1. art and entertainment
2. visual art and design
3. design

1
Case study on anti-windup compensation Micro-actuator control in a hard-disk drive
Guido Herrmann, Matthew C. Turner, and Ian Postlethwaite
Control and Instrumentation Research Group,
Department of Engineering,
University of Leicester
Leicester,
LE1 7RH, U.K.
[email protected], [email protected], [email protected]
This chapter demonstrates the use of anti-windup compensation in the control loop of
a micro-actuator which is nominally controlled by a linear, discrete robust controller.
The micro-actuator is part of a hard disk drive dual-stage servo-control system for
positioning of the read/write head. The actuator inputs are constrained to retain the
micro-actuator’s displacement range of less than 0.4 µ m for mechanical protection.
In the first part of the chapter, the anti-windup compensation scheme exemplifies an
approach suggested by Weston & Postlethwaite [22]. Here, the scheme is posed as a
discrete full-order compensator and the closed loop analysis uses a generalized circle
citerion approach. The design of the compensator is posed in LMI-form.
In the second part of the chapter, it is shown how the linear micro-actuator control
loop with anti-windup compensation is incorporated into the non-linear servo-control
scheme for positioning of the read/write head in a hard disk drive.
1.1 Introduction
Micro-actuators have been gaining of importance in practical systems during recent
years. For instance, it is nowadays the target to integrate actuator, sensor and electronics for powerful computations in one device of micro or nano-scale. These technologies can be useful in optical communication systems, in electromechanical signal processing systems or in healthcare systems, such as BIO-MEMS for microchiplab diagnostics or micro-devices for therapeutic targeting and delivery. Mechanical
micro-actuators for nano-positioning have been of interest for the University of Leicester due to its importance in the servo-controller for the positioning of the readwrite head in hard disk data-storage systems [5, 8, 11]. A micro-actuator is being
used in a dual-stage control system to achieve high-banwidth positioning control.
2
Guido Herrmann, Matthew C. Turner, and Ian Postlethwaite
Fig. 1.1. Schematic of Hard Disk Drive with PZT-actuator
Significant research effort on hard-disk drive (HDD)-servo techniques has been invested in the area of dual-stage servo control [17, 18, 14]. The reason for this is the
continuous increase in the track density and in storage capacity of HDDs. Recently,
a track density of above 420 kTPI (TPI- track per inch) has been demonstrated (see
[23, 2]) in a laboratory environment and about 149 kTPI density HDDs are nowadays
available in the consumer market. In addition to the significant increase in data density, the increased demand for higher data rates requires the improved performance
of the head-positioning servo system in a hard disk drive. A promising way to meet
these demands is to augment the conventional voice coil motor (VCM) actuator with
a second-stage, high bandwidth micro-actuator. Dual-stage servo systems in HDDs
are now a feasible alternative to the single stage VCM-servo system. PZT-based
micro-actuators using PZT-elements embedded in the head suspension are popular,
e.g. the ‘FUMA’-actuator in [19] (Figure 1.1). However, the displacement range of
secondary actuators is very limited, typically less than 1-2 µ m, and the input signal
for the actuator is limited to prevent damage. In dual-stage servo-systems, the two
actuators have to deal with the following servo-tasks: seek/settling and track following. Seek/settling control has to ensure a fast movement of the read/write head from
one track to another. For track following, high bandwidth controllers are necessary to
ensure good error rejection capabilities while counteracting disturbances. Therefore,
the primary VCM-actuator is required for larger displacement and the secondary actuator provides large bandwidth.
For servo-control of such a dual-stage actuator system, the method of [11, 12] is
employed. It is based on a well known decoupled dual-stage controller structure
of [13], where design and stability for the primary VCM-control loop and the secondary PZT-control loop are guaranteed independently. It will be shown [11, 12]
that the primary and secondary loop remain stable independently regardless of the
seek/settling/track-following control method used for the VCM-loop, providing the
secondary control loop is stable in the presence of saturation limits. Hence, it seems
Title Suppressed Due to Excessive Length
3
logical to use for the secondary loop an AW compensator to guarantee overall large
and small signal stability despite actuator saturation limits. AW compensators are
most suitable, as they have been developed to retain the nominal performance of the
original control system [9, 7, 20], e.g. high-bandwidth tracking in the servo-control
of hard disk drives.
This example study on AW-compensation will consider the following issues:
1. controller design for the micro-actuator loop and wind-up problems due actuator
limits,
2. discrete anti-windup compensator design, anti-windup compensation for the
micro-actuator control loop
3. the micro-actuator control loop as part of the overall seek-settling scheme for
the hard disk drive.
We will consider for reasons of simplicity the micro-actuator loop at first.
1.2 The micro-actuator control loop and windup-problems
The model of a micro-actuator is usually very simple. Ignoring high frequency resonances, the model of the micro-actuator could be considered to be of constant gain
only (Figure 1.2).
However, in practice these resonances at 6.5 kHz and 9.6 kHz are significant. Resonances are usually subject to phase and gain uncertainty. The center frequency of a
resonance might even shift due to the influence of temperature. This usually forces
the control designer to retain the open and closed loop bandwidth lower than 50 %
of the smallest significant resonance. Hence, for our micro-actuator, an open loop
crossover frequency of not more than 3 kHz can be achieved.
It must be also noted that hard disk drive technology is usually controlled using digital technology. The sampling frequency is directly correlated to the rotational speed
of the hard disk and the servo-information which is placed along the concentric data
tracks. The amount of servo-information will limit the available space for user data.
Hence, it is necessary to limit the amount of servo-information causing also a limited sampling frequency (Figure 1.3). In our case, we have used a sampling frequency
of 27 kHz which is a practically relevant sampling frequency in modern hard disk
drives. However, this sampling frequency is rather low, since micro-actuators often have also resonance frequencies at 20 kHz and above (not depicted here), i.e.
above the Nyquist frequency of 13.5 kHz. Thus, a hard disk drive servo system is a
sampled-data control system, where it is necessary to use discrete or sampled-data
control methods to design the servo-controller.
In the hard disk drive industry, it is common practice to counteract resonances by
simple notch filters. In our case, this may be done by using two discrete notch filters
4
Guido Herrmann, Matthew C. Turner, and Ian Postlethwaite
Log. Magn. [µ m/V]
PZT−model
0
10
−1
10
−2
10
1
10
2
10
3
10
Frequency [Hz]
4
10
Phase [deg]
200
0
−200
−400
10
1
10
2
10
Frequency [Hz]
3
4
10
Fig. 1.2. Continuous model of a PZT-actuator
Fig. 1.3. Hard-disk with servo information and data tracks
which are digitally implemented (see Figure 1.4). Hence, these notch filters are easily augmented to the input signal of the PZT-actuator via a digital-to-analogue unit
(DAU). In general, a saturation is placed between the filter and the DAU to protect
the actuator from any damage due to high voltage peaks (see Figure 1.5 for a Matlab
respresentation). The saturation limits are also tuned in such a way to protect the
micro-actuator from too large displacement.
The micro-actuator augmented with the notch filters is easily modelled as a second
order system PPZT (z) (see Figure 1.6):
Title Suppressed Due to Excessive Length
5
Notch filters
Log. Magn. [µ m/V]
10
10
10
0
−1
−2
10
1
2
3
10
10
10
4
Frequency [Hz]
Phase [deg]
0
−50
−100
−150
−200
10
1
2
3
10
4
10
10
Frequency [Hz]
Fig. 1.4. Frequency response of discrete notch filter
sys_notch_d1*sys_notch_d2
PZT
NotchFilter
PZT actuator
Saturation1
Zero−Order
Hold1
Fig. 1.5. Matlab-Simulink model of PZT-actuator with notch filter and protective saturation
element
PPZT =
−0.07997z − 0.05363
z2 − 0.7805z + 0.3097
(1.1)
The first step in the closed loop control design for this micro-actuator is to design a
suitable linear controller K(z) based on robust µ -design methods. The design problem is standard. hWe arei minimizing the µ -value for the following control problem
S
with two blocks WWusSK
and [ WT T ]:
·
¸
Ws S
 Wu SK 
£
¤
WT T
where S =
1
1+KPPZT
and T =
KPPZT
1+KPPZT
(see Figure 1.7).
The weights (Figure 1.8) are given by
6
Guido Herrmann, Matthew C. Turner, and Ian Postlethwaite
Log. Magn. [µ m/V]
Discrete PZT−model with notch
10
10
−1
−2
10
1
2
3
10
10
10
4
Frequency [Hz]
Phase [deg]
200
0
−200
−400
1
10
2
3
10
10
4
10
Frequency [Hz]
Fig. 1.6. Zero-order hold discretization of PZT-model with notch (line); Second order model
of PZT-actuator (dash)
Fig. 1.7. µ -control problem
WT =
1.3637(z + 0.04294)
−0.25664(z − 2.578)
, Ws =
, Wu = 0.000001.
z + 0.6843
z − 0.9605
The design of the controller is easily achieved using the µ -toolbox of Matlab. However, a small trick has to be used. Matlab does not provide µ -tools for discrete control
problems. Hence, the discrete control problem has to be converted into a continuoustime problem using a bilinear transformation [3, 5]. Note that the bilinear transfor-
Title Suppressed Due to Excessive Length
7
Log. Magn. [µ m/V]
µ−design weights
10
10
1
0
10
1
2
3
10
10
10
4
Frequency [Hz]
50
Phase [deg]
0
−50
−100
−150
−200
1
2
10
3
10
10
4
10
Frequency [Hz]
Fig. 1.8. µ -control problem weights (WT (line), Ws (dashed))
mation creates an equivalent continuous-time µ -problem. The discrete controller can
be obtained from the solution of the continuous-time control problem by using again
the bilinear transformation approach. The discrete controller will be always stabilizing and µ -(sub)-optimal with the same µ -value as obtained from the continuous-time
design. Thus,√for our design problem, a controller is obtained using DK-iteration for
a µ -value of 2. Balanced truncation methods allow to obtain a third order controller
which perfectly matches the originally designed controller. The discrete controller of
third order is:
K(z) =
−6.584z3 − 1.403z2 + 3.15z − 2.079
z3 + 0.4509z2 − 0.9169z − 0.4211
The control-loop is easily simulated considering a sine sweep in the frequency range
from 10 Hz to 500 Hz as demand for the position. For small demand amplitude of 0.2
µ m, the controller is well able to follow this demand without significant phase lag
but with a small amplitude loss (Figure 1.9). However, for large demand amplitude
of 1 µ m, the actuator saturation limit of 1.54 V is activated, limiting also the actuator
displacement range. Thus, in this case, the controller is not able to track the controller
demand as the actuator displacement is limited to a magnitude of less than 0.5 µ m.
Hence, the actuator starts to oscillate and the controller features a lag (Figure 1.10).
These two issues of the resonance and the lag can be easily resolved by introducing
an anti-windup compensator to recover quickly from the performance loss due to
saturation. The anti-windup compensator of interest for us will be discussed next.
8
Guido Herrmann, Matthew C. Turner, and Ian Postlethwaite
0.2
0.15
0.1
time [s]
0.05
0
−0.05
−0.1
−0.15
−0.2
0
0.01
0.02
0.03
0.04 0.05 0.06
postion [µm]
0.07
0.08
0.09
0.1
Fig. 1.9. Control result for 0.2 µ m demand amplitude (demand (dashed), actuator-position
(line))
1
0.8
0.6
0.4
time [s]
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0
0.01
0.02
0.03
0.04 0.05 0.06
postion [µm]
0.07
0.08
0.09
0.1
Fig. 1.10. Control result for 1 µ m demand amplitude (demand (dashed), actuator-position
(line))
1.3 Anti-windup compensation for discrete linear control systems
We consider the system in Figure 1.11 as introduced in [21, 22] for continuoustime anti-windup (AW) compensation and in [7] for discrete-time control systems.
Title Suppressed Due to Excessive Length
9
Fig. 1.11. Conditioning with M(z)
Fig. 1.12. Equivalent representation of conditioning with M(z)
P(z) is the discrete plant and K(z) is the nominal linear discrete controller. The AWcompensator is given by the blocks, M(z) − I and PM(z). The anti-windup compensation is designed using the free parameter M(z).
The control signal is constrained by the limits of a saturation function. The saturation
function is defined as
sat(u) := [sat1 (u1 ), . . . , satm (um ))]T
(1.2)
where sati (ui ) := sign(ui ) × min {|ui |, u¯i }, where u¯i > 0 is the i’th saturation limit.
The following identity holds
Dz(u) = u − sat(u)
(1.3)
where Dz(u) is the deadzone function. For the deadzone nonlinearity Dz(u), it follows that there exists a diagonal matrix W such that
10
Guido Herrmann, Matthew C. Turner, and Ian Postlethwaite
Dz(u)0W (u − Dz(u)) ≥ 0, u ∈ Rm
(1.4)
This inequality will be used later for stability analysis employing the S-procedure
[1]. This is the discrete-time version of the continuous time configuration introduced
in [21, 22].
As in [21, 22], it is straightforward to show that, using the identity (1.3), Figure
1.11 can be re-drawn as Figure 1.12. The representation in both of these diagrams
essentially casts the anti-windup problem as the problem of choosing an appropriate
M(z). However, notice that Figure 1.12 reveals an attractive decoupling into nominal
linear system, nonlinear loop and disturbance filter.
As noted in [22], most linear conditioning schemes can be interpreted in the framework of Figure 1.11. In [7], the mapping T : ulin 7→ yd was picked as a measure of the
anti-windup compensator’s performance (Figure 1.12). We shall choose to minimise
the l2 gain, kT ki,l2 , in our anti-windup synthesis.
The detectable plant, P(z), has the following state-space description
½
P(z) ∼
x p (k + 1) = A p x p (k) + B p um (k)
y(k) = C p x p (k) + D p um (k)
(1.5)
where x p ∈ Rn p is the plant state, um ∈ Rm is the actual control input to the plant,
y ∈ Rq is the output which is fed back to the controller. We are making the assumption
that the plant P(z) is asymptotically stable is |λmax (A p )| < 1 for global stability of
the non-linear control system with anti-windup compensation.
As in [22] for continuous-time, M(z) can be chosen as a coprime factor of P(z).
So if P(z) = N(z)M −1 (z), we can search for a coprime factor of P(z) such that the
anti-windup closed-loop has the best performance in terms of the gain of T . This
approach is also related to that of [16] and, to a lesser extent, that of [15]. To achieve
full-order stabilisation we would like to choose coprime factors, which share the
same state space and are of order equal to that of P(z). Employing Figure 1.12, such
coprime factorisations can be characterised by
·


¸
Ap + BpF Bp
M(z) − I
∼
F
0 
N(z)
Cp + D p F D p
(1.6)
where u(k)
˜
= Dz(ulin (k) − ud (k)). Note that these equations are parameterised by
the free parameter F and therefore we attempt to choose F such that kT ki,l2 is minimised.
Theorem 1. There exists a dynamic compensator Θ (z) = [M(z)0 − I (P(z)M(z))0 ]0
which solves strongly the anti-windup problem if there exist matrices Q > 0,U =
Title Suppressed Due to Excessive Length
11
diag(µ1 , . . . µm ) > 0, L ∈ R(m+q)×m and a scalar γ > 0 such that the following linear
matrix inequality is satisfied


−Q −L0 0 QC0p + L0 D0p QA0p + L0 B0p
 ? −2U I

UD0p
UB0p


 ?
<0
? −γ I
0
0


 ?

?
?
−γ I
0
?
?
?
?
−Q
(1.7)
Furthermore, if this inequality is satisfied, a suitable F for the coprime factorisation
(1.6) achieving kT ki,l2 < γ , is given by F = LQ−1 .
Proof: Let us choose a Lyapunov function candidate as V (k) = x(k)0 Px(k) > 0. We
define the Lyapunov difference as ∆ V (k) := V (k + 1) −V (k). Next we consider the
function ∆ V˜ (k) which is defined as
1
∆ V˜ (k) := ∆ V (k) + 2u(k)
˜ 0W [ulin (k) − ud (k) − u(k)]
˜
+ kyd (k)k2 − γ kulin (k)k2
γ
(1.8)
This function is a combination of the Lyapunov difference (first term), the sector
bounds from (1.4) associated with the deadzone nonlinearity (second term), and two
final terms which ensure we have a certain level of l2 performance. If we can ensure
that equation (1.8) is negative definite, we have
1. Asymptotic stability When ulin (k) = 0 and
1
∆ V˜ (k) = ∆ V (k) + 2u(k)
˜ 0W [ulin (k) − ud (k) − u(k)]
˜
+ kyd (k)k2 < 0
|
{z
} γ
| {z }
≥0
(1.9)
≥0
for [x(k) u(k)
˜ ulin (k)] 6= 0 asymptotic stability is implied from ∆ V (k) < 0.
2. l2 gain < γ .
Summing ∆ V˜ (k) from 0 to ∞ gives:
∞
∞
k=0
k=0
1
˜ 0W [ulin (k) − ud (k) − u(k)]
˜
+ kyd k2l2 − γ kulin k2l2 < 0
∑ ∆ V (k) + 2 ∑ u(k)
γ
As
∑∞
k=0 ∆ V (k) = V (∞) −V (0)
(1.10)
we get
12
Guido Herrmann, Matthew C. Turner, and Ian Postlethwaite
∞
1
V (∞) −V (0) + 2 ∑ u(k)
˜ 0W [ulin (k) − ud (k) − u(k)]
˜
+ kyd k2l2 − γ kulin k2l2 < 0
| {z }
γ
k=0
|
{z
}
>0
≥0
for [x(k) u(k)
˜
ulin (k)] 6= 0, which implies
fore kT ki,l2 < γ .
(1.11)
kyd k2l2
<
γ 2 ku
2
lin kl2
+ V (0) and there-
This procedure of extending the Lyapunov difference by some extra non-negative
terms is well established as S-procedure [1]. Strictly speaking m + 1 terms are included. For the sector non-linearity (1.4), m terms are included, while the m + 1-th
term is contributed by the l2 -gain constraint. It is well known that the inclusion of
one term only, creates an equivalent inequality for both conditions to be satisfied.
However, once more than one term is considered, sufficiency is only achieved and
conservatism is introduced. Furthermore, the sector bound as given in (1.4) may also
introduce conservatism as discussed earlier. These facts are well-known and accepted
trade-offs [1, 4] as they allow practically feasible solutions (e.g. [10]).
Substituting for x(k), ud (k) and yd (k) in (1.8), we have that ∆ V˜ (k) < 0 if and only if

0 


x(k)
VF11 VF12 0
x(k)
 u(k)
  ? VF22 W   u(k)
 < 0,
˜
˜
ulin (k)
?
? −γ I
ulin (k)
|
{z
}
[x(k) u(k)
˜ ulin (k)] 6= 0 (1.12)
VF
where
1
VF11 = (A p + B p F)0 P(A p + B p F) − P + (C p + D p F)0 (C p + D p F)
γ
1
VF12 = (A p + B p F)0 PB p − F 0W + (Cp + D p F)0 D p
γ
1 0
0
VF22 = −2W + D p D p + B p PB p .
γ
(1.13)
(1.14)
(1.15)
The remainder of the proof has to show that VF < 0 is equivalent to (1.7). This
follows by standard Schur complement and congruence transformation arguments.
The Schur complement implies that (1.12) holds if and only if

−P −F 0W
 ? −2W

 ?
?

 ?
?
?
?

0 C0p + F 0 D0p A0p + F 0 B0p

W
D0p
B0p

<0
0
0
−γ I


?
−γ I
0
?
?
−P−1
(1.16)
Title Suppressed Due to Excessive Length
13
The next step is to multiply the left and right of the matrix inequality with

−P−1 0
 ? W −1

 ?
?

 ?
?
?
?

000
0 0 0

I 0 0
<0
? I 0
??I
(1.17)
so that

−P−1 −P−1 F 0
 ? −2W −1

 ?
?

 ?
?
?
?

0 P−1C0p + P−1 F 0 D0p P−1 A0p + P−1 F 0 B0p

I
W −1 D0p
W −1 B0p

<0
−γ I
0
0


?
−γ I
0
?
?
−P−1
(1.18)
If we define L = FP−1 , U = W −1 and Q = P−1 , then (1.7) follows.
Hence, considering equation (1.9), internal stability, follows. The non-linear operator
kT ki,l2 has a finite l2 gain with an upper bound of γ > 0 which is easily implied from
equation (1.11). Furthermore, note that as there is no ‘direct feedthrough’ term in the
nonlinear loop, well-posedness is ensured.
¤¤
1.4 Anti-windup compensation for the micro-actuator
It is now straightforward to design an anti-windup compensator for the linear control
scheme of Section 1.2. The model used for controller design (1.1) delivers an antiwindup compensator of (1.6) as given by the state space representation of the second
order system
·
Ap =
¸
·
¸
£
¤
0.5000
0.7805 −0.6195
, Bp =
, Cp = −0.1599 −0.2145 , D p = 0
0.5000 0
0
and the suitable state feedback gain F as known from (1.6):
£
¤
F = −1.2403 1.7618 .
The l2 gain has been minimized to a value of γ = 0.2616.
14
Guido Herrmann, Matthew C. Turner, and Ian Postlethwaite
1
0.8
0.6
0.4
time [s]
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0
0.01
0.02
0.03
0.04 0.05 0.06
postion [µm]
0.07
0.08
0.09
0.1
Fig. 1.13. Control result for 1 µ m demand amplitude (demand (dashed), actuator-position
(line))
The application of this computed AW-compensator to the control system of Section
1.2 with saturation limit improves the closed loop (Figure 1.13). The oscillations observed without AW-compensation are minimized and the lag seems to be eradicated
(Figure 1.13 and 1.10) for the sine sweep with 1 µ m amplitude.
Thus, AW-compensation can achieve a significantly improved tracking performance
considering the fact that the micro-actuator has a displacement limit of about ±0.5µ m.
1.5 The micro-actuator control loop as part of a hard-disk drive
servo-system
The micro-controller is to be incorporated into the control scheme for the servocontrol of a hard disk drive actuator. The micro-actuator is directly embedded in the
suspension of the voice-coil motor (VCM) actuator (Figure 1.1). A linear model of
the actuator is given by the superposition of the two models of the PZT-actuator,
PPZT , and the VCM-actuator, PVCM :
[PPZT PVCM ]
The VCM actuator can be modeled as a double integrator which is affected by high
frequency resonances and the dynamics of friction in low frequency. The VCMactuator is usually controlled by a (proximate)-time-optimal control scheme [3, 6,
Title Suppressed Due to Excessive Length
15
Fig. 1.14. Simplified seek/settle/trackfollowing scheme
Fig. 1.15. Equivalent representation of the servo scheme
11] which achieves fast seeking for fast positioning of the read/write head, while a
smooth transfer to a linear track-following scheme needs to be achieved for trackfollowing (see [3, 6, 11] for a more detailed explanation). To achieve a higher trackfollowing controller bandwidth, the secondary PZT-actuator is used. The constraints
on both actuators (in particular for the PZT-actuator) need to be incorporated into the
servo-control scheme. The approach is to use a decoupled control scheme as from
[13], which incorporates the traditional time-optimal seek-settling scheme for the
VCM-actuator [6, 11] and it allows an independent controller design for the PZTmicro-actuator so that the controller design of Sections 1.2-1.3 can be reused. The
16
Guido Herrmann, Matthew C. Turner, and Ian Postlethwaite
Fig. 1.16. Simplified seek/settle/trackfollowing scheme with observer
2.5
postion [µm]
2
1.5
1
0.5
0
0
0.005
0.01
0.015
0.02
time [s]
0.025
0.03
0.035
0.04
Fig. 1.17. Control result for 2 µ m seek step without AW-compensation (demand (dashed),
actuator-position (line))
control scheme works on the assumption that the absolute position of the PZT-microactuator is measurable (see Figure 1.14).
Employing the superposition principle, it is easily seen that the control scheme of
Figure 1.14 is equivalent to the controller configuration of Figure 1.15, where the
control loops for the PZT and the VCM-actuator are decoupled. Hence, both controllers can be designed independently in terms of stability. For the implementation
of the scheme, it is necessary to use an observer which obtains the absolute position
Title Suppressed Due to Excessive Length
17
2.5
postion [µm]
2
1.5
1
0.5
0
0
0.005
0.01
0.015
0.02
time [s]
0.025
0.03
0.035
0.04
Fig. 1.18. Control result for 2 µ m seek step with AW-compensation(demand (dashed),
actuator-position (line))
of the PZT-actuator (see Figure 1.16). It is easily verified that observer and controller
separate due to the linearity of the plant.
Using now a non-linear seek-settle control scheme for the VCM-actuator as presented in [6, 11] and the linear control loop from Sections 1.2-1.3 with and without
anti-windup compensation for the controller of the PZT-actuator, it is easily verified
that the AW-compensation scheme significantly improves on seeking performance
(see Figures 1.17 and 1.18). The controller with AW-compensation prevents for a 2
µ m-seek step a very large overshoot and allows fast settling to assume track following of the read/write head as quickly as possible.
1.6 Summary
The control system of a PZT-micro-actuator has been investigated for its feasible
range, i.e. the available displacement range of the micro-actuator. It has been shown
that anti-windup compensation can improve tracking of demands which are not feasible. It limits controller lags and suppresses high frequency resonances for a practically valid hard disk drive micro-actuator. In connection with the recently established dual-stage track-seek/following scheme [6, 11], it has been shown that the
AW-compensator suppresses large overshoots and enhances settling speed.
18
Guido Herrmann, Matthew C. Turner, and Ian Postlethwaite
References
1. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in
System and Control Theory. Society for Industrial and Applied Mathematics, 1994.
2. C. Du, L. Xie, G. Guo, J. Zhang, Q. Li, and B. Hredzak. A generalized kyp lemma based
control design and application for 425 ktpi servo track writing. In Proceedings of the
2006 American Control Conference, Minneapolis, Minnesota, USA, 2006.
3. G. F. Franklin, J. D. Powell, and M . L. Workman. Digital Control of Dynamic Systems.
Addison-Wesley Publishing Company, Reading, Massachusetts, 2nd edition, 1990.
4. G. Grimm, J. Hatfield, I. Postlethwaite, A. R. Teel, M. C. Turner, and L. Zaccarian. Antiwindup for stable linear systems with input saturation: An LMI based synthesis. IEEE
Transactions on Automatic Control, 48(9):1509–1525, 2003.
5. G. Herrmann and G. Guo. HDD dual-stage servo-controller design using a µ -analysis
tool. Control Engineering Practice, 12(3):241–251, 2003.
6. G. Herrmann, B. Hredzak, M. C. Turner, I. Postlethwaite, and G. Guo. Improvement of a
novel dual-stage large-span track-seeking and track-following method using anti-windup
compensation. In Proceedings of the 2006 American Control Conference, Minneapolis,
Minnesota, USA, 2006.
7. G. Herrmann, M. C. Turner, and I. Postlethwaite. Discrete time and sampled data antiwindup synthesis: stability and performance. International Journal of Systems Science,
37(2):91–113, 2006.
8. G. Herrmann, M. C. Turner, I. Postlethwaite, and G. Guo. Practical implementation of a
novel anti-windup scheme in a hdd-dual-stage servo-system. IEEE/ASME Transactions
on Mechatronics, 9(3):580–592, 2004.
9. G. Herrmann, M.C. Turner, and I. Postlethwaite. Discrete time anti-windup - part 2:
extension to sampled data case. In Proc. of the European Control Conf., 2003.
10. G. Herrmann, M.C. Turner, I. Postlethwaite, and G. Guo. Application of a novel antiwindup scheme to a hdd-dual-stage actuator. Proceedings of the American Control Conference, 2003.
11. B. Hredzak, G. Herrmann, and G. Guo. A proximate-time-optimal-control design and
its application to a hard disk drive dual-stage actuator system. IEEE Transactions on
Magnetics, 42(6):1708 – 1715, 2005.
12. B. Hredzak, G. Herrmann, and G. Guo. Short and long-span track seek control for hard
disk drive dual-stage servo actuators. In Proceedings of IEEE Industrial Electronics Society Conference, Raleigh, North Carolina, 2005.
13. M. Kobayashi and R. Horowitz. Track seeking control for hard disc dual-stage servo
systems. IEEE Transactions on Magnetics, 37(2):949–954, 2001.
14. M. Kobayashi, S. Nakagawa, T. Atsumi, and T. Yamaguchi. High-bandwidth servo control
designs for magnetic disc drives. In Proc. IEEE/ASME Intern. Conf. Adv. Intel. Mechatr.,
Como, Italy, pages 1124–1129, 2001.
15. M.V. Kothare, P.J. Campo, M. Morari, and C.N. Nett. A unified framework for the study
of anti-windup designs. Automatica, 30(12):1869–1883, 1994.
16. S. Miyamoto and G. Vinnicombe. Robust control of plants with saturation nonlinearity based on comprime factor representations. Proc. IEEE Conference on Decision and
Control, pages 2838–2840, 1996.
17. K. Mori, T. Munemoto, H. Otsuki, Y. Yamaguchi, and K. Akagi. A dual-stage magnetic
disk drive actuator using a piezoelectric device for high track density. IEEE Trans. on
Magnetics, 27(6):5298–5300, 1991.
Title Suppressed Due to Excessive Length
19
18. S. J. Schroeck, W. C. Messner, and R. J. McNab. On compensator design for linear timeinvariant dual-input single-output systems. IEEE Trans. Mechatr., 6(1):50–57, 2001.
19. M. Tokuyama, T. Shimizu, H. Masuda, S. Nakamura, M. Hanya, O. Iriuchijima, and
J. Soga. Development of a φ -shaped actuated suspension for 100-ktpi hard disk drives.
IEEE Transactions on Magnetics, 37(4):1884–1886, 2001.
20. M. C. Turner, G. Herrmann, and I. Postlethwaite. Discrete-time anti-windup: Part 1 - stability and performance. In Proceedings of the European Control Conference, Cambridge,
UK, 2003.
21. M.C. Turner and I. Postlethwaite. A new perspective on static and low order anti-windup
synthesis. International Journal of Control, 77(1):27–44, 2004.
22. P.F. Weston and I Postlethwaite. Analysis and design of linear conditioning schemes for
systems containing saturating actuators. IFAC Nonlinear Control System Design Symposium, 1998.
23. J. Zheng, C. Du, G. Guo, Y. Wang, J. Zhang, Q. Li, and B. Hredzak. Phase lead peak
filter method to high tpi servo track writer with microactuators. In Proceedings of the
2006 American Control Conference, Minneapolis, Minnesota, USA, 2006.