Resonance and Friction Compensations in a Micro Hard Drive

Transcription

1 Resonance and Friction Copensations in a Micro Hard Drive * School of Electrical Engineering, Institute of Engineering Suranaree University of Technology Nakhon Ratchasia, Thailand, *corresponding author: sarawut@sut.ac.th Abstract: - This paper presents dynaic copensations in a icro hard drive. It reviews dynaic odels of the drive in low-and high-frequency regions. The nonlinear friction copensation for low-frequency dynaic is achieved via a fuzzy logic controller. Forward and backward icro-step otion of the read/write head can be nicely perfored. Resonance copensation for high-frequency dynaic is achieved via linear copensation. The paper presents soe coparison studies of using a cascaded lead copensator, a coplex lead-lag copensator, and a searched polynoial copensator. The copensated syste s perforance is enhanced further by stable nonlinear control. Detailed descriptions of odelling, design, siulation results, and analysis can be found in the paper. Key-Words: - Resonance, Friction, Copensation, Adaptive tabu search, Fuzzy logic, Hard drive. 1. Introduction High speed data accessibility is a very deanding specification for today s hard drives. It can be achieved by using effective control technology. Proper servo systes for a hard drive require two controllers naely track-seeking, and trackfollowing controllers, respectively. The control systes are usually subjected to repeatable and nonrepeatable runouts, which need appropriate copensations [1-3]. A high-frequency bandwidth specification is also iposed on a current servo syste of a hard drive. Due to drive s iperfection, a hard drive is not rigid and contains any flexible odes that raise vibrations. The resonance odes severely degrade the hard drive perforance, and are the causes of the nonrepeatable runout. Hence, resonance odes ust be treated properly by copensation in high frequency. Regarding this, the voice-coil-otor (VCM) actuator can be accurately odeled by a transfer function of various resonance odes as in the equation (1) [4, ] KT ωnk G (1) Js s + ζ ω s+ ω k 1 k nk nk where K T torque constant, J inertia, ζ k daping ratio and ω natural frequency of the nk th k resonance ode. In a icro hard drive, the effects of nonlinear friction in the pivot bearing and the data flex in the VCM becoe even ore pronounced. Even though the VCM used as a read/write head has a high-frequency bandwidth, the data flex connected to it does not. The data flex behaves like a nonlinear daper during its expansion and contraction phases. These oveent phases always occur when the read/write head oves away fro or back to its hoe position. Moreover, the friction fro the pivot bearing, and the data flex causes severe errors in track following oveent of the head. Thus, the low-frequency dynaic of the read/write head is influenced by the nonlinear friction and characteristics caused by the data flex and the pivot bearing. If such nonlinearities were not copensated properly, a great deal of errors in data retrieval due to the head being isplaced would occur. Fig. 1 shows the echanical structures of a hard drive. Chen et. al. [5] addressed these probles with their proposed coposite nonlinear feedback (CNF) control. Fig.1 Mechanical structures of a hard drive. ISSN: Issue, Volue 8, February 00

2 Intelligent control is also an alternative for the servo probles of a hard drive such as use of fuzzy logic [6, 7], etc. Recently, an effective use of resonant filter has been proposed for trackfollowing control [8]; a cobined use of reference generator and nonlinear feedback controller has been proposed for track-seeking control []; a pointto-point otion control algorith has been applied for short stroke servo control in a hard drive []; Wang and Du et. al. [11, 1] have successfully applied the sliding ode and the nonlinear tracking control approaches to accoplish non-overshoot servoechaniss of hard drives. Extreu seeking control for a hard drive can also be achieved by using intelligent search, e.g. genetic algorith [13], etc. The reviews of these literatures, even though not exhaustive, give us useful inforation on odelling of hard drives as well as roos available for testing soe new ideas on linear, nonlinear and intelligent control approaches to the servo probles of hard drives. In this paper, the authors deonstrate the design of a ixed type of controllers using rulebased and fuzzy logic to treat the effects of nonlinear friction. A few production rules have been added in order to handle the sub-transient dynaic of the head. The overall structure of the controller is very siple and like a switched-type controller. Two or ore controllers, each of which is switched into operation during a different period of tie in order to obtain desired perforance, are eant by the switched controller in this context. As a atter of fact, a fuzzy logic controller behaves like a switching function in its own. As described further, the copensated response of the head possesses ore-or-less equal settling tie to that achieved by a PID controller, however without any overshoot. Section of this paper presents the dynaic odel of the head at low-frequency together with the nonlinear friction odel. Section 3 presents our controller design and siulation results. Our paper also addresses the resonance proble in a icro hard drive. Since the resonance occurs in high-frequency region and can be treated in a linear anner, we present the design coparisons using a lead copensation found in standard textbooks [14-16], for instance, a coplex lead-lag copensation [17], and a polynoial copensator optiized by the adaptive tabu search (ATS) [18-0]. Section 4 of the paper presents the copensation design and siulation results, while the resonance-ode odel is described in the last part of section. Conclusion follows in section 5.. Dynaic Models The dynaic of the read/write head at lowfrequency is highly influenced by nonlinear characteristics and friction. To provide appropriate copensation requires accurate odels of the head dynaic. Extensive theoretical and experiental studies have been conducted by Chen et. al. [1]. They reported the odelling of the read/write head as expressed by the equations ()-(5). && 8 6 y.35 u arctan( y) + T () f uy+ 0.01( y) & sgn( y& ) 8.6 y&, y& 0 Tf (3) T, y& 0, T T e e s T sgn( T ), y& 0, T > T s e e s 8 T arctan( y) + u (4) e [ ] 6 4 u y 0 0 T s (5) where T f nonlinear frictional torque (N), T e external torque (N), T s static frictional torque (N), u input voltage (V), u 0 initial input voltage (V), y displaceent of the head (), and y 0 initial displaceent of the head (). Fig. illustrates various displaceent curves in accordance with different input voltages fed to the VCM. These curves are obtained fro the odels in ()-(5). Nonlinearities exhibit their effects quite clearly in these response curves which contain large overshoots and steady-state errors. Fig. Displaceent curves of the read/write head corresponding to various inputs. ISSN: Issue, Volue 8, February 00

3 At high-frequency, the dynaic of a icro hard drive contains several resonance odes [1] as described by the equations (6)-(11). Fig. 3 discloses that the drive is inherently unstable G G r..1 Gr.. s G G G G..1 r..3 r..4 r..5 (6) 0.870s + 176s r s s (7) 0.33s 805.8s r.. s s (8) 1.07s + 5.1s+ 1.7 r..3 s s+ 1.7 () 0.54s + 8.s+.514 r..4 s s+.514 () r..5 s + 61s (11) G G G G 3. Friction Copensation and Siulation Results Our head control syste can be represented by the block-diagra shown in Fig. 4. The proposed controller is a switched type having one set of production rules and the other of fuzzy control rules. Fig. 4 Read/write head control syste. These rules are obtained heuristically based on the siulation results of the uncontrolled head. The rule-based controller is activated during the initial tie t 0 sec until tie t 1.6 sec. The controller possesses the following siple rules: Begin: u 0.08 V IF (x 0.6 ) THEN (u -0.0 V) IF (t sec AND t sec) THEN (u 0.01 V). (a) (b) Fig. 3 (a) Tie (b) frequency responses of an uncopensated icro hard drive. Such siple rules are effective to suppress subtransient overshoot. The figures given in the rules are specific for 15V-input as an exaple. Once the tie of 1.6 sec collapses, the fuzzy logic controller is switched into action. The fuzzy controller design considers inputs, and 1 output. The displaceent errors (e), and the change in errors ( e) are the inputs, while the change in control ( u) is the output of the fuzzy control rules. Five fuzzy sets serve as the descriptions of the inputs naely negative large (NL), negative sall (NS), about zero (ZE), positive sall (PS), and positive large (PL), respectively. Triangular and trapezoidal ebership grades are used correspondingly, and shown in Fig. 5. Six fuzzy sets of Sugeno s type are used as the descriptions of the output. These are extra largely decrease (XLD), largely decrease (LD), oderately decrease (MD), slightly decrease (SD), no change (NC), slightly increase (SI), oderately increase (MI), largely increase (LI) and extra largely increase (XLI), respectively (see Fig. 6). By the tie t 1.6 sec, the fuzzy controller is switched into action by the production rule IF (t > sec) THEN (u new u old F con u old ). Fcon stands for the outcoe obtained fro the fuzzy-rule inference. Table 1 suarizes the 5 fuzzy control rules. Soe of the, for instance, can be read as follows: ISSN: Issue, Volue 8, February 00

4 IF ( e is NL AND e is NL) THEN ( u is XLI ) IF ( e is NL AND e is NS) THEN ( u is LI ) M IF ( e is PL AND e is PL) THEN ( u is XLI). where u s change in control obtained fro Sugeno s inference, and k singleton. As an exaple, consider the following 4 rules to be fired: Fig. 5 Mebership grades of the inputs. 1. IF ( e is NL AND e is PS) THEN ( u is SI ). IF ( e is NL AND e is PL) THEN ( u is NC) 3. IF ( e is NS AND e is PS) THEN ( u is NC) 4. IF ( e is NS AND e is PL) THEN ( u is SD) Assue that the quantity e -0.6, and e 0.6, Fig. 7 illustrates the echaniss of rule firing in accordance with the above 4 rules. Notice that the quantity e belongs to the fuzzy sets NL, and SN; e belongs to the sets PS, and PL, respectively. Fig. 8 and the relations (1) and (13) serve to explain the Sugeno s inference echanis. Fig. 6 Mebership grades of the output. Table1 Fuzzy control rules. Change in errors ( e) NL NS ZE PS PL NL XLI LI MI SI NC F con 0. ( 0.5) (13) errors (e) NS LI MI SI NC SD ZE MI SI NC SD MD PS SI NC SD MD LD PL NC SD MD LD XLI Fig. Siulation results of closed-loop syste. The rule inference follows Sugeno s ethod []. At the instance of rule execution, possibly 1 up to 4 rules can be fired and Sugeno s inference provides the final outcoe, F con. F con can be expressed as F con L 1 L u ( k ) k 1 s u ( k ) s (1) Siulation results of the closed-loop fuzzy control syste are shown in Fig.. For coparison purposes, the step responses under the PID control, the CNF with and without nonlinearity copensators have been taken fro the reference [1]. Table suarizes the settling tie of each case. It can be noticed that our proposed fuzzy controller can provide a sooth response of the read/write head with zero steady-state errors, and no overshoot as also shown in Fig.. Even though the response is not so fast as that controlled by the CNF, the structure and the design of the controller are uch sipler. Moreover, the proposed controller can be ISSN: Issue, Volue 8, February 00

5 1. IF ( e is NL AND e is PS) THEN ( u is SI). IF ( e is NL AND e is PL) THEN ( u is NC) 3. IF ( e is NS AND e is PS) THEN ( u is NC) 4. IF ( e is NS AND e is PL) THEN ( u is SD) Fig. 7 Firing of fuzzy rules. Fig. 8 Sugeno s inference. ISSN: Issue, Volue 8, February 00

6 Fig. Response curves of the head due to 15V-step input. Table Settling ties of each case. Controller PID CNF Fuzzy 3% settling tie (sec) odified to handle a icro-step otion control of the head. The fuzzy rules reain the sae; only the production rules are odified in accordance with forward and backward directions of otion of the head. Due to the nonlinearity of the syste, the rules have been heuristically odified to deonstrate this icro-stepping otion. Responses of the head with the corresponding control signals are illustrated in Figs. 11 and 1, respectively. The controlled head can ove soothly at 1 µ each step in both directions with reasonable agnitudes of the control signals. This reflects an advantage of using the proposed fuzzy controller. Moreover, a systeatic optiization for this nonlinear control regie is still an open proble. Fig. 1 Control signals of the case icro-stepping. 4. Resonance Copensation and Siulation Results As entioned in section, the high-frequency dynaic of a icro hard drive is doinated by various resonance odes that can be odeled by the transfer function in the equations (6)-(11). This paper presents soe coparison studies of the resonance copensation between a cascaded lead copensator, a coplex lead-lag copensator, and a polynoial copensator via search. For the cascade copensator, we apply the standard design procedures appeared in textbooks such as in [14-16]. The design ethod in [17] is applied to obtain the coplex lead-lag copensator. The corresponding design steps are given in the appendix A. The last approach is to use search algorith to search for a copensator of the sae 4 th -order as the coplex lead-lag one with its poles and zeros being strictly real. The search ethod applied is the adaptive tabu search (ATS) [18-0], whose brief description represented by a flow diagra can be found in the appendix B. The required specifications are as follows: percent overshoot %, settling tie sec, steady-state error %, GM 6 db, and PM 50. Using the conventional lead copensation approach, we have obtained the third-order copensator described by the equation (14). Fig. 13 shows the closed-loop frequency response of the copensated syste having the -3dB bandwidth of 5,360 rad/sec with the corresponding GM.73 db and PM 4.1. Fig. 11 Micro-step responses. s s Gc 8.77 s s s+ 134 s (14) ISSN: Issue, Volue 8, February 00

7 Fig. 13 Closed-loop frequency response of the copensated hard drive via a lead copensator. The coplex lead-lag ethod results in the copensator of 4th-order expressed as 4 8 s s+ 3.4 Gc.44 5 s s s s s s (15) in which the following paraeters are used: 1 st set: φ ax 45 o 4, ω 4. rad/sec, ζ 0., and nd set: φ ax 30 o 3, ω 4.53 rad/sec, ζ 0.8. Fig. 15 Closed-loop frequency response of the copensated hard drive via a searched copensator. The ATS has provided the copensator described by the equation (16). The following search paraeters are used: search spaces for poles, zeros, and gain [0 0,000], search radius R, neighborhood N 50, terination criteria J or ax_iteration 0,000, allowed solution cycling 5 before an activation of the backtracking echanis, and 3 levels of adaptive search radius echanis (if J 0 then R 8, if J 15 then R 6, and if J 1 then R 4, respectively). The closed-loop frequency response in Fig. 15 indicates that the -3dB bandwidth 3,780 rad/sec. In addition, the copensated syste has GM 7.1dB, and PM 75. s+ 03. s+ 77 Gc 0.1 s+ 03. s (16) s+ 640 s+ 43 s+ 80 s Fig. 14 Closed-loop frequency response of the copensated hard drive via a coplex lead-lag copensator. The closed-loop frequency response plot in the Fig. 14 indicates the -3dB bandwidth of,850 rad/sec. In addition, the corresponding GM and PM are 7.53 db and 43.5, respectively. Fig. 16 Coparison of step responses. ISSN: Issue, Volue 8, February 00

8 Fig. 16 illustrates the step responses of the copensated systes for coparison purposes. The cascaded lead copensator provides the response with the shortest rise-tie in an exchange of the largest overshoot. The copensator via ATS ethod provides the soothest response with a oderate rise-tie. The quality of the perforance obtained fro using the coplex lead-lag copensator is in between the two. Under the consideration of ±% steady-state error, these copensated perforances settle at about the sae tie of 5 sec. however, the closed-loop syste with the ATS-based copensator is the ost robust one in ters of stability. The GMs and PMs as well as the P.O. of the responses of the systes copensated by the other two types of copensators do not eet the required specifications. using this control approach having ± 0. saturation liits, K, 3, and 4, respectively. With K, the response settles nicely within 1 sec, and the overshoot is bounded within %. Fig. 1 Nyquist plot for the syste with saturation characteristic. Fig. 17 Block-diagra of nonlinear copensation of a icro drive. We attepted further to enhance the closedloop perforance of the icro-drive by incorporating gain and nonlinear eleent into the copensated syste as represented by the diagra in Fig. 17. The linear plant is represented by the odel G( s ) of the equation (6), while the copensator, Gc ( s ), is of the case ATS-based ethod according to the equation (16). The saturation characteristic with the gain K can be viewed as a sector bounded nonlinearity depicted in Fig. 18. To apply the circle criterion [3, 4] for absolute stability consideration, it is a special case of having the slope α 0. Hence, the circle becoes a straight line as shown in Fig. 1. Since the gain K affects the slope of Fig. 18 Sector bounded nonlinearity. the saturation characteristic and it is bounded by the straight line of slopeβ, the syste is always stable and the gain K can be adjusted freely as far as the Nyquist plot of the linear part dose not touch or cut the straight line show in Fig. 1. Fig. 0 shows the results of Fig. 0 Step responses of the icro hard drive having an optiized copensator with a nonlinear characteristic. 5. Conclusion The switched-type fuzzy controller has been proposed to copensate for the nonlinear friction in a icro hard drive. The controller consists of a set of production rules, and another one of fuzzy control rules. Each rule set is switched into operation according to the dynaic response of the read/write head. The production rules coe into action fro the initial tie t 0 sec until 1.6 sec such that the sub-transient overshoot of the head could be suppressed. Fro then on, the fuzzy control rules are activated to govern the head during the rest of the transient interval up to the steady-state operation. With this arrangeent, a sooth response with zero steady-state errors of the head can be achieved. The ISSN: Issue, Volue 8, February 00

9 head responds fast enough coparable to the use of a PID controller and a CNF controller. Micro-step otion control of the head is also possible through this regie as deonstrated in the paper. The production rules need a suitable design enhanceent to cover the nonlinear behaviour of the icro drive. High-frequency resonance odes have been copensated for using linear control approach. Aong the cascaded lead, the coplex lead-lag, and the ATS-optiized polynoial copensators, the optiized copensator outperfors the rest in all aspects of perforance and stability. The linearly copensated perforance has been further iproved by adding nonlinear saturation and gain to the control loop without sacrificing its stability. The paper deonstrates that the drive step response settles within 1 sec with its overshoot bounded by %. Acknowledgeents The authors are thankful to the HDD Cluster, NECTEC, Thailand, Suranaree University of Technology (SUT), and HDD-HRD Center, SUT, for the research grants. References [1] L. Guo, A new disturbance rejection schee for hard disk drive control, Proc. Aerican Control Conference, pp , 18. [] G. Jang, D. Ki and J.E. Oh, New frequency doain ethod of nonrepeatable runout easureent in a hard disk drive spindle otor, IEEE Trans. on Magnetics, vol 35, pp , 1. [3] T. Ohi, Non-repeatable runout of ballbearing spindle-otor for.5 HDD, IEEE Trans. on Magnetic, vol 3, pp , 16. [4] G.F. Franklin, J.D. Powell and M. Workan, Digital Control of Dynaical Systes (3rd. ed.), Addison-Wesley, 17. [5] B.M. Chen, T.H. Lee, K. Peng and V. Venkataraanan, Coposite nonlinear feedback control for linear systes with input saturation: theory and an application, IEEE Trans. on Autoatic Control, vol. 43, no. 3, pp , 003. [6] J-Y. Yen, F-J. Wang and Y-Y. Chen, Fuzzy scheduling controller for a coputer disk file track-following servo, IEEE Trans. on Industrial Electronics, vol. 40, no., pp. 66-7, 13. [7] E.L. Branch, M. Bikdash and A. Hoaifar, Fuzzy and tie-suboptial control for dual track following and seeking drive, Proc. 5 th Biannual World Autoation Congress,Vol. 13, pp. 37-4, 007. [8] T. Atsui, A Okuyaa and M. Kobayashi, Track-following control using resonant filter in hard disk drives, IEEE/ASME Trans. on Mechatronics, vol.1, no. 4, pp , 007. [] Y. Li, V. Venkataraanan, G. Guo and Y. Wang, Dynaic nonlinear control for fast seek-settling perforance in hard disk drives, IEEE Trans. on Industrial Electronics, vol. 54, no., pp. 51-6, 007. [] Y-M. Choi, J. Jeong and D-G. Gweon, Modified daping scheduling proxiate tie optial servoechanis for iproveents in short strokes in hard disk drives, IEEE Trans. on Magnetics, vol. 44, no. 4, pp , 008. [11] Q. Hu, C. Du, L. Xie and Y. Wang, Discrete-tie sliding ode control with tie-varying surface for hard disk drives, IEEE Trans. on Control Syste Technology, vol. 17, no. 1, pp , 00. [1] J. Zheng, M. Fu, Y. Wang and C. Du, Nonlinear tracking control for a hard disk drive dual-stage actuator syste, IEEE Trans. on Mechatronics, vol. 13, no. 5, pp , 008. [13] K-S. Low and T-S. Wong, A ultiobjective genetic algorith for optiization the perforance of hard disk drive otion control syste, IEEE Trans. on Industrial Electronics, vol. 54, n. 3, pp , 007. [14] B.C. Kuo, Autoatic Control Systes, Prentice-Hall, 11. [15] K. Ogata, Modern Control Engineering, Prentice-Hall, 00. [16] J. Dorsey, Continuous and Discrete Control Systes, McGraw-Hill, 00. [17] W.C. Messner, M.D. Bedillion, L. Xia and D.C. Karns, Lead and lag copensators with coplex poles and zeros, IEEE Control Systes Mag., pp , February, 007. [18] D. Puangdownreong, S. Sujitjorn and T. Kulworawanichpong, Convergence analysis of adaptive tabu search ScienceAsia, vol. 30, no., pp , 004. [1] D. Puangdownreong and S. Sujitjorn, ISSN: Issue, Volue 8, February 00

10 Iage approach to syste indentification, WSEAS Trans. on Systes, vol. 5, no., pp , 006. [0] J. Kluabwang, D. Puangdownreong and S. Sujitjorn, Manageent agent for search algoriths with surface optiization applications, WSEAS Trans. on Coputers, vol. 7, no. 6, pp , 007. [1] B.M. Chen, T.H. Lee, K. Peng and V Venkataranan, Hard Disk Drive Servo Systes, Springer-Verlag, 006. [] T. Takagi and M. Sugeno, Fuzzy identification of syste and its application to odeling and control, IEEE Trans. on SMC, vol.15, pp , 185. [3] J-J.E. Slotine and W. Li, Applied Nonlinear Control, Prentice-Hall, 11. [4] H.K. Khalil, Nonlinear Systes, Pearson Education, 000. B. Algoriths of the ATS. Appendices A. Design steps for coplex lead-lag copensation [17]. Step. 1 Choose ω, φ ax and ζ (arbitrarily). Step. Calculate p ( tan ax tan ax 1) ( tan ax tan ax 1) ω ω ζ φ + ζ φ + ω ω ζ φ + ζ φ + z ω p s + ζω zs+ ω z Gc ω z s ζω ps ω + + p Step. 3 Correct the DC-gain. ISSN: Issue, Volue 8, February 00