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Application of Modern Control to Disk Drive Actuator Positioning
9d-Ol 2
Copyright © 1996 IFAC 13th Triennial World Congress, San Francisco, USA
APPLICATION OF MODERN CONTROL TO DISK DRIVE ACTUATOR POSITIONING Otis L. Funches Advanced Servo Technology, Seagate Technology, Inc., Oklahoma City, OK 73123,FAX:(405) 324-3637, [email protected]
Abstract: Hard disk position control has two objectives: moving the magnetic recording heads from one data track to another in minimum time and maintaining position at a destination data track center while rejecting disturbance inputs. These objectives have not changed but the technology has evolved rapidly over the years. In the 1980's, analog servo position control could no longer provide solutions to the demand for smaller drives with higher capacity and significantly lower access times. This paper chronicles the evolution in design from the analog designs of the past to the modem control approach of today. Keywords: current, voltage, actuator, velocity control, position control, analog control, digital control, observer.
1. INTRODUCTION Hard disk drive (HOD) technology has evolved at a high rate since the early 1980's characterized by: smaller physical size, extremely large capacity, significantly faster access, and a large decrease in price relative to cost per megabyte of memory. In the late 1980's, analog design for position control began to reach a plateau when it could no longer provide solutions for the increasingly complex control problem brought on by increasing data track density, faster access time requirements, and the smaller circuit board area forced by smaller disk drive size. Analog control design provided robust solutions to the positioning problem for over two decades, but the combination of higher track density and faster access time requirements forced designers into a corner. Solutions to some of the fundamental problems of analog circuits such as offset and component tolerance required additional circuitry for adaptive compensation if performance goals were to be met, but at significantly more cost. There was less circuit board area available due to the transition from 5.25 inch to the much smaller 3.5 inch form-factor drives. Not only did the
use of digital control, using a single DSP chip in combination with the development of LSI (large scale integration) chips, solve the limited board area problem, but its use proved to be cost effective while significantly improving performance.
2. THE DISK DRIVE ACTUATOR POSITION CONTROL PROBLEM 2.1 Description of positioning mechanism. Physical description. Most disk drives use rotary actuators. The rotary actuator mechanical structure can be described as a solid cylinder pivoted at center of the top and bottom surfaces and free to rotate so that the heads span the useable area ofthe magnetic disk surfaces. A short extrusion on one side of the cylinder holds a coil which extends into a fixed magnet structure. Opposite the coil extrusion are a series of extrusions (arms) spaced in coincidence with the drive's magnetic disks and span an area from the disk's outer radius to an inner radius of about 0.75 inch for a drive with a 3.5 inch disk diameter. Heads are mounted at the end of the
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of head position relative to the surface of the disk with fme position measurement, PES, and coarse position measurement, P A, where PES is a measurement of head position relative to the nearest track center and PAis a digital number representing the absolute address of that track.
2.3 Position control mode descriptions. Track-follow control mode. The primary function of the track-follow mode is to hold the heads at the track center in the presence of disturbances such as shock and vibration inputs so that position error is never greater than about +110% of a track width. The track width for a 4500 TPI drive will be 222 micro inches, so that 10% of the track would be 22.2 microinches.
An additional function of the track-follow loop is to handle the initial conditions present at the transition from seek to track-follow so that the heads will reach track center with no more than about 5% of a track width undershoot or overshoot. This track-follow function is sometimes given a special name, such as settle mode control. The amount of undershoot or overshoot depends on initial conditions passed on by the seek loop and how the track-follow loop responds to the initial conditions. Excessive overshoot or undershoot during Settle mode can add a significant amount of time to drive access time. Seek control mode. The function of positioning the heads from one track to another track is known as the seek mode and can be accomplished in a number of ways. Velocity transducers were eliminated from HDD designs in the early 1980's, and designers had to resort to a mechanization which estimated the velocity state from the position state measurement. The basic mechanization for the seek loop has a reference input which is modified as a function of distance to destination track center with feedback provided by estimated velocity. The seek is initiated by control logic which sets the control loop to seek mode, whereby the initial input to the trajectory generator is the commanded destination track, causing an initial velocity demand input to the loop. As the seek to the destination track progresses, the demand input to the loop will be a decreasing function which approaches zero as the destination track is reached.
3.0 DISK DRIVE ACTUATOR POSITION CONTROL DESIGN
The actuator mechanism, head and position demodulator designs have significant impact on head positioning performance. These designs usually reflect the latest technological
advances at the time of introduction. Nevertheless, there will be limitations which require innovation ifperformance goals are to be reached. For certain, access time requirements will be lower and track density will be higher. For example, the actuator or heads may contain resonance modes which adversely affect performance. Actuator peak torque output may not be sufficient to meet access time goals without new seek mode control strategy. These examples are typical of the forces which motivated the move from analog to digital control and fmally to the use of some modern control concepts in today's position control designs.
3.1. Analog position control.
Analog track-follow control. PID control has been used many years for on-track positioning. One of the weaknesses of PID control for disk drive position control was the large integrator time constant needed to maximize loop phase margin and low frequency gain for systems with low bandwidth. As a result, there was sluggish response to some types of disturbance inputs. The well-known PID controller equation is given by, Uc 1 Tv'S --(s)=Kp+-+-Xdm Ti'S 1!,s+ 1
(3)
where Kp is proportional gain, Ti is the integrator time constant and Tv is the differentiator time constant. Typical open loop parameters of 400 Hz crossover frequency and 35 degrees phase margin were typical for designs up to the late 1980's. Analog seek control. Minimization of average seek time with analog circuits was a formidable task because so many uncontrolled variables, such as loop gain variation, power supply variation, and large variation in actuator peak torque degraded performance. Loss of deceleration capability could give severe overshoot for seeks which require high velocity, resulting in high velocity initial conditions at transition from seek to track-follow control. As a result, the trajectory design had to be based on absolute worse case conditions which resulted in a conservative design and longer seek times. A simplified block diagram representation ofthe seek loop is shown in Figure 2, where Vr is the velocity reference input, Xdm is position measurement, Xd is destination track, Xe is distance to destination track, F(Xe) is trajectory generator function, Vd is demand velocity, X is head position, Kdm is demodulator gain, and Vf is estimated velocity.
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products, with many of them at track densities of 4500 tracks per inch or more. The need to increase TPI to gain more capacity has motivated a move from a single dedicated servo surface to the embedded servo approach where servo position information is embedded on each surface at a much lower sample rate. The dedicated servo approach gave adequate position control for the other disk surfaces as long as the mechanical motion between the dedicated surface and the other surfaces was small relative to track width. This is no longer true at the track densities of today's new products. A large sample rate reduction has severe impact on trackfollow and seek performance with classically based digital control. The reduction in sample frequency to bandwidth ratio requires a bandwidth reduction to maintain adequate phase margin. For the seek mode, reduced bandwidth reduces the ability of the loop to follow the aggressive velocity trajectory needed to reduce average seek time for new products. The results of simulation studies indicated that classically-based control at low sample rate would result in an increase in average seek time. Study, analysis, and the simulation of modem control concepts has led to observer-based designs that offer promise towards attaining seek performance goals.
Track-follow control with observer. A reduced order observer with an augmented plant model for bias estimation was implemented during the preliminary design phase for a new product. The basic structure for the design is shown in Figure 3. The observer is a reduced order current estimator and the observer state equations are given by, Xe(k);Xp(k)+io[X(k)-Xp(k)]
(8)
Xp(k);AoXe(k-l)+BoUc(k-l)
(9)
where Ao and Bo are the observer state-transition and distribution matrices, respectively, lo the observer gain matrix, Xe(k) the observer state estimate, and Xp(k) the observer predicted estimate. The observer error is given by, Xer(k+ 1);[Ao-AoloCo]Xer(k)
(10)
Figure 3. Observer with bias estimator. The system state equation is given by, X(k+ 1);[A -BKo]X(k)+BUc(k)
(11)
where Ko is the system gain matrix, and A and B· are the plant transition and distribution matrices, respectively, based on a double integrator plant model. The complete system is described by the coupled observer and system equations, but through the use of the Separation Principle, the poles for the observer and system can be determined separately using pole placement or LQR methods. Equation (11) is augmented with the bias model to provide bias estimation for the system.
Seek control with observer. A move from one track to another with observer control can be accomplished in a positional mode when a step input representing the demand address is summed with Xes(k), the observer position estimate. However, the observer can operate in velocity mode and the time for the move will be considerably less for a velocity mode seek if the observer can handle a realizable near-time-optimal trajectory design. For a velocity mode seek: Kx and Kw are set to zero; the demand trajectory is summed with Ves(k), the observer velocity estimate; the observer continues to compute Xes(k); and settle mode occurs at Xe(k)=0.5 track. A simulation of the preliminary design shows that even at low sample rate the design is robust, relative to trajectory following ability, and has good settle characteristics. In the design, the sample frequency is 5 KHz, and the model of the plant in the simulation includes the compensated power amplifier with saturation (see equation 2). In the simulation, the seek length is one third of a full stroke, for which the seek time will be a close
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Copyright © 1996 IFAC 13th Triennial World Congress, San Francisco, USA
APPLICATION OF MODERN CONTROL TO DISK DRIVE ACTUATOR POSITIONING Otis L. Funches Advanced Servo Technology, Seagate Technology, Inc., Oklahoma City, OK 73123,FAX:(405) 324-3637, [email protected]
Abstract: Hard disk position control has two objectives: moving the magnetic recording heads from one data track to another in minimum time and maintaining position at a destination data track center while rejecting disturbance inputs. These objectives have not changed but the technology has evolved rapidly over the years. In the 1980's, analog servo position control could no longer provide solutions to the demand for smaller drives with higher capacity and significantly lower access times. This paper chronicles the evolution in design from the analog designs of the past to the modem control approach of today. Keywords: current, voltage, actuator, velocity control, position control, analog control, digital control, observer.
1. INTRODUCTION Hard disk drive (HOD) technology has evolved at a high rate since the early 1980's characterized by: smaller physical size, extremely large capacity, significantly faster access, and a large decrease in price relative to cost per megabyte of memory. In the late 1980's, analog design for position control began to reach a plateau when it could no longer provide solutions for the increasingly complex control problem brought on by increasing data track density, faster access time requirements, and the smaller circuit board area forced by smaller disk drive size. Analog control design provided robust solutions to the positioning problem for over two decades, but the combination of higher track density and faster access time requirements forced designers into a corner. Solutions to some of the fundamental problems of analog circuits such as offset and component tolerance required additional circuitry for adaptive compensation if performance goals were to be met, but at significantly more cost. There was less circuit board area available due to the transition from 5.25 inch to the much smaller 3.5 inch form-factor drives. Not only did the
use of digital control, using a single DSP chip in combination with the development of LSI (large scale integration) chips, solve the limited board area problem, but its use proved to be cost effective while significantly improving performance.
2. THE DISK DRIVE ACTUATOR POSITION CONTROL PROBLEM 2.1 Description of positioning mechanism. Physical description. Most disk drives use rotary actuators. The rotary actuator mechanical structure can be described as a solid cylinder pivoted at center of the top and bottom surfaces and free to rotate so that the heads span the useable area ofthe magnetic disk surfaces. A short extrusion on one side of the cylinder holds a coil which extends into a fixed magnet structure. Opposite the coil extrusion are a series of extrusions (arms) spaced in coincidence with the drive's magnetic disks and span an area from the disk's outer radius to an inner radius of about 0.75 inch for a drive with a 3.5 inch disk diameter. Heads are mounted at the end of the
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of head position relative to the surface of the disk with fme position measurement, PES, and coarse position measurement, P A, where PES is a measurement of head position relative to the nearest track center and PAis a digital number representing the absolute address of that track.
2.3 Position control mode descriptions. Track-follow control mode. The primary function of the track-follow mode is to hold the heads at the track center in the presence of disturbances such as shock and vibration inputs so that position error is never greater than about +110% of a track width. The track width for a 4500 TPI drive will be 222 micro inches, so that 10% of the track would be 22.2 microinches.
An additional function of the track-follow loop is to handle the initial conditions present at the transition from seek to track-follow so that the heads will reach track center with no more than about 5% of a track width undershoot or overshoot. This track-follow function is sometimes given a special name, such as settle mode control. The amount of undershoot or overshoot depends on initial conditions passed on by the seek loop and how the track-follow loop responds to the initial conditions. Excessive overshoot or undershoot during Settle mode can add a significant amount of time to drive access time. Seek control mode. The function of positioning the heads from one track to another track is known as the seek mode and can be accomplished in a number of ways. Velocity transducers were eliminated from HDD designs in the early 1980's, and designers had to resort to a mechanization which estimated the velocity state from the position state measurement. The basic mechanization for the seek loop has a reference input which is modified as a function of distance to destination track center with feedback provided by estimated velocity. The seek is initiated by control logic which sets the control loop to seek mode, whereby the initial input to the trajectory generator is the commanded destination track, causing an initial velocity demand input to the loop. As the seek to the destination track progresses, the demand input to the loop will be a decreasing function which approaches zero as the destination track is reached.
3.0 DISK DRIVE ACTUATOR POSITION CONTROL DESIGN
The actuator mechanism, head and position demodulator designs have significant impact on head positioning performance. These designs usually reflect the latest technological
advances at the time of introduction. Nevertheless, there will be limitations which require innovation ifperformance goals are to be reached. For certain, access time requirements will be lower and track density will be higher. For example, the actuator or heads may contain resonance modes which adversely affect performance. Actuator peak torque output may not be sufficient to meet access time goals without new seek mode control strategy. These examples are typical of the forces which motivated the move from analog to digital control and fmally to the use of some modern control concepts in today's position control designs.
3.1. Analog position control.
Analog track-follow control. PID control has been used many years for on-track positioning. One of the weaknesses of PID control for disk drive position control was the large integrator time constant needed to maximize loop phase margin and low frequency gain for systems with low bandwidth. As a result, there was sluggish response to some types of disturbance inputs. The well-known PID controller equation is given by, Uc 1 Tv'S --(s)=Kp+-+-Xdm Ti'S 1!,s+ 1
(3)
where Kp is proportional gain, Ti is the integrator time constant and Tv is the differentiator time constant. Typical open loop parameters of 400 Hz crossover frequency and 35 degrees phase margin were typical for designs up to the late 1980's. Analog seek control. Minimization of average seek time with analog circuits was a formidable task because so many uncontrolled variables, such as loop gain variation, power supply variation, and large variation in actuator peak torque degraded performance. Loss of deceleration capability could give severe overshoot for seeks which require high velocity, resulting in high velocity initial conditions at transition from seek to track-follow control. As a result, the trajectory design had to be based on absolute worse case conditions which resulted in a conservative design and longer seek times. A simplified block diagram representation ofthe seek loop is shown in Figure 2, where Vr is the velocity reference input, Xdm is position measurement, Xd is destination track, Xe is distance to destination track, F(Xe) is trajectory generator function, Vd is demand velocity, X is head position, Kdm is demodulator gain, and Vf is estimated velocity.
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products, with many of them at track densities of 4500 tracks per inch or more. The need to increase TPI to gain more capacity has motivated a move from a single dedicated servo surface to the embedded servo approach where servo position information is embedded on each surface at a much lower sample rate. The dedicated servo approach gave adequate position control for the other disk surfaces as long as the mechanical motion between the dedicated surface and the other surfaces was small relative to track width. This is no longer true at the track densities of today's new products. A large sample rate reduction has severe impact on trackfollow and seek performance with classically based digital control. The reduction in sample frequency to bandwidth ratio requires a bandwidth reduction to maintain adequate phase margin. For the seek mode, reduced bandwidth reduces the ability of the loop to follow the aggressive velocity trajectory needed to reduce average seek time for new products. The results of simulation studies indicated that classically-based control at low sample rate would result in an increase in average seek time. Study, analysis, and the simulation of modem control concepts has led to observer-based designs that offer promise towards attaining seek performance goals.
Track-follow control with observer. A reduced order observer with an augmented plant model for bias estimation was implemented during the preliminary design phase for a new product. The basic structure for the design is shown in Figure 3. The observer is a reduced order current estimator and the observer state equations are given by, Xe(k);Xp(k)+io[X(k)-Xp(k)]
(8)
Xp(k);AoXe(k-l)+BoUc(k-l)
(9)
where Ao and Bo are the observer state-transition and distribution matrices, respectively, lo the observer gain matrix, Xe(k) the observer state estimate, and Xp(k) the observer predicted estimate. The observer error is given by, Xer(k+ 1);[Ao-AoloCo]Xer(k)
(10)
Figure 3. Observer with bias estimator. The system state equation is given by, X(k+ 1);[A -BKo]X(k)+BUc(k)
(11)
where Ko is the system gain matrix, and A and B· are the plant transition and distribution matrices, respectively, based on a double integrator plant model. The complete system is described by the coupled observer and system equations, but through the use of the Separation Principle, the poles for the observer and system can be determined separately using pole placement or LQR methods. Equation (11) is augmented with the bias model to provide bias estimation for the system.
Seek control with observer. A move from one track to another with observer control can be accomplished in a positional mode when a step input representing the demand address is summed with Xes(k), the observer position estimate. However, the observer can operate in velocity mode and the time for the move will be considerably less for a velocity mode seek if the observer can handle a realizable near-time-optimal trajectory design. For a velocity mode seek: Kx and Kw are set to zero; the demand trajectory is summed with Ves(k), the observer velocity estimate; the observer continues to compute Xes(k); and settle mode occurs at Xe(k)=0.5 track. A simulation of the preliminary design shows that even at low sample rate the design is robust, relative to trajectory following ability, and has good settle characteristics. In the design, the sample frequency is 5 KHz, and the model of the plant in the simulation includes the compensated power amplifier with saturation (see equation 2). In the simulation, the seek length is one third of a full stroke, for which the seek time will be a close
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