CN109003631A - The multiple dimensioned approximate explicit model forecast Control Algorithm of disk drive system - Google Patents
The multiple dimensioned approximate explicit model forecast Control Algorithm of disk drive system Download PDFInfo
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- CN109003631A CN109003631A CN201810771561.XA CN201810771561A CN109003631A CN 109003631 A CN109003631 A CN 109003631A CN 201810771561 A CN201810771561 A CN 201810771561A CN 109003631 A CN109003631 A CN 109003631A
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- G—PHYSICS
- G11—INFORMATION STORAGE
- G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
- G11B5/00—Recording by magnetisation or demagnetisation of a record carrier; Reproducing by magnetic means; Record carriers therefor
- G11B5/48—Disposition or mounting of heads or head supports relative to record carriers ; arrangements of heads, e.g. for scanning the record carrier to increase the relative speed
- G11B5/58—Disposition or mounting of heads or head supports relative to record carriers ; arrangements of heads, e.g. for scanning the record carrier to increase the relative speed with provision for moving the head for the purpose of maintaining alignment of the head relative to the record carrier during transducing operation, e.g. to compensate for surface irregularities of the latter or for track following
- G11B5/596—Disposition or mounting of heads or head supports relative to record carriers ; arrangements of heads, e.g. for scanning the record carrier to increase the relative speed with provision for moving the head for the purpose of maintaining alignment of the head relative to the record carrier during transducing operation, e.g. to compensate for surface irregularities of the latter or for track following for track following on disks
- G11B5/59683—Disposition or mounting of heads or head supports relative to record carriers ; arrangements of heads, e.g. for scanning the record carrier to increase the relative speed with provision for moving the head for the purpose of maintaining alignment of the head relative to the record carrier during transducing operation, e.g. to compensate for surface irregularities of the latter or for track following for track following on disks for magnetoresistive heads
-
- G—PHYSICS
- G11—INFORMATION STORAGE
- G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
- G11B5/00—Recording by magnetisation or demagnetisation of a record carrier; Reproducing by magnetic means; Record carriers therefor
- G11B5/48—Disposition or mounting of heads or head supports relative to record carriers ; arrangements of heads, e.g. for scanning the record carrier to increase the relative speed
- G11B5/58—Disposition or mounting of heads or head supports relative to record carriers ; arrangements of heads, e.g. for scanning the record carrier to increase the relative speed with provision for moving the head for the purpose of maintaining alignment of the head relative to the record carrier during transducing operation, e.g. to compensate for surface irregularities of the latter or for track following
- G11B5/60—Fluid-dynamic spacing of heads from record-carriers
- G11B5/6005—Specially adapted for spacing from a rotating disc using a fluid cushion
- G11B5/6088—Optical waveguide in or on flying head
Abstract
The multiple dimensioned approximate explicit model forecast Control Algorithm of disk drive system, includes the following steps: that step 1) models disk drive system, obtains Parametric optimization problem；Step 2) piecewise linearity insertion tentatively obtains a kind of approximation control rule；Step 3) adaptive layered approximation to function, the form of conversion approximation control rule；Step 4) introduces center of gravity function and obtains the rule of the approximation control based on center of gravity function using barycentric interpolation；The multiple dimensioned approximate explicit model PREDICTIVE CONTROL of step 5) disk drive system.The present invention improves the real-time of magnetic disk drve control system, reduces control complexity, reduces the demand of controller memory capacity, saves in the line computation time, and possesses good control effect.
Description
Technical field
The present invention relates to a kind of optimal control methods of disk drive system.
Background technique
Disk drive system is the important component of computer, and will be used wider and wider general.Disc driver is also known as
" disc unit " is the storage device using disk as record information medium, includes mainly floppy disk drive, hard disk drive is also
CD drive etc..Data in disc driver reading disk, pass to processor, it is seen that disk drive system reads information
Speed will have a direct impact on the progress of computer overall work, therefore find reasonable control method control disk drive to closing
It is important.
For handling Multivariable Constrained optimal control problem, model predictive control method is a kind of very effective method,
It by years of researches and explores, achieves significant progress and be used widely.Model Predictive Control uses prediction mould
The new control strategy such as type, rolling optimization, feedback compensation and multi-step prediction, enables it effectively to inhibit to be to a certain extent
Influence of the inaccurate and external interference of system model for system control performance.But Model Predictive Control have the shortcomings that it is very big just
It is that Model Predictive Control is only applicable to slow procedure, has sizable limitation in the faster field of processing speed.It studies thus
Personnel propose explicit model PREDICTIVE CONTROL.
Explicit model PREDICTIVE CONTROL (Explicit Model Predictive Control) introduces multi-parametric programming reason
By carrying out convex division to the state region of system, and establish the optimal control law of the optimization problem on corresponding each Condition Areas
Explicit function relationship (being restrained for the Linear Control of state) between state；This method also has its limitation, it is only applicable to about
The system of beam, and complexity can be in exponential increase with the increase of problem scale, i.e., when input number increases or controls
Time domain processed just needs very big memory space when elongated, increases so that searching control law and handling the difficulty of problem.
Summary of the invention
The present invention proposes a kind of more rulers of disk drive system to overcome the disadvantages mentioned above of existing disk drive system
Spend approximate explicit model forecast Control Algorithm.
Gridding processing is carried out by the state space obtained to accurate explicit model PREDICTIVE CONTROL, so that Condition Areas becomes
At the rectangle of rule, approximation control rule is obtained, by the way that maximum level status Condition Areas quantity is arranged, so that conveniently online search
Process.
When being controlled using explicit model PREDICTIVE CONTROL, online progress solving optimization problem is not had to, off-line calculation is good
The control law of each Condition Areas, finds the subregion where current system conditions online, just can determine that the optimal of parameter current
Control amount.But when inputting number increase or elongated control time domain, complexity can be exponentially increased, so that online search control
Rule difficulty becomes larger.For the disadvantage, the present invention provides a kind of new multiple dimensioned approximation method, by seeking the thinking of approximate solution,
State space carries out the gridding processing of rule, convenient to search control rate online, can also change state by setting level
Divide domain number.
On multiple dimensioned approximate explicit prediction model control method algorithm based on explicit model forecast Control Algorithm, introduce
Piecewise linearity insertion and adaptive layered function approximation method, and combine barycentric coodinates and barycentric interpolation method.Pass through segmentation
Linear interpolation carries out lattice to subspace method, describes mesh point with basic function, the in due course described point of use has just started first big
The division subspace of cause, with layering basic function again to those there are no the region of enough approximations carry out it is subdivided, it is continuous in this way
Constantly divide layer by layer, until all regions are all by approximation, finally obtain one based on layering detail index it is close
Like control law.In order to facilitate processing higher-dimension problem, and adaptive layered approximation to function method is introduced, approximate control law is suitably become
Shape obtains another form of approximation control rule, is finally introducing the method for center of gravity function and center of gravity function interpolation for pairing approximation control
Make the feasibility of rule and the proof of stability.
To be more clear the object, technical solutions and advantages of the present invention, below just to technical solution of the present invention make into
The description of one step.The multiple dimensioned approximate display model forecast Control Algorithm of disk drive system, includes the following steps:
Step 1) establishes disk drive system model；
Main physical quantity is torque T in disk control system, electric current I, and rotational speed omega etc. is mainly studied between this three
Internal relation.Pass through given parameter such as armature inductance L, motor carry-over factor Km, armature resistance R, amplifier gain ka, rub
Coefficient f is wiped, arm and magnetic head rotary inertia J etc. obtain following formula:
KmI=T (2)
Only consider interference are as follows: D=V1x1+V2x2+ b obtains the control structure model of disk drive system are as follows:
For the second-order model, design when, will make disk operate in resonant frequency as much as possible, to enhance system
Stability, is embodied in the settling position that is just desirable to state variable in state finally and can tend to default i.e. zero is attached
Closely.Therefore, the constraint condition of design point variable X here are as follows: Xmax=-Xmin=[0.6,0.6]T, while output variable Y is set
Constraint condition are as follows: Ymax=-Ymin=[0.6,0.6]T, design the constraint condition of input variable U are as follows: Umax=-Umin=
0.1, setting prediction step is 10.Performance index function is as follows:
S.t x (τ+1)=A (τ) x (τ)+B (τ) u (τ) τ=t ..., t+T-1 (6)
umin≤u(τ)≤umax
xmin≤x(τ)≤xmax
Wherein Q is state weight matrix, and R is weighted input matrix, QfinalIt is SOT state of termination weight, u is input vector, x
For state vector, T is the sampling time；Based on the above performance indicator and system state space expression formula, it is handled and is counted
It calculates；Then by disk drive system performance index function J*It is converted, converts thereof into a Parametric optimization problem u*(x), this
A Parametric optimization problem is exactly the object of last desired approximation.
After obtaining disk drive system performance index function J, using piecewise linearity insertion by disk drive system index
The corresponding polyhedral subspace method of function J is divided, and introduces adaptive layered function, to the approximation control obtained
Rule has carried out deformation appropriate, here it is having carried out the division of height rule to control law corresponding to Condition Areas, while again
Approximation has been carried out, and has met system feasibility and stability.
The processing of step 2) piecewise linear interpolation；
The cell cube Ω tieed up with dd=[0,1]dInstead of subspace method χ, function u (x): R is consideredd→ R, x=
(x1,...,xd), use ΩdIn point come to cell cube carry out lattice.It allows l as level of discretization, uses hl=2-lTo indicate
Sizing grid.This d rectangular mesh tieed up is set to Ωl。ΩlOn mesh point be represented as
Here i indicates Ω with multiple indexeslOn point coordinate.
It selects one-dimensional cap function phi (x) and converts and derive to describe mesh point, φ (x) is converted to a segmentation
D Wiki function:
Basic function φl,i(x) it is used to the SPACE V of building segmentation d dimension functionl d, this segmentation d dimension function is:
Vl d:=span { φl,i: 0≤i≤2l} (9)
Each multi-variable function ul(x)∈Vl dIt can be expressed as unique φl,i(x) weighted sum:
Vl dIt can be described as being segmented d dimensional linear functionD dimension hierarchical function space sum, then it is each is changeable
Flow function ul(x)∈Vl dWrite as a weighted sum:
Here wk,iReferred to as it is layered detail index.By defining ψk,i=φk,i(x), i ∈ Ik, and write as:
The approximation control rule based on layering detail index is obtained.It is to sum up exactly using above-mentioned mathematical method, first
In due course described point is carried out, rough subspace is divided, it is then still subdivided without the region progress of enough approximations to those again,
It continuously divides layer by layer in this way, until all regions are all by approximation.
Step 3) quotes adaptive layered approximation to function method, and approximate control law is become another form；
Introduce adaptive layered approximation to function method.Consider function u (x) ∈ R, x:=(x1,...,xd)∈Ωd, set first
One rough primary grid coefficient l0>=0, for l0Mesh point, store relevant functional valueThen mesh point obtains
Continuous processing has been arrived until desired horizontal lmax.In each step, those parts for being unsatisfactory for particular requirement will be obtained more
Fine processing.For the mesh point in k level newly obtained, functional value is not u (xk), but in horizontal k-1
The difference of functional value is:
This difference can be stored, wk,iReferred to as it is layered detail.It can be nearly by adaptive layered approximation to function method
It is indicated depending on control law are as follows:
Λ is the set of relevant level index.By the property of hereinbefore involved basic function, this is approximately to connect
Continuous.
Step 4) introduce the method for center of gravity function and barycentric interpolation for pairing approximation control law feasibility and stability into
Line justification；
3.1, for setHere conv (R) is convex set, and extr (R) is pole, introduces barycentric coodinates function fv
(x), wherein x ∈ S, v ∈ extr (S),
fv(x) >=0 positive value (15)
A function is inserted on a grid, according to the property of barycentric coodinates function, the functional value only on vertex is used
To carry out interpolation arithmetic.What adaptive layered approximation to function method obtained is some hypermatrix, these hypermatrix are by interpolation operation
It limits.Because hypermatrix is convex polytope, approximation control rule ensures that feasibility, stability and performance range.
3.2, by approximate closed-loop systemLiapunov function verify the feasible of these regions
Property, stability and performance range.Approximation control rule has been obtained in hierarchical function in step 2 described above, then to every
One hypermatrix region R ∈ Rh,It can be write as the form obtained with center of gravity function interpolation:
For problemAnd if only ifTo be with all v ∈ extr (R) it is feasible, that
Approximation control ruleIt is exactly a feasible solution of optimal problem (2-1).
If be defined onGravity's center control rule aboveAll be to all v ∈ extr (R) it is feasible, then:
For set R*:={ x ∈ R:R ∈ Rh, err (R) >=0 }, approximate functionIt is a Liapunov letter
Number.If R*This region is constrained, then from(R*Boundary) and Jmin(OnMinimum value)
Find out setIt is restrained in approximation controlUnder it is constant, so control law is stable.
The multiple dimensioned approximate explicit model PREDICTIVE CONTROL of step 5) disk drive system；
The multiple dimensioned explicit model PREDICTIVE CONTROL course of work of disk drive system is divided into two parts；When off-line calculation, press
According to disk drive system Control performance standard, using above-mentioned steps 1)-step 4) establish disk drive system state region it is convex
It divides, is drawn the corresponding polyhedral subspace method of disk drive system target function J using piecewise linearity insertion
Point, and adaptive layered function is introduced again, deformation appropriate has been carried out to the approximation control rule obtained；In line computation,
Rotational speed omega when by measurement disk operation, the physical quantitys such as electric current I and torque T, then by given parameters to find out disk current
State in which, and which subregion of state be in by determining current time system of tabling look-up, and according on the subregion most
Excellent control law calculates the optimum control amount at current time.After disk drive system, which is powered, to be worked normally, using in control circuit
Single-chip microcontroller initialized, magnetic head is placed in disc center at this time.Spindle motor will start and with height after the completion of initialization
Floating magnetic head, is then placed in the initial magnetic track of disc surface, constantly transmits information and instruction by control circuit by speed rotation,
Information therein just includes the good control law of off-line calculation, finally disk drive system is allowed to operate normally.
The invention has the following advantages that
1. the present invention solves, original disk drive explicit model forecast Control Algorithm complexity is too high, real-time is insufficient
Problem by obtaining disk drive explicit model approximation control rule, and changes original storage in the storage of Condition Areas
Mode brings great convenience to online search procedure using very regular coarse gridding.
2. this method is applied in disk drive control problem by the present invention, the real-time of disk drive control is substantially increased
Property, reduce the demand of controller memory capacity, save in the line computation time, and possesses good control effect.
3. the present invention passes through disk drive using multiple dimensioned thought for the actual requirement of magnetic disk drve control system
Compromise between control performance, control complexity, realtime control and controller capacity meets disk drive control system
Various controls of uniting require and performance constraints.
Detailed description of the invention
Fig. 1 is disk drive system hardware structure diagram
Fig. 2 is disk drive system control structure block diagram
Fig. 3 is multiple dimensioned approximate explicit model PREDICTIVE CONTROL flow chart
Fig. 4 is the Condition Areas that accurate explicit model PREDICTIVE CONTROL obtains
Fig. 5 is the Condition Areas that the multiple dimensioned approximation method that maximum level is 6 obtains
Fig. 6 is the Condition Areas that the multiple dimensioned approximation method that maximum level is 7 obtains
Fig. 7 is the Condition Areas that the multiple dimensioned approximation method that maximum level is 8 obtains
Fig. 8 is the state change trajectory diagram that exact method obtains
Fig. 9 is the state change rule figure that multiple dimensioned approximation method obtains
The control sequence figure that Figure 10 exact method obtains
Figure 11 is the control sequence figure that multiple dimensioned approximation method obtains
Specific embodiment
The present invention will be further described below with reference to the accompanying drawings:
Multiple dimensioned approximate explicit model of the invention predicts disk drive optimal control method, is as shown in Figure 1 application pair
As for disk drive system hardware, Fig. 2 is disk drive system Control system architecture block diagram, while specifically includes the following steps:
Step 1) establishes disk drive system model；
Main physical quantity is torque T in disk control system, electric current I, and rotational speed omega etc. is mainly studied between this three
Internal relation.Pass through given parameter such as armature inductance L, motor carry-over factor Km, armature resistance R, amplifier gain ka, rub
Coefficient f is wiped, arm and magnetic head rotary inertia J etc. obtain following formula:
KmI=T (2)
Only consider interference are as follows: D=V1x1+V2x2+ b obtains the control structure model of disk drive system are as follows:
For the second-order model, design when, will make disk operate in resonant frequency as much as possible, to enhance system
Stability, is embodied in the settling position that is just desirable to state variable in state finally and can tend to default i.e. zero is attached
Closely.Therefore, the constraint condition of design point variable X here are as follows: Xmax=-Xmin=[0.6,0.6]T, while output variable Y is set
Constraint condition are as follows: Ymax=-Ymin=[0.6,0.6]T, design the constraint condition of input variable U are as follows: Umax=-Umin=
0.1, setting prediction step is 10.Performance index function is as follows:
S.t x (τ+1)=A (τ) x (τ)+B (τ) u (τ) τ=t ..., t+T-1 (6)
umin≤u(τ)≤umax
xmin≤x(τ)≤xmax
Wherein Q is state weight matrix, and R is weighted input matrix, QfinalIt is SOT state of termination weight, u is input vector, x
For state vector, T is the sampling time；Based on the above performance indicator and system state space expression formula, it is handled and is counted
It calculates；Then by disk drive system performance index function J*It is converted, converts thereof into a Parametric optimization problem u*(x), this
A Parametric optimization problem is exactly the object of last desired approximation.
After obtaining disk drive system performance index function J, using piecewise linearity insertion by disk drive system index
The corresponding polyhedral subspace method of function J is divided, and introduces adaptive layered function, to the approximation control obtained
Rule has carried out deformation appropriate, here it is having carried out the division of height rule to control law corresponding to Condition Areas, while again
Approximation has been carried out, and has met system feasibility and stability.
The processing of step 2) piecewise linear interpolation；
The cell cube Ω tieed up with dd=[0,1]dInstead of subspace method χ, function u (x): R is consideredd→ R, x=
(x1,...,xd), use ΩdIn point come to cell cube carry out lattice.It allows l as level of discretization, uses hl=2-lTo indicate
Sizing grid.This d rectangular mesh tieed up is set to Ωl。ΩlOn mesh point be represented as
Here i indicates Ω with multiple indexeslOn point coordinate.
It selects one-dimensional cap function phi (x) and converts and derive to describe mesh point, φ (x) is converted to a segmentation
D Wiki function:
Basic function φl,i(x) it is used to the SPACE V of building segmentation d dimension functionl d, this segmentation d dimension function is:
Vl d:=span { φl,i: 0≤i≤2l} (9)
Each multi-variable function ul(x)∈Vl dIt can be expressed as unique φl,i(x) weighted sum:
Vl dIt can be described as being segmented d dimensional linear functionD dimension hierarchical function space sum, then it is each is changeable
Flow function ul(x)∈Vl dWrite as a weighted sum:
Here wk,iReferred to as it is layered detail index.By defining ψk,i=φk,i(x), i ∈ Ik, and write as:
The approximation control rule based on layering detail index is obtained.It is to sum up exactly using above-mentioned mathematical method, first
In due course described point is carried out, rough subspace is divided, it is then still subdivided without the region progress of enough approximations to those again,
It continuously divides layer by layer in this way, until all regions are all by approximation.
Step 3) quotes adaptive layered approximation to function method, and approximate control law is become another form；
Introduce adaptive layered approximation to function method.Consider function u (x) ∈ R, x:=(x1,...,xd)∈Ωd, set first
One rough primary grid coefficient l0>=0, for l0Mesh point, store relevant functional value u (xl0), then mesh point obtains
Continuous processing has been arrived until desired horizontal lmax.In each step, those parts for being unsatisfactory for particular requirement will be obtained more
Fine processing.For the mesh point in k level newly obtained, functional value is not u (xk), but in horizontal k-1
The difference of functional value is:
This difference can be stored, wk,iReferred to as it is layered detail.It can be nearly by adaptive layered approximation to function method
It is indicated depending on control law are as follows:
Λ is the set of relevant level index.By the property of hereinbefore involved basic function, this is approximately to connect
Continuous.
Step 4) introduce the method for center of gravity function and barycentric interpolation for pairing approximation control law feasibility and stability into
Line justification；
3.1, for setHere conv (R) is convex set, and extr (R) is pole, introduces barycentric coodinates function fv
(x), wherein x ∈ S, v ∈ extr (S),
fv(x) >=0 positive value (15)
A function is inserted on a grid, according to the property of barycentric coodinates function, the functional value only on vertex is used
To carry out interpolation arithmetic.What adaptive layered approximation to function method obtained is some hypermatrix, these hypermatrix are by interpolation operation
It limits.Because hypermatrix is convex polytope, approximation control rule ensures that feasibility, stability and performance range.
3.2, by approximate closed-loop systemLiapunov function verify the feasible of these regions
Property, stability and performance range.Approximation control rule has been obtained in hierarchical function in step 2 described above, then to every
One hypermatrix region R ∈ Rh,It can be write as the form obtained with center of gravity function interpolation:
For problemAnd if only ifTo be with all v ∈ extr (R) it is feasible, that
Approximation control ruleIt is exactly a feasible solution of optimal problem (2-1).
If be defined onGravity's center control rule aboveAll be to all v ∈ extr (R) it is feasible, then:
For set R*:={ x ∈ R:R ∈ Rh, err (R) >=0 }, approximate functionIt is a Liapunov letter
Number.If R*This region is constrained, then from(R*Boundary) and Jmin(OnMinimum value)
Find out setIt is restrained in approximation controlUnder it is constant, so control law is stable.Entirely
Process is as shown in Figure 3.
The multiple dimensioned approximate explicit model PREDICTIVE CONTROL of step 5) disk drive system；
The multiple dimensioned explicit model PREDICTIVE CONTROL course of work of disk drive system is divided into two parts；When off-line calculation, press
According to disk drive system Control performance standard, using above-mentioned steps 1)-step 4) establish disk drive system state region it is convex
It divides, is drawn the corresponding polyhedral subspace method of disk drive system target function J using piecewise linearity insertion
Point, and adaptive layered function is introduced again, deformation appropriate has been carried out to the approximation control rule obtained；In line computation,
Rotational speed omega when by measurement disk operation, the physical quantitys such as electric current I and torque T, then by given parameters to find out disk current
State in which, and which subregion of state be in by determining current time system of tabling look-up, and according on the subregion most
Excellent control law calculates the optimum control amount at current time.After disk drive system, which is powered, to be worked normally, using in control circuit
Single-chip microcontroller initialized, magnetic head is placed in disc center at this time.Spindle motor will start and with height after the completion of initialization
Floating magnetic head, is then placed in the initial magnetic track of disc surface, constantly transmits information and instruction by control circuit by speed rotation,
Information therein just includes the good control law of off-line calculation, finally disk drive system is allowed to operate normally.
Analysis of cases
The present invention presents the pre- observing and controlling of multiple dimensioned explicit model by carrying out emulation experiment by object of disk drive system
Method processed specifically shows in disk drive system, by contrast and experiment, embodies superior function of the invention.
It is calculated with accurate EMPC, step-length 10, Condition Areas is as shown in figure 4, region sum is 347.In identical item
Under part, error coefficient is set as ε=0.5, and step-length 10, the Condition Areas that multiple dimensioned approximation explicit model PREDICTIVE CONTROL obtains is as schemed
Shown in 5,6,7, their level is respectively 6,7,8.By emulation it can be found that maximum level is less than when error coefficient is 0.5
When equal to 7, the Condition Areas of the disk drive system obtained with the multiple dimensioned approximation method of explicit model PREDICTIVE CONTROL is few
In 347 subregions, respectively 322,226,88,40,16,4.It can significantly be obtained from the result that comparison obtains, for
It is pre- with explicit model when for 0.5, maximum level is less than or equal to 7 to selection error coefficient for disk drive system
The Condition Areas that observing and controlling system obtains scale approximation method is fewer than the subregion obtained with explicit model forecast Control Algorithm, institute
It can be reduced with the space complexity after off-line calculation, along with being stored with the grid of height rule, be looked into online in this way
The efficiency looked for can greatly improve.
When to one original state x of system0=[- 0.5,0.5]T, the state change of system is obtained with two different methods
Track, Fig. 8 are the state change tracks that exact method obtains, Fig. 9 is that the multiple dimensioned approximation method of explicit model PREDICTIVE CONTROL is maximum
The state change track that level is 7.Abscissa indicates step-length, and ordinate indicates state, and the line of two different colours respectively indicates
Two different states of disk drive system.Two methods have finally all reached stable state, and the comparison from two width figures can
The state change of system is relatively gentle when using exact method out, and the speed for reaching stable state is slower, with explicit mould
When the multiple dimensioned approximation method of type PREDICTIVE CONTROL, the variation steeper of system mode reaches the fast speed of stable state.
It is x in primary condition0=[- 0.5,0.5]TWhen, the control sequence obtained with two different methods, Figure 10 is essence
The control sequence that true method obtains.The control sequence obtained with multiple dimensioned approximation method is as shown in figure 11.Their changing rule and
State trajectory is similar, by comparison it can be seen that reaching stable speed faster with multiple dimensioned approximate explicit model PREDICTIVE CONTROL.
By a series of comparison and analysis shows, control for disk drive system, explicit model PREDICTIVE CONTROL is more
Scale approximation method is better than explicit model forecast Control Algorithm.
Content described in this specification embodiment is only enumerating to the way of realization of inventive concept, protection of the invention
Range should not be construed as being limited to the specific forms stated in the embodiments, and protection scope of the present invention is also and in art technology
Personnel conceive according to the present invention it is conceivable that equivalent technologies mean.
Claims (1)
1. a kind of multiple dimensioned approximate explicit model forecast Control Algorithm of disk drive comprising the steps of:
Step 1) establishes disk drive system model；
Main physical quantity is torque T in disk control system, electric current I, and rotational speed omega etc. is mainly studied interior between this three
In relationship；Pass through given parameter such as armature inductance L, motor carry-over factor Km, armature resistance R, amplifier gain ka, friction system
Number f, arm and magnetic head rotary inertia J etc. obtain following formula:
KmI=T (2)
Only consider interference are as follows: D=V1x1+V2x2+ b obtains the control structure model of disk drive system are as follows:
For the second-order model, design when, will make disk operate in resonant frequency as much as possible, to enhance the stabilization of system
Property, it is embodied near the settling position that is just desirable to state variable in state finally and can tend to default i.e. zero；Cause
This, the constraint condition of design point variable X here are as follows: Xmax=-Xmin=[0.6,0.6]T, while the pact of output variable Y is set
Beam condition are as follows: Ymax=-Ymin=[0.6,0.6]T, design the constraint condition of input variable U are as follows: Umax=-Umin=0.1, if
Setting prediction step is 10；Performance index function is as follows:
Wherein Q is state weight matrix, and R is weighted input matrix, QfinalIt is SOT state of termination weight, u is input vector, and x is shape
State vector, T are the sampling time；Based on the above performance indicator and system state space expression formula, it is handled and is calculated；So
Afterwards by disk drive system performance index function J*It is converted, converts thereof into a Parametric optimization problemThis ginseng
Number optimization problem is exactly the object of last desired approximation；
After obtaining disk drive system performance index function J, using piecewise linearity insertion by disk drive system target function J
Corresponding polyhedral subspace method is divided, and introduces adaptive layered function, to the approximation control obtained restrain into
It has gone deformation appropriate, here it is having carried out the division of height rule to control law corresponding to Condition Areas, while having carried out again
Approximation, and meet system feasibility and stability；
The processing of step 2) piecewise linear interpolation；
The cell cube Ω tieed up with dd=[0,1]dInstead of subspace method χ, function u (x): R is consideredd→ R, x=(x1,...,
xd), use ΩdIn point come to cell cube carry out lattice；It allows l as level of discretization, uses hl=2-lTo indicate that grid is big
It is small；This d rectangular mesh tieed up is set to Ωl；ΩlOn mesh point be represented as
Here i indicates Ω with multiple indexeslOn point coordinate；
It selects one-dimensional cap function phi (x) and converts and derive to describe mesh point, φ (x) is converted to the d dimension of a segmentation
Basic function:
Basic function φl,i(x) it is used to the SPACE V of building segmentation d dimension functionl d, this segmentation d dimension function is:
Vl d:=span { φl,i: 0≤i≤2l} (9)
Each multi-variable function ul(x)∈Vl dIt can be expressed as unique φl,i(x) weighted sum:
Vl dIt can be described as being segmented d dimensional linear functionD dimension hierarchical function space sum, then by each multivariable letter
Number ul(x)∈Vl dWrite as a weighted sum:
Here wk,iReferred to as it is layered detail index；By defining ψk,i=φk,i(x), i ∈ Ik, and write as:
The approximation control rule based on layering detail index is obtained；It is to sum up exactly first to be carried out using above-mentioned mathematical method
In due course described point divides rough subspace, then still subdivided without the region progress of enough approximations to those again, in this way
It continuously divides layer by layer, until all regions are all by approximation；
Step 3) quotes adaptive layered approximation to function method, and approximate control law is become another form；
Introduce adaptive layered approximation to function method；Consider function u (x) ∈ R, x:=(x1,...,xd)∈Ωd, one is set first
Rough primary grid coefficient l0>=0, for l0Mesh point, store relevant functional valueThen mesh point obtains
Continuous processing is until desired horizontal lmax；In each step, those parts for being unsatisfactory for particular requirement will obtain more fine
Processing；For the mesh point in k level newly obtained, functional value is not u (xk), but it is in the function of horizontal k-1
The difference of value is:
This difference can be stored, wk,iReferred to as it is layered detail；Myopia can be controlled by adaptive layered approximation to function method
System rule indicates are as follows:
Λ is the set of relevant level index；By the property of hereinbefore involved basic function, this is approximately continuous；
Step 4) introduces feasibility and stability of the method for center of gravity function and barycentric interpolation for pairing approximation control law and is demonstrate,proved
It is bright；
3.1, for setHere conv (R) is convex set, and extr (R) is pole, introduces barycentric coodinates function fv(x),
Wherein x ∈ S, v ∈ extr (S),
fv(x) >=0 positive value (15)
A function is inserted on a grid, according to the property of barycentric coodinates function, only the functional value on vertex be used into
Row interpolation operation；What adaptive layered approximation to function method obtained is some hypermatrix, these hypermatrix are limited by interpolation operation
's；Because hypermatrix is convex polytope, approximation control rule ensures that feasibility, stability and performance range；
3.2, by approximate closed-loop systemLiapunov function verify the feasibility in these regions,
Stability and performance range；Approximation control rule has been obtained in hierarchical function in step 2 described above, then to each
Hypermatrix region R ∈ Rh,It can be write as the form obtained with center of gravity function interpolation:
For problemAnd if only ifTo being feasible with all v ∈ extr (R), then closely
Like control lawIt is exactly a feasible solution of optimal problem (2-1)；
If be defined onGravity's center control rule aboveAll be to all v ∈ extr (R) it is feasible, then:
For set R*:={ x ∈ R:R ∈ Rh, err (R) >=0 }, approximate functionIt is a liapunov function；Such as
Fruit R*This region is constrained, then from(R*Boundary) and Jmin(OnMinimum value) can find out
SetIt is restrained in approximation controlUnder it is constant, so control law is stable；
The multiple dimensioned approximate explicit model PREDICTIVE CONTROL of step 5) disk drive system；
The multiple dimensioned explicit model PREDICTIVE CONTROL course of work of disk drive system is divided into two parts；When off-line calculation, according to magnetic
Disc driving system Control performance standard, using above-mentioned steps 1)-step 4) establishes convex stroke of state region of disk drive system
Point, the corresponding polyhedral subspace method of disk drive system target function J is divided using piecewise linearity insertion,
And adaptive layered function is introduced again, deformation appropriate has been carried out to the approximation control rule obtained；In line computation, pass through
Rotational speed omega when disk operation, the physical quantitys such as electric current I and torque T are measured, then finds out disk by given parameters and is presently in
State, and which subregion of state be in by determining current time system of tabling look-up, and according to the optimal control on the subregion
System rule calculates the optimum control amount at current time；After disk drive system, which is powered, to be worked normally, the list in control circuit is utilized
Piece machine is initialized, and magnetic head is placed in disc center at this time；Spindle motor will start and to revolve at a high speed after the completion of initialization
Turn, floating magnetic head is then placed in the initial magnetic track of disc surface, information and instruction are constantly transmitted by control circuit, wherein
Information just include the good control law of off-line calculation, finally disk drive system is allowed to operate normally.
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