Robot manipulators have been widely used in industry to increase flexibility and productivity. Dynamics of a manipulator are described by a set of highly coupled nonlinear differential equations. The objective of this project is to develop high performance nonlinear control algorithms for the coordinated control of robot manipulators in various applications:
Today’s information storage industry is forced to move toward micro hard-disk-drives (micro-drives) for laptop computers and smaller hand-held devices as well as high performance drives with extreme large storage capacity and fast data retrieval/storage time. This trend has posted a great challenge to the design of servo controllers for the moving parts of the information storage devices, as the current industrial servo design techniques are no longer able to deliver the required accuracy and speed, which is due to either the fundamental performance limitations coming from the artificial constraint of using only linear controller structures or the inability of the controller in dealing with the ever-increasing noticeable effect of nonlinear disturbance forces such as the pivot bearing friction in micro-drives. Here it is proposed to deal with these servo design problems by applying the recently formulated nonlinear adaptive robust control proposed by the PI. Specifically, based on the nonlinear dynamics of the servo-actuators with the consideration of mechanical flexibility of the actuator arm, a nonlinear robust control law with adjustable model compensation will be designed so that the effect of various model uncertainties is attenuated as much as possible for a guaranteed baseline performance in general. In addition, learning mechanisms such as parameter adaptation law will be sought to adjust the model compensation on-line to reduce the model uncertainties caused by unknown terms possessing certain invariant properties; terms like the repeatable run-out and nonlinear pivot dynamic frictions. The result will be an adaptive robust servo controller which can deliver ultra high precision motion tracking at fast speeds in spite of the potential parameter variations and nonlinearities associated with the modern information storage systems. An experimental system with advanced controller implementation hardware and various state-of-the-art industrial hard-disk drives has been set up at the recently established Ruth and Joel Spira Laboratories for Electro-mechanical Systems, and the proposed algorithm will be implemented to test the proposed strategy. Industrial partnerships will be sought to enlarge the impact of the proposed work.
Information
storage systems always involve certain moving parts such as the voice coil
magnetic (VCM) actuator arm in a hard disk drive shown in Fig.1. In a hard disk
drive, the read/write heads located at the slider is mounted at the tip of an
actuator arm moved by a VCM actuator. The information of each bit is stored at
certain positions evenly spaced on various tracks as illustrated by the red dots
in Fig.2, the enlarged graph of the disk platters and the spindle shaft shown in
Fig.1. The mechanical operation principle of a hard-disk drive is that, by
spinning the disk platters at certain speeds and moving the arm over the disk
surfaces, the read/write heads are able to access all the bit positions on the
disk surfaces for bit information retrieval and storage. It is thus clear that,
for fast and correct information storage and retrieval, it is necessary that the
head (or the tip of the arm) can be moved from one track to another track
quickly, which is often referred to as the track seeking mode in hard-disk drive
industry [1,2,3,4]. At the same time, the head should be able to settle down at
the target track within a very short time for fast data retrieval/storage
operations and be able to track the actual target track profile within an
accuracy normally ten times less than the track width (i.e., the distance
between two adjacent tracks) for correct data retrieval/storage [1]; the latter
is normally referred to as track tracking mode.
To precisely position the read/write head, a feedback controller is needed to control motion of the actuator arm. To have a better understanding of the difficulties in controlling such a seemingly simple electro-mechanical device, let us take a close look at the block diagram of the current industrial servo controllers used for the arm as shown in Fig. 3. In the figure, the position error signal (PES) [5] represents the position error between the actual coded target track profile and the actual read/write head position, which is picked up by some sensors at the slider. The goal of servo design is to synthesize a feedback controller C(s) such that, based on the actual feedback of PES, the electro-magnetic (EM) force generated by the voice-coil motor (VCM) is able to move the tip of the arm (or the head) to follow the target track profile precisely in spite of various output disturbances and nonlinear disturbance forces acting on the arm. Currently, the design of such an industrial servo controller is carried out either in frequency domain using the classical loop-shaping techniques [6] or in the time-domain by the repetitive control techniques [7].
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Fig.3. Industrial Servo Controllers |
The difficulties in synthesizing the needed precision motion controller come
from the fact that the output disturbances and nonlinear disturbance forces seen
on the actual drives are normally very hard to characterize due to the
complicated natures of these disturbances. As illustrated in Fig.1 and 2, the
output disturbances could come from (i) the non-circular track profiles due to
the unavoidable imperfection when coding the track profile information on the
disks [1], (ii) the non-circular rotational motion of the coded tracks due to
the spindle shaft eccentricity of the spinning disk [7], and (iii) vibrations of
the disk platters and the base of the actuator arm caused by various external
shocks [2]. The major nonlinear disturbance forces are (i) the pivot bearing
friction of the actuator arm [8], and (ii) the flow-induced aero-elastic forces
at the slider [9]. Since current industrial servo controllers are all
based on linear control design techniques, they cannot handle the effect of
nonlinear disturbance forces such as the pivot friction force directly. As a
result, these nonlinear terms can only be treated as pure disturbances in the
design of industrial servo controllers, which rely solely on fast (usually high
gain) feedback to attenuate the effect of these nonlinear terms. Furthermore,
due to the artificial constraint of using only linear controller structures,
which is in contrast with the nonlinear decision making process of our brains,
the theoretical achievable performance of these industrial servo designs is also
much limited.
As
today’s market moves toward the micro-drives for laptop computers and smaller
hand-held devices, the sizes and the weights of the drive and the actuator arm
have to be reduced dramatically. As a result, the effect of nonlinear pivot
friction force on the head tracking error is becoming increasingly noticeable,
and, in fact, has been one of the major obstacles in improving the tracking
performance of certain micro-drives [8]. At the same time, the customer demand
for high performance drives with a much increased data storage capacity and a
faster data retrieval/storage speed is so high that the information storage
industry is forced to increase the disk area density dramatically while reducing
the track seek time, which is evident by the phenomenal area density growth rate
of about 60% per year in recent years [1]. This trend is likely to
continue, if not accelerate, in the near future. As predicted in [1], even
with half of this area density growth were to come from higher track density
(i.e., smaller track width)[1], today’s control engineers would have to
contend with 25000 tracks per inch (TPI) disks, which is indeed the focus
of current hard-disk drive industry. With such a high TPI, the tracking accuracy
of the read/write head along the target track has to be less than 50 nanometers
for correct data retrieval and storage. Furthermore, this ultra-high precision
motion tracking has to be realized by taking into account the practical
situation that target tracks may experience possible non-circular rotational
motion with a current disk spinning speed around 7000rpm as explained before.
Such a stringent performance requirement necessitates the accurate structural
modeling of various nonlinear elements (e.g., pivot friction) along with the use
of learning mechanisms (e.g., parameter adaptation) to explicitly compensate for
the effect of those nonlinear terms, instead of simply treating those nonlinear
terms purely as disturbances as in the current industrial servo designs. As
such, high performance nonlinear adaptive and robust control techniques, which
are briefly reviewed below, have to be employed to handle the various
nonlinearities and the model uncertainties associated with modern information
storage systems directly to face the above servo design challenges, which is the
focus of the proposal.
Control
of nonlinear dynamics with uncertainties has been one of the main areas of focus
in control community during the past twenty years, due to the industrial needs
for high performance controllers. Two approaches have been popular: adaptive
control [10,11] and deterministic robust control (DRC) (e.g., sliding mode
control, SMC) [12,13]. The PI has been doing research in the fields of both
adaptive control and DRC during the past decade and has published a substantial
number of journal and conference papers (e.g., by using DRC in [14,15,16] and by
using adaptive control in [17]. Those theoretical and practical experiences have
helped the PI to develop a deep understanding of the limitations and advantages
of both adaptive control and DRC. Recently, a breakthrough was made. A new
approach, named adaptive robust control (ARC) [18-21], is developed for
the high performance robust control of uncertain nonlinear systems. The approach
effectively combines the design techniques of adaptive control (AC) and those of
deterministic robust control (DRC), and improves performance by preserving the
advantages of both AC and DRC while overcoming their practical limitations.
Comparative experimental results for trajectory tracking control of a hydraulic
arm [22] and the precision motion control of an industrial machine tool [23] as
well as a high-speed linear motor drive system [24,25] have shown the advantages
of the proposed ARC and the substantial improvement of performance in actual
applications.
This
work will generalize the ARC approach to the ultra precision control of modern
information storage systems because of the high performance and strong
robustness of the ARC approach to various model uncertainties.
Collaborating with Professor Raman, an expert in the modeling of nonlinear dynamics and spinning disks, an experimental system shown in Fig.4 is being set-up at the Spira Electromechanical Systems Laboratories. As shown, the test-bed consists of the following major components: an industrial HDD with direct access to the current input of the VCM actuator, a power supply for spinning the disk, a Laser Doppler Vibrometer (LDV), a current probe, an advanced dSPACE system for quick controller implementation, and a host PC. The position and motion of the read/write head is picked up directly by the LDV. The position signal is then fed back to the servo controller implemented through the dSPACE system. Based on the proposed control strategy and the position signal feedback, the servo controller generates the correct control inputs to drive the VCM motor through the power amplifier. The host PC is used as a user interface only. The current probe is used to feedback the actual current sent to the VCM actuator, which could be used to identify the electrical dynamics to isolate the electrical dynamics from the arm dynamics for a better understanding of the problem. The set-up is intended to be set-up for studying both the fundamental problems in the nonlinear dynamics modeling and the ultra precision control of information storage systems.
The
controller design will focus on the fundamental issues associated with HDD
drives. Significant practical problems such as the actuator bandwidth limitation
due to sampling frequency and computational delay will be studied. The following
specific issues will be first addressed.
(A). Control Oriented Nonlinear Pivot Friction Modeling and Compensation
As
mentioned before, pivot friction has become a major source of nonlinearities
that have to be deal with explicitly in micro-drives. As such, accurate
control-oriented nonlinear friction modeling and compensation are needed in
order to improve the drive performance. The PI and his students have gained
substantial theoretical experiences in the nonlinear modeling and compensation
of friction, either the static friction compensation using neural network based
adaptive robust control strategy in [26] or the dynamic friction compensation
for ultra-high precision motion control in [27]. The proposed work provides an
excellent opportunity to test our theoretical results while solving the
practical issues facing in the current HDD industry.
(B).
Development of Novel Nonlinear Adaptive Robust Control Algorithms to explicitly
compensate for repeatable run-out while attenuating non-repeatable run-out
As
pointed out in introduction, some of the major sources of causing large disk
head tracking error are output disturbances. To be able to improve the tracking
performance of conventional drives, it is essential to see if the particular
structural information of certain output disturbances can be intelligently
utilized to achieve a better model compensation. Along this line, the following
strategy will be adopted.
Among
the three types of output disturbance sources discussed in introduction, the
first two posses certain invariant properties that could be fully utilized for a
better model compensation. Namely, the output disturbance due to the track
coding error and spindle shaft eccentricity are repeatable over different disk
rotations. Therefore, certain known harmonic functions with unknown weights may
be used to approximate these repeatable but unknown output disturbances well.
The adaptive robust control strategy [21] can then be employed to adapt the
unknown weights on-line over different disk rotations for a better performance.
At the same time, effective robust control law will be constructed to attenuate
non-repeatable output disturbances as much as possible for a guaranteed
performance.
(C).
Development of Simple and yet Effective Nonlinear Adaptive Robust Controllers
for High-order Systems with Partial State Feedback or Output Feedback
Unlike
the nonlinear systems studied in previous ARC designs in which full state
feedback is normally required, for HDD, the signal available for feedback is
usually the PES signal only. Furthermore, due to the stringent performance
requirement, the closed-loop bandwidth has been pushed to kHz range, which is
normally higher than the first several flexible modes of the mechanical arm. As
such, some of the flexible modes should be explicitly included in the arm
dynamics when designing the servo controller. This may substantially increase
the order of the system dynamics to be deal with. It is thus very important to
be able to construct simple and yet effective adaptive robust control algorithms
for high order systems using partial or output feedback information only. It is
anticipated that the output feedback adaptive robust control strategy developed
in [28] for uncertain linear systems will be generalized to accomplish this
goal.
(D).
Integrating Advanced Flow-Induced Aero-Elastic Force Modeling into ARC
Controller Design for Further Performance Improvement
It
has been recognized that the flow induced aero-elastic forces acting on the arm
is also a significant contributor of the head tracking error [9]. At this
stage, the flow-induced aero-elastic force modeling is still quite complicated
and the phenomenon is not well understood yet. Fortunately, Professor Raman from
the School of ME has been actively working on the problem. The PI will actively
collaborate with Prof. Raman to look for the possibility of incorporating Prof.
Raman’s research results into the proposed ARC designs to further improve
drive performance.
The
PI has been maintaining a close interaction with Dr. Lin Guo, senior manager of
advanced servo designs at Maxtor Inc., and Dr. M. White at IBM Almaden Research
Center; Maxtor and IBM are two of the three largest HDD companies in US.
At this stage, Maxtor has donated us four HDD drives specially modified for
control research. It is naturally to expect that both IBM and Maxtor will
continue donating advanced HDD drives such as the micro-drives and the
dual-stage actuator drives for the research. Support from other companies will
be actively sought also.
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