

2Validation of the tape drive modelFigure 1 shows the Tape Path schematic. Assuming thatpositive motor current moves the reels in the counter-clockwise direction, the basic equations of motion of thedrive are given by:

J1dx1

dtþ b1x1 � r1T ¼ K1i1 ð1Þ

J2dx2

dtþ b2x2 þ r2T ¼ �K2i2 ð2Þ

v1 ¼ _d1 ¼ r1x1 ð3Þv2 ¼ _d2 ¼ r2x2 ð4Þd1 ¼ r1h1 ð5Þd2 ¼ r2h2 ð6ÞThe tape tension is given by

T ¼ KTðd2 � d1Þ ð7ÞThe velocity of the tape at the head is given by

v ¼ v1 þ v2

2ð8Þ

Instead of controlling the velocity at the head, we shallcontrol the linear velocity of one of the reels, say theMachine reel, so throughout this paper, we take

v ¼ v2 ð9ÞLet

x2n1 ¼

r21KT

J1; x2

n2 ¼r2

2KT

J2ð10Þ

and

x2n ¼ x2

n1 þ x2n2 ð11Þ

Make the simplifying assumption

a ¼ b1

J1¼ b2

J2ð12Þ

The mathematical model for the system for control systemdesign was developed in a manner similar to the one in [8].Since tension measurements are not available, we nowtreat this to be a two-input, one-output system. Taking the

input vector u ¼ ½u1 u2�T ¼ ½i1 i2�T, and the output vectory ¼ y1 ¼ v, we have the following transfer function.

Transfer function from i2 to v ¼ G12ðsÞ

¼ �K2

J2

s2 þ asþ x2n1

ðsþ aÞðs2 þ asþ x2nÞ

ð13Þ

Fig. 1. Tape path schematic

54

Plant parameters including the tape path spring constantKT are calculated using the method in [8]. With a series offrequency response tests and matching the measured G12M

( jx), with the corresponding modeled transfer function,we determine parameters such as a, xn, xn1, and xn2.Transfer function G12M(s) includes the appropriate gainsfor the measurement circuits. Figure 2 shows a compari-son of the model and measured transfer function while thedrive is running at a steady Read/Write speed after thetransients have settled down. The constants ‘a’, xn, andxn1 are adjusted to match the plant model to the measureddata. Originally, we denoted ‘a’ as representative of thedamping in the reel motors. It is worthwhile to note thatthe way the tape drive model is validated, ‘a’ now repre-sents the damping of both the reels and the tape path. Theslight inaccuracy in the model caused by the use of atension transducer instead of the actual read/write head isnot material to the system model used for control andestimation purposes.

3Tension error estimationTension error estimation is carried out when the drive isoperating in the velocity mode. The state space model ofthe system in the velocity mode is described by

_x ¼ Axþ Bu ð14Þy ¼ Cx ð15Þwhere the state vector is given by

x ¼ ½x1 x2 x3�T ð16Þwith x1 = Machine reel velocity error (full-tach/sampleperiod), x2 = Tension error (N), x3 = Tension errorderivative (N/s) and the input and output vectors aregiven in Sect. 2. The system matrices can be derived as

A ¼�a r2

ky

J20

0 0 10 �x2

n �a

24

35 ð17Þ

B ¼0 �K2

ky

J2

0 0�r1KT

k1

J1�r2KT

k2

J2

24

35 ð18Þ

C ¼ 1 0 0½ � ð19ÞIt can be seen that the pair ðA;CÞ is completely observable.We can thus use the machine velocity error to estimate thetension error and tension error derivative and feedbackthe estimated errors as if these are the actual errors. This isthe use of the standard separation principle of the esti-mator/controller design where the estimator and thecontroller can be designed separately and yet used to-gether [2]. A sampling frequency of 1.667 kHz (sampleperiod = 0.6 ms) is used. Matrices F, G, and H, are dis-crete-time versions of the A, B, C matrices leading to thediscrete-time plant equations:

xðkþ 1Þ ¼ FxðkÞ þ GuðkÞ ð20ÞyðkÞ ¼ HxðkÞ ð21ÞA full-order current estimator design is implemented [2].The estimation equation is given by

x̂ðkÞ ¼ ðF � LcHFÞx̂ðk� 1Þ þ ðG� LcHGÞuðk� 1Þþ LcyðkÞ ð22Þ

where x̂ðkÞ is the estimated state, and Lc is a 3� 1estimator gain matrix which is determined by pole-placement technique with the matrix pair (F, HF). Theestimator poles are placed in the z-plane such that theestimator bandwidth is about 3 times the controllerbandwidth.

Figure 3 shows the results of the tension error estimationtests. A tension transducer was placed in the test deck formonitoring purposes. It is seen that the estimated tensionerrors and the measured tension errors do not correlatewell. While operating in the steady state velocity mode, thetension errors are dominated by the errors induced by thereel eccentricities, or the so-called once arounds. The looperrors are relatively small. Therefore, the estimator/con-troller design technique is not pursued any further.

4Feedback controller design – DLQR technique

4.1Velocity-pseudo tension controlWe now consider the system as Multi-Input, Multi-Output2� 2 system as detailed in [8] where tension is measuredand is available for feedback. We carry out the controllerdesign as in [8] assuming tension measurement is avail-able; however, we ignore the tension feedback gains. Thisis equivalent to saying that the tension error, tension errorderivative, and tension error integral estimates are all zero.We term this as pseudo tension control because the driveis designed for a certain tension loop bandwidth whichinfluences the velocity controller design. The drive is op-erated in open loop tension mode applying only the feedforward currents to develop the desired tension.

The state space model of the velocity-tension control isdescribed by

Fig. 2. Comparison of magnitude and phase of measured andmodel transfer functions, machine current to machine velocity

55

_x ¼ Af xþ Bf u ð23Þy ¼ Cf x ð24Þwhere the state vector is given by

x ¼ x1 x2 x3 x4 x5½ �T ð25Þwith x1 = Machine reel velocity error (full-tach/sampleperiod), x2 = Tension error (N), x3 = Tension errorderivative (N/s), x4 = Machine reel velocity error integral(full-tach s/sample period), x5 = Tension error integral(N-s). The input vector

u ¼ u1 u2½ �T ð26Þwith u1 = File reel current (amps), u2 = Machine reelcurrent (amps). The output vector

y ¼ y1 y2½ �T ð27Þwith y1 = Machine reel velocity error = x1, y2 = Tensionerror = x2.

The system matrices can be derived as [8]

Af ¼

�a � r2ky

J2

� �0 0 0

0 0 1 0 00 �x2

n �a 0 01 0 0 0 00 1 0 0 0

266664

377775

ð28Þ

Bf ¼

0 � K2ky

J2

� �

0 0

� r1KTk1

J1

� �� r2KT

k2

J2

� �

0 0

0 0

2666664

3777775

ð29Þ

Cf ¼1 0 0 0 0

0 1 0 0 0

� �ð30Þ

It can be seen that ðAf ;Bf Þ form a completely controllablepair. The pair, (Af ;Cf ) is not completely observable,however, without the integrators the system is completelyobservable.

A sampling frequency of 1.6 kHz (sample period =0.6 ms) is used. Matrices Ff ;Gf , and Hf are discrete-timeversions of the Af ;Bf , and Cf matrices leading to thediscrete-time plant equations:

xðkþ 1Þ ¼ Ff xðkÞ þ Gf uðkÞ ð31ÞyðkÞ ¼ Hf xðkÞ ð32Þ

Control law is obtained via DLQR design technique [2, 8].This is done by minimizing the cost function

JðxðkÞ;uðkÞÞ ¼ 1

2

X1

k¼0

ðxTðkÞQxðkÞ þ uTðkÞRuðkÞÞ ð33Þ

where R = positive definite cost matrix for input variables,Q = positive definite cost matrix for state variables.

This leads to the linear static feedback control law

uðkÞ ¼ �KxðkÞ ð34ÞTypical choices for Q and R matrices are

Q ¼ diag q11 q22 0 q44 q55½ � ð35Þand

R ¼ diag r11 r22½ � ð36Þwhich leads to the feedback gain matrix with thestructure

Fig. 3. Comparison ofestimated and measuredtension errors, center-of-tape,tape moving forward

56

K ¼ k11 k12 k13 k14 k15

k21 k22 k23 k24 k25

� �ð37Þ

Since tension measurement is not available, the columns 2,4, and 5 of the K matrix are not utilized.

4.1.1Choice of R and Q matricesSince both the reels have similar power amplifier elec-tronics and motors, the R matrix is taken to be the identitymatrix multiplied by a positive constant. The choice of thispositive constant is immaterial. The choice of this constantaffects the parameters of the Q matrix. The Q matrix istaken to be diagonal, and the q44 and q55 elements deter-mine the gains for the integrators of the velocity andtension errors. These are taken to be relatively smallnumbers compared to q11 and q22. A large value of q11

penalizes the velocity error heavily where as a large q22

penalizes the tension error heavily. Even though the ve-locity and tension loops are coupled [3, 6, 8], the weighingfunction, i.e., the Q matrix controls the closed loop polelocations, thus indirectly controls the bandwidth for thevelocity and tension loops as if these were uncoupled.Judicious choice of the components of the Q matrix isrequired depending on the system performance require-ments. If the controller is made too aggressive, i.e., theclosed loop poles are close to the origin in the z-plane,then the input currents could saturate very quickly leadingto system instability especially in the presence of systemdisturbances. A couple of iterations for choosing the Qmatrix may be required in arriving at the optimum valuesfor the components of the Q matrix which provide a bal-ance between the tracking performances and controllereffort (input current) requirements. We have provided aguidance for choosing the Q and R matrices in the fol-lowing in order to minimize the number of iterations inarriving at a final design.

The final cost matrices are thus chosen based on theclosed loop pole locations and the desired performancelevels for the velocity and tension errors. We have chosen

Q ¼ diag kv

rc1

� �2ktr1ð Þ2 0 1

9:821

1252

� �ð38Þ

R ¼ diag 1322

1322

� �ð39Þ

The constants kv, c, and kt are chosen such that the closedloop pole locations are uniform as the File reel radiuschanges from end to end. This is gain scheduling and it isdone via File reel radius with equally spaced bins fromminimum to maximum File reel radius.

4.2Position-pseudo tension controlThe position-tension control is carried out in a mannersimilar to the velocity-tension control. The details are notshown here. We shall only point out that operation of thedrive with the selection of the set of state variables File reelposition error, File reel velocity error, Tension error,Tension error derivative, and Tension error integral hasbeen successful. We could have chosen the set of statevariables as the Machine reel position error, Machine reel

velocity error, Tension error, Tension error derivative, andTension error integral as well.

5Tape path friction compensationA tension ramping scheme is employed while the drive isoperating in the position mode. The tension rampingscheme consists of operating the drive at a lower tension(say 0.56 N) while the drive is at stoplock or standstill andraising the tension to the nominal read/write tension(1.12 N) as the drive reaches 60% of the nominal read/write speed. The reverse process is carried out as the drivedecelerates from the nominal read/write speed to stand-still. The tension ramping avoids excessive stiction while atstandstill requiring less motor currents for starting thedrive. It also keeps the maximum tape tension to a rea-sonable value well below the tension that could cause creepin the tape as the drive accelerates from standstill to thenominal read/write speed when the tension transients areat the maximum.

Since there are no air bearings in the tape path, theguides and D-bearings are fixed. The friction in the tapepath varies considerably during the acceleration phase andis a function of the tape velocity. Tape path friction and itsvariation with velocity must be taken into account in orderto maintain proper tension at the Read/Write Head and forproper operation of the drive. Figure 4 shows the ReelTension Ratio and is utilized to calculate the tensioncurrents to be applied to the file and machine reels formaintaining proper tension at the head. The Reel TensionRatio is obtained analytically from the geometry of thetape path, the surfaces where the tape makes contact, andthe expected coefficient of friction between the tape andcontact surface at the desired tape velocity, and the desiredtape tension at the read/write head.

6Tape integrity in transducerless environmentIt is absolutely essential that tape stretch and tape break-age be avoided under all conditions. When the drive isprovided with a tension transducer, excessive or low tapetension condition is easily detected and the drive shutsdown under those conditions preserving tape integrity.However, in the absence of a tension transducer, someother method must be devised to ensure tape protection.

Fig. 4. Reel tension ratios during acceleration

57

When tachometers are available in both the motors, alinear velocity difference scheme is employed to monitortape integrity. There are two global position registers, onefor each motor. The absolute value of the instantaneousvelocity difference at sampling instant k is calculated asfollows.

v1ELðkÞ ¼ ðh1ðkÞ � h1ðk� 1ÞÞr1=Ts ð40Þv2ELðkÞ ¼ ðh2ðkÞ � h2ðk� 1ÞÞr2=Ts ð41ÞvdiffELðkÞ ¼ absðv1ELðkÞ � v2ELðkÞÞ ð42Þwhere v1ELðkÞ = estimated linear velocity of File reel atsampling instant k, m/s, v2ELðkÞ = estimated linear velocityof Machine reel at sampling instant k, m/s, vdiffELðkÞ =absolute value of linear velocity difference between the tworeels at sampling instant k, m/s. When the absolute valueof the linear velocity difference exceeds certain thresholdvalue, it indicates that either the tape has dangerously highor low tension and the drive is shut down.

7Test resultsFigures 5 through 7 show the results of the drive perfor-mance for velocity error, position error, and tension errorfor the drive as it accelerates from a stopped position to asteady read/write velocity. Figure 6 shows the velocity athead as measured by the servo frame rate with a maximumvariation of at most 1%. During the tests, a tensiontransducer was placed on the tape path. The read/writehead was replaced with a dummy head with the sameshape as the actual read/write head. A hole was made atthe center of the head and a pneumatic assembly wasconstructed to measure the tension with a tension trans-ducer in a manner very similar to the one described in[10]. The head was moved so that the hole, through whichair flows to create a pressure proportional to the tension, isat the center of the tape. The tension so measured wasused for monitoring and gauging the tension performanceduring acceleration, deceleration, and steady state running

condition. Figure 7 shows the tension performance whichis very good considering that there was no tension feed-back for control purposes. The fluctuation in the tensionerror is due to reel eccentricities. Because of lack of ten-sion feedback and inability of estimating the tension errorfrom velocity measurement alone, the controller designcompensates for any velocity errors but not the tensionfluctuations due to reel eccentricities.

It is worthwhile to note that the performance of thetension controller per se can’t be improved by increasingthe encoder resolution. It may be possible to use (7) toestimate tension provided extremely high resolution en-coders are used on both the reels. But use of such encoderswould be expensive and defeat the very purpose of notusing tension transducer in the first place which was toreduce the cost. Also, just increasing the sampling ratewould not improve the tension performance. Currentsampling rate is of the order of 15 times the band width of

Fig. 5. Control system performance from stoplock to R/W speed

Fig. 6. Tape speed measured at head during R/W cruise

Fig. 7. Tension error measured during cruise at R/W speed

58

the velocity/tension loops. Increasing the sampling rateany higher would not improve the performance.

8ConclusionsIn this paper, we have presented the modeling, controlsystem design, and operation of reel-to-reel tape drivesystem without any tension transducer. It was not possibleto carry out the estimator/controller design. The controllerdesign using optimal control technique along with pseudotension control has been proved to be successful. We haveprovided a method for friction/stiction compensation asthe drive accelerates from stopped condition to read/writespeed. This design technique can be applied for both theposition and the velocity loops when there is only oneposition encoder or tachometer with minor modificationsto account for the side on which the tachometer is located.This method of controller design can also be used for thevelocity loop design in case there are no tachometersavailable on any of the reels with the velocity feedbacksignal generated off the prewritten tape of a track followingtape drive. A method for preventing tape damage due toexcessive tension has been provided. This is done via theinstantaneous linear velocity difference technique whentwo tachometers, one on each reel, are available. Thevelocity and tension goals for read/write operation as wellas for other tasks performed by the drive are met withoutany difficulties. The modeling and control efforts alongwith innovative designs for feedback and feed forwardcompensations have resulted in a reliable and robust reelcontrol servo.

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