Microsystem Technologies

, Volume 19, Issue 9, pp 1351–1355

Feedforward stability control of active slider in sub-nanometer spacing regime

Authors

  • G. Sheng
    • Marshall University
    • Auckland University of Technology
  • J.-Y. Chang
    • National Tsing Hua University
Technical Paper

DOI: 10.1007/s00542-013-1819-7

Cite this article as:
Sheng, G., Huang, L. & Chang, J. Microsyst Technol (2013) 19: 1351. doi:10.1007/s00542-013-1819-7
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Abstract

This paper proposes a feedforward control scheme to control the bouncing instability of active-head air-bearing slider. The principle of the scheme for stability control of bouncing slider is discussed. Simulation results show that the control scheme is proved to be able to substantially reduce the bouncing vibrations. Compared to other controllers, the proposed scheme is less computationally intensive and is thus suitable for real time implementation.

1 Introduction

Storage of 10 Tb/in2 in hard disk drives within the next decade requires a significant change to reduce the physical spacing as little as 0.25 nm at the read-write transducer location. At such a small spacing intermittent contact between the slider and disk surface becomes inevitable and the current MEMS-based thermal fly-height control (TFC) technology is unlikely to affordable (Canchi and Bogy 2010; Hua et al. 2009; Salas et al. 2012; Ono 2009; Tani et al. 2009; Vakis et al. 2009; Xu et al. 2009; Knigge and Talke 2001; Mate et al. 2004; Xu et al. 2005; Kiely and Hsia 2008; Yu et al. 2012; Zheng and Bogy 2012; Sheng 2011; Canchi et al. 2012). To solve this problem, MEMS-based piezoelectric fly-height control (PFC) which has a faster dynamic response has been explored to overcome the shortcomings of the common TFC active slider (Naniwa et al. 2009). How to control the slider to reduce touchdown instability and eventually eliminate bouncing has been a pressing and challenging research topic.

The dynamics of the slider in a ultra-small space from the disk surface is very complex due to disk morphology, interface instability and nonlinear interface forces such as intermolecular force and contact forces which are hard to be modeled and quantified. At the sub-nanometer ultra-low clearance, several significant tribological effects such as adhesion, friction and contact have been the stability design concerns and have been widely investigated (Ono 2009; Yu et al. 2012; Zheng and Bogy 2012). The control of adhesion and friction effects in lubricant-solid contact (surfing state) has been shown to be critical. Adhesion force is shown to mainly affect the second air-bearing pitch mode and instability, friction force affects instability of both first and second air-bearing pitch mode and stability.

On the other hand, it could be too idealistic to assume that the dynamics of active air-bearing slider in sub-nanometer spacing regime can be modeled accurately (Sheng 2011; Canchi et al. 2012). With this observation, a feedforward control scheme is proposed in this paper to control the high frequency slider bouncing in touchdown process without needing accurate system model and identification. Unlike the approach proposed in (Boettcher et al. 2011) where the dynamic flying height adjustment in hard disk drives was attained through feed forward control, in this paper the idea of feedforward control is used to change the behavior of the interface nonlinear properties by applying a properly chosen input function or dither excitation. The dither excitation used feedforward control is also likely to reduce the interface friction. Such an dither excitation approach has been used for vibration control (Gelb and Warren 1973; Gelb and Velde 1968; Lee and Meerkov 1991; Morgul 1999; Thomsen 1999; Feeny and Moon 2000), and it is attractive because of its simplicity that no measurements and no extra sensors are needed. It is especially advantageous for ultrafast processes and nanometer level where measuring system variables are extremely difficulty. The high frequency dither excitation has also proved to be useful to substantially reduce interface friction (Hesjedal and Behme 2002; Dinelli et al. 1997; Cuberes 2007; Badertscher et al. 2007; Kaajakari’ et al. 2000). Considering the special features of computer hard disk drive head-disk interface model that includes air-bearing force, adhesion force, contact force and friction force, the feedforward control is analyzed and the dither effect is analyzed. The feedforward controller is developed and optimized. The feasibility is verified by simulation of slider in touchdown process. The proposed approach is not computationally intensive and is suitable for real time implementation. The control strategy is proved to be able to substantially reduce the bouncing vibrations of active slider.

2 Motion equation

The air-bearing slider system used computer hard disk drive can be further simplified to be a single-degree-of-freedom (1DOF) system. Fig. 1 shows the schematic of a 1DOF model of TFC slider in touchdown process.
https://static-content.springer.com/image/art%3A10.1007%2Fs00542-013-1819-7/MediaObjects/542_2013_1819_Fig1_HTML.gif
Fig. 1

Schematic of 1DOF nonlinear HDI model

The equation of motion of the 1DOF model is given by,
$$m\ddot{x}(t) + f[s(t),\;\dot{s}(t)]x(t) = F{}_{s}[s(t)] + c[s(t)]\dot{d}(t) + k[s(t)]d(t) $$
(1)
in which \(m\) is modeled mass of slider, \(s(t)\) is transient clearance, \(x(t)\) is vibration displacement, \(f[s(t),\;\dot{s}(t)]\) is the air-bearing force coefficient, \(F{}_{s}[s(t)]\) is the interfacial force acting on slider. \(d(t)\) is due to the effect of lubricant surface profile and/or disk topographic effect. The lubricant surface profile effect and disk topographies effect on slider dynamics have been investigated. The effects can be assumed as \(d(t) = D\sin \omega_{n} t\), in which \(D,\;\omega_{n}\) are, respectively the amplitude and the specific frequency. The lubricant-slider interaction with specific frequency could occur when slider clearance was in the sub-5 nm range. Under such low clearance, shear effects started to dominate, and two types of lubricant redistribution patterns were identified and coined as “moguls” and “ripples”. Moguls are an incoherent pattern associated with disk topography, whereas ripples originate from slider instability leading to coherent lubricant corrugations at the air-bearing frequency. Both have been shown to add to slider modulation, as well as to account for lubricant loss from the disk to the slider in previous researches. Consider TFC slider in touchdown process, if we assume that the clearance is reduced at a constant speed \(v_{0}\), and the initial clearance before actuation is \(s_{0}\), then the instantaneous clearance is given by \(s(t) = s_{0} - v_{0} t - d(t) + x(t)\). After the interference get saturated when power supply is increased to a critical level, the clearance could reach to and remain at a relative steady level, \(s_{f} = s_{1} - d(t) + x(t)\). The interfacial force acting on slider \(F{}_{s}[s(t)]\) has been widely studied. The air-bearing force acting on slider and the corresponding stiffness and damping can be parameterized by numerically solving the generalized Reynolds equation. The air-bearing force coefficient corresponding to air-bearing force could be parameterized approximately as power law form,
$$f[s(t),\dot{s}(t)] = a_{0} + a_{1} s(t) + b_{1} \dot{s}^{2} (t) + a_{2} s^{2} (t) + b_{2} \dot{s}^{2} (t) + \cdots $$
(2)
in which \(a_{i} ,\;b_{i}\) are the parameters from data fitting of the numerical results of the generalized Reynolds equation.
The interfacial force consists of multiple terms, \(F_{s} [s(t)] = F_{imf} + F_{elec} + F_{cs} + F_{cl}\), in which \(F_{imf}\) is intermolecular force, \(F_{elec}\) electrostatic force, \(F_{cs}\) contact force between solid asperities of slider and disk, \(F_{cl}\) contact force between slider and lubricant on disk. Intermolecular force is given by,
$$F_{imf} = - \frac{A}{{[s(t)]^{3} }} + \frac{B}{{[s(t)]^{9} }} $$
(3)
in which the constants \(A,\;B\) are constants depending on air-bearing surface design and the materials of slider/lubricant/disk. The electrostatic force is given by,
$$F_{elec} = - \frac{{cA_{0} E^{2} }}{{[s(t)]^{2} }} $$
(4)
in which \(c,\;A_{0} ,\;E\) are, respectively the constant, effective contact area, and potential difference. The contact force between solid asperities of slider and disk can be approximated by power law form,
$$F_{cs} = \left\{ {\begin{array}{ll} 0,&\quad s(t) > \delta_{s} \\ - c_{2} [s(t) - \delta ]^{{p_{s} }}, &\quad s(t) < \delta_{s} \\ \end{array} } \right. $$
(5)
in which \(\delta_{s}\) is the critical separation of the onset of contact between slider and disk that could be specified in terms of contact criterion. \(c_{2} ,\;p_{s}\) are parameters. The contact force between slider and lubricant on disk can be treated in same way.
$$F_{cl} = \left\{ {\begin{array}{ll} 0,&\quad s(t) > \delta_{l}\\ - c_{3} [s(t) - \delta ]^{{p_{l} }} ,&\quad s(t) < \delta_{l} \\ \end{array} } \right. $$
(6)
in which \(\delta_{l}\) is the critical separation of the onset of contact between slider and lubricant on disk. \(c_{2} ,\;p_{s}\) are parameters. Both slider-disk solid contact force and slider-lubricant contact force are function of contact depth or penetration (when separation is smaller than a value, separation is measured from the mean of asperity heights of the two rough surfaces), and can be approximately simplified as power law form. If pitch modes are considered, the friction force that is affected by the normal forces should be added for SDOF reflecting pitch mode.
The nonlinear vibration equation of air-bearing slider in the sub-nanometer clearance or proximity can be represented as,
$$m\ddot{x} + c\dot{x} + kx + F_{n} (x,\dot{x},h_{0} ) = F(t) $$
(7)
in which \(m,c,k\) are mass of slider, spring constant and damping constants of suspension. \(F_{n} (x,\dot{x},h_{0} )\) is nonlinear force due to interfacial interactions, which consists of the air-bearing force, intermolecular force, electrostatic force, lubricant-solid, solid–solid contact forces and friction force. \(F(t)\) is the excitation from disk roughness and lubricant ripples. The touchdown instability and bouncing due to the effects of strong nonlinearity of interface force have been widely investigated (Canchi and Bogy 2010; Hua et al. 2009; Salas et al. 2012; Ono 2009; Tani et al. 2009; Vakis et al. 2009; Xu et al. 2009; Knigge and Talke 2001; Mate et al. 2004; Xu et al. 2005; Kiely and Hsia 2008; Yu et al. 2012; Zheng and Bogy 2012; Sheng 2011; Canchi et al. 2012).

3 Suppression of instability of nonlinear system using dithering and forward control

The dynamics of the slider in a ultra-small space from the disk surface is very complex due to the uncertainty of disk and lubricant morphology, interface instability and nonlinear interface forces such as intermolecular force and contact forces which are hard to be modeled and quantified. It is too idealistic to assume it can be modeled accurately. With this observation, a feedforward control scheme is proposed to control the high frequency slider bouncing in touchdown process. The feedforward control such as dither can be introduced electronically or mechanically by an actuator (Hesjedal and Behme 2002; Dinelli et al. 1997; Cuberes 2007; Badertscher et al. 2007; Kaajakari’ et al. 2000). Dithering is to artificially input a high frequency external signal into a nonlinear system to obtain several possible objectives which include augmenting the linearity of the open or closed loop system, robustness, and asymptotic stability, reduction of quantization noise in data convertors; and adaptive enhancement of the closed loop linearity. The dithering can also be utilized to affect the dynamic behavior of the system and stop undesired chaotic behavior or undesired limit cycle oscillations in the system.

The most important effect of dithering is linearization of hard nonlinear characteristics, i.e. the original nonlinearity is transformed to another one which has a smaller nonlinearity or smoother system. This is attained by the fact that the dither effectively acts as a moving average filter, and applying this kind of process to a hard nonlinearity, will always make it softer, provided that the proceeding filter is able to omit the undesirable spurious components at the output. The typical feedforward control such as dither as a simple way to reduce system’s nonlinear discontinuous type force such as friction has been used for a long time. For the system characterized by Eq. (7), the idea of feedforward control is to change the behavior of the interface nonlinear properties by applying a properly chosen input function \(d_{i} (t)\) or external excitation \(f_{d} (t)\), and accordingly, the system motion equation is given by,
$$m\ddot{x} + c\dot{x} + kx + F_{n} (x,\dot{x},h_{0} ) = F(t) + f_{d} (t) $$
(8)

The excitation can reflect influence of some physical action, e.g. external force/field, or it can be some parameter perturbation (modulation). Such an approach is attractive because of its simplicity: no measurements or extra sensors are needed. It is especially advantageous for ultrafast processes and nanometer level where measuring system variables are extremely difficulty.

A number of authors discovered that high frequency excitation can stabilize the unstable equilibrium of a nonlinear system. Gelb pioneered the dither control of nonlinear dynamics (Gelb and Warren 1973; Gelb and Velde 1968). Morgul (1999) proposed the use of piecewise constant dither control to modify system dynamics (nonlinearity shape, equilibrium points, etc.). Thomsen (1999), Feeny and Moon (2000) discussed that dither in general has a stabilizing effect on the instability in friction-induced oscillations. For the above motion Eq. (8), there exists a strong nonlinearity due to adhesive force and the discontinuity due to contact bouncing. The main effects of the artificial high frequency excitation on mechanical systems has been widely proved that it is likely to result in three kinds of positive effects on the strong nonlinear system with discontinuity: (a) stiffening-it is the ability of high frequency excitation to alter the effective stiffness of the system, with respect to slow motions; one of the consequences of this is the ability to stabilize or destabilize equilibrium through changing the sign of the effective stiffness; (b) biasing- it is the ability of high frequency excitation to attract the system to a new steady state, e.g. a quasi-equilibrium or a steady-state velocity; (c) smoothening- it is the ability of high frequency excitation to smoothen discontinuous nonlinearities on the average. The solution of Eq. (8) can be decomposed as a fast component \(z\) and a slow component \(y\). The averaging approach could be used to obtain the equations governing the slow motions of the system under high frequency excitation.
$$m\ddot{y} + c\dot{y} + ky + \bar{F}_{n} (y,\dot{y}) = 0 $$
(9)
Proper dithering could render the effect of nonlinear force \(\bar{F}_{n} (y,\dot{y})\) to have weaker nonlinearity and less discontinuity compared with original interface nonlinear forces. The effective nonlinear force can be approximated as,
$$\bar{F}_{n} (y,\dot{y}) = \beta \int {F_{n} } (x + d_{i} ,\dot{x} + \dot{d}_{i} ,h_{0} )dt $$
(10)

The dither \(d_{i}\) could be developed to allow \(\bar{F}_{n} (y,\dot{y})\) to have less nonlinearity in terms of either velocity or displacement.

4 Simulation

In the simulation, the dither in the form of square waves with magnitude 0.85 and frequency of 400 kHz is applied on the system which has the following nominal parameters: \(m = 1.18\;{\text{mg, }}\)\(c = 0.05{\text{ kg/s}}\) and \(k = 1.3\,e5N/m\)\(F_{\text{i}} (x, \dot{x},h_{0} ) = \sum\nolimits_{i = 0}^{13} {a_{i} x^{i} }\), where \(a_{i}\) are taken from (Yu et al. 2011) (Table 1):
Table 1

Coefficients of interface forces of SDOF

\(a_{0} = - 9.327e - 1\)

\(a_{1} = - 1.2\)

\(a_{2} = 5.899\)

\(a_{3} = - 2.493\)

\(a_{4} = - 2.016\)

\(a_{5} = 5.722e - 1\)

\(a_{6} = 6.463e - 1\)

\(a_{7} = - 1.966e - 1\)

\(a_{8} = - 7.459e - 2\)

\(a_{9} = 3.317e - 2\)

\(a_{10} = 4.672e - 4\)

\(a_{11} = - 1.859e - 3\)

\(a_{12} = 3.043e - 4\)

\(a_{13} = - 1.546e - 5\)

 
Figures 2 and 3 shows the vibration without and with control, respectively. The results show that the vibration magnitude is reduced by 90 % after optimized dither control is applied.
https://static-content.springer.com/image/art%3A10.1007%2Fs00542-013-1819-7/MediaObjects/542_2013_1819_Fig2_HTML.gif
Fig. 2

Vibration without control

https://static-content.springer.com/image/art%3A10.1007%2Fs00542-013-1819-7/MediaObjects/542_2013_1819_Fig3_HTML.gif
Fig. 3

Vibration with control

5 Discussion

In the above we discussed the feedforward instability control of slider using dithering, which was accomplished from the system dynamics perspective. Actually, the application of dithering to the slider could directly alter interface friction and adhesion properties. The friction can be reduced by allowing a sliding part to have high-frequency vibrations (Hesjedal and Behme 2002; Dinelli et al. 1997; Cuberes 2007; Badertscher et al. 2007; Kaajakari’ et al. 2000). Depending on the direction of oscillation in relation to the direction of movement, different local effects can be attained in interface in addition to the mechanism of global effect described in above section. The physical effect of high frequency vibrations or ultrasound induced lubricity was reported due to out-of-plane or vertical normal ultrasonic vibration. In addition to the dither effects on system dynamics, in principle, the added input dither function also has the following functions (Hesjedal and Behme 2002; Dinelli et al. 1997; Cuberes 2007; Badertscher et al. 2007): reduce contact areas; change interface properties such as viscoelastic behavior due to its ultrasonic waveform feature (surface acoustic waves (SAWs). The effect of friction reduction caused by Rayleigh-type surface acoustic waves has been demonstrated for out-of-plane vertical oscillation component, instead of the effect of in-plane polarized Love waves. Moreover, the application of dithering to the slider could directly alter interface lubricant-induced adhesion (meniscus force/bridge) that is likely to appear in interface (Ono 2009; Yu et al. 2011).

6 Conclusion

By considering the special features of the interface model that includes air-bearing force, adhesion force, contact force and friction force, the feedforward control is proposed and the favorable dither effect is analyzed. The feasibility of the approach is verified by simulation results. Besides the advantageous dither effects on nonlinear system dynamics, the proper deployment of dithering is likely to directly generate the benefits of reducing contact areas/friction and favorably changing interface properties and lubricant-solid contact through inherent ultrasonic waveform feature. Future work includes the implementation of the control scheme on a physical system.

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© Springer-Verlag Berlin Heidelberg 2013