CN108631674B - Linear permanent magnet motor position servo system based on high-order sliding mode algorithm - Google Patents

Linear permanent magnet motor position servo system based on high-order sliding mode algorithm Download PDF

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CN108631674B
CN108631674B CN201810450065.4A CN201810450065A CN108631674B CN 108631674 B CN108631674 B CN 108631674B CN 201810450065 A CN201810450065 A CN 201810450065A CN 108631674 B CN108631674 B CN 108631674B
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multiplier
sliding mode
module
value
function module
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CN108631674A (en
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纪科辉
苏明垢
鲁文其
姚炳兴
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Zhejiang University of Technology ZJUT
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Zhejiang University of Technology ZJUT
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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
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/0007—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using sliding mode control
    • 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
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/18—Estimation of position or speed
    • 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
    • H02P6/14—Electronic commutators
    • H02P6/16—Circuit arrangements for detecting position
    • H02P6/18—Circuit arrangements for detecting position without separate position detecting elements

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  • Power Engineering (AREA)
  • Control Of Linear Motors (AREA)

Abstract

The invention provides a linear permanent magnet motor position servo system based on a high-order sliding mode algorithm, which comprises the following steps: the device comprises a sliding mode controller, a resonance suppression module, a notch filter, a low-pass filter, a current loop PI controller, a PARK conversion module, a space vector control module, an inverter, a Clark conversion module, a PARK inverse conversion module and a linear motor with a position grating ruler; because the large inertia delay link of the speed closed loop is removed, the position-current double-loop control structure is used for replacing the traditional three-loop control structure, the response speed of the system can be improved, and the dynamic performance is better. By adopting the high-order sliding mode controller, the buffeting phenomenon can be obviously weakened, the sliding mode control precision is ensured, and the dynamic characteristic and the robust performance of the system can be further improved.

Description

Linear permanent magnet motor position servo system based on high-order sliding mode algorithm
Technical Field
The invention relates to a position servo control method based on a linear permanent magnet motor, in particular to a high-performance direct drive position servo system and a method.
Background
The permanent magnet linear synchronous motor has the advantages of high power density, high thrust-volume ratio, good dynamic performance and the like, can realize direct high-speed driving, avoids the defects of insufficient reverse clearance, inertia, friction force, rigidity and the like in indirect mechanical transmission, can obtain high-speed and high-precision moving performance, has excellent stable state and dynamic performance, and is very suitable for a linear direct-drive system. With the development of intelligent equipment manufacturing and automatic control technology, a linear permanent magnet synchronous motor-based position servo system with the advantages of fast response, high accuracy, high overload capacity and the like is gradually and widely applied to direct drive equipment in industrial production as an execution component, such as the fields of numerical control machines, semiconductor production, robots, XY platform driving and the like. For a high-speed and high-precision linear position servo system, a high-performance and high-response control method is one of key technologies.
The high-performance position servo system has high requirements on the dynamic performance of system position response, the traditional position servo system is composed of three closed loops, namely a position closed loop serving as an outer loop, a speed closed loop serving as an intermediate loop and a current closed loop serving as an inner loop, the speed closed loop serving as a series link in a control structure reduces the dynamic response performance of system position adjustment, the order of the whole system is improved, and the debugging difficulty of the system is increased. The two-loop position servo without a speed closed loop link is adopted, and the large inertia delay link of the speed closed loop is omitted, so that the response speed to the position command change is higher, the dynamic performance is better, and the direct-drive type position servo motor is suitable for direct-drive position control of a permanent magnet linear servo motor. After the two-ring system is adopted, the output of the position controller is the given quantity of a current ring, the performance of a servo system can be influenced by electric parameters and external disturbance, a high-order sliding mode algorithm is introduced into the position controller of the two-ring system, and the designed sliding mode controller is insensitive to the change of the electric parameters and can inhibit load disturbance. The high-order sliding mode control algorithm is an extension of the traditional sliding mode, does not act on a discontinuous function and a first derivative of the sliding modulus, but acts on a second derivative of the sliding modulus, can obviously weaken the shaking phenomenon, and has the characteristics of simple algorithm, strong robustness and easy realization.
Accordingly, there is a need for improvements in the art.
Disclosure of Invention
The invention aims to provide an efficient linear permanent magnet motor position servo system based on a high-order sliding mode algorithm.
In order to solve the technical problem, the invention provides a linear permanent magnet motor position servo system based on a high-order sliding mode algorithm, which comprises the following steps: the device comprises a sliding mode controller, a resonance suppression module, a notch filter, a low-pass filter, a current loop PI controller, a PARK conversion module, a space vector control module, an inverter, a Clark conversion module, a PARK inverse conversion module and a linear motor with a position grating ruler;
giving a position instruction p through a host system*Sending the signal to a resonance suppression module and a first subtracter;
linear motor outputs p through position grating rulerbThe signal is sent to a first subtracter; linear motor outputs two-phase stator current iaAnd ibTo a Clark transformation module;
the resonance suppression module is used for suppressing the resonance according to a given position instruction p*(ii) a The operation results in a smoothed instruction position pfAnd the smoothed instruction position p isfSending to a second subtractor;
the first subtracter is based on a given position instruction p*And pbSignal, calculating to obtain an error signal p*-pbAnd apply the error signal p*-pbSending to a second subtractor; the first subtracter operates on the given position instruction p*Subtracting pbA signal;
the second subtractor is based on the error signal p*-pbAnd smoothed instruction position pfCalculating to obtain a position error signal sigma, and sending the position error signal sigma to the sliding mode controller; the second subtracter operates on the error signal p*-pbSubtracting instruction position pf；
The sliding mode controller calculates to obtain an output i according to the position error signal sigmamAnd will output imSending the signal to a low-pass filter;
the low-pass filter is based on the output i of the sliding mode controllermFiltered to obtain a filtered signal im *And will filter the signal im *Sending the signal to a notch filter;
the notch filter is based on the filtered signal im *Calculating to obtain a given value i of quadrature axis currentq *And the quadrature axis current is set to a given value iq *Sending to a third subtracter;
clark conversion moduleAccording to two-phase stator current iaAnd ibAnd calculating to obtain a transformed stator current iαAnd iβAnd converting the stator current iαAnd iβSending the data to a PARK inverse transformation module;
the PARK inverse transformation module is used for transforming the stator current iαAnd iβCalculating to obtain quadrature axis current feedback value iqAnd a direct axis current feedback value idAnd feeding back the quadrature axis current to the value iqSending the direct axis current feedback value i to a third subtracterdSending to a fourth subtracter;
the third subtracter is based on the given value i of quadrature axis currentq *And quadrature axis current feedback value iqObtaining the quadrature axis current error value i through calculationq *-iqAnd sending the quadrature axis current error value to a current loop PI controller; the operation method of the third subtracter is that the given value i of the quadrature axis current isq *Subtracting quadrature axis current feedback value iq；
A straight shaft current set value i is obtained through an upper systemd *Sending to a fourth subtracter;
the fourth subtracter is based on the given value i of the direct-axis currentd *And a direct axis current feedback value idObtaining a direct-axis current error value i through calculationd *-idAnd the error value i of the direct-axis currentd *-idSending the current to a current loop PI controller; the fourth subtracter adopts the operation method of setting the direct-axis current value id *Subtracting the direct axis current feedback value id；
The current loop PI controller is based on the quadrature axis current error value iq *-iqAnd the direct axis current error value id *-idCalculating to obtain quadrature axis voltage uqAnd straight axis direct pressure udAnd applying the quadrature axis voltage uqAnd straight axis direct pressure udSending to a PARK conversion module;
PARK conversion module according to quadrature axis voltage uqAnd straight axis direct pressure udAnd calculating to obtain the stator voltage component u under the two-phase static coordinate systemα、uβAnd the stator voltage component u under the two-phase static coordinate system is measuredα、uβSending the vector to a space vector control module;
the space vector control module is used for controlling the stator voltage component u according to the two-phase static coordinate systemα、uβSix paths of PWM signals are obtained through operation and are sent to the inverter; and driving the linear motor to operate through the inverter.
As an improvement of the linear permanent magnet motor position servo system based on the high-order sliding mode algorithm, the invention comprises the following steps:
the transfer function of the resonance suppression module is:
Figure GDA0003051052880000031
in the formula: kfAs a thrust constant, M is the total mass of the mover and load of the linear motor, ω0NIs the bandwidth, ξ, of the resonance suppression module0Is the damping ratio;
as a further improvement of the linear permanent magnet motor position servo system based on the high-order sliding mode algorithm, the invention comprises the following steps:
the sliding mode controller comprises a fifth subtracter, a first sign function module, a first multiplier, a first integral function module, a first absolute value evolution function module, a third multiplier, a first adder, a second integral function module, a second absolute value evolution function module, a second multiplier, a second sign function module, a first absolute value function module, a fourth multiplier, a fifth multiplier, a second adder, a sixth multiplier and a third sign function module;
the second subtractor sends the position error signal sigma to a fifth subtractor;
the fifth subtracter is used for estimating the position error signal z output by the second integral function module according to the position error signal sigma0Computing to obtain a deviation signal z0σ, and the deviation signal z0- σ is sent to a first sign function module and a first absolute value evolution function module, respectively;
first symbolThe function module being dependent on the deviation signal z0σ, the sign (z) is obtained by operation0σ) and sign (z)0- σ) to a first multiplier and a second multiplier;
the first multiplier is based on sign (z)0σ) operating to obtain an estimate of the first derivative of the error signal
Figure GDA0003051052880000041
And an estimate of the first derivative of the error signal
Figure GDA0003051052880000042
Sending the data to a first integral function module;
the first integral function module is based on an estimate of a first derivative of the error signal
Figure GDA0003051052880000043
Position error signal estimated value z is obtained by integral operation1And estimating the position error signal z1Sending the data to a first adder;
the first absolute value square function module is used for calculating the deviation signal z0σ, the operation results in
Figure GDA0003051052880000044
And will be
Figure GDA0003051052880000045
To a second multiplier;
a second multiplier based on
Figure GDA0003051052880000046
And sign (z)0σ) is computed to obtain
Figure GDA0003051052880000047
And will be
Figure GDA0003051052880000048
Sending to a third multiplier;
a third multiplier is based on
Figure GDA0003051052880000049
Operation gives z2And is combined with z2Sending the data to a first adder;
the first adder being dependent on z1And z2Calculating to obtain a derivative
Figure GDA00030510528800000410
And will be derived from
Figure GDA00030510528800000411
Sending to a second integral function module;
the second integral function module is based on the derivative
Figure GDA00030510528800000412
Integral operation to obtain estimated value z of position error signal0And an estimate z of the position error signal is determined0Sending the signal to a fifth subtracter;
Figure GDA00030510528800000413
λ1＝1.2，λ21.7, L satisfies the constraint
Figure GDA00030510528800000414
Figure GDA00030510528800000415
The maximum acceleration of the rotor is obtained;
the second integral function module also sends an estimate z of the position error signal0To a second absolute value evolution function module and a first absolute value function module;
the first absolute value function block is based on an estimate z of the position error signal0Operated to obtain | z0And will | z0Sending | to a second symbol function module;
the second absolute value function of the root of the equation0Is calculated to obtain
Figure GDA00030510528800000416
And will be
Figure GDA00030510528800000417
Sending to a fourth multiplier;
the second sign function module is based on | z0I, calculating to obtain sign (| z)0| and sign (| z) is given0|)) to a fourth multiplier;
a fourth multiplier based on
Figure GDA00030510528800000418
And sign (| z)0| obtained by operation
Figure GDA00030510528800000419
And will be
Figure GDA00030510528800000420
To a fifth multiplier;
a fifth multiplier based on
Figure GDA0003051052880000051
Is obtained by operation
Figure GDA0003051052880000052
And will be
Figure GDA0003051052880000053
Sending the data to a second adder;
the first multiplier also sends an estimate of the first derivative
Figure GDA0003051052880000054
To a second adder;
a second adder based on
Figure GDA0003051052880000055
And an estimate of the first derivative
Figure GDA0003051052880000056
OperationsObtaining the sliding form quantity
Figure GDA0003051052880000057
And measuring the sliding form
Figure GDA0003051052880000058
Sending the symbol function to a third symbol function module;
the third sign function module is based on the sliding mode quantity
Figure GDA0003051052880000059
Is obtained by operation
Figure GDA00030510528800000510
And will be
Figure GDA00030510528800000511
Sending to a sixth multiplier;
a sixth multiplier based on
Figure GDA00030510528800000512
Calculating to obtain output i of sliding mode controllerm；
Figure GDA00030510528800000513
In the formula: i.e. imAlpha is a constant greater than 0, which is the output of the sliding mode controller,
Figure GDA00030510528800000514
and u is1Satisfy the constraint condition
Figure GDA00030510528800000515
As a further improvement of the linear permanent magnet motor position servo system based on the high-order sliding mode algorithm, the invention comprises the following steps:
the operation method of the low-pass filter comprises the following steps:
Figure GDA00030510528800000516
in the formula: τ is the filter time constant.
As a further improvement of the linear permanent magnet motor position servo system based on the high-order sliding mode algorithm, the invention comprises the following steps:
the operation method of the notch filter comprises the following steps:
Figure GDA00030510528800000517
in the formula: omega2NIs a notch frequency, xi2Is the damping ratio.
As a further improvement of the linear permanent magnet motor position servo system based on the high-order sliding mode algorithm, the invention comprises the following steps:
the first, second and third symbol function modules are defined as:
Figure GDA00030510528800000518
because the large inertia delay link of the speed closed loop is removed, the invention introduces the following advantages of a linear servo system:
1. the position-current double-loop control structure is used for replacing the traditional three-loop control structure, the response speed of the system can be improved, and the dynamic performance is better. By adopting the high-order sliding mode controller, the buffeting phenomenon can be obviously weakened, the sliding mode control precision is ensured, and the dynamic characteristic and the robust performance of the system can be further improved.
2. The resonance suppression algorithm can smooth the instruction position obtained by operation, suppress instruction noise, reduce vibration of load caused by acceleration sudden change and reduce tracking error; the overshoot and setting time is reduced to the maximum extent.
3. The trap filter filters the resonance interference signal generated by the elastic coupling of the load and the resonance interference signal of the decoder. The low-pass filter further filters high-frequency interference signals generated by the sliding mode algorithm.
Drawings
The following describes embodiments of the present invention in further detail with reference to the accompanying drawings.
FIG. 1 is a structural block diagram of a linear permanent magnet motor position servo system based on a high-order sliding mode algorithm;
fig. 2 is a block diagram of a sliding mode surface algorithm structure of the sliding mode controller 4 in fig. 1;
fig. 3 is a block diagram of a sliding mode function structure of the sliding mode function counter 4 in fig. 1.
Detailed Description
The invention will be further described with reference to specific examples, but the scope of the invention is not limited thereto.
Embodiment 1, a linear permanent magnet motor position servo system based on a high-order sliding mode algorithm, as shown in fig. 1 to 3, includes a sliding mode controller 4, a resonance suppression module 1, a notch filter 6, a low pass filter 5, a current loop PI controller 8, a PARK transformation module 9, a spatial vector control module 10, an inverter 11, a Clark transformation module 13, a PARK inverse transformation module 14, and a linear motor 12 with a position grating scale 16.
Giving a position instruction p through a host system*Sending the signal to a resonance suppression module 1 and a first subtracter 2;
the linear motor 12 outputs p through the position grating ruler 16bThe signal is sent to a first subtracter 2; the linear motor 12 outputs a two-phase stator current iaAnd ibTo a Clark transformation module 13;
the resonance suppression module 1 responds to a given position command p*Operation to obtain smoothed instruction position pfAnd the smoothed instruction position p isfTo the second subtractor 3;
the first subtracter 2 is based on a given position instruction p*And pbSignal, calculating to obtain an error signal p*-pbAnd apply the error signal p*-pbSending to the second subtractor 3; the first subtracter 2 operates on a given position instruction p*Subtracting pbA signal;
the second subtractor 3 is based on the error signal p*-pbAnd after smoothingIs given by the instruction position pfCalculating to obtain a position error signal sigma, and sending the position error signal sigma to the sliding mode controller 4; the second subtracter 3 operates on the error signal p*-pbSubtracting instruction position pf；
The sliding mode controller 4 calculates to obtain an output i according to the position error signal sigmamAnd will output imTo the low-pass filter 5;
the low-pass filter 5 is based on the output i of the sliding mode controller 4mFiltered to obtain a filtered signal im *And will filter the signal im *Sent to the notch filter 6;
the notch filter 6 is based on the filtered signal im *Calculating to obtain a given value i of quadrature axis currentq *And the quadrature axis current is set to a given value iq *Sending to the third subtractor 7;
clark conversion module 13 according to two-phase stator current iaAnd ibAnd calculating to obtain a transformed stator current iαAnd iβAnd converting the stator current iαAnd iβSent to the PARK inverse transform module 14;
the PARK inverse transformation module 14 transforms the stator current iαAnd iβCalculating to obtain quadrature axis current feedback value iqAnd a direct axis current feedback value idAnd feeding back the quadrature axis current to the value iqSending the feedback value to a third subtracter 7 to obtain a direct-axis current feedback value idTo the fourth subtractor 15;
the third subtracter 7 gives a value i according to the quadrature axis currentq *And quadrature axis current feedback value iqObtaining the quadrature axis current error value i through calculationq *-iqAnd sends the quadrature axis current error value to the current loop PI controller 8; the operation method of the third subtracter 7 is that the given value i of the quadrature axis current isq *Subtracting quadrature axis current feedback value iq；
A straight shaft current set value i is obtained through an upper systemd *(id *0) to the fourth subtractor 15;
the fourth subtracter 15 gives a value i according to the direct-axis currentd *0 and direct current feedback value idObtaining a direct-axis current error value i through calculationd *-idAnd the error value i of the direct-axis currentd *-idSending to a current loop PI controller 8; the fourth subtracter 15 operates on the given value i of the direct-axis currentd *Subtracting the direct axis current feedback value i from 0d；
The current loop PI controller 8 is based on the quadrature axis current error value iq *-iqAnd the direct axis current error value id *-idCalculating to obtain quadrature axis current uqAnd straight axis direct pressure udAnd applying the quadrature axis current uqAnd straight axis direct pressure udSending to the PARK transformation module 9;
PARK conversion module 9 based on quadrature axis current uqAnd straight axis direct pressure udAnd calculating to obtain the stator voltage component u under the two-phase static coordinate systemα、uβAnd the stator voltage component u under the two-phase static coordinate system is measuredα、uβSending to the space vector control module 10;
the space vector control module 10 controls the stator voltage component u according to the two-phase stationary coordinate systemα、uβSix paths of PWM signals are obtained through operation and are sent to the inverter 11; the linear motor 12 is driven to operate by the inverter 11.
The resonance suppression module 1 adopts a second-order low-pass filter, and the transfer function is as follows:
Figure GDA0003051052880000081
in the formula: kfAs a thrust constant, M is the total mass of the mover and load of the linear motor 12, ω0NIs the bandwidth of the resonance suppression module 1, can be adjusted according to the design requirements of the system, xi0The damping ratio is adjustable, the damping ratio is adjusted according to the load and inertia of the motor, generally 0.5 to 0.7 is taken, and S is a Laplace function operator;
the operation method of the sliding mode controller 4 is as follows:
the sliding-mode controller 4 comprises a fifth subtractor 17, a first sign function module 18, a first multiplier 19, a first integral function module 20, a first absolute value open-square function module 21, a third multiplier 22, a first adder 23, a second integral function module 24, a second absolute value open-square function module 25, a second multiplier 32, a second sign function module 26, a first absolute value function module 33, a fourth multiplier 27, a fifth multiplier 28, a second adder 29, a sixth multiplier 30 and a third sign function module 31.
The second subtractor 3 sends the position error signal σ to the fifth subtractor 17;
the fifth subtractor 17 calculates an estimated value z of the position error signal output from the second integration function block 24 based on the position error signal sigma0Computing to obtain a deviation signal z0σ (estimate of position error signal z)0Subtracting the error signal σ) and applying the deviation signal z0- σ is sent to the first sign function module 18 and the first absolute value evolution function module 21, respectively;
the first sign function module 18 is based on the deviation signal z0σ, the sign (z) is obtained by operation0σ) and sign (z)0σ) to the first multiplier 19 and to the second multiplier 32; the first sign function block 18 operates by applying a deviation signal z0- σ is introduced into sign ();
the first multiplier 19 is based on sign (z)0σ) operating to obtain an estimate of the first derivative of the error signal
Figure GDA0003051052880000082
And an estimate of the first derivative of the error signal
Figure GDA0003051052880000083
To the first integral function module 20; the first multiplier 19 operates by using sign (z)0σ) and
Figure GDA0003051052880000084
multiplying;
the first integral function block 20 is based on an estimate of the first derivative of the error signal
Figure GDA0003051052880000085
Position error signal estimated value z is obtained by integral operation1And estimating the position error signal z1To the first adder 23;
the first absolute value square function module 21 depends on the deviation signal z0σ, the operation results in
Figure GDA0003051052880000091
And will be
Figure GDA0003051052880000092
To the second multiplier 32; the first absolute value square function module 21 is operated by dividing the deviation signal z0Introduction of sigma
Figure GDA0003051052880000093
Performing the following steps;
second multiplier 32 is based on
Figure GDA0003051052880000094
And sign (z)0σ) is computed to obtain
Figure GDA0003051052880000095
And will be
Figure GDA0003051052880000096
To the third multiplier 22; the operation method of the second multiplier 32 is
Figure GDA0003051052880000097
And sign (z)0- σ) multiplication;
the third multiplier 22 is based on
Figure GDA0003051052880000098
Operation gives z2And is combined with z2To the first adder 23; operation method of third multiplier 22Is composed of
Figure GDA0003051052880000099
And
Figure GDA00030510528800000910
multiplying;
the first adder 23 being dependent on z1And z2Calculating to obtain a derivative
Figure GDA00030510528800000911
And will be derived from
Figure GDA00030510528800000912
To the second integral function module 24; the first adder 23 operates by z1And z2Adding;
second integral function module 24 depends on the derivative
Figure GDA00030510528800000913
Integral operation to obtain estimated value z of position error signal0And an estimate z of the position error signal is determined0To the fifth subtractor 17.
The sliding mode surface algorithm of the complete sliding mode controller 4 is shown as follows:
Figure GDA00030510528800000914
in the formula of1＝1.2，λ21.7, L satisfies the constraint
Figure GDA00030510528800000915
In the case of the linear motor 12,
Figure GDA00030510528800000916
the maximum acceleration of the rotor can be obtained according to the maximum thrust of the linear motor 12 and the mass of the rotor;
the first, second and third symbol function modules 18, 26, 31 are defined as:
Figure GDA00030510528800000917
the second integral function module 24 also sends an estimate z of the position error signal0To the second absolute value square function module 25 and the first absolute value function module 33;
the first absolute value function block 33 is based on the estimated value z of the position error signal0Operated to obtain | z0And will | z0Sending | to the second sign function module 26; the first absolute value function module 33 is operated by using z0Introducing into | () |;
the second absolute value square function module 25 depends on z0Is calculated to obtain
Figure GDA0003051052880000101
And will be
Figure GDA0003051052880000102
To a fourth multiplier 27; the second absolute value square function module 25 is operated by dividing z0Introduction of
Figure GDA0003051052880000103
Performing the following steps;
the second sign function module 26 depends on | z0I, calculating to obtain sign (| z)0| and sign (| z) is given0|) to a fourth multiplier 27; the second sign function block 26 operates by applying | z0I is introduced into sign ();
a fourth multiplier 27 based on
Figure GDA0003051052880000104
And sign (| z)0| obtained by operation
Figure GDA0003051052880000105
And will be
Figure GDA0003051052880000106
Send to the fifth multiplierA flange 28; the fourth multiplier 27 operates by
Figure GDA0003051052880000107
And sign (| z)0I) multiplication;
a fifth multiplier 28 according to
Figure GDA0003051052880000108
Is obtained by operation
Figure GDA0003051052880000109
And will be
Figure GDA00030510528800001010
To the second adder 29; the fifth multiplier 28 operates by
Figure GDA00030510528800001011
Multiplying by beta;
the first multiplier 19 also sends an estimate of the first derivative
Figure GDA00030510528800001012
To the second adder 29;
a second adder 29 based on
Figure GDA00030510528800001013
And an estimate of the first derivative
Figure GDA00030510528800001014
Calculating to obtain sliding mode quantity
Figure GDA00030510528800001015
And measuring the sliding form
Figure GDA00030510528800001016
To the third sign function module 31; the second adder 29 operates by adding
Figure GDA00030510528800001017
And an estimate of the first derivative
Figure GDA00030510528800001018
Adding;
the third sign function module 31 depends on the sliding mode quantity
Figure GDA00030510528800001019
Is obtained by operation
Figure GDA00030510528800001020
And will be
Figure GDA00030510528800001021
To the sixth multiplier 30; the third sign function module 31 is operated by sliding mode quantity
Figure GDA00030510528800001022
Introducing sign ();
a sixth multiplier 30 based on
Figure GDA00030510528800001023
The operation obtains the output i of the sliding mode controller 4m；
Figure GDA00030510528800001024
The sixth multiplier 30 operates by
Figure GDA00030510528800001025
Multiplication by-alpha;
output i of sliding mode controller 4mThe operation method comprises the following steps:
Figure GDA00030510528800001026
in the formula: i.e. imWhich is the output of the sliding mode controller 4, alpha is a constant greater than 0,
Figure GDA0003051052880000111
and u is1Satisfy the constraint condition
Figure GDA0003051052880000112
According to
Figure GDA0003051052880000113
The integration operation may result in a position error signal sigma.
The low-pass filter 5 is calculated by:
Figure GDA0003051052880000114
in the formula: τ is an adjustable filter time constant.
The low-pass filter 5 is a first-order low-pass filter 5 and can filter high-frequency interference signals generated by the sliding mode algorithm.
The operation method of the notch filter 6 is:
Figure GDA0003051052880000115
in the formula: omega2NTo notch the frequency, xi, can be adjusted according to the design requirements of the system2For adjustable damping ratio, 0.4-0.7 is generally adopted. The notch filter 6 is used for filtering the resonance interference signal generated by the elastic connection of the load and the resonance interference signal of the decoder, and the output value g of the notch filter2(s) is the given value i of quadrature axis currentq *。
The linear motor 12 is a permanent magnet synchronous linear motor and adopts id *The linear motor 12 satisfies L in the 0-field directional control methodd＝LqThe electromagnetic thrust is expressed as:
Figure GDA0003051052880000116
Ld、Lqa direct axis inductor and a quadrature axis inductor respectively; i.e. id、iqIs a stator current vector under a rotating coordinate system; psifMagnetic potential generated for the rotor permanent magnets; τ is the motor pole pitch, Ld、Lq、ψfAnd τ, etc. are all motor parameters.
From this, the given value i of quadrature axis current outputted from notch filter 6 is knownq *Can realize the effective control of the thrust of the linear motor 12, pbThe signal is detected by the grating ruler 16 to obtain the given position instruction p*The comparison results in an error signal p*-pbThe error signal p*-pbAs an input value of the position ring, an electromagnetic thrust FeThe size of the mover determines the moving speed of the mover, thereby realizing the control of the mover of the linear motor 12.
Finally, it is also noted that the above-mentioned lists merely illustrate a few specific embodiments of the invention. It is obvious that the invention is not limited to the above embodiments, but that many variations are possible. All modifications which can be derived or suggested by a person skilled in the art from the disclosure of the present invention are to be considered within the scope of the invention.

Claims (6)

1. A linear permanent magnet motor position servo system based on a high-order sliding mode algorithm is characterized in that: the device comprises a sliding mode controller (4), a resonance suppression module (1), a notch filter (6), a low-pass filter (5), a current loop PI controller (8), a PARK conversion module (9), a space vector control module (10), an inverter (11), a Clark conversion module (13), a PARK inverse conversion module (14) and a linear motor (12) with a position grating ruler (16);
giving a position instruction p through a host system*Sending the signal to a resonance suppression module (1) and a first subtracter (2);
the linear motor (12) outputs p through the position grating ruler (16)bThe signal is sent to a first subtracter (2); the linear motor (12) outputs a two-phase stator current iaAnd ibTo a Clark transformation module (13);
the resonance suppression module (1) is used for suppressing resonance according to a given position instruction p*(ii) a The operation results in a smoothed instruction position pfAnd the smoothed instruction position p isfTo a second subtractor (3);
a first subtractor (2) is based on a given position instruction p*And pbSignal, calculating to obtain an error signal p*-pbAnd apply the error signal p*-pbSending the signal to a second subtracter (3); the first subtracter (2) operates on a given position instruction p*Subtracting pbA signal;
a second subtractor (3) based on the error signal p*-pbAnd smoothed instruction position pfCalculating to obtain a position error signal sigma, and sending the position error signal sigma to a sliding mode controller (4); the second subtracter (3) operates on the error signal p*-pbSubtracting instruction position pf；
The sliding mode controller (4) calculates to obtain an output i according to the position error signal sigmamAnd will output imSending to a low-pass filter (5);
the low-pass filter (5) is based on the output i of the sliding mode controller (4)mFiltered to obtain a filtered signal im *And will filter the signal im *To a notch filter (6);
the notch filter (6) is based on the filtered signal im *Calculating to obtain a given value i of quadrature axis currentq *And the quadrature axis current is set to a given value iq *Sending to a third subtractor (7);
the Clark conversion module (13) is based on the two-phase stator current iaAnd ibAnd calculating to obtain a transformed stator current iαAnd iβAnd converting the stator current iαAnd iβSending the data to a PARK inverse transformation module (14);
the PARK inverse transformation module (14) is used for transforming the stator current iαAnd iβCalculating to obtain quadrature axis current feedback value iqAnd a direct axis current feedback value idAnd feeding back the quadrature axis current to the value iqSending the feedback value to a third subtracter (7) to feed back the direct-axis current idTo a fourth subtractor (15);
a third subtracter (7) according to a given value i of the quadrature axis currentq *And quadrature axis current feedback value iqObtaining the quadrature axis current error value i through calculationq *-iqAnd sending the quadrature axis current error value to a current loop PI controller (8); third subtractionThe operation method of the device (7) is that a quadrature axis current given value iq *Subtracting quadrature axis current feedback value iq；
A straight shaft current set value i is obtained through an upper systemd *To a fourth subtractor (15);
a fourth subtractor (15) based on the given value i of the direct-axis currentd *And a direct axis current feedback value idObtaining a direct-axis current error value i through calculationd *-idAnd the error value i of the direct-axis currentd *-idSending the current to a current loop PI controller (8); the fourth subtracter (15) operates on the given value i of the direct-axis currentd *Subtracting the direct axis current feedback value id；
The current loop PI controller (8) is based on the quadrature axis current error value iq *-iqAnd the direct axis current error value id *-idCalculating to obtain quadrature axis voltage uqAnd straight axis direct pressure udAnd applying the quadrature axis voltage uqAnd straight axis direct pressure udSending the data to a PARK conversion module (9);
the PARK conversion module (9) is used for converting the quadrature axis voltage uqAnd straight axis direct pressure udAnd calculating to obtain the stator voltage component u under the two-phase static coordinate systemα、uβAnd the stator voltage component u under the two-phase static coordinate system is measuredα、uβSending the data to a space vector control module (10);
the space vector control module (10) controls the stator voltage component u according to the two-phase static coordinate systemα、uβSix paths of PWM signals are obtained through operation and are sent to an inverter (11); the linear motor (12) is driven to operate through the inverter (11).
2. The linear permanent magnet motor position servo system based on the high-order sliding mode algorithm according to claim 1, is characterized in that:
the transfer function of the resonance suppression module (1) is:
Figure FDA0003051052870000021
in the formula: kfM is the total mass of the mover and the load of the linear motor (12) as a thrust constant0NIs the bandwidth, ξ, of the resonance suppression module (1)0Is the damping ratio.
3. The linear permanent magnet motor position servo system based on the high-order sliding mode algorithm according to claim 2, is characterized in that:
the sliding mode controller (4) comprises a fifth subtracter (17), a first sign function module (18), a first multiplier (19), a first integral function module (20), a first absolute value square-root function module (21), a third multiplier (22), a first adder (23), a second integral function module (24), a second absolute value square-root function module (25), a second multiplier (32), a second sign function module (26), a first absolute value function module (33), a fourth multiplier (27), a fifth multiplier (28), a second adder (29), a sixth multiplier (30) and a third sign function module (31);
the second subtractor (3) sends the position error signal sigma to a fifth subtractor (17);
a fifth subtractor (17) based on the position error signal sigma and the estimated value z of the position error signal output by the second integral function module (24)0Computing to obtain a deviation signal z0σ, and the deviation signal z0- σ is sent to a first sign function module (18) and a first absolute value evolution function module (21), respectively;
the first sign function module (18) is responsive to the deviation signal z0σ, the sign (z) is obtained by operation0σ) and sign (z)0- σ) to a first multiplier (19) and a second multiplier (32);
the first multiplier (19) is based on sign (z)0σ) operating to obtain an estimate of the first derivative of the error signal
Figure FDA0003051052870000031
And an estimate of the first derivative of the error signal
Figure FDA0003051052870000032
To a first integral function module (20);
a first integral function module (20) is responsive to an estimate of a first derivative of the error signal
Figure FDA0003051052870000033
Position error signal estimated value z is obtained by integral operation1And estimating the position error signal z1To a first adder (23);
the first absolute value square function module (21) is based on the deviation signal z0σ, the operation results in
Figure FDA0003051052870000034
And will be
Figure FDA0003051052870000035
To a second multiplier (32);
a second multiplier (32) based on
Figure FDA0003051052870000036
And sign (z)0σ) is computed to obtain
Figure FDA0003051052870000037
And will be
Figure FDA0003051052870000038
To a third multiplier (22);
a third multiplier (22) based on
Figure FDA0003051052870000039
Operation gives z2And is combined with z2To a first adder (23);
the first adder (23) is based on z1And z2Calculating to obtain a derivative
Figure FDA00030510528700000310
And will be derived from
Figure FDA00030510528700000311
To a second integral function module (24);
the second integral function module (24) is based on the derivative
Figure FDA00030510528700000312
Integral operation to obtain estimated value z of position error signal0And an estimate z of the position error signal is determined0Sending to a fifth subtractor (17);
Figure FDA00030510528700000314
λ1＝1.2，λ21.7, L satisfies the constraint
Figure FDA0003051052870000041
Figure FDA00030510528700000422
The maximum acceleration of the rotor is obtained;
the second integral function module (24) also transmits an estimate z of the position error signal0To a second absolute value function block (25) and to a first absolute value function block (33);
a first absolute value function block (33) is responsive to an estimate z of the position error signal0Operated to obtain | z0And will | z0Sending | to a second symbol function module (26);
a second absolute value square function block (25) based on z0Is calculated to obtain
Figure FDA0003051052870000042
And will be
Figure FDA0003051052870000043
To a fourth multiplier (27);
a second sign function module (26) based on | z0I, calculating to obtain sign (| z)0| and sign (| z) is given0|) to a fourth multiplier (27);
a fourth multiplier (27) based on
Figure FDA0003051052870000044
And sign (| z)0| obtained by operation
Figure FDA0003051052870000045
And will be
Figure FDA0003051052870000046
To a fifth multiplier (28);
a fifth multiplier (28) based on
Figure FDA0003051052870000047
Is obtained by operation
Figure FDA0003051052870000048
And will be
Figure FDA0003051052870000049
To a second adder (29);
the first multiplier (19) also sends an estimate of the first derivative
Figure FDA00030510528700000410
To a second adder (29);
a second adder (29) based on
Figure FDA00030510528700000411
And an estimate of the first derivative
Figure FDA00030510528700000412
Calculating to obtain sliding mode quantity
Figure FDA00030510528700000413
And measuring the sliding form
Figure FDA00030510528700000414
To a third sign function module (31);
a third sign function module (31) according to the sliding mode quantity
Figure FDA00030510528700000415
Is obtained by operation
Figure FDA00030510528700000416
And will be
Figure FDA00030510528700000417
To a sixth multiplier (30);
a sixth multiplier (30) based on
Figure FDA00030510528700000418
The output i of the sliding mode controller (4) is obtained by operationm；
Figure FDA00030510528700000419
In the formula: i.e. imIs the output of the sliding mode controller (4), alpha is a constant greater than 0,
Figure FDA00030510528700000420
and u is1Satisfy the constraint condition
Figure FDA00030510528700000421
4. The linear permanent magnet motor position servo system based on the high-order sliding mode algorithm according to claim 3, is characterized in that:
the low-pass filter (5) is calculated by the following method:
Figure FDA0003051052870000051
in the formula: τ is the filter time constant.
5. The linear permanent magnet motor position servo system based on the high-order sliding mode algorithm according to claim 4, is characterized in that:
the method for operating the notch filter (6) comprises the following steps:
Figure FDA0003051052870000052
in the formula: omega2NIs a notch frequency, xi2Is the damping ratio.
6. The linear permanent magnet motor position servo system based on the high-order sliding mode algorithm according to claim 5, is characterized in that:
the first (18), second (26) and third (31) symbol function modules are defined as:
Figure FDA0003051052870000053
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