CN116208035B - Control method of brush direct current motor - Google Patents

Control method of brush direct current motor Download PDF

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Publication number
CN116208035B
CN116208035B CN202310472837.5A CN202310472837A CN116208035B CN 116208035 B CN116208035 B CN 116208035B CN 202310472837 A CN202310472837 A CN 202310472837A CN 116208035 B CN116208035 B CN 116208035B
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liquid crystal
relation
display device
crystal display
sliding mode
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CN116208035A (en
Inventor
何龙
汪凤翔
章烁
颜秉洋
贺鸿彬
夏安俊
黄东晓
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Quanzhou Institute of Equipment Manufacturing
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Quanzhou Institute of Equipment Manufacturing
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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
    • H02P7/00—Arrangements for regulating or controlling the speed or torque of electric DC motors
    • H02P7/06—Arrangements for regulating or controlling the speed or torque of electric DC motors for regulating or controlling an individual dc dynamo-electric motor by varying field or armature current
    • H02P7/18—Arrangements for regulating or controlling the speed or torque of electric DC motors for regulating or controlling an individual dc dynamo-electric motor by varying field or armature current by master control with auxiliary power
    • H02P7/24—Arrangements for regulating or controlling the speed or torque of electric DC motors for regulating or controlling an individual dc dynamo-electric motor by varying field or armature current by master control with auxiliary power using discharge tubes or semiconductor devices
    • H02P7/28—Arrangements for regulating or controlling the speed or torque of electric DC motors for regulating or controlling an individual dc dynamo-electric motor by varying field or armature current by master control with auxiliary power using discharge tubes or semiconductor devices using semiconductor devices
    • 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
    • H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
    • 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
    • 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
    • H02P21/22—Current control, e.g. using a current control loop
    • 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
    • H02P7/00—Arrangements for regulating or controlling the speed or torque of electric DC motors
    • H02P7/03—Arrangements for regulating or controlling the speed or torque of electric DC motors for controlling the direction of rotation of DC motors
    • H02P7/04—Arrangements for regulating or controlling the speed or torque of electric DC motors for controlling the direction of rotation of DC motors by means of a H-bridge circuit

Abstract

The invention relates to a motor control method, in particular to a brush direct current motor control method, a driving circuit of the brush direct current motor adopts an H bridge circuit, the H bridge circuit is provided with four switching tubes, and then the two ends of the motor of the brush direct current motor have three voltage states which are respectively as follows
Figure ZY_1
、
Figure ZY_2
And 0, the control method comprises the steps of establishing a brush direct current motor model, controlling gain optimization, designing a generalized proportional integral disturbance observer based on a sliding mode approach law of a preset time, controlling current and the like, and ensuring that a control system converges in a fixed time by designing the sliding mode approach law of the preset time, wherein the convergence speed is high, the current control precision is relatively high, and simultaneously, real-time estimating and compensating model parameters and external disturbance by designing the generalized proportional integral observer based on the sliding mode approach law of the preset time and the control gain optimizer, so that the anti-interference capability of the control system in a complex environment is improved.

Description

Control method of brush direct current motor
Technical Field
The invention relates to a motor control method, in particular to a brush direct current motor control method.
Background
The brush direct current motor has simple structure and low cost and is widely applied to equipment such as massage chairs and the like. Conventional brush direct current motors generally employ linear PI control based on pulse width modulation techniques, and current control accuracy is relatively low.
Some limited time control strategies are proposed by students at home and abroad for the current control precision of a motor system, such as a limited time control method based on fuzzy control, a limited time control method with interference compensation effect and the like, but the convergence time is generally related to an initial state, and in some practical cases, the initial state of the system is difficult to acquire, the convergence time changes along with the initial state and is gradually stable, the convergence speed is influenced, and the current control precision still needs to be improved.
In addition, when the brush direct current motor is applied to a complex environment, factors such as motor parameter change, external disturbance and the like can seriously influence the performance of a control system, for example, a creeping phenomenon can occur at a low speed, a larger static difference and limit cycle oscillation can be displayed at a steady state, and the anti-interference capability is relatively poor.
In view of this, the applicant has conducted intensive studies on a method for controlling a brushed dc motor, and has produced the present invention.
Disclosure of Invention
The invention aims to provide a brush direct current motor control method which is relatively high in current control precision and relatively good in anti-interference capability.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a brush direct current motor control method, the drive circuit of the brush direct current motor adopts an H bridge circuit, the H bridge circuit has four switch tubes, then the two ends of the motor of the brush direct current motor have three voltage states, which are respectively
Figure SMS_1
、
Figure SMS_2
And 0, the control method comprising the steps of:
s1, a brush direct current motor model is built as follows,
Figure SMS_3
in the method, in the process of the invention,
Figure SMS_4
representing disturbance term representing parameter mismatch and external disturbance, < ->
Figure SMS_5
Indicating control gain, ++>
Figure SMS_6
Representing the stator voltage of said brushed dc motor, a +.>
Figure SMS_7
Representing the differentiation of the stator current of the brushed direct current motor, i representing the order of the derivative of the disturbance term, n representing the highest order of the derivative of the disturbance term used, d representing the value of the derivative of the disturbance term n, and->
Figure SMS_8
Differentiation, f, of the ith derivative representing the disturbance term i+1 Represents the (i+1) th derivative of the disturbance term,>
Figure SMS_9
differentiation of the nth derivative representing the disturbance term;
s2, controlling gain optimization, wherein the specific method comprises the following steps:
in the case of a steady-state condition,
Figure SMS_11
the n+1 order differential of the brush DC motor model is 0, the n+1 order differential of the brush DC motor model is
Figure SMS_13
Hereby is obtained a certain moment->
Figure SMS_14
The expression of (2) is +.>
Figure SMS_16
The method comprises the steps of carrying out a first treatment on the surface of the Will->
Figure SMS_18
The estimation system of the time is defined as
Figure SMS_19
Wherein->
Figure SMS_20
Is->
Figure SMS_10
Estimated value of ∈10->
Figure SMS_12
Is->
Figure SMS_15
The estimation error is defined as
Figure SMS_17
；
The minimum of the following objective function is solved,
Figure SMS_21
in the method, in the process of the invention,
Figure SMS_22
，/>
Figure SMS_23
is an adjustable parameter;
s3, designing a generalized proportional-integral disturbance observer based on a predetermined time sliding mode approach law, wherein the specific method comprises the following steps:
s3.1, designing a sliding mode approach law of a preset time as follows:
Figure SMS_24
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_25
t is a predefined time, & lt/L & gt, for differentiation of the slide surface>
Figure SMS_26
Is a parameter of the approach law, and has a value range of
Figure SMS_27
The approach time for obtaining the sliding mode approach law in the preset time is calculated as follows:
Figure SMS_28
the process is carried out by the steps of,
Figure SMS_29
and->
Figure SMS_30
The maximum convergence time is T;
s3.2, the predicted value
Figure SMS_31
Substituting the brush direct current motor model to obtain a relation formula I:
Figure SMS_32
the generalized proportional-integral observer is designed as a relation two:
Figure SMS_33
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_34
differential of the stator current estimate, +.>
Figure SMS_35
Differential of the estimated value of the i-th derivative of the disturbance term,/-, and>
Figure SMS_36
and subtracting the relation one from the relation two to obtain a relation three for differentiating the disturbance term n-order derivative estimated value:
Figure SMS_37
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_38
differential of the current estimation error, +.>
Figure SMS_39
Differential of the estimated error for the disturbance term i-th derivative,/->
Figure SMS_40
Differential of the estimated error for the disturbance term nth derivative,/->
Figure SMS_41
，/>
Figure SMS_42
The sliding mode surface is designed as +.>
Figure SMS_43
And according to the predetermined time sliding mode approach law, obtaining a relation four:
Figure SMS_44
；
s4, controlling the current, wherein the specific method comprises the following steps:
will predict the value
Figure SMS_45
Substituting the relation one to obtain a relation five: />
Figure SMS_46
The design sliding die surface is as follows:
Figure SMS_47
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_48
is a predefined convergence time, +.>
Figure SMS_49
The time differential of the slip plane is then the relationship six:
Figure SMS_50
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_51
differential for current-controlled slip-plane, +.>
Figure SMS_52
Is the differentiation of the reference current and the feedback current error;
calculating the sliding mode surface at the k+1 time to obtain a relation seven
Figure SMS_53
Wherein->
Figure SMS_54
For controlling the period, according to the predetermined time sliding mode approach law, the target sliding mode surface at the time k+1 is represented by a relation eight:
Figure SMS_55
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_56
is->
Figure SMS_57
Predefined convergence time, defining a cost function of sliding mode predictive current control as
Figure SMS_58
And combining the relation five, the relation six and the relation7. And obtaining a relation nine by the relation eight and the cost function:
Figure SMS_59
will respectively
Figure SMS_60
、/>
Figure SMS_61
And 0 are respectively substituted into the relation nine to obtain the corresponding cost function value as follows:
Figure SMS_62
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_63
，/>
Figure SMS_64
，/>
Figure SMS_65
=0, selecting the cost function value +.>
Figure SMS_66
And outputting a corresponding voltage vector according to the corresponding i value.
As an improvement of the invention, in step S2,
Figure SMS_67
，/>
Figure SMS_68
the method is adopted for determination:
order the
Figure SMS_69
Can calculate +.>
Figure SMS_70
Step->
Figure SMS_71
The value of (2) is
Figure SMS_72
Expressed in the z-domain as:
Figure SMS_73
the closed loop system is expressed as:
Figure SMS_74
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_75
and->
Figure SMS_76
All are characteristic equations, and according to Jury criterion, the sufficient and necessary conditions for system stability are as follows:
Figure SMS_77
thereby can obtain
Figure SMS_78
，/>
Figure SMS_79
The selection mode is as follows: />
Figure SMS_80
。
The technical scheme has the following beneficial effects:
1. the invention ensures that the control system converges in fixed time by designing the predefined time sliding mode approach law, has high convergence speed and relatively high current control precision, and simultaneously improves the anti-interference capability of the control system in complex environment by designing the generalized proportional integral observer and the control gain optimizer based on the predefined time sliding mode approach law to estimate and compensate model parameters and external disturbance in real time.
2. The direct output switch signal controls the brush direct current motor by minimizing the control target error, thereby reducing the switch frequency and the switch loss.
Drawings
FIG. 1 is a first connection state of an H-bridge circuit according to an embodiment;
FIG. 2 is a second connection state of the H-bridge circuit according to the embodiment;
FIG. 3 is a third connection state of the H-bridge circuit according to the embodiment;
FIG. 4 is a fourth connection state of the H-bridge circuit according to the embodiment;
Detailed Description
The invention will be further illustrated with reference to specific examples.
The invention provides a control method of a brush direct current motor, a driving circuit of the brush direct current motor adopts a conventional H bridge circuit, the H bridge circuit is provided with four switching tubes, a signal generated by a control system of a motor of the brush direct current motor controls the on and off of the four switching tubes, in general, if only one switching tube is conducted and can not form a passage, more than two switching tubes are conducted and short circuit can occur, therefore, when the brush direct current motor is used, only two switching tubes are conducted simultaneously, four connection states as shown in fig. 1-4 can be generated, wherein the voltages at two ends of the motor in the two connection states are 0, that is, the two ends of the motor of the brush direct current motor share three voltage states, namely, the two ends of the motor of the brush direct current motor respectively
Figure SMS_81
、/>
Figure SMS_82
And 0.
The control method of the brush direct current motor provided by the embodiment is performed based on the driving circuit, and specifically comprises the following steps:
s1, a mathematical model of a brush direct current motor based on disturbance can be written as:
Figure SMS_83
or alternatively
Figure SMS_84
In the method, in the process of the invention,
Figure SMS_86
、/>
Figure SMS_88
、/>and->
Figure SMS_92
The stator voltage, current, inductance and resistance of the brush direct current motor are respectively; />
Figure SMS_93
Representing back emf; />
Figure SMS_94
、/>
Figure SMS_95
Respectively representing the proportionality coefficient and the motor speed. From the above, it can be seen that the brush DC motor model is inaccurate due to the variation of the parameters such as inductance, resistance, rotation speed, etc., assuming that the rated inductance is L n Rated resistance is R n Rated proportionality coefficient of k n Deviation of the actual inductance from the nominal inductance +.>
Figure SMS_85
Deviation of the actual resistance from the nominal resistance +.>
Figure SMS_87
Deviation of the actual proportionality coefficient from the nominal proportionality coefficient +.>
Figure SMS_89
Then->
Figure SMS_91
。
Order the
Figure SMS_96
Representing disturbance term representing parameter mismatch and external disturbance, < ->
Figure SMS_97
Representing the control gain, it can be rewritten as +.>
Figure SMS_98
Let->
Figure SMS_99
Is n-th order conductive, then it can be rewritten as: />
Figure SMS_100
In the method, in the process of the invention,
Figure SMS_101
indicating parameter mismatch, ++>
Figure SMS_102
Indicating control gain, ++>
Figure SMS_103
Representing the stator voltage of said brushed dc motor, a +.>
Figure SMS_104
Representing the stator current of the brushed DC motor, i representing the order of the derivative of the disturbance term, n representing the highest order of the derivative of the disturbance term used, d representing the value of the derivative of the disturbance term n, f i Representing the ith derivative, f of the disturbance term i+1 Representing the (i+1) th derivative of the disturbance term, f n Represents the nth derivative of the disturbance term, +.>
Figure SMS_105
Differential representing the stator current of the brushed DC motor,/I>
Figure SMS_106
Differential representing the ith derivative of the disturbance term, +.>
Figure SMS_107
Representing the derivative of the nth derivative of the disturbance term.
S2, controlling gain optimization, wherein the specific method comprises the following steps:
under steady state conditions (steady state refers to the state that the system maintains when all input variables remain constant after all transient effects have disappeared),
Figure SMS_109
the n+1 order differential of the brush DC motor model is 0, the n+1 order differential of the brush DC motor model is
Figure SMS_110
Hereby is obtained a certain moment->
Figure SMS_111
The expression of (2) is +.>
Figure SMS_113
The method comprises the steps of carrying out a first treatment on the surface of the Will->
Figure SMS_115
The estimation system of the time is defined as
Figure SMS_116
Wherein->
Figure SMS_118
Is->
Figure SMS_108
Estimated value of ∈10->
Figure SMS_112
Is->
Figure SMS_114
The estimation error is defined as
Figure SMS_117
；
Solving the following objective function
Figure SMS_119
In the objective function, e represents the estimated current and measured current error, the minimization of which will achieve an improvement in the accuracy of the current estimation; />
Figure SMS_120
And->
Figure SMS_121
Constraint on the rate of change of the estimated control gain, wherein +.>
Figure SMS_122
The gain change rate is controlled taking into account the estimates at the k and k-1 instants,
Figure SMS_123
the gain change speed is controlled taking into account the estimates of the next time instant (k+1) and the current time instant k.
Figure SMS_124
In the method, in the process of the invention,
Figure SMS_125
，/>
Figure SMS_126
is an adjustable parameter and->
Figure SMS_127
，/>
Figure SMS_128
Preferably, the following method is used:
order the
Figure SMS_129
Can calculate +.>
Figure SMS_130
Step->
Figure SMS_131
The value of (2) is
Figure SMS_132
The spatial domain that samples a continuous-time system and processes the sampled signal is called the z-domain) is expressed as: />
Figure SMS_133
The closed loop system is expressed as:
Figure SMS_134
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_135
and->
Figure SMS_136
All are characteristic equations, and the specific calculation process is as follows: />
Figure SMS_137
。
According to Jury criterion (Jury criterion: whether the feature root is strictly located in a unit circle on a Z plane according to the coefficient of a closed loop feature equation of a discrete system is a stability criterion directly applied in the Z domain), zhu Li stability criterion is described as follows:
let the characteristic equation of the n-order discrete system be
Figure SMS_138
Characteristic equation
Figure SMS_139
Is that all of the root of (2) lie strictly within a unit circle in the z-plane
1)
Figure SMS_140
2)
Figure SMS_141
3) The following (n-1) constraints are satisfied
Figure SMS_142
，/>
Figure SMS_143
，/>
Figure SMS_144
，………，/>
Figure SMS_145
The discrete system is stable only if the above conditions are met, otherwise the system is unstable.
The sufficient requirements for system stability are:
Figure SMS_146
thus, the first and second substrates are bonded together,
Figure SMS_147
，/>
Figure SMS_148
the selection mode is as follows: />
Figure SMS_149
S3, designing a generalized proportional-integral disturbance observer based on a predetermined time sliding mode approach law, wherein the specific method comprises the following steps:
s3.1, designing a sliding mode approach law of a preset time as follows:
Figure SMS_150
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_151
t is a predefined time, & lt/L & gt, for differentiation of the slide surface>
Figure SMS_152
Is a parameter of the approach law, and has a value range of
Figure SMS_153
The approach time for obtaining the sliding mode approach law in the preset time is calculated as follows: />
Figure SMS_154
The process is carried out by the steps of,
Figure SMS_155
and->
Figure SMS_156
The maximum convergence time is T; the specific calculation process is as follows:
Figure SMS_157
Figure SMS_158
。
s3.2, the predicted value
Figure SMS_159
Substituting the brush direct current motor model to obtain a relation formula I: />
Figure SMS_160
The generalized proportional-integral observer is designed as a relation two:
Figure SMS_161
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_162
differential of the stator current estimate, +.>
Figure SMS_163
Differential of the estimated value of the i-th derivative of the disturbance term,/-, and>
Figure SMS_164
and subtracting the relation one from the relation two to obtain a relation three for differentiating the disturbance term n-order derivative estimated value:
Figure SMS_165
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_166
differential of the current estimation error, +.>
Figure SMS_167
Differential of the estimated error for the disturbance term i-th derivative,/->
Figure SMS_168
Differential of the estimated error for the disturbance term nth derivative,/->
Figure SMS_169
，/>
Figure SMS_170
The sliding mode surface is designed as +.>
Figure SMS_171
And according to the predetermined time sliding mode approach law, obtaining a relation four: />
Figure SMS_172
。
S4, controlling the current, wherein the specific method comprises the following steps:
will predict the value
Figure SMS_173
Substituting the relation one to obtain a relation five: />
Figure SMS_174
The design sliding die surface is as follows:
Figure SMS_175
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_176
is a predefined convergence time, +.>
Figure SMS_177
The time differential of the slip plane is then the relationship six: />
Figure SMS_178
Wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_179
differential for current-controlled slip-plane, +.>
Figure SMS_180
Is the differentiation of the reference current and the feedback current error;
calculating the sliding mode surface at the k+1 time to obtain a relation seven
Figure SMS_181
Wherein->
Figure SMS_182
For controlling the period, according to the predetermined time sliding mode approach law, the target sliding mode surface at the time k+1 is represented by a relation eight:
Figure SMS_183
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_184
is->
Figure SMS_185
Predefined convergence time, defining a cost function of sliding mode predictive current control as
Figure SMS_186
And combining the relation five, the relation six, the relation seven, the relation eight and the cost function to obtain a relation nine: />
Figure SMS_187
Will respectively
Figure SMS_188
、/>
Figure SMS_189
And 0 are respectively substituted into the relation nine to obtain the corresponding cost function value as follows:
Figure SMS_190
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_191
，/>
Figure SMS_192
，/>
Figure SMS_193
the control system selects said cost function value->
Figure SMS_194
The corresponding i value is controlled and output to corresponding voltage vector, thereby realizing the control of the brush direct current motor, thus being capable of estimating and compensating model parameters and external disturbance in real time, improving the anti-interference capability of the control system under complex environment, directly outputting a switch signal to control the brush direct current motor by minimizing control target error, reducing the switch frequency and reducing the switch loss.
The present invention has been described in detail, but the embodiments of the present invention are not limited to the above embodiments, and those skilled in the art can make various modifications to the present invention according to the prior art, which fall within the scope of the present invention.

Claims (2)

1. A brush direct current motor control method, the drive circuit of the brush direct current motor adopts an H bridge circuit, the H bridge circuit has four switch tubes, then the two ends of the motor of the brush direct current motor have three voltage states, which are respectively
Figure QLYQS_1
、/>
Figure QLYQS_2
And 0, characterized in that the control method comprises the steps of:
s1, a brush direct current motor model is built as follows,
Figure QLYQS_3
，
in the method, in the process of the invention,
Figure QLYQS_4
representing disturbance term representing parameter mismatch and external disturbance, < ->
Figure QLYQS_5
Indicating control gain, ++>
Figure QLYQS_6
Representing the stator voltage of said brushed dc motor, a +.>
Figure QLYQS_7
Representing the differentiation of the stator current of the brushed direct current motor, i representing the order of the derivative of the disturbance term, n representing the highest order of the derivative of the disturbance term used, d representing the value of the derivative of the disturbance term n, and->
Figure QLYQS_8
Differentiation, f, of the ith derivative representing the disturbance term i+1 Represents the (i+1) th derivative of the disturbance term,>
Figure QLYQS_9
differentiation of the nth derivative representing the disturbance term;
s2, controlling gain optimization, wherein the specific method comprises the following steps:
in the case of a steady-state condition,
Figure QLYQS_11
the n+1 order differential of the brush DC motor model is 0, the n+1 order differential of the brush DC motor model is
Figure QLYQS_12
Hereby is obtained a certain moment->
Figure QLYQS_14
The expression of (2) is +.>
Figure QLYQS_16
The method comprises the steps of carrying out a first treatment on the surface of the Will->
Figure QLYQS_17
The estimation system of the moment is defined as +.>
Figure QLYQS_18
Wherein->
Figure QLYQS_20
Is->
Figure QLYQS_10
Estimated value of ∈10->
Figure QLYQS_13
Is->
Figure QLYQS_15
The estimation error is defined as
Figure QLYQS_19
；
The minimum of the following objective function is solved,
Figure QLYQS_21
，
in the method, in the process of the invention,
Figure QLYQS_22
，/>
Figure QLYQS_23
is an adjustable parameter;
s3, designing a generalized proportional-integral disturbance observer based on a predetermined time sliding mode approach law, wherein the specific method comprises the following steps:
s3.1, designing a sliding mode approach law of a preset time as follows:
Figure QLYQS_24
，
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure QLYQS_25
t is a predefined time, & lt/L & gt, for differentiation of the slide surface>
Figure QLYQS_26
Is a parameter of the approach law, and has a value range of
Figure QLYQS_27
The approach time for obtaining the sliding mode approach law in the preset time is calculated as follows:
Figure QLYQS_28
，
the process is carried out by the steps of,
Figure QLYQS_29
the maximum convergence time is T;
s3.2, the predicted value
Figure QLYQS_30
Substituting the brush direct current motor model to obtain a relation formula I:
Figure QLYQS_31
，
the generalized proportional-integral observer is designed as a relation two:
Figure QLYQS_32
，
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure QLYQS_33
differential of the stator current estimate, +.>
Figure QLYQS_34
Differential of the estimated value of the i-th derivative of the disturbance term,/-, and>
Figure QLYQS_35
and subtracting the relation one from the relation two to obtain a relation three for differentiating the disturbance term n-order derivative estimated value:
Figure QLYQS_36
，
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure QLYQS_37
differential of the current estimation error, +.>
Figure QLYQS_38
Differential of the estimated error for the disturbance term i-th derivative,/->
Figure QLYQS_39
Differential of the estimated error for the disturbance term nth derivative,/->
Figure QLYQS_40
，/>
Figure QLYQS_41
The sliding mode surface is designed as +.>
Figure QLYQS_42
Then according to the preset time sliding mode trendThe law is closed, and the relation four can be obtained:
Figure QLYQS_43
；
s4, controlling the current, wherein the specific method comprises the following steps:
will predict the value
Figure QLYQS_44
Substituting the relation one to obtain a relation five: />
Figure QLYQS_45
The design sliding die surface is as follows:
Figure QLYQS_46
，
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure QLYQS_47
is a predefined convergence time, +.>
Figure QLYQS_48
The time differential of the slip plane is then the relationship six:
Figure QLYQS_49
，
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure QLYQS_50
differential for current-controlled slip-plane, +.>
Figure QLYQS_51
Is the differentiation of the reference current and the feedback current error;
calculating the sliding mode surface at the k+1 time to obtain a relation seven
Figure QLYQS_52
Wherein->
Figure QLYQS_53
For controlling the period, according to the predetermined time sliding mode approach law, the target sliding mode surface at the time k+1 is represented by a relation eight:
Figure QLYQS_54
，
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure QLYQS_55
is->
Figure QLYQS_56
Predefined convergence time, defining a cost function of sliding mode predictive current control as
Figure QLYQS_57
And combining the relation five, the relation six, the relation seven, the relation eight and the cost function to obtain a relation nine:
Figure QLYQS_58
，
will respectively
Figure QLYQS_59
、/>
Figure QLYQS_60
And 0 are respectively substituted into the relation nine to obtain the corresponding cost function value as follows:
Figure QLYQS_61
，
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure QLYQS_62
，/>
Figure QLYQS_63
，/>
Figure QLYQS_64
selecting the cost function value->
Figure QLYQS_65
And outputting a corresponding voltage vector according to the corresponding i value.
2. The method for controlling a brushed DC motor according to claim 1, wherein, in step S2,
Figure QLYQS_66
，/>
Figure QLYQS_67
the method is adopted for determination:
order the
Figure QLYQS_68
Can calculate +.>
Figure QLYQS_69
Step->
Figure QLYQS_70
The value of (2) is
Figure QLYQS_71
Expressed in the z-domain as:
Figure QLYQS_72
，
the closed loop system is expressed as:
Figure QLYQS_73
，
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure QLYQS_74
and->
Figure QLYQS_75
All are characteristic equations, and according to Jury criterion, the sufficient and necessary conditions for system stability are as follows:
Figure QLYQS_76
，
thereby can obtain
Figure QLYQS_77
，/>
Figure QLYQS_78
The selection mode is as follows:
Figure QLYQS_79
。
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