CN109223093A - A kind of bone surgery subtle bone drill of pen type hand pressure - Google Patents
A kind of bone surgery subtle bone drill of pen type hand pressure Download PDFInfo
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- CN109223093A CN109223093A CN201811192040.5A CN201811192040A CN109223093A CN 109223093 A CN109223093 A CN 109223093A CN 201811192040 A CN201811192040 A CN 201811192040A CN 109223093 A CN109223093 A CN 109223093A
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- 210000000988 bone and bone Anatomy 0.000 title claims abstract description 44
- 238000001356 surgical procedure Methods 0.000 title claims abstract description 23
- 230000008878 coupling Effects 0.000 claims abstract description 15
- 238000010168 coupling process Methods 0.000 claims abstract description 15
- 238000005859 coupling reaction Methods 0.000 claims abstract description 15
- 230000033228 biological regulation Effects 0.000 claims abstract description 5
- 239000011159 matrix material Substances 0.000 claims description 45
- 238000004804 winding Methods 0.000 claims description 27
- 238000012937 correction Methods 0.000 claims description 9
- 230000006870 function Effects 0.000 claims description 8
- 230000000694 effects Effects 0.000 claims description 7
- 241001270131 Agaricus moelleri Species 0.000 claims description 6
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 claims description 3
- 238000001914 filtration Methods 0.000 claims description 3
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- 238000005070 sampling Methods 0.000 claims description 3
- 230000009466 transformation Effects 0.000 claims description 3
- 230000005611 electricity Effects 0.000 claims 1
- 230000008450 motivation Effects 0.000 claims 1
- 208000010392 Bone Fractures Diseases 0.000 description 4
- 206010017076 Fracture Diseases 0.000 description 4
- 238000004364 calculation method Methods 0.000 description 4
- 238000000034 method Methods 0.000 description 4
- 238000010586 diagram Methods 0.000 description 3
- 238000011161 development Methods 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 238000005457 optimization Methods 0.000 description 2
- 208000002565 Open Fractures Diseases 0.000 description 1
- 230000003044 adaptive effect Effects 0.000 description 1
- 238000011217 control strategy Methods 0.000 description 1
- 201000010099 disease Diseases 0.000 description 1
- 208000037265 diseases, disorders, signs and symptoms Diseases 0.000 description 1
- 230000017525 heat dissipation Effects 0.000 description 1
- 230000005389 magnetism Effects 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 230000004044 response Effects 0.000 description 1
- 230000000717 retained effect Effects 0.000 description 1
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B17/00—Surgical instruments, devices or methods
- A61B17/16—Instruments for performing osteoclasis; Drills or chisels for bones; Trepans
- A61B17/1613—Component parts
- A61B17/1626—Control means; Display units
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B17/00—Surgical instruments, devices or methods
- A61B17/16—Instruments for performing osteoclasis; Drills or chisels for bones; Trepans
- A61B17/1613—Component parts
- A61B17/1628—Motors; Power supplies
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
- H02P6/34—Modelling or simulation for control purposes
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B17/00—Surgical instruments, devices or methods
- A61B17/56—Surgical instruments or methods for treatment of bones or joints; Devices specially adapted therefor
- A61B2017/564—Methods for bone or joint treatment
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Abstract
The invention belongs to bone surgery equipment technical fields, disclose a kind of subtle bone drill of bone surgery pen type hand pressure, and the bone surgery presses subtle bone drill to be provided with shell with pen type hand；The enclosure interior is disposed with drive rod, micro-gearbox, motor and battery from front end to rear end；Drill bit is provided in front of the shell；The drill bit rear is provided with drive rod, and the front end of the drive rod passes through shaft coupling and drill bit；The drive rod is connected by shaft coupling with micro-gearbox；The micro-gearbox is connected by shaft coupling with motor；The hull outside is provided with motor switch and speed regulation button, and front end screw is fixed with fixed frame.The present invention realizes the function that subtle bone drill adjusts the speed when in use；Motor switch is arranged in index finger location, facilitates operation, while the configuration of the present invention is simple, firm in structure, easy to operate.
Description
Technical field
The invention belongs to bone surgery equipment technical fields more particularly to a kind of bone surgery pen type hand to press subtle bone
It bores.
Background technique
Currently, children's open fracture be mostly caused by high-energy external force, such as not in time processing can cause it is serious concurrent
Disease and development sequelae.Adult is mostly used to be performed the operation in traditional children's fracture operation with surgical instrument, however adult operation
Instrument haves the shortcomings that volume is big, weight is big, is not suitable with the needs of the tiny fracture operation of children, can perform the operation to medical worker
Certain inconvenience is caused in operation；Also, traditional bone drill does not have speed-regulating function, there is biggish limitation when in use
Property.
Brushless direct current motor is one to get up with the development of power electronic technique and microelectric technique in modern age
The novel variable-speed motor of kind, rotor is permanent magnetism, and there are many prominent advantages compared with other type motors.With AC electrical
Machine is compared, and has the characteristics that small in size, light-weight, high-efficient, rotary inertia is small, control is relatively easy；With dc motor phase
Than without mechanical commutator, when commutation does not generate spark, reliable for operation, is not limited, can be accomplished big by mechanical commutation condition
Capacity, high revolving speed, therefore, brushless direct current motor had both had simple, reliable for operation, easy to maintain excellent of AC motor structure
Point, while the excellent mechanical property of dc motor is also retained, it is widely used in SERVO CONTROL, numerically-controlled machine tool, robot, family
The fields such as electrical appliance.
With the continuous expansion of brushless direct current motor application field, its speed-regulating system is required to have in many applications
Quick dynamic response, higher stable state accuracy and stronger anti-interference ability.Due to pid control algorithm is simple, precision is higher,
It is highly reliable, it is most widely used and most mature control method in X in brushless DC motor control at present, but PID is controlled
Device parameter optimization processed is difficult, anti-interference ability is weak, poor to the adaptability of load.
In conclusion problem of the existing technology is:Traditional bone drill haves the shortcomings that volume is big, weight is big, no
The needs for adapting to the tiny fracture operation of children, can cause certain inconvenience to medical worker on surgical procedure；Also, it passes
The bone drill of system does not have speed-regulating function, there is biggish limitation when in use；
Existing brushless direct current motor parameter optimization is difficult, anti-interference ability is weak, poor to the adaptability of load.
Summary of the invention
In view of the problems of the existing technology, the present invention provides a kind of bone surgery pen type hands to press subtle bone drill.
The invention is realized in this way a kind of bone surgery presses subtle bone drill, the bone surgery pen type with pen type hand
Hand presses subtle bone drill to be provided with shell；
Enclosure interior is disposed with drive rod, micro-gearbox, motor and battery from front end to rear end；Before shell
Side is provided with drill bit；Drill bit rear is connect by shaft coupling with drive rod；Drive rod is connected by shaft coupling with micro-gearbox；
Micro-gearbox is connected by shaft coupling with motor；Hull outside is provided with motor switch and speed regulation button, housing forward end
Screw is fixed with fixed frame.
Further, housing side offers heat release hole, convenient for heat dissipation, prevents internal temperature is excessively high from damaging.
Further, motor uses brushless direct current motor, and brushless direct current motor uses Optimal state-feedback strategy, answers
For Speed Regulating System of Brushless DC Motor, to obtain preferable speed adjusting performance.
Further, brushless direct current motor work is conducted under 6 condition mode of star three-phase two, and no middle line is drawn, instead
EMF waveform is the trapezoidal wave that flat-top width is 120 ° of electrical angles, and magnetic circuit is unsaturated during the work time for motor, disregards vortex
And magnetic hystersis loss, three-phase windings are full symmetric, then the voltage equation of three-phase windings is
In formula: ua、ub、ucIt is stator phase winding voltage, V；
ia、ib、icIt is stator phase winding electric current, A；
ea、eb、ecIt is stator phase winding counter electromotive force, V；
R is the resistance of stator phase winding, Ω；
L is the self-induction of every phase winding, H；
M is mutual inductance between every two phase winding, H；
D is differential operator (D=d/dt)；
Since three-phase windings are star-like connection and no middle line, then have:
ia+ib+ic=0 (2)
Formula (1) abbreviation can be by joint type (1), (2)
Electromagnetic torque equation is
In formula: Te is electromagnetic torque, Nm；ω is motor rotor machinery angular speed, rad/s；
Mechanical motion equation is
In formula: TLFor load torque, Nm；J is motor rotary inertia, kgm2；
Ideal commutation situation, each moment only have two to be conducted, and electric current enters from one phase flow, flow out from another phase, then by formula
(3) it can obtain:
U=2ri+2 (L-M) di/dt+2ep (6)
In formula: u is the branch voltage that two-phase is connected, V；I is the branch current that two-phase is connected, A；Ep is the opposite of conducting phase
Electromotive force, V；
It can be obtained by formula (4):
Te=2epi/ω (7)
Since back emf waveform is the trapezoidal wave that flat-top width is 120 ° of electrical angles, when being often conducted, counter electromotive force
It is always in plateau region, then is had:
ep=Keω (8)
Ke is power coefficient, V/ (rad/s) in formula；
Formula (5)~(8) progress Laplace transformation can be obtained:
Load torque TLIt regards a kind of interference as, according to no-load condition, can be obtained by formula (9):
ByIt can obtain:
N is motor speed (r/min) in formula；
Formula (11) are substituted into formula (10) and are arranged:
In formula:
If d1、d2For s2Unequal of 2 of+bs+c=0, keep link according to zeroth order, carry out transform to formula (12)
:
In formula:
T is sampling period, s；
Take state x1(k)=n (k), x2(k)=x1(k+1)-Au (k), then formula (13) can be written as following state space side
Formula:
For brushless direct current motor, G, H, C are constant matrices in formula (14), C=[1 0].
Further, in order to realize the optimum feedback control of brushless direct current motor, need to know the state vector x of system
(k), however due to brushless direct current motor often in the disturbance of various random disturbances and noise under, therefore need to seek state
Estimated value x^ (k), and make it as far as possible close to its true value x (k), can use Kalman filter and carry out state estimation；
According to formula (14), the state space equation of the brushless direct current motor equipped with random disturbances and noise is
In formula: ξ (k) is dynamic noise vector；ε (k) be measure noise, if its be all irrelevant mean value be zero it is white
Noise sequence, then the state estimation equation of Kalman filter be
In formula: x^ (k) is state estimation；X (k) is state forecast value；K (k) is correction matrix；G, H, C are known
State outputs and inputs permanent matrix；The correction matrix K (k) of Kalman filter can be calculated by formula (17):
In formula: P (k) is the covariance matrix of evaluated error [x (k)-x^ (k)]；For prediction errorCovariance matrix；Q is the variance matrix of the positive semidefinite of ξ (k)；R is the variance of the positive definite of ε (k)
Matrix；Due toK (k), P (k) are unrelated with state, can with off-line calculation, according to the initial value of Q, R matrix and P (0) of selection,
According to formula (17) after successive ignition calculates, the steady-state value of the correction matrix K (k) of Kalman filter can get；
The effect of optimum feedback control is exactly that objective function is made to reach minimum value, that is, is had:
In formula: V (k)=diag { vi, k } be state x (k) the symmetrical weight matrix of positive semidefinite；W (k-1)=diag { wi, k-1 }
For the symmetrical weight matrix of positive definite for inputting u (k)；
It is planned using dynamic optimal, objective function J () can be made for minimum, and optimum control effect u can be exported*.It is dynamic
State optimum programming can be indicated with the formula of one group of solution by recursion formula:
u*(N-k)=- Λ (N-k+1) Gx (N-k) (19)
Λ (N-k+1)=[HTV0(N-k+1)H+
W(N-k)]-1HTV0(N-k+1) (21)
In formula: k=1 ..., N；- Λ (N-k+1) G is known as Optimal Feedback gain matrix；Referred to as loss matrix；V0(N-k
+ 1) the calculating gained matrix to be determined by formula (20)；For a stational system, G, H are permanent matrix in above-mentioned formula, such as nothing
Special requirement, V, W also do not become generally with markers k, therefore can use formula (20)~(22) and carry out off-line calculation.Selection is appropriate
Weight matrix V, W, and enableΛ (N-k+1) can be made finally to tend to a steady-state value through successive ignition.Enable L=- Λ
G, and using Kalman filtering state estimation as a result, then the control amount of optimal state feed-back control is
Advantages of the present invention and good effect are as follows: the present invention devises subtle bone by using the characteristics of children's skeletal size
The needs for more adapting to the tiny fracture operation of children are bored, it is greatly convenient to bring on surgical procedure to medical worker；Pass through
Increase micro-gearbox, realizes speed-regulating function and it is made to adapt to more occasions.
The present invention derives the state-space model of brushless direct current motor, using the state estimation of Kalman filter,
It proposes a kind of optimal state feed-back control strategy based on Dynamic Programming, a kind of adaptive control algorithm is given, for compensating
Input signal is disturbed and the deviation that generates, so that motor is had preferable speed adjusting performance, to meet the height in bone surgery
Required precision.
Detailed description of the invention
Fig. 1 is that bone surgery pen type hand provided in an embodiment of the present invention presses subtle bone drill structural schematic diagram；
Fig. 2 is that bone surgery pen type hand provided in an embodiment of the present invention presses subtle bone drill bit, drive rod connection structure
Schematic diagram；
Fig. 3 is Speed Regulating System of Brushless DC Motor structural schematic diagram provided in an embodiment of the present invention；
In figure: 1, shell；2, drill bit；3, drive rod；4, micro-gearbox；5, motor；6, battery；7, shaft coupling；
8, fixed frame；9, button is adjusted the speed；10, motor switch.
Specific embodiment
In order to further understand the content, features and effects of the present invention, the following examples are hereby given, and cooperate attached drawing
Detailed description are as follows.
Structure of the invention is explained in detail with reference to the accompanying drawing.
As depicted in figs. 1 and 2, it includes: shell that bone surgery pen type hand provided in an embodiment of the present invention, which presses subtle bone drill,
1, drill bit 2, drive rod 3, micro-gearbox 4, motor 5, battery 6, shaft coupling 7, fixed frame 8, speed regulation button 9, motor
Switch 10.
Drive rod 3, micro-gearbox 4, motor 5 and battery 6 are disposed with inside shell 1 from front end to rear end；
Drill bit 2 is provided in front of shell；2 rear of drill bit is provided with drive rod 3, and the front end of drive rod 3 passes through shaft coupling 7 and drill bit 2；It passes
Lever is connected by shaft coupling 7 with micro-gearbox 4；Micro-gearbox 4 is connected by shaft coupling 7 with motor 5；Hull outside
It is provided with motor switch 10 and speed regulation button 11, front end screw is fixed with fixed frame.1 side of shell offers heat release hole.
Motor 5 uses brushless direct current motor, and brushless direct current motor uses Optimal state-feedback strategy, is applied to nothing
Brush DC motor speed-regulating system, to obtain preferable speed adjusting performance.
Brushless direct current motor work is conducted under 6 condition mode of star three-phase two, and no middle line is drawn, counter electromotive force wave
Shape is the trapezoidal wave that flat-top width is 120 ° of electrical angles, and magnetic circuit is unsaturated during the work time for motor, disregards vortex and magnetic hysteresis damage
Consumption, three-phase windings are full symmetric, then the voltage equation of three-phase windings is
In formula: ua、ub、ucIt is stator phase winding voltage, V；
ia、ib、icIt is stator phase winding electric current, A；
ea、eb、ecIt is stator phase winding counter electromotive force, V；
R is the resistance of stator phase winding, Ω；
L is the self-induction of every phase winding, H；
M is mutual inductance between every two phase winding, H；
D is differential operator (D=d/dt)；
Since three-phase windings are star-like connection and no middle line, then have:
ia+ib+ic=0 (2)
Formula (1) abbreviation can be by joint type (1), (2)
Electromagnetic torque equation is
In formula: Te is electromagnetic torque, Nm；ω is motor rotor machinery angular speed, rad/s；
Mechanical motion equation is
In formula: TLFor load torque, Nm；J is motor rotary inertia, kgm2；
Ideal commutation situation, each moment only have two to be conducted, and electric current enters from one phase flow, flow out from another phase, then by formula
(3) it can obtain:
U=2ri+2 (L-M) di/dt+2ep (6)
In formula: u is the branch voltage that two-phase is connected, V；I is the branch current that two-phase is connected, A；Ep is the opposite of conducting phase
Electromotive force, V；
It can be obtained by formula (4):
Te=2epi/ω (7)
Since back emf waveform is the trapezoidal wave that flat-top width is 120 ° of electrical angles, when being often conducted, counter electromotive force
It is always in plateau region, then is had:
ep=Keω (8)
Ke is power coefficient, V/ (rad/s) in formula；
Formula (5)~(8) progress Laplace transformation can be obtained:
Load torque TLIt regards a kind of interference as, according to no-load condition, can be obtained by formula (9):
ByIt can obtain:
N is motor speed (r/min) in formula；
Formula (11) are substituted into formula (10) and are arranged:
In formula:
If d1、d2For s2Unequal of 2 of+bs+c=0, keep link according to zeroth order, carry out transform to formula (12)
:
In formula:
T is sampling period, s；
Take state x1(k)=n (k), x2(k)=x1(k+1)-Au (k), then formula (13) can be written as following state space side
Formula:
For brushless direct current motor, G, H, C are constant matrices in formula (14), C=[1 0].
In order to realize the optimum feedback control of brushless direct current motor, need to know the state vector x (k) of system, however
Due to brushless direct current motor often in the disturbance of various random disturbances and noise under, therefore need to seek the estimated value of state
X^ (k), and it is made close to its true value x (k), to can use Kalman filter as far as possible and carry out state estimation；
According to formula (14), the state space equation of the brushless direct current motor equipped with random disturbances and noise is
In formula: ξ (k) is dynamic noise vector；ε (k) be measure noise, if its be all irrelevant mean value be zero it is white
Noise sequence, then the state estimation equation of Kalman filter be
In formula: x^ (k) is state estimation；X (k) is state forecast value；K (k) is correction matrix；G, H, C are known
State outputs and inputs permanent matrix；The correction matrix K (k) of Kalman filter can be calculated by formula (17):
In formula: P (k) is the covariance matrix of evaluated error [x (k)-x^ (k)]；For prediction errorCovariance matrix；Q is the variance matrix of the positive semidefinite of ξ (k)；R is the variance of the positive definite of ε (k)
Matrix；Due toK (k), P (k) are unrelated with state, can with off-line calculation, according to the initial value of Q, R matrix and P (0) of selection,
According to formula (17) after successive ignition calculates, the steady-state value of the correction matrix K (k) of Kalman filter can get；
The effect of optimum feedback control is exactly that objective function is made to reach minimum value, that is, is had:
In formula: V (k)=diag { vi, k } is the symmetrical weight matrix of positive semidefinite of state x (k)；W (k-1)=diag { wi, k-
It 1 } is the symmetrical weight matrix of positive definite of input u (k)；
It is planned using dynamic optimal, objective function J () can be made for minimum, and optimum control effect u can be exported*.It is dynamic
State optimum programming can be indicated with the formula of one group of solution by recursion formula:
u*(N-k)=- Λ (N-k+1) Gx (N-k) (19)
Λ (N-k+1)=[HTV0(N-k+1)H+
W(N-k)]-1HTV0(N-k+1) (21)
In formula: k=1 ..., N；- Λ (N-k+1) G is known as Optimal Feedback gain matrix；Referred to as loss matrix；V0(N-k+
1) the calculating gained matrix to be determined by formula (20)；For a stational system, G, H are permanent matrix in above-mentioned formula, such as nothing
Special requirement, V, W also do not become generally with markers k, therefore can use formula (20)~(22) and carry out off-line calculation.Selection is appropriate
Weight matrix V, W, and enableΛ (N-k+1) can be made finally to tend to a steady-state value through successive ignition.Enable L=- Λ
G, and using Kalman filtering state estimation as a result, then the control amount of optimal state feed-back control is
In use, bone surgery presses subtle bone drill with pen type hand, and battery 6 is fully charged, drill bit alignment is needed to punch
Position, press motor switch 10, motor 5 starts turning, and drives drill bit 2 to rotate by shaft coupling 7, to drill；When
Different speed is needed, motor switch 10 is unclamped, stops operating to motor 5.Fast button 11 is clicked, is adjusted the speed, is being pressed
Motor switch 10 is pressed, can be used continuously to the rotation of motor 5.
The above is only the preferred embodiments of the present invention, and is not intended to limit the present invention in any form,
Any simple modification made to the above embodiment according to the technical essence of the invention, equivalent variations and modification, belong to
In the range of technical solution of the present invention.
Claims (5)
1. a kind of bone surgery presses subtle bone drill with pen type hand, which is characterized in that the bone surgery presses subtle bone with pen type hand
It is drilled with and is equipped with shell；
Enclosure interior is disposed with drive rod, micro-gearbox, motor and battery from front end to rear end；It is set in front of shell
It is equipped with drill bit；Drill bit rear is connect by shaft coupling with drive rod；Drive rod is connected by shaft coupling with micro-gearbox；It is miniature
Gearbox is connected by shaft coupling with motor；Hull outside is provided with motor switch and speed regulation button, housing forward end screw
It is fixed with fixed frame.
2. bone surgery as described in claim 1 presses subtle bone drill with pen type hand, which is characterized in that housing side offers scattered
Hot hole.
3. bone surgery as described in claim 1 presses subtle bone drill with pen type hand, which is characterized in that motor is using brushless straight
Galvanic electricity motivation, brushless direct current motor use Optimal state-feedback strategy, are applied to Speed Regulating System of Brushless DC Motor.
4. bone surgery as claimed in claim 3 presses subtle bone drill with pen type hand, which is characterized in that brushless direct current motor work
Work is conducted under 6 condition mode of star three-phase two, and no middle line is drawn, and back emf waveform is that flat-top width is 120 ° of electrical angles
Trapezoidal wave, magnetic circuit is unsaturated during the work time for motor, disregards vortex and magnetic hystersis loss, and three-phase windings are full symmetric, then three
The voltage equation of phase winding is
In formula: ua、ub、ucIt is stator phase winding voltage, V；
ia、ib、icIt is stator phase winding electric current, A；
ea、eb、ecIt is stator phase winding counter electromotive force, V；
R is the resistance of stator phase winding, Ω；
L is the self-induction of every phase winding, H；
M is mutual inductance between every two phase winding, H；
D is differential operator (D=d/dt)；
Since three-phase windings are star-like connection and no middle line, then have:
ia+ib+ic=0 (2)
Formula (1) abbreviation can be by joint type (1), (2)
Electromagnetic torque equation is
In formula: Te is electromagnetic torque, Nm；ω is motor rotor machinery angular speed, rad/s；
Mechanical motion equation is
In formula: TLFor load torque, Nm；J is motor rotary inertia, kgm2；
Ideal commutation situation, each moment only have two to be conducted, and electric current enters from one phase flow, flow out from another phase, then can by formula (3)
:
U=2ri+2 (L-M) di/dt+2ep (6)
In formula: u is the branch voltage that two-phase is connected, V；I is the branch current that two-phase is connected, A；Ep is the opposite electronic of conducting phase
Gesture, V；
It can be obtained by formula (4):
Te=2epi/ω (7)
Since back emf waveform is the trapezoidal wave that flat-top width is 120 ° of electrical angles, when being often conducted, counter electromotive force is always located
In plateau region, then have:
ep=Keω (8)
Ke is power coefficient, V/ (rad/s) in formula；
Formula (5)~(8) progress Laplace transformation can be obtained:
Load torque TLIt regards a kind of interference as, according to no-load condition, can be obtained by formula (9):
ByIt can obtain:
N is motor speed (r/min) in formula；
Formula (11) are substituted into formula (10) and are arranged:
In formula:
If d1、d2For s2Unequal of 2 of+bs+c=0 keep link according to zeroth order, carry out transform to formula (12) and obtain:
In formula:
T is sampling period, s；
Take state x1(k)=n (k), x2(k)=x1(k+1)-Au (k), then formula (13) can be written as following state space equation formula:
For brushless direct current motor, G, H, C are constant matrices in formula (14), C
=[1 0].
5. bone surgery as claimed in claim 3 presses subtle bone drill with pen type hand, which is characterized in that utilize Kalman filter
State estimation is carried out to the state estimation x^ (k) of system, makes it as far as possible close to its true value x (k):
According to formula (14), the state space equation of the brushless direct current motor equipped with random disturbances and noise is
In formula: ξ (k) is dynamic noise vector；ε (k) is to measure noise, if it is all the white noise that irrelevant mean value is zero
Sequence, then the state estimation equation of Kalman filter be
In formula: x^ (k) is state estimation；X (k) is state forecast value；K (k) is correction matrix；G, H, C be known state,
Output and input permanent matrix；The correction matrix K (k) of Kalman filter can be calculated by formula (17):
In formula: P (k) is the covariance matrix of evaluated error [x (k)-x^ (k)]；For prediction errorCovariance matrix；Q is the variance matrix of the positive semidefinite of ξ (k)；R is the variance of the positive definite of ε (k)
Matrix；According to formula (17) after successive ignition calculates, the steady-state value of the correction matrix K (k) of Kalman filter can get；
The effect of optimum feedback control is exactly that objective function is made to reach minimum value, that is, is had:
In formula: V (k)=diag { vi, k } be state x (k) the symmetrical weight matrix of positive semidefinite；W (k-1)=diag { wi, k-1 } and it is defeated
Enter the symmetrical weight matrix of positive definite of u (k)；
Dynamic optimal planning can be indicated with the formula of one group of solution by recursion formula:
u*(N-k)=- Λ (N-k+1) Gx (N-k) (19)
Λ (N-k+1)=[HTV0(N-k+1)H+W(N-k)]-1HTV0(N-k+1) (21)
In formula: k=1 ..., N；- Λ (N-k+1) G is known as Optimal Feedback gain matrix；Referred to as loss matrix；V0(N-k+1) it is
Matrix obtained by the calculating determined by formula (20)；Enable L=- Λ G, and using Kalman filtering state estimation as a result, then optimal shape
The control amount of state feedback control is
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| CN110403678A (en) * | 2019-07-18 | 2019-11-05 | 朱颖妍 | A kind of automatic pricking method formula scalpel |
| CN110522493A (en) * | 2019-08-14 | 2019-12-03 | 蚌埠医学院第一附属医院 | A kind of operation of opening cranium skull milling cutter |
| CN110912471A (en) * | 2019-12-11 | 2020-03-24 | 重庆科技学院 | Intelligent controller with current protection for miniature direct current motor |
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