CN1266525A

CN1266525A - Disc drive with robust track following servo controller

Info

Publication number: CN1266525A
Application number: CN98808113A
Authority: CN
Inventors: J·C·莫里斯
Original assignee: SICHATER TEHC CO Ltd
Current assignee: SICHATER TEHC CO Ltd
Priority date: 1997-08-07
Filing date: 1998-05-15
Publication date: 2000-09-13
Also published as: GB2341481A; KR20010022679A; GB9928819D0; WO1999008267A1; JP2001512881A; DE19882560T1

Abstract

A servo system in a disc drive (110) provides robust servo control during track following operations. The disc drive (110) includes a rotatable disc (112) having a disc surface (180, 182) with information arranged in tracks on the disc surface (180, 182). The disc drive (110) also includes a transducer (144) for accessing the information on the disc surface (180, 182). An actuator arm (126) is operably coupled to the transducer (144). An actuator (173) is operably coupled to the actuator arm (126) to move the transducer (144) relative to the disc surface (180, 182) to follow one of the tracks during track following. A model-based servo controller (190) is operably coupled to the actuator (173) to control movement of the actuator (173). The model-based servo controller (190) provides robust track following control over a desired frequency range.

Description

Disk drive with robust track following servo controller

Technical Field

The present invention relates generally to servo systems for disk drives. More particularly, the present invention relates to a disk drive having a model-based robust servo control system.

Background

A typical disc drive includes one or more discs that are fixed for rotation on a hub or spindle. Typical disk drives also include one or more transducers supported by hydrodynamic air bearings (hydro-dynamic air bearings), which fly above each disk. The transducer and hydrodynamic air bearing are collectively referred to as a data head. Conventionally, a drive controller is used to control a disk drive system in accordance with commands received from a host system. The drive controller controls the disk drive to retrieve information from the disk and to store information on the disk.

The electromechanical actuator operates within a negative feedback closed loop servo system. The actuator generally includes an actuator arm for supporting a flexure of the flexure assembly, which in turn supports the data head. An actuator moves the data head radially over the disk surface to perform a seek operation and to cause the transducer to face a track on the disk surface to perform a track following operation.

Information is typically stored on the disk by providing a write signal to the data head to encode a flux reversal (flux relief) on the disk surface that represents the data to be stored. When retrieving data from the disk, the drive controller controls the electromechanical actuator to fly the data head over the disk, thereby sensing magnetic flux reversals on the disk, and generating a read signal based on these magnetic flux reversals. The drive controller then decodes the read signal to recover the data represented by the flux reversals stored on the disk that are subsequently embodied in the read signal provided by the data head.

Accurate positioning of the data head over the disk track is extremely important in writing data to and reading data from the disk.

In prior systems, the servo operation was done based on a dedicated servo head. In a dedicated servo type system, all servo information is written on a dedicated surface of the disk in the disk drive. All heads in a disk drive are mechanically coupled to a servo head for accessing servo information. Thus, all heads in a dedicated servo disk drive are positioned based on the servo information read from the servo surface. This type of system allows the disk drive to perform read and write parallel operations with great ease. In other words, using appropriate circuitry in the drive controller, reading and writing can be performed in a parallel fashion with multiple data heads mounted on the actuator, which are simultaneously positioned according to the servo information read from the dedicated servo surface.

However, the track density of magnetic disks has continued to increase over the years. The increased track density on magnetic disks requires more precise positioning and higher resolution. The mechanical offset between heads in a dedicated servo system can exceed one track width. Thus, in some applications, the industry has turned to embedding servo information.

In an embedded servo system, servo information is embedded on each track of each surface of each disk. Thus, each data head can return a position signal independently of the other data heads. Therefore, when a particular data head is accessing information on a disk surface, the data head can be positioned with a servo actuator. The positioning is performed with the embedded servo data of the track and then the data head is floated over the track.

Although this may improve positioning accuracy and resolution during positioning (since the data head is positioned independently of any other data head), there are some drawbacks due to increased head density and mechanical considerations. One disadvantage is that in typical embedded servo systems, the ability to perform read and write parallel operations with multiple heads is lost. This is because the servo system is positioned based on information received by a single data head, and mechanical tolerances are not suitable for accurately positioning the remaining data heads in a high track density system. In addition, actuators to date are not capable of independently positioning the data head. Thus, embedded servo systems have not been able to perform read and write parallel operations, such as simultaneously reading or writing an entire cylinder of tracks on a disk drive, to date.

Because of these differences between dedicated servo systems and embedded servo systems, a tradeoff needs to be made between servo sampling rate and efficient user data storage.

In addition, both systems suffer from a number of problems that affect the positioning accuracy of the servo system. The following are some of the most important issues:

1. the servo sampling rate. In embedded servo systems, the sampling rate is limited by the speed of the spindle and the number of servo sectors per track.

2. Structural modes of arm and head suspension.

3. External shock and vibration. They may be linear or rotational, or both.

4. And writing the position error. When writing to a servo track, a writing position error is caused by the occurrence of a tracking error. This results in repeatable runout. Runout refers to the total error in positioning when performing track following operations. When tracking over long periods of time, runout is commonly referred to as static offset. Since the write position error is synchronized with the spindle speed, it is called repeatable runout.

5. The bearing is non-linear. This non-linearity can lead to rotational damping and hysteresis, especially when the actuator is moving at low speeds.

6. Non-linearity due to flex circuit bias force acting on the actuator. In other words, the actuator is coupled to the disk drive controller through a flex circuit. When the actuator positions the transducer at different radial positions on the disk, the flex circuit biasing force acting on the actuator changes.

7. Disk jitter that results in unrepeatable runout. The amount of disk jitter depends on the spindle speed and the stiffness of the disk substrate.

8. The gain variation is generated due to the non-linear cross-track (cross-track) of the magnetic transducer.

9. Position error sampling noise due to media magnetic changes and electronic noise, etc.

Conventional prior art servo controllers include a Proportional Integral Derivative (PID) controller, which is made up of two components: an observer and a regulator. Each time a servo sector is crossed, the observer receives input position information and estimates a position and a velocity. The regulator then provides feedback on the observed signal. In seek mode, the regulator generally regulates the error between the reference velocity trajectory and the observed velocity to zero. In track following mode, the adjuster adjusts the error between the desired track position and the observed track position to zero. The regulator is controlled according to PID control techniques.

However, a PID controller may not be advantageous or desirable in all disk drive applications. For example, it may be desirable to provide a micro-actuator between the flexure assembly and the transducer or slider assembly, or on the actuator arm, or on the suspension or flexure assembly. When the microactuator is provided, the servo actuation system becomes a multiple-input multiple-output (MIMO) system from a single-input single-output (SISO) system where the input is an error signal and the output is a voice coil current signal, the MIMO system receiving various inputs from the microactuator and providing a position output signal to the voice coil motor and each microactuator. Although such systems can be controlled by just a decentralized PID controller, problems remain. For example, if multiple heads are to be positioned simultaneously, the positioning of a data head may be affected by simultaneously positioning other adjacent or neighboring data heads. In addition, the higher bandwidth positioning can excite driver structural modes and initiate vibration, ringing (ringing), or other disturbances that can affect the positioning of adjacent data heads.

In addition, many problems arise when attempting to implement a discrete time system for a fixed point digital signal processor in a disk drive. For example, the computational power provided in a digital signal processor that a disk drive may use is often quite limited. This causes a number of significant problems. The number of sizes of registers in a digital signal processor may be quite limited. When performing matrix calculations, the number of bits required to store the intermediate calculation results may exceed the capacity of the registers in the data signal processor. Therefore, overflow becomes a big obstacle. In addition, the computational speed and structure and memory of the digital signal processor render some matrix calculations completely infeasible simply because of the number of computations that must be performed. Furthermore, substantially all of the digital signal processors are fixed-point processors. Therefore, it is simply not feasible to implement a linear discrete time system in a digital signal processor. In addition, the quantization error in conventional DSPs is so large that the control accuracy of the DSP in the disc drive servo system is not achieved.

The present invention addresses at least some of these and other problems and provides other benefits over the prior art.

Disclosure of Invention

The present invention is directed to a system that may address one or more of the problems set forth above.

The servo system of the disk drive performs robust servo control during head tracking. A disk drive includes a rotatable disk having a disk surface with information disposed in tracks on the disk surface. The disk drive also includes a transducer for accessing disk surface information. An actuator arm is operatively coupled to the transducer. An actuator is operatively coupled to the actuator arm to move the transducer relative to the disk surface to track a track during track following. A model-based servo controller is operatively coupled to the actuator to control movement of the actuator. The model-based servo controller provides robust track following control over a desired frequency range.

Brief description of the drawings

FIG. 1 illustrates a disk drive in accordance with an embodiment of the present invention.

FIG. 2 illustrates an actuator assembly in accordance with an embodiment of the present invention.

FIG. 3 illustrates a head gimbals assembly (head gimbals assembly) in accordance with a feature of the present invention.

FIG. 4 is a block diagram illustrating a portion of a disk drive in accordance with one embodiment of the present invention.

FIG. 5 is a block diagram illustrating a portion of a servo control circuit in accordance with one embodiment of the present invention.

FIG. 6 is a flow chart illustrating a servo control algorithm structure in accordance with an aspect of the present invention.

FIG. 7 is a block diagram illustrating an actuator model in accordance with an aspect of the present invention.

FIG. 8 is a graph of a nominal model showing measurement data and average measurement data obtained when a positional disturbance is introduced into the system.

9-1 through 9-4 illustrate additive and multiplicative uncertainties and weighting functions in accordance with an aspect of the present invention.

10-1 through 10-3 are graphs showing estimated additive and multiplicative uncertainties and phase errors for an actual disk drive.

FIG. 11 is a block diagram illustrating a track following control integration interconnect in accordance with an aspect of the present invention.

FIG. 12 is a block diagram illustrating Linear Fractional Transforms (LFTs) with respect to the track following control synthesis interconnect shown in FIG. 11.

FIG. 13 is a graph illustrating model validation in accordance with an aspect of the present invention.

FIG. 14 is a flow diagram illustrating a model verification technique in accordance with an aspect of the present invention.

FIG. 15 is a flow chart illustrating an implementation of a servo controller and digital signal processor in accordance with an aspect of the present invention.

Detailed description of the preferred embodiments

FIG. 1 is a plan view showing a typical disk drive 110. Disk drive 110 includes a disk pack 112 that is secured to a spindle motor (not shown) by a disk clamp 114. In a preferred embodiment, disk pack 112 includes a plurality of disks mounted for coaxial rotation about a central axis 115. Each disk surface that stores data has an associated Head Gimbal Assembly (HGA)116 that is attached to an actuator assembly 118 of the disk drive 110. The actuator assembly shown in fig. 1 is an actuator assembly known as a rotary motion coil actuator that includes a Voice Coil Motor (VCM), shown schematically at 120. Under the control of electronic circuitry housed within the disk drive 110, the voice coil motor 120 rotates the actuator assembly 118 and the HGA116 attached thereto about pivot 121 to position the HGA116 over a desired data track in the associated disk surface.

Specifically, actuator assembly 118 pivots about axis 121 to rotate head gimbal assemblies 116 generally along arc 119 to position each head gimbal assembly 116 over a desired one of the disk surfaces of disk pack 112. HGA116 may move from a track at the innermost radius of the disk to a track at the outermost radius of the disk. Each head gimbal assembly 116 has a gimbal that resiliently supports a slider relative to a load beam (load beam) so that the slider can track the topography of the disk (topographiy). And the slider includes a transducer for encoding flux reversals on the disk surface floating above it and reading the flux reversals from the disk surface.

Fig. 2 is a perspective view of the actuator assembly 118. Actuator assembly 118 includes a base 122, a plurality of actuator arms 126, a plurality of load beams 128, and a plurality of head gimbal assemblies 116. The bottom portion 122 has an aperture that, in the preferred embodiment, is coupled to pivot about an axis 121. Actuator arms 126 extend from the base 122 and each is connected to a first end of one or both load beams 128. A second end of each load beam 128 is coupled to one of the head gimbal assemblies 116.

FIG. 3 is a highly enlarged view of head gimbal assembly 116. Head gimbal assembly 116 includes a gimbal 130 having a pair of

stays

132 and 134 and a gimbal coupling tongue 136. Head gimbal assembly 116 further includes a slider 138, slider 138 having an upper surface 140 and an underlying air bearing surface 142. In addition, the transducer 144 is preferably located at the leading edge of the slider 138. The particular connection between the slider 128 and the gimbal 130 may be accomplished in any desired manner. Briefly, in a preferred embodiment, a flexible sheet is preferably coupled between the upper surface of the slider 138 and the lower surface of the gimbal bonding tongue 138 with an adhesive. The flexible sheet allows relative lateral movement between the slider 138 and the gimbal engaging tongue 136. The flexible sheet is preferably a polyester film having a thickness of about 150 microns. In addition, the gimbal coupling tongue 136 preferably terminates at the trailing edge of the slider 138 with a retaining tab 146, the slider 138 being secured to the gimbal coupling tongue 136 on the surface provided by the tab.

FIG. 4 is a block diagram of a portion of disk drive 110 illustrating servo position control circuitry in accordance with an aspect of the present invention. The disk drive portion shown in FIG. 4 includes an actuator assembly 118, a disk pack 112, a microactuator (collectively microactuator 158) associated with each head gimbal assembly, a preamplifier 160, data and clock recovery circuitry 162, error detection circuitry 164, a drive controller 166, data conditioning circuitry 168, a servo control processor 170, a power amplifier 172, and an optional microactuator controller 174.

The drive controller 166 is preferably a microprocessor or digital computer, or other suitable microcontroller, which is connected via bus 111 to a host system or another drive controller that controls multiple drives.

The disk pack 112 includes a shaft 176 that supports a plurality of coaxially disposed magnetic disks 178. Each disk 178 is mounted for rotation with the spindle 176 about the rotational axis 115. Each disk has a first side 180 and a second side 182. The disk surfaces 180 and 182 include a number of concentric tracks for receiving and storing data encoded on the tracks in the form of flux reversals.

As described with reference to fig. 2 and 3, the actuator assembly 118 includes a base 122 for supporting a plurality of actuator arms 126. Each actuator arm 126 is coupled to at least one load beam 128. And each load beam 128 supports a head gimbal assembly 116 (labeled in fig. 3) positioned on a

corresponding disk surface

180 or 182 for accessing data in tracks on the disk surfaces. Each gimbal assembly also includes at least one microactuator 158 for positioning the transducer on the head gimbal assembly in one track of the disk 178 or in one of a plurality of different tracks. As shown in fig. 4, the micro-actuator 158 may be provided on the actuator arm 126, on the load beam 128, on the gimbal (or other flexure) 130, between the gimbal 130 and an associated slider, or at any other suitable location. The microactuator 158 may be made of PZT material, electrostatic material, which is capacitively, fluidically, electromagnetically, magnetostatically, or thermally excited for corresponding biasing.

In operation, the drive controller 166 typically receives command signals from a host system indicating that portions of one or more disks 178 are to be accessed. In response to the command signals, the driver controller 166 provides position signals (or reference signals) 165 to the servo control processor 170 that indicate the particular cylinder on which the head gimbal assembly 116 is to be positioned by the actuator assembly 118. The servo control processor 170 converts the position signal to an analog signal, which is amplified by a power amplifier 172 and provided to a voice coil motor in the actuator assembly 118. In response to the analog position signal, actuator assembly 118 positions load beam 128 and its associated head gimbal assembly 116 over a desired cylinder.

The head gimbal assembly 116 generates a read signal containing data from embedded servo position data stored in selected portions of each track of the disk to be read, as well as normal data to be retrieved from the selected portions of the disk to be read. The read signal is provided to preamplifier 160, and preamplifier 160 amplifies the read signal and provides it to data and clock recovery circuit 162. The data and clock recovery circuit 162 recovers the data encoded on the disk surface from the read signal as it is written to the disk surface in a known manner. Of course, the data and clock recovery circuit 162 may be a Partial Response Maximum Likelihood (PRML) path, or another suitable type of read channel.

Once the data is recovered, it is provided to error detection circuit 164 which detects whether the data read back from disk has errors. Error detection circuit 164 provides an output 167. Error correction is performed in a known manner using error detection circuitry 164 or drive controller 166, or a combination of both.

During head positioning, the drive controller 166 provides position signals to the servo control processor 170 to cause the actuator assembly 118 to position the head gimbal assembly 116 over a selected cylinder. In a sector servo positioning drive (or an embedded servo positioning drive), a portion of each sector on the disk surface contains position information that is encoded on the disk surface, read by the data head, and provided to the servo control processor 170 via a read channel. The positioning information not only gives coarse position information indicating the particular track over which the data head is flying, but also provides tuning feedback to the servo control processor for better positioning. The servo control processor 170 reacts to the position information read from the disk and positions the head gimbal assembly 116 accordingly.

In a preferred embodiment, the servo control processor 170 is used to control not only the coarse actuator (voice coil motor), but also the micro-actuator 158. In another preferred embodiment, a separate microactuator controller (or multiple independent microactuator controllers) 174 is provided for controlling the microactuator 158 in response to position request signals from the drive controller 166 and in response to embedded position information read from the disk.

To write information to the disks, the drive controller 166 receives not only the location of the information to be written on the disk pack 112, but also the actual data to be written. The position information is provided as a reference signal to the servo control processor 170 (and optionally the microactuator controller 174) to coarsely position the data head relative to the corresponding disk surface. The drive controller 166 then provides the data to be written to the data conditioning circuit 168, and the data conditioning circuit 168 provides this information at output 169 to the particular transducer on the head gimbal assembly 116 for writing the data to the disk surface in a known manner.

In the preferred embodiment, the microactuator 158 has a range of motion that exceeds the worst case mechanical mounting error between any two head gimbal assemblies 116 supported by the actuator assembly 118. In a preferred embodiment, the range of motion of each microactuator 158 exceeds one track width, and more preferably exceeds multiple track widths. Additionally, in the preferred embodiment, the read channel provided by disk drive 110 (which, in the embodiment shown in FIG. 4, includes preamplifier 160, data and clock recovery circuit 162, and error detection circuit 164) is capable of receiving multiple simultaneous and parallel data signals, and of processing these data signals in parallel, and then providing them in parallel to host system and/or drive controller 166. In addition, in the preferred embodiment, the data conditioning circuit 168 is also preferably adapted to provide multiple simultaneous and parallel write signals to the data head in order to perform simultaneous and parallel write operations. In addition, in the preferred embodiment, the servo controller processor 170 and optional microactuator controller 174 are adapted to simultaneously provide positioning signals to the microactuator 158 to simultaneously position all or at least a plurality of the microactuators to simultaneously align a plurality of heads with tracks on a plurality of disk surfaces in the disk stack 112.

With this structure, many advantages can be obtained. For example, precise position control may be performed for each of a plurality of data heads. This allows for precise and simultaneous track following of multiple data heads, allowing for parallel read and write operations. In addition, since the operating bandwidth of the microactuator is much greater than the bandwidth of the voice coil motor, this configuration can significantly increase the track density for any given disk surface because it accommodates bearing nonlinearities and other problems limiting track density in the current art in a much better manner than track following using a voice coil motor alone.

In addition, since in the preferred embodiment the range of motion of each microactuator exceeds a plurality of data tracks, the microactuator itself can be used to perform short seek operations (seek operations that seek tracks within the range of motion of the microactuator). This minimizes excitation of structural modes in the disk drive and allows for a wide bandwidth servo control during short seeks.

The microactuator 158 may be controlled in any of a number of ways in accordance with the present invention. For example, a servo controller used as a single input/single output (SISO) system controls a voice coil motor in a conventional disk drive. The input is a head position measurement obtained from embedded servo data, and the output typically drives a voice coil motor through a power amplifier 172. However, in controlling the microactuator 158, the servo control system of the present invention must have multiple inputs and multiple outputs. The inputs include the position of the head read from the embedded servo information, the head is flying above it, and also optionally the relative position of one or more micro-actuators with respect to the voice coil motor (or coarse actuator). The plurality of outputs includes an output for driving a single coarse positioner (VCM) and N micro-actuators.

In prior architectures where multiple data heads were positioned simultaneously, there was a potential problem in that the positioning of one data head could be affected by the simultaneous positioning of adjacent or nearby other data heads. The higher bandwidth positioning can excite structural modes of the drive and cause vibration or other disturbances that can affect the positioning of adjacent data heads. Thus, in the preferred embodiment of the present invention, the servo control processor 170 or microactuator controller 174 accounts for the motion of other data heads on the actuator assembly 118.

A preferred architecture includes a single servo controller that includes a MIMO servo controller that functions as a Digital Signal Processor (DSP). The DSP inputs indicate the head position of each head, the relative position of each microactuator, and a reference signal from the main or disk drive controller 166.

FIG. 5 illustrates an embodiment in which the servo control processor 170 and the microactuator controller 174 incorporate a single servo controller for use as the DSP 190. The DSP190 receives as its inputs the reference signal from the host system or disk drive controller 166, and the head position signal for each head 180 (head 0-head N) that represents the position of the head. The output of DSP190 is provided to Voice Coil Motor (VCM)173, which drives actuator assembly (or E-block) 118. FIG. 5 also shows that the DSP190 provides output signals to all of the microactuators 158 (microactuator 0-microactuator N, as represented by reference numerals 159-161) coupled to the actuator assembly 118. Thus, the inputs to DSP190 also include head position signals 171 from the respective heads, and relative position signals 179 of each head with respect to VCM 173. In the figure, each micro-actuator is coupled to a magnetic head 181. In addition, each microactuator has an associated position sensor 183 for sensing the relative position of the microactuator with respect to the voice coil motor (or actuator assembly 118). Relative position sensor 183 may include any suitable sensor, such as a capacitive sensor or any other suitable position sensor. It can be seen that the DSP190 provides a coarse positioning signal to the voice coil motor 173 in order to position the entire actuator assembly 118. The DSP190 also provides a fine positioning signal to the micro-actuator 158.

In a preferred embodiment, the DSP190 takes into account not only the head position and relative position associated with each head, but also the movement of adjacent or neighboring heads (i.e., taking into account the cross-coupling of the heads) when providing the micro-actuator output for each head-associated micro-actuator. In this manner, DSP190 accounts for structural mode excitations as each head is positioned. Additionally, in the preferred embodiment, the DSP190 controls to provide interference rejection, account for run-out, prevent actuator over-current, and provide noise immunity.

The DSP190 shown in FIG. 5 preferably embodies a model-based algorithm. FIG. 6 (e.g., block 191-199) is a flow chart illustrating a method of designing a servo control system in which the DSP190 is implemented in accordance with the present invention. Each block in FIG. 6 is discussed briefly generally as an overview, and then in more detail.

First, a standard model is constructed, which is mainly a set of differential equations, and expresses the structure dynamics of the disk drive. As represented by block 192 in fig. 6. When constructing a standard model, it is desirable to have an accurate understanding of the drive dynamics. Knowledge in this respect is preferably obtained using empirical/measured data. This type of information is used to define the parameters in the system model and all this information is used to construct the model according to the first principle (or differential equation).

Next, an uncertainty description (uncertainly description) of the disk drive is constructed. As represented by block 194 of fig. 6. The uncertainty description is preferably designed to collect drive characteristics and variations associated with a large number of drives. This data is used to modify the model constructed in block 192.

Then, a performance target for the system is specified. As represented by block 196 of fig. 6. These goals are provided to ensure that the model is compatible with existing and commercially available tools to optimize and finalize the design of control algorithms that can be executed in a variety of ways directly on the disk drive.

Then, the model is verified. As represented by block 197 of fig. 6. In short, the model constructed so far is a robust control model, which is a system model, and contains not only a model of system dynamics, but also uncertainty descriptions and noise descriptions. In general, the model validation problem is formulated as a linear, time-invariant system with uncertainties and experimental data constructed with norm bounding. Model verification is performed by considering model verification problems in the frequency domain. Using what is known as μ assay and μ_gThe technique of analyzing determines whether the model is consistent with the data and whether the controller is consistent with the model.

Finally, the model is optimized with commercially available optimization software. Algorithms for calculating μ and optimizing are available under the trade names MATLAB μ -Analysis and Synthesis Toolbox. This is indicated by block 198 in fig. 6.

A. Actuator model

FIG. 7 illustrates a servo actuator model 201 in accordance with an aspect of the present invention. Fig. 7 includes

blocks

200, 202 and 204. Block 200 represents the servo actuator transfer function Gnom. Block 204 represents the additive uncertainty description and block 202 represents the multiplicative uncertainty description.

1. Standard model

Gnom is the actuator standard model. The role of the standard model is to accurately characterize typical system dynamics. This means that the standard model must be the average expected behavior of the system observed across the entire class of disk drives being simulated. In a preferred embodiment, the standard model is designed by adding a lot of accurate knowledge about the drive.

In a preferred embodiment, the standard model is constructed in the frequency domain, since the worst extreme case in system dynamics may include many higher frequency structural modes that will result in highly variable transient behavior in the time domain. Since the disk drive is unstable open loop, data is collected closed loop. This is achieved by introducing disturbances to the loop and measuring the input and output of the drive actuator. For example, in a preferred embodiment, empirical work is used to collect frequency domain input and output information. In addition, time domain responses to different types of inputs (such as pulse or step inputs) are collected. Such information is used to define parameters in the system model. Additionally, in a preferred embodiment, finite element analysis is performed to obtain structural data for various physical elements in the system. Preferably, all of these information structure models are used according to the first principle (or differential equation).

FIG. 8 is a graph of frequency 203 versus log amplitude showing the open loop transfer function of a typical disk drive. Data is collected when performing track following operations by introducing sinusoidal position disturbances to the measured head position, while measuring the voice coil motor dynamics and head position. Reference numeral 206 denotes a standard model of a disk drive. Reference numeral 208 denotes measured data when tracking a PID controller in a disk drive, and reference numeral 210 is an average of the measured data. For

heads

0, 1 and 3, data was collected at the inner radius, middle radius and outer radius of the disk. The position disturbance amplitude is 2% -20% of the track width.

The standard model is chosen to be the cascade of a second order system, which can be represented by the following equation:

equation 1

Wherein KDC is actuator Direct Current (DC) gain; n is the number of resonant modes, for the ith resonant mode (i ═ 1, …, n); zeta_z，iAnd

is the damping and natural frequency of the zero; and ζ_p，iAnd

is the damping and natural frequency of the pole. Similarly, ζ and ω_nThe low frequency characteristics of the driver are defined.

In addition, in the standard model expressed in equation 1, the delay can be simulated. Various sources of latency exist in magnetic disk drives. For example, Pulse Width Modulation (PWM) filters, power amplifiers, voice coil time constants, and other sources can introduce delays into the system. The standard procedure for modeling the pure delay of continuous time is to use the following pade approximation:

equation 2

Wherein t is_dDelay in seconds; s is a frequency parameter; and mouth { } tableThe laplacian transform of the vector.

To model the time delay, generally a low order Pad is approximately appropriate (e.g., first order or second order). Other robust approximations may also be used.

2. Description of uncertainty

Because a rigorous mathematical model of the actuator system is not possible in a disk drive, the uncertainty descriptions represented by

blocks

202 and 204 in FIG. 7 are used. A rigorous model means that the system can be represented by a set of differential equations, and all the parameters of the differential equations are known. Under normal circumstances, it is not possible to accurately simulate a disk drive. However, a set of models may be determined, covering the characteristics of the disk drive. Uncertainty simulation is one way to determine the set of models.

In a typical disc drive, the disc drive structure itself has a high frequency resonant mode. In addition, the natural frequency and damping of the low frequency modes is somewhat amplitude dependent. In other words, it is determined by some non-linear dynamics (most likely caused by bearing hysteresis, flex circuit biasing forces, etc.). In the uncertainty description, these variations can be collected most efficiently.

Block 204 illustrates adding an additive uncertainty to the standard model represented by block 200. The additive uncertainty describes the following set of systems:

equation 3

g：G(s)＝G_nom(s)+W_a(s) Δ(s), | Δ | < 1 where Δ(s) is a norm-bounded uncertainty perturbation, and W_a(s) is a frequency domain weighting function. Uncertainty perturbation Δ(s) is norm-bounded, so a weighting function is typically used to specify the degree of dependence of any frequency on the magnitude of uncertainty. Kinetic uncertainties are generally characterized by an applicable uncertainty. Thus, the uncertainty perturbation Δ(s) is generally considered to be a full matrix of complex numbers at each frequency.

The additive uncertainty is generally most effectively used to model high frequency dynamics uncertainties such as resonant modes in disk drives. For example, in the frequency range above about 2kHz, there is little or no reliable information about disk drive dynamics. The main reason is that the natural frequencies and damping of these structural modes vary from system to system.

Uncertainty weight w may be added_aThe task of (1) is to introduce a minimum value (floor) to the system gain at high frequencies.

Fig. 9-1 and 9-2 are graphs of frequency 209 versus value 211, illustrating the use of an applicable uncertainty. In fig. 9-1, the standard model is denoted by 212 and the actual measured value is denoted by 214. The additive uncertainty used to account for the unmodeled dynamics is an envelope, represented by 216. Fig. 9-2 illustrates one embodiment of the additive uncertainty weighting function 218.

Multiplicative uncertainty describes the following set of systems:

equation 4

g：G(s)-G_nom(I+W_m(s) Δ (s)), | Δ | < 1 where Δ(s) is a norm-bounded perturbation of uncertainty, and W_m(s) is a frequency domain weighting function. As with the additive uncertainty, the uncertainty perturbation Δ(s) is generally considered to be a full matrix of complex numbers at each frequency.

Multiplicative uncertainty is very effective in simulating low frequency gain variations. Fig. 9-3 shows the multiplicative uncertainty being used to account for gain variations. Fig. 9-3 is similar to fig. 9-1 and like parts are indicated by like reference numerals. However, reference numeral 216 represents the envelope of a group of systems with multiplicative uncertainty at low frequencies. Multiplicative uncertainty weight W_mThe task of (a) is to provide an envelope around the standard transfer function. In many cases, up to about 100Hz, the envelope will increase or decrease by about 50% and then gradually decrease to less than 1%. Fig. 9-4 illustrates a multiplicative uncertainty weight function 218 with respect to the uncertainty illustrated in fig. 9-3.

For the model shown in FIG. 7, the designer's task is to select the uncertainty weight W_mAnd W_aThey can adequately cover the data collected from the disk drive, but are not overly conservative. Some simple estimates are given in fig. 10-1 to 10-3, which plot frequency 215 against amplitude 217 and phase error 219.

FIGS. 10-1, 10-2, and 10-3 illustrate summable uncertainty levels in a typical disk drive. Fig. 10-1 shows the estimated multiplicative uncertainty 220. Fig. 10-2 shows the estimated additive uncertainty 222, while fig. 10-3 shows the phase error 224 (for delay estimation) as a function of frequency. Note that the additive multiplicative uncertainty can be used for uncertainty models for low, medium, and high frequencies. The uncertainty model is chosen by design to be simply weighted. In addition, a plurality of summable multiplicative uncertainties may be used.

B.H_∞Mu Integrated controller design

Once the actuator model 201 shown in FIG. 7 is obtained, the next step is to specify performance goals and design an optimal controller for controlling the modeled actuators. FIG. 11 is a block diagram illustrating a track following control global interconnect 230 for a disk drive. Note that the system 230 includes an actuator model 201. The controller is designed to optimize the weighted interconnect 230.

In FIG. 11, the system blocks preferably include a controller block 232; an actuator model 201; an ideal actuator model 234; integrated weight 231 (W)_u) And 233 (W)_p) Which are respectively located on current and tracking error signals 235(u) and 237 (y); external inputs including command offset position 239(r), position sensor noise 241(n), signal 269 (y)_m) Weight 267 (w)_n) Current disturbance 243 (d)_i) Input weight 259 (w)_di) Output weight 261 (w)_do) And location interference 245 (d)_o) (ii) a And controlled outputs 247(z1) and 249(z2) which correspond to current loss (penalty) and tracking error, respectively.

In the preferred embodiment, the controller block 232 is preferably provided in a two degree of freedom control configuration including the compensator K₂And a precompensator K₁. Comprising a precompensator K₁To improve the transient response of the closed loop system.

The interconnect shown in fig. 11 is preferably designed to satisfy the following equations, which describe the current loss and tracking error of the actuator.

Equation 5

z_{1} = W_{u} K \frac{_{1}}{1 - {PK}_{2}} W_{r} r + W_{u} \frac{{GK}_{2}}{1 - {GK}_{2}} W_{d_{i}} d_{i}

+ W_{u} \frac{K_{2}}{1 - {GK}_{2}} W_{d_{o}} d_{o} + W_{u} \frac{K_{2}}{1 - {GK}_{2}} W_{n} n

Equation 6

z_{2} = W_{p} (\frac{{GK}_{1}}{1 - {GK}_{2}} - G_{ideal}) W_{r} r + W_{P} \frac{G}{1 - {GK}_{2}} W_{d_{i}} d_{i}

{+ W}_{P} \frac{1}{1 - {GK}_{2}} W_{d_{o}} d_{o} + W_{P} \frac{G K_{2}}{1 - {GK}_{2}} W_{n} n

The interconnection shown in fig. 11 can be simplified to the equivalent linear fractional transform shown in fig. 12, which includes controller 261, actuator 263, and uncertainty 265. In modern control theory, Linear Fractional Transforms (LFTs) are often used to simplify the representation of linear system interconnections and can be seen as a mathematical representation of a block diagram consisting of linear blocks with feedback.

LFT according to FIG. 12, resulting in H_∞The optimization criterion is as follows:

equation 7

<math> <mrow> <mi>K</mi> <mo>=</mo> <mi>arg</mi> <mi>min</mi> <mo>|</mo> <mo>|</mo> <msub> <mi>F</mi> <mi>L</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>F</mi> <mi>U</mi> </msub> <mrow> <mo>(</mo> <mi>Δ</mi> <mo>,</mo> <mi>G</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>K</mi> <mo>)</mo> </mrow> <msub> <mrow> <mo>|</mo> <mo>|</mo> </mrow> <mo>∞</mo> </msub> <mi>where</mi> <msubsup> <mo>,</mo> <munder> <mrow> <msub> <mi>Δ</mi> <mi>m</mi> </msub> <mo>,</mo> <msub> <mi>Δ</mi> <mi>e</mi> </msub> <mi>ϵC</mi> </mrow> <mrow> <mo>|</mo> <mo>|</mo> <mi>Δ</mi> <msub> <mrow> <mo>|</mo> <mo>|</mo> </mrow> <mo>∞</mo> </msub> <mo>≤</mo> <mn>1</mn> </mrow> </munder> <mrow> <mi>Δ</mi> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>Δ</mi> <mi>m</mi> </msub> </mtd> <mtd> <mi>O</mi> </mtd> </mtr> <mtr> <mtd> <mi>O</mi> </mtd> <mtd> <msub> <mi>Δ</mi> <mi>a</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> </msubsup> </mrow> </math>

Wherein,

F₁(Fu (Δ, G), K) denotes feedback interconnection w → z;

‖.‖_∞an derived ∞ norm representing the vector; and

c is a set of complex numbers.

For robust performance, the closed loop system should have a controller K that can stabilize the plant set:

equation 8

{P∶P＝F_u(Δ, G),  Δ ε β Δ }, wherein

βΔ₁＝{ΔεΔ₁∶‖Δ‖_∞＝≤1}

And also meets the following performance objectives:

equation 9

‖F₁(F_u(Δ，G)，K)‖_∞＜1ΔεβΔ，

Thus, from equations 5, 6 and 7, the following norm inequalities can be derived:

equation 10

‖ω_j-z_i‖_∞≤‖ω-z‖_∞ i, j wherein | w → z |)_∞＝‖F₁(F_u(Δ，G)，K)‖_∞And w is_j→z_iIs from w_jTo z_iThe transfer function of (2).

Therefore, if the controller K is designed to satisfy | w → z |)_∞< gamma, then H is given according to equation 7_∞The optimization criterion, and the norm inequality given by equation 10, holds the following performance inequality at each frequency ω.

Equation 11

<math> <mrow> <mo>|</mo> <mfrac> <msub> <mi>GK</mi> <mn>1</mn> </msub> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>GK</mi> <mn>2</mn> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <mi>jw</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>G</mi> <mi>ideal</mi> </msub> <mrow> <mo>(</mo> <mi>jw</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo><</mo> <mrow> <mo>(</mo> <mo>|</mo> <msub> <mi>W</mi> <mi>P</mi> </msub> <mrow> <mo>(</mo> <mi>jw</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> <msub> <mi>W</mi> <mi>r</mi> </msub> <mrow> <mo>(</mo> <mi>jw</mi> <mo>)</mo> </mrow> <mo>|</mo> <msup> <mo>)</mo> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mi>γ</mi> </mrow> </mrow> </math>

Equation 12

Equation 13

Equation 14

Further, the following actuator penalty inequality (actuator inequality) also holds:

equation 15

Equation 16

Equation 17

Equation 18

It can be seen that the performance inequalities shown in equations 11-14 serve as a set of performance constraints imposed on the system. Equation 11 defines the tracking constraint, equation 12 defines the input interference rejection (rotational vibration) constraint, equation 13 defines the position interference rejection constraint, which includes current interference rejection, write error rejection, repeatable runout rejection, non-repeatable runout rejection, and bias current error, and equation 14 is the noise rejection constraint.

The tracking constraint set forth in equation 11 is imposed on the system by selecting the weight 233 (w)_p) And 251 (w)_r) The designer may force the controller to meet any desired response, if any. For example, a designer may wish to have a step response to an actuator to take some form (appearance) in the frequency domain (e.g., when moving a track or performing a read-write offset). Typically, the weights are chosen such that the tracking constraints are strongly suppressed. Ringing can excite structural modes in the drive, while strong damping tends to avoid this problem. It should be noted that by providing the controller K as a two degree of freedom controller, the present invention provides one additional degree of freedom to further enforce tracking constraints. Further, it is preferable that the transfer function G in the formula 11 is_idealDesigned to provide a desired response to a command bias. Thus, the performance target given by equation 11 forces the disk drive to respond with G_idealThe responses of (a) match. Such a tracking target is hereinafter referred to as explicit model tracking (explicit modeling). There are also implicit techniques that do not require embedding the model in the global interconnect, which avoids additional states. However, explicit techniques are preferred because often they are simpler to design.

The input and output interference rejection performance constraints set forth in equations 12 and 13 enable the track following servo system to reject interference from external sources (exogenous sources) and thus maintain tight tracking performance under these normal operating conditions. For example, the seek arrival (seekarrrival) causes an actuator position and velocity error when the tracking controller is turned on. In addition, the user structure causes the disk drive to vibrate and vibrate translationally and rotationally. Thus, good tracking performance requires the servo system to respond quickly and to attenuate continuous and stepped or pulsed bias current, torque, position and velocity disturbances. Furthermore, in such systems, generally, constant ringing at too high an amplitude or for too long a time is highly undesirable. These requirements are well achieved by applying a norm constraint to a particular transfer function. The effects of bias current and torque disturbances can be minimized over some specified frequency range by attenuation of the norm constraint as set forth by the following equation:

equation 19

The greater attenuation from dc to critical frequencies results in a fast response. Reaching a peak in the transfer function results in ringing.

Similarly, by attenuation, positional disturbances are minimized:

equation 20

By setting the performance weights in equations 12 and 13, attenuation equations 19 and 20 can be obtained.

Although the system does not filter out or suppress sensor noise, it is preferable to design it so that it does not contribute to the noise. This may occur if there is a peak in the transfer function set forth in equation 14. Term peaking generally represents a gain of 0dB or higher in some frequency domains. Typically, the peak is used to represent unwanted amplification in the closed loop transfer function. It should be noted that in the presence of large gains, this transfer function approximates 1. Thus, if there is excessive noise in those frequencies where the controller is expected to have high performance, it is generally desirable to incorporate a noise filter that uses a priori information about the noise spectrum. This is typically done in disk drives by using a repeatable runout compensator, which locks in repeatable noise caused by write errors from the servo track writing system.

The actuator constraints set forth in equations 15-18 include a tracking constraint (equation 15), an input interference constraint (equation 16), an output interference constraint (equation 17), and a noise constraint (equation 18).

The task of the designer is to select the frequency weights w_p、w_u、w_r、w_di、w_doAnd w_nThey gather performance requirements for the disk drive. The weight selection is simple if the performance requirements are easily expressed in the frequency domain. However, in general, there may also be time domain requirements. For example, these requirements may include overshoot, rise time, settling time, and ringing, where they must be converted to equivalent properties in the frequency domain (e.g., bandwidth, attenuation, peak, etc.).

The actuator constraints (or objectives) set forth in equations 15-18 degrade the actuator control signal. This preferably serves several purposes. For systems with little or no uncertainty, these goals may force the controller to roll off, thereby limiting bandwidth. However, these objectives are typically used to define the amplitude of the control signal to minimize the likelihood of control signal saturation in the servo actuator.

Adjusting the correlation weights is an iterative process that uses data from simulations and tests to determine the appropriate weights.

C. Robustness and model validation and optimization

Once the model is built and the appropriate weights are selected, the robustness of the model is verified. In the preferred embodiment, H is used_∞And μ synthesis techniques to accomplish this. The matrix function μ can be calculated and used to analyze the stability and performance characteristics of the interconnect structure set forth in fig. 12, including the controller 261, the actuator 263, and the uncertainty 265. Mu-analysis is used to analyze the stability and performance characteristics of an interconnected system subject to norm-bounded structural uncertainty. Fig. 12 presents a generic interconnect with structural uncertainty, which is suitable for μ analysis and μ synthesis.

After the matrix function mu is calculated for the system, the function mu is calculated_g。μ_gIs an extension of the μ framework, where the interference box is layered into two groups, one satisfying a maximum norm constraint (similar to μ) and the other satisfying a minimum norm constraint. As can be seen, such a formula solves the model validation problem. Commonly known as mu_sCan be calculated.

Essentially, after the integrated controller, μ determines the maximum measure of interference, noise and model uncertainty for the closed loop system to maintain stability and performance. For a given data set, the model confirms μ_sThe analysis determines the minimum scale of interference, noise and model instability required by the model to fit these data. The closed loop system is robust if the controller can maintain stability and performance for the actual system. If μ (ω) is smaller than μ_g(ω)  ω ε Ω, then (p ω t) is simply presented, so the model is consistent with the data and the controller is consistent with the model. Thus, the closed loop system is robust over the frequency group Ω.

FIG. 13 is a graph of frequency 271 versus amplitude 273 illustrating stability and performance robustness for a closed loop tracking controller. 242 designates μ_gA function. 244 specifies μ (ω) for performance targets and 246 specifies μ (ω) for stability. At each frequency, if μ is less than μ_gThe closed loop system is very stable. In the case of an indeterminate structural pattern (i.e., above about 1-2KHz)Critical frequency ranges occur in disk drives. Thus, as can be seen from fig. 13, the closed loop system may lose stability in the frequency range of 2kHz to 4 kHz. Within this range frequencies may occur at which μ for stability and performance analysis_gBoth fall below μ (ω).

Robustness of stability can be improved by iterating over uncertainty and performance weights. This requires either an increased level of uncertainty or a reduced level of performance required (or both). Each iteration requires recalculation of the μ robustness analysis and appropriate adjustment of uncertainty and performance weights.

The controller according to the invention is preferably adjusted in two stages. The first phase is simulation and the second phase is implementation. In both phases, open and closed loop data are used to assess the effectiveness of the control design. Based on this data, the standard model, uncertainty weights or control performance weights, or all of these quantities, are adjusted.

A simple tuning technique is to adjust the frequency weights w in the performance constraints set forth in equations 11-14_p. This directly affects all relevant performance goals. In this way, w can be reduced_pMultiplied by a scalar to easily adjust the bandwidth of the controller without resorting to the more complex process of adjusting each of the other frequency weights in the performance constraints set forth in equations 11-14.

Such adjustments may be advantageously employed when initializing a new servo controller on a new disk drive product. The weights of the previous generation design can be applied while scaling w_pTo reduce bandwidth on the new disk drive product until the design specified weighting is completed. This may help to initialize new products faster.

Furthermore, it is advantageously possible to adjust a parameter, i.e. the loop gain of the servo controller, online. In practice, it may even be preferable to adjust the loop gain according to each driver. For example, by scaling the servo controller, the loop gain can be increased or decreased, resulting in an increase or decrease in the closed loop bandwidth.

FIG. 14 is a flow chart including block 308-330 and illustrates the process described above by which the disk drive model is validated and optimized. First, the model is designed by the designer choosing all weights for uncertainty description and performance constraints. Of course, these items may be selected either intuitively or through experimentation. This is represented by blocks 310 and 312.

Next, a matrix function μ (ω) is calculated to perform μ analysis for stability and performance. This is indicated by block 320. The function μ (ω) may be calculated (or the upper and lower bounds of the function may be calculated) using the techniques described above or any other known technique.

Then, the weight calculation μ selected in block 310 is applied_g(ω). This is indicated by block 322. Once μ (ω) and μ are calculated, as described above_g(ω), two things are known. First, the minimum of uncertainty needed to fit (or agree with) the data according to a μ g known model. Furthermore, the maximum value of uncertainty that the controller can tolerate and still maintain stability and meet performance constraints is also known (in terms of μ).

The next step is then to combine mu with mu_gBy comparison, to ensure that μ is less than μ at all desired frequencies_g. If this does not hold, there are frequencies in the frequency range in question at which the controller cannot achieve robust performance. In other words, there are some frequencies that undermine the stability of the controller, or performance constraints cannot be met, or both. In this case, processing reverts to block 310, where a new weighting function is selected. This is indicated by block 324, whereupon μ (ω), e.g., μ for performance and stability analysis, is recalculated by the new weighting function_gThat way. This is represented by block 310- "322.

However, if at block 324, it is determined that μ is less than μ at all desired frequencies_gThen when the weighting function selected at block 310 is applied, the sum ofRobust performance achieved by the controller. This is indicated by block 326.

Next, it is determined whether further optimization of the model is desired. If so, processing reverts to block 310 where a new weighting function is again selected. To optimize the system, the weighting functions may be adjusted to provide better performance or less uncertainty, or both. Using those new values, mu and mu are calculated_gTo determine whether the controller still provides robust performance. This can be repeated until the optimization reaches the desired level. In other words, this may be repeated until the amount of conservation in the model is reduced to achieve the desired level of performance, while still maintaining a controller that provides robust performance over the frequency range in question. Once this occurs and no further optimization is required, the model can be validated and the controller optimized to the desired extent and the design substantially complete so that the controller can be implemented. This is represented by blocks 328 and 330.

D. Implementing a controller in a Digital Signal Processor (DSP)

After obtaining the transfer function of the controller as described above, the frequency domain transfer function has a discrete time state-space implementation as follows:

equation 21

x(k+1)＝Ax(k)+Bu(k)

y (k) ═ Cx (k) + Du (k) where

x∈RⁿIs the controller state;

u∈R^mfor controller input (e.g., derived from a Position Error Signal (PES));

y∈R^pis a controller output (e.g., output to a voice coil motor and/or micro-actuator);

A. b, C, D is a matrix of appropriate size; and

Rⁿ、R^mand R^pN-dimensional, m-dimensional and p-dimensional real vectors, respectively.

However, implementing such a discrete-time system on a digital signal processor may be problematic. As described in the background section of the present application, those problems generally relate to intermediate calculations to handle the capacity of the overflow registers, the total computational power and memory capacity of conventional signal digital processors, the discrete time system to fixed point processor transformation, and the reduction and elimination of quantization errors in the controller.

Fig. 15 is a flow diagram including a block 339-349 illustrating one preferred technique for implementing a controller on a digital signal processor in accordance with an aspect of the present invention. Each block in fig. 16 will be discussed briefly, and then discussed in more detail later in this application.

First, as described above, a matrix for discrete time state-space implementation represented by equation 21 is obtained. This is indicated at 340.

The state of the controller is then scaled. In a preferred embodiment, the limits of the controller states are determined under worst case assumptions and state transitions are performed to scale the limits to a desired level. This significantly reduces the likelihood of overflow during intermediate controller calculations. This is indicated by block 342.

The state of the controller is then transformed to a more desirable configuration. In a preferred embodiment, the state of the controller is transformed into a bi-diagonals (bi-diagnol) structure, which significantly reduces the computation time and memory requirements of the digital signal processor. This is indicated by block 344.

Finally, the matrices are transformed so as to change the controller parameters from a floating point format to a fixed point format. In doing so, care is taken to significantly reduce the quantization error induced to an acceptable level. In a preferred embodiment, the matrices are formatted as fractional binary numbers, whereby the dots represented by the fractional binary numbers are placed at desired locations. This is indicated by block 346.

1. Scaling controller states to reduce overflow

The state development for the discrete-time implementation indicated by equation 21 is given below:

equation 22

Wherein x (0) is an initial state.

The present invention minimizes or at least reduces the chance of overflow being encountered in the intermediate controller calculation. In the preferred embodiment, this is done by automatically scaling the state of the controller. Thus, at each sample k, it can be assumed (without loss of generality) that for each input u_i：

Equation 23

|u_i(k)|≤M_iM_i＞0，i＝1...m，

Where m is defined as the number of inputs to the controller. Then, under worst case assumptions, the kth sample of the state in the controller satisfies the following bounds:

equation 24

Wherein M and M_jDefined as shown in equation 23.

For a stable system (i.e., ρ (A) < 1), there is some integer N, so that A^NAnd gradually becomes smaller. Then, from equation 24, the state described by equation 24 satisfies the following bounds:

equation 25

<math> <mrow> <msub> <mi>max</mi> <mrow> <mi>k</mi> <mo>&RightArrow;</mo> <mo>∞</mo> </mrow> </msub> <mo>|</mo> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>≤</mo> <mrow> <mo>(</mo> <munderover> <mi>Σ</mi> <mrow> <mi>v</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>|</mo> <msup> <mi>A</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>v</mi> </mrow> </msup> <mo>|</mo> <mo>)</mo> </mrow> <mo>|</mo> <mi>B</mi> <mo>|</mo> <msup> <mrow> <mo>[</mo> <msub> <mi>M</mi> <mn>1</mn> </msub> <msub> <mi>M</mi> <mn>2</mn> </msub> <mo>…</mo> <msub> <mi>M</mi> <mi>m</mi> </msub> <mo>]</mo> </mrow> <mi>T</mi> </msup> </mrow> </math>

The limits on the controller state given in equation 25 (bearing in mind that this is a limit for the worst case sample) can be used to form the state transition.

First, T is defined as follows:

equation 26

Where diag () is defined as the diagonal matrix whose main diagonal is the vector marked by the vector. Then, the state transition z ═ t (x) will satisfy the limit

Equation 27

max_k→∞|z(k)|≤1

Thus, the new controller is implemented as follows:

equation 28

z(k+1)＝TAT^-1z(k)+TBu(k)

y(k)＝CT^-1z(k)+Du(k)

It should be noted that a controller implementing a pure integrator cannot be stable because ρ (a) ═ 1. In this case, there is no such integer N, so that A^NClose to 0. However, in many cases (especially in H)_∞And μ integrated), the controller does not have a pure integrator, but may have a spectral radius of approximately 1. Thus, there will be such an integer N, thus A^NClose to 0. However, the integer N may be very large. This means that the state transition represented by equation 26 will result in extremely conservative bounds for all states except the integration state. Thus, where the controller's spectral radius is approximately 1, appropriate inverse integrator termination (windup) techniques are also implemented to further reduce the likelihood of integrator overflow, as described above for the remaining controller states.

2. Transforming scaled states to reduce computational power and memory capacity requirements of a DSP

The discrete-time system shown in equation 21 may have any elements in the matrices A, B, C and D. Thus, at each sample, up to (n + p) × (m + m) multiplications, and (n + p) × (n + m-1) additions may be required. This is very inconvenient as it may cause the controller to perform an impractically large number of arithmetic operations (multiplications and additions). However, using state transitions, the number of multiplications and additions can be significantly reduced.

In embodiments where the controller is implemented as a single input/single output (SISO) controller, a canonical form may be utilized to obtain significant simplification of the computation. In this embodiment, the controller implementation represented by equation 21 is preferably in the regular form of a controller as follows:

equation 29

z(k+1)＝A_cz(k)+b_cu(k)

y(k)＝C_cz (k) + du (k) wherein C_cAnd d is an arbitrary matrix; and

A_cand b_cThe definition is as follows:

equation 30

Equation 31

Wherein n is the number of states in the controller; and

a_is in a characteristic polynomial of A^n-iThe coefficient of the term.

Thus, as can be seen from equations 29-31, at each sample, there are only 2n +1 multiplications and 2n additions for the regular form implementation of the controller. This is a great reduction compared to the (n +1) × (n +1) multiplications and n × (n +1) additions implemented as shown in equation 21.

While such state transformations may be highly desirable for implementing SISO, the canonical form is not universally applicable to multiple-input multiple-output (MIMO) systems. Thus, in practicing MIMO, a dual diagonal implementation can be utilized to significantly simplify the computation.

For the purposes of the present invention, a dual diagonal implementation refers to a box diagonal matrix that separates the matrix in equation 21 into real eigenvalues and complex conjugate pairs. This results in the transformation of the implementation represented by equation 21 to the implementation as follows:

equation 32

z(k+1)＝A_bdz(k)+B_bdu(k)

y(k)＝C_bdz (k) + Du (k) wherein B_bd、C_bdAnd D is an arbitrary matrix; and

equation 33

Where r is the number of real eigenvalues of the controller;

c is the number of pairs of complex conjugate eigenvalues (n ═ r + 2C);

each lambda_iThe ith eigenvalue corresponding to a in equation 21; and

each one of which isA 2x 2 matrix of j-th complex conjugate eigenvalue pairs corresponding to a.

Thus, as can be seen from equations 32 and 33, forAchieved on the double diagonal, there will be n × (m +1) + p × (n + m) +2c multiplications and n × m + p × (n + m-1) +2c additions per sample. In other words, for each sample, the dual diagonal line represented by equations 32 and 33 achieves n less²N-2c multiplications and n²N-2c additions. Furthermore, as the number of states increases (corresponding to the number of controller inputs and outputs), the calculations implemented by the dual diagonals are linear with the number of states and quadratic with the standard shown in equation 21. It should also be noted that the dual diagonal transformation may be applied before the transformation used to scale and bound the states of the controller. This allows the integration state to be isolated prior to scaling to minimize or prevent overflow in intermediate calculations.

3. Matrix conversion to fixed-point format

Since the digital signal processor is a fixed-point controller, the matrix defining the discrete-time controller must be converted to a fixed-point format to allow the controller to be implemented on a DSP. Floating point numbers can be converted to fixed point equivalents using a fractional binary number. The decimal binary number is represented as a binary number followed by a binary point followed by a binary decimal number. For example, a decimal binary number may be represented as follows:

equation 34

Where N is the word length (or number of bits in a binary word);

q is the position of the binary point; and

(b_N-1，b_N-2，...b₁，b₀) Are bits in a binary word.

For the purposes of this application, a decimal binary number will be denoted by Qn, where n is the position of the binary point. For example, the decimal binary number Q15 represents a binary number 15 bits after the binary point.

The elements of the matrix represented by the dual diagonal implementation in equation 32 are preferably converted to decimal binary numbers. In the preferred embodiment, this is done by right shifting the elements of each matrix until the matrix can be represented in the desired fractional binary number format. Thus, the fixed point dual diagonal implementation represented in equation 32 will be represented as:

equation 35

2 (k + 1 = 2^{s_{A}} A_{bd}^{2_{A}} z (k) + 2^{s_{B}} B_{bd}^{s_{B}} u (k)

y (k) = 2^{s_{C}} C_{bd}^{s_{C}} z (k) + 2^{s_{D}} D^{s_{D}} u (k)

Wherein s is_A、s_B、s_CAnd s_DIs a positive number equal to the number of right shifts required to represent each matrix in the format of a fractional binary number (Qn); and

and

respectively correspond to

And

is denoted by Qn.

In a preferred embodiment, the discrete time controller implementation represented by format 21 is implemented on a 16-bit fixed point digital signal processor, with standard Arithmetic Logic Units (ALUs) providing signed and unsigned multiply and add instructions for 16-bit arguments. Internally, the sum of products is stored in 32-bit form. In one preferred embodiment, the processor is a DSP core commercially known as TMS320C2xLP, available from Texas Instruments. Experiments have shown that using 16 bits (i.e., Q15 format) for the controller matrix, measurements, and outputs provides acceptable operation. However, for state operations, 32 bits (Q31 format) are preferred.

The present invention thus provides a highly advantageous disk drive in which a model-based servo controller can be implemented. The servo controller controls the movement of the actuator to cause the transducer to move relative to the rotating disc surface in the disc drive. The model-based servo controller provides robust track-following control of the servo system over a desired frequency range.

In a preferred embodiment, the servo controller 190 is synthesized based on a servo controller model 201, wherein the servo controller model 201 accounts for standard performance 200 of the disk drive 110,

uncertainty descriptions

202, 204 characterizing the disk drive 110, and track following performance constraints on the servo controller model 201. In another preferred embodiment, a plurality of transducers 181 are provided on a plurality of disk faces 180, 182. The actuator arm 118 includes an arm portion 126 and a plurality of

suspension assemblies

128 and 116, wherein each

suspension assembly

128 and 116 supports one transducer 144 relative to a

respective disk face

180 and 182. In this embodiment, the actuator 173 includes a coarse actuator coupled to the arm portion and a plurality of micro-actuators 158, at least one of the plurality of micro-actuators 158 being operatively connected to the arm portion 126 and the corresponding transducer 144 for controllably moving the corresponding transducer 144 relative to the arm portion 126.

In another preferred embodiment, the servo controller 190 includes a plurality of error inputs for receiving the error signals 171 from the transducer 144 and a plurality of control outputs for providing control signals to the plurality of micro-actuators 158 and the coarse actuators 173 based on the command signals 165 and the error signals 171. Additionally, in another preferred embodiment, the servo controller 190 includes a plurality of relative position inputs for receiving a plurality of relative position signals 179 indicative of the relative position of the plurality of microactuators 158 with respect to the coarse actuator 173. In the preferred embodiment, a plurality of relative position sensors 183 are operatively coupled to the plurality of microactuators 158 and provide a plurality of relative position signals 179.

In another preferred embodiment, servo controller 190 is configured to adjust the servo control signals to compensate for structural resonances, positional input disturbances, and/or substantially simultaneous movement of the

multiple actuators

118 and 158 in disk drive 110.

It is to be understood that even though numerous characteristics and advantages of various embodiments of the present invention have been set forth in the foregoing description, together with details of the structure and function of various embodiments of the invention, this description is illustrative only, and changes may be made in detail, especially in matters of structure and arrangements of parts within the principles of the present invention to the full extent indicated by the broad general meaning of the terms in which the appended claims are expressed. For example, the particular components may vary depending on the particular drive or drive type while maintaining substantially the same functionality without departing from the scope and spirit of the present invention.

Claims

1. A servo system for controlling the positioning of a transducer relative to a surface of a rotatable disk in a disk drive, the surface having tracks containing information, the servo system comprising:

an actuator arm operatively coupled to the transducer;

an actuator operatively coupled to the actuator arm for moving the transducer relative to the disk surface to track a track during track following; and

a model-based servo controller operatively coupled to the actuator for providing servo control signals to control movement of the actuator, the model-based servo controller being configured to provide the servo control signals to account for changes in servo system operating parameters relative to standard operating parameters to provide stable track following control of the servo actuator at a desired performance level over a desired frequency range.

2. The servo system of claim 1 wherein the model-based servo controller comprises:

a servo controller synthesized from a servo controller model that accounts for standard performance of the disk drive, an uncertainty description characterizing the disk drive, and track following performance constraints placed on the servo controller model.

3. The servo system of claim 2 wherein the transducer provides an error signal indicative of a tracking position error and the servo controller comprises;

an error input configured to receive an error signal;

a command input configured to receive a command signal indicative of a track to be tracked; and

a control output coupled to the actuator, the servo controller configured to provide a servo control signal to the actuator based on the error signal and the command signal.

4. The servo system of claim 3 wherein said disc drive further comprises a plurality of disc faces and a plurality of transducers, and said actuator arm comprises;

an arm portion; and

a plurality of suspension assemblies, each suspension assembly supporting a transducer relative to a respective disk face;

wherein the actuator includes a coarse actuator coupled to the arm portion and a plurality of micro-actuators, at least one of the plurality of micro-actuators being operatively coupled to the arm portion and the respective transducer for controllably moving the respective transducer relative to the arm portion; and is

The servo controller comprises

A plurality of error inputs configured to receive error signals from the transducers; and

a plurality of control outputs configured to provide control signals to the plurality of micro-actuators and the coarse actuator based on the command signal and the error signal.

5. The servo system of claim 4 wherein the servo controller comprises a plurality of relative position inputs configured to receive a plurality of relative position signals indicative of the relative position of the plurality of micro-actuators with respect to the coarse actuator.

6. The servo system of claim 5, further comprising:

a plurality of relative position sensors operatively coupled to the plurality of micro-actuators and providing the plurality of relative position signals.

7. The servo system of claim 1 wherein the model-based servo controller comprises:

a controller, which is H_∞And the mu controller is synthesized by a model.

8. The servo system of claim 4 wherein the operating parameter varies in response to vibration caused by structural resonance in the disc drive, and wherein the servo controller is configured to adjust the servo control signal to compensate for structural resonance in the disc drive and for variations in an operating parameter of the disc drive, the operating parameter selected from the group consisting of:

positional input disturbance to the servo controller:

moving the plurality of micro-actuators substantially simultaneously.

9. A disc drive, comprising:

a rotatable magnetic disk having a disk surface with signals disposed in tracks on the disk surface;

a transducer;

an actuator arm operatively coupled to the transducer;

a model-based servo controller operatively coupled to the actuator to control movement of the actuator, the model-based servo controller providing robust track following control over a desired frequency range.

10. The servo disk drive of claim 9 wherein said model-based servo controller comprises:

a controller which utilizes H_∞And the combination of the mu controller is formed by combining a model.