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Neural-Network Based Automatic PID Gain Tuning in the Presence of Time-Varying Disturbances in Hard Disk Drives

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Abstract and Figures

In hard disk drive (HDD) systems, disturbances commonly contain different frequency components that are time-varying in nature. Different HDD systems may subject to different excitation disturbances. In this case, it is difficult for fixed-gain PID controllers to maintain a good overall performance. When the characteristics of the disturbances change, or when servos are designed for different drive products, the PID gains have to be retuned. This paper presents automatic online gain tuning of PID controllers based on neural networks. The proposed control scheme can automatically adjust the PID parameters online in the presence of time-varying disturbances, or for different disturbances among different HDD products, and find the optimal sets of PID gains through the self-learning ability of neural networks.
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*Corresponding author: Liting Sun
The author is a Ph. D student in University of Science and Technology of China. Currently she is a visiting student researcher in
University of California at Berkeley, supervised by Professor Masayoshi Tomizuka. This work is performed during the visiting period
in UC Berkeley.
Liting Sun1*, Xu Chen2, Masayoshi Tomizuka2
1University of Science and Technology of China, Hefei, Anhui, 230027, China
litingsun@me.berkeley.edu
2University of California, Berkeley
Department of Mechanical Engineering, University of California, Berkeley, CA, 94720, USA
Email: {maxchen, tomizuka}@me.berkeley.edu
Introduction
In hard disk drive (HDD) systems, disturbances
commonly contain different frequency components
that are time-varying in nature. Different HDD
systems may subject to different excitation
disturbances. In this case, it is difficult for fixed-gain
PID controllers to maintain a good overall
performance. When the characteristics of the
disturbances change, or when servos are designed for
different drive products, the PID gains have to be re-
tuned. This paper presents automatic online gain
tuning of PID controllers based on neural networks.
The proposed control scheme can automatically
adjust the PID parameters online in the presence of
time-varying disturbances, or for different
disturbances among different HDD products, and
find the optimal sets of PID gains through the self-
learning ability of neural networks.
Neural network has been widely applied in control
systems due to its self-learning ability, adaptability,
and nonlinear mapping between its inputs and
outputs. Gao et. al [1] and Zhang et. al [2] both
adopted an adaptive PID controller based on neural
network in an electro-hydraulic position system and
a crank angular speed control system where coupling
effect between the motor and mechanism was
considered. High adaptability and strong robustness
of the controller were observed. Seung [3] used a
primary PID controller and an auxiliary controller
based on neural network for learning and
compensating for the inherent nonlinearities in a
pneumatic servo system, which improved the
tracking performance and enhanced the robustness of
the controller. Cheng et. al [4] applied the neural-
network-based-PID controller in a nanopositioning
system driven by ultrasonic motor and achieved a
positioning accuracy of 10nm. Yang et. al [5]
effectively improved the positioning performance of
a micro-positioning stage using an adaptive neural-
fuzzy PID controller, which improved the
positioning accuracy from 92nm to 23nm at the X
axis and from 102nm to 28nm at the Y axis.
In this paper, the self-learning ability of the neural
network is employed to improve the adaptability and
robustness of the PID controller with time-varying or
product-dependent disturbances. The PID gains will
be automatically tuned and optimized online for
different HDD products with different disturbance
characteristics.
Neural-Network Based Automatic PID Gain Tuning in the
Presence of Time-Varying Disturbances in Hard Disk Drives
1
Copyright © 2013 by ASME
Proceedings of the ASME 2013 Conference on Information Storage and Processing Systems
ISPS2013
June 24-25, 2013, Santa Clara, California, USA
ISPS2013-2948
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The Structure of Neural-Network based PID
Controller
Fig.1 shows the structure of neural-network based
PID controller and the structure of a two-layer back-
propagation neural network (BPNN) [6]. In Fig.1(b),
1
()
p
Gz
represents the dynamics of the HDD system
and
is the disturbance signal. Our goal is to
automatically tune the PID gains for a better
regulation performance to match the current
disturbance characteristics. In the neural-network
based PID controller, PID gains are the outputs of
the back-propagation neural network, as shown in
Fig.1(a).
Fig.1 Structure of a two-layer back-propagation
neural network (a) and the neural-network based PID
controller (b)
The central idea for the BPNN based PID controller
is to find a set of PID parameters that minimizes the
cost function E = e2(k)/2
through the online update process of the neural
network parameters, denoted as W and V in Fig. 1(a).
e(k) in the feedback loop depends on PID gains
[Kp(k), KI(k), Kd(k)], which are functions of the
weighting parameters W and V. Hence e(k) depends
on W and V. It thus makes sense to minimize the cost
function with respect to W and V.
As shown in Fig.1(a), the structure of the BPNN
adopted in this paper is 4-7-3. The input nodes
include the position error signal (PES), the derivative
of PES, the second differential of PES and the sum
of PES. The order of the hidden layer is selected
based on the empirical formula [7, 8]. In selecting
this value, many factors such as the training
algorithm, the training dataset, the input and the
output neuron numbers and the complexity of the
activation functions have to be considered. There is
no guide about how to compute the optimal order of
the hidden layer and it is obtained by trimming the
network size without degrading its performance. It
should be noted that the order of the hidden layer has
nothing to do with the order of the plant to be
controlled. This is one benefit of the neural network
as it requires no information on the plant model.
The working principle of the BPNN can be
expressed as follows.
Input layer: for each node i, the input and the output
are
1, 1,
, 1,2,3,4;
ii
y xi= =
(1)
where
1,i
x
are 2
(), (), (), ()
ek ek ek ek∆∆
.
Hidden layer: for each node j, the input and the
output relation is
4
2, 1 2, 1 1,
1
1
() ( )
()
j j i ij
i
xx
xx
y fx f yw
ee
fx ee
=
= =
=
+
(2)
where
ij
w
is the updated weight coefficients that
connect the nodes in the input and the hidden layers,
and 1
()fx
is called the activation function of the
hidden layer.
Output layer: for each node k, the input and the
output relation is
7
3, 2 3, 2 2,
1
2
() ( )
1
() 1
k k j jk
j
x
y fx f yv
fx e
=
= =
=
+
(3)
2
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where the weight coefficient
jk
v
connects the nodes
in the hidden and the output layers, and
2
()fx
is the
activation function of the hidden layer.
Online Update Algorithm. In order to automatically
tune the PID gains in the presence of time-varying
disturbances or dramatic disturbance changes, the
weight coefficients
ij
w
and
jk
v
are updated online to
minimize the PES. By using the idea that is similar
in adaptive inverse control, the mean square error is
first approximated by the instantaneous error square
2( )/2E ek=, and the update law is derived by using
the steepest descent method and the backward error
propagation concept:
3, 3, '
2 2,
3,
2, 2, '
1 1,
2, 2, 2,
2,
3,
'
1 1, 3, 2,
... ( )
()
( () )
()
kk
jk j
jk k jk
jj
ij i
ij j j ij j
jk j
j
k
ikkj
yx
E Ee e
v e sgn f y
v eu x v u
yx
EE E
w fy
w yxw y
vy
y
e
f y e sgn ux y
e
e sgn u
ηη η
ηη η
η
η
∂∂
∂ ∂∂
∆=− = =⋅
∂∂ ∂
∂∂
∂∂ ∂
∆=− = =
∂ ∂∂


= −⋅ 
∂∂ ∂


= ⋅
''
1 1, 2, 2i j jk
k
fy y fv
(4)
( 1) ( ) ( ( ) ( 1))
( 1) ( ) ( ( ) ( 1))
ij ij ij c ij ij
jk jk jk c jk jk
wk wk w mwk wk
vk vk v mvk vk
η
η
+ = +∆ +
+ = +∆ +
(5)
In Eq. (4), sgn(x) is the sign function: i.e. sgn(x)=1 if
x>0 and sgn(x)=-1 if x<0.
η
is the learning rate of the
weight coefficients and
c
m
is the
momentum adopted to avoid local minima.
Application to Time-varying Disturbance
Rejection
To illustrate the effectiveness of the BPNN based
automatic PID gains tuning process, the HDD
benchmark [9] is used to study disturbance rejection
with time-varying frequencies. We take a piecewise
sinusoidal signal as the disturbance signal, as shown
in Fig.2. Each segment has a different frequency,
ranging from 20Hz to 200Hz.
Fig.3 shows a comparison of the results using a
traditional fixed-gain PID controller and a BPNN
based PID controller with automatic gain tuning. It
can be seen that the BPNN based PID controller
exhibits a better overall rejection performance with
time-varying disturbances. This comes at the cost of
a larger computational amount because the neural
network weights have to be updated online to tune
the PID1
.
Fig.4 also shows the tuning process of the PID
parameters: Kp, Ki and Kd. As the frequency of the
disturbance varies, the PID gains are tuned
automatically and converge to different values for
different disturbance characteristics.
00.5 11.5 2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time(s)
Displacement
Disturbance signal
Fig.2 Disturbance signal with time-varying
frequencies
0.5 11.5 2
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Time(s)
Disturbance
PID Controller with Fixed Gains
BPNN Based Automatic Tuning PID Controller
Fig. 3 Disturbance rejection results
1 With this simulated BPNN structure, it requires 49 (=4*7+7*3)
multiplications and 39 (=3*7+6*3) additions in the feedforward process and
147 (=3*49) multiplications and 117 (=3*39) additions during the error back-
propagation process. So with simple BPNN structure, the computational
amount still remains reasonable.
3
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Conclusion
In this paper, automatic gain tuning of PID
controllers based on neural-network is developed for
suppressing time-varying disturbance. Using the
self-learning ability of the neural network, this
controller can adjust PID gains online for different
disturbances to get an improved overall disturbance
rejection performance. The design concepts are
supported by simulation results on a HDD
benchmark problem.
00.5 11.5 2
0
10
20 parameter Kp
Time(s)
00.5 11.5 2
0
0.05
0.1 parameter Ki
Time(s)
00.5 11.5 2
0
100
200 parameter Kd
Time(s)
Fig. 4 Evolution of the PID parameters Kp, Ki and
Kd
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4
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... The servo system is subjected to both repeatable (periodic) and non-repeatable (random) disturbances/noises that are due to the imperfection in fabrication and assembly processes, internal and external vibrations Sun et al. (2014Sun et al. ( , 2013; Zheng et al. (2014a,b), and electronic interferences. Fig. 1.2 (left) can be adopted to abstract the block diagram of a single stage HDD servo system in track-following mode. ...
Thesis
Full-text available
Control methodologies for deterministic disturbance rejection and trajectory tracking have been of great interest to researchers in the elds of controls, mechatronics, robotics and signal processing in the past two decades. The applications of these methods span a wide range from satellite attitude control requiring an accuracy of a few meters, to positioning of the read/write head in hard disk drives with an accuracy of less than one nanometer. This dissertation addresses the problem of trajectory tracking and deterministic disturbance rejection in discrete time systems when the trajectory/disturbance is unknown, but can be realized as an a ne combination of known basis functions. Despite the prior work on this problem that assumes known and time invariant plant dynamics, we consider multi input single output systems with unknown dynamics. Moreover, we investigate the cases where the disturbance or system dynamics varies slowly or abruptly but infrequently. Within the broad class of disturbances/trajectories that satisfy the stated criteria, an elaborate study is conducted on periodic and superposition of multiple sinusoidal sequences. We propose two novel adaptive control methods for the aforementioned problem. The rst scheme can be classi ed as an indirect adaptive algorithm since it consists of two parts, namely a system identi cation mechanism that provides a dynamic model of the closed loop system, and the adaptive compensator which deploys the aforementioned dynamic model to synthesize the control law. The second proposed method is a direct adaptive controller, meaning that the control law is generated directly and the stated separation is not possible. Besides providing theoretical guarantees, we experimentally evaluate our algorithms on a challenging control task for nano scale positioning of the read write head in a dual stage hard disk drive (HDD). Even with the advent of NAND ash based data storage devices, the HDD continues to thrive as the most cost e ective, reliable solution for rewritable, very high density data storage. It remains a key technology particularly with the tremendously growing popularity of server based cloud computing and novel hybrid enterprise storage solutions. We described that the control methodologies that can address the problem under our study are crucial for Bit Patterned Media Recording which is one of the two breakthroughs in magnetic recording that have been immensely investigated in the past few years. Extensive computer simulations and implementation on a digital signal processor unit are performed to validate the e ectiveness of our proposed algorithms in full spectrum compensation of the repeatable runout in dual stage HDDs. This application introduces unique control challenges since it requires estimating a very large number of parameters that is order(s) of magnitude greater than prior work and frequency contents span from 120Hz to extremely large values (above 20KHz) where the plant dynamic uncertainties are large.
... Besides track seeking, nonlinear PID has also been applied for track following performance enhancement. For example, [10] proposed to make the propositional gain and the derivative gain nonlinear functions, and formulated an optimization problem to enhance disturbance rejection during track following; [11] proposed PID gain tuning method based on neural-network to deal with time-varying disturbance in HDDs. There are also some other nonlinear algorithms to unify track seeking and track following, and improve the transient performance of HDDs, [12] and [13] among others. ...
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Technical Commitee for Novel Nanoscale Servo Control
IEEJ, Technical Commitee for Novel Nanoscale Servo Control, "NSS benchmark problem of hard disk drive systems," http://mizugaki.iis.utokyo.ac.jp/nss/, 2007.
Artificial Neural Networks: An Introduction, The Society of Photo-Optical Instrumentation Engineers
  • Kevin L Priddy
  • Paul E Keller
Kevin L. Priddy and Paul E. Keller, 2005, Artificial Neural Networks: An Introduction, The Society of Photo-Optical Instrumentation Engineers, WA, USA.