CN113517832A - Low-voltage servo discrete linear active disturbance rejection control method - Google Patents

Low-voltage servo discrete linear active disturbance rejection control method Download PDF

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CN113517832A
CN113517832A CN202110677419.0A CN202110677419A CN113517832A CN 113517832 A CN113517832 A CN 113517832A CN 202110677419 A CN202110677419 A CN 202110677419A CN 113517832 A CN113517832 A CN 113517832A
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CN113517832B (en
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邢科新
权欣文
林叶贵
吴昊
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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
    • 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
    • H02P21/14—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
    • 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
    • H02P2205/00—Indexing scheme relating to controlling arrangements characterised by the control loops
    • H02P2205/01—Current loop, i.e. comparison of the motor current with a current reference
    • 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
    • H02P2205/00—Indexing scheme relating to controlling arrangements characterised by the control loops
    • H02P2205/07—Speed loop, i.e. comparison of the motor speed with a speed reference

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  • Power Engineering (AREA)
  • Control Of Electric Motors In General (AREA)
  • Feedback Control In General (AREA)

Abstract

A low-voltage servo discrete linear active disturbance rejection control method comprises the steps of determining the order of a controlled object of a speed ring and a current ring of a low-voltage servo driver according to a current differential equation and a motion equation of a servo motor, determining the order of a linear active disturbance rejection controller according to the order of the controlled object, designing a continuous linear active disturbance rejection controller for the speed ring and the current ring, discretizing the continuous controller by an Euler discretization method, and determining the corresponding relation of each matrix of the continuous controller and the discrete controller; the method for identifying the parameters of the rotary inertia and the inductance of the motor is used for designing a compensation factor of the linear active disturbance rejection controller, and a digital controller of a current loop is subjected to time delay consideration in parameter setting to set corresponding parameters. The discrete mode of the linear active disturbance rejection controller is applied to the low-voltage servo driver, and the stability, the disturbance rejection, the rapidity, the robustness and the like of the permanent magnet synchronous motor control system can be improved by means of a discrete linear active disturbance rejection control algorithm.

Description

Low-voltage servo discrete linear active disturbance rejection control method
Technical Field
The invention relates to the field of low-voltage servo motor control, in particular to a discrete linear active disturbance rejection control method for a low-voltage servo driver.
Background
The low-voltage servo motor has the remarkable advantages of no need of brush phase change, simple structure, high operation precision, low power supply voltage, small volume, light weight, high working efficiency, flexible modification of design appearance and size under the basic design condition and the like. In the coming of the 4.0 times of industry, power devices and permanent magnet materials are developed vigorously, the control precision of a low-voltage servo motor is improved to a great extent, the low-voltage servo motor is slowly and widely applied to the fields of robot control, hydraulic devices, aerospace, medical equipment, ship and naval vessel equipment and the like, and the cost of replacing an electric brush at the later stage is saved because the electric brush is not required to be used for phase change, so that the occupation ratio of the low-voltage brush motor is replaced in a certain field. However, because there is no brush, the controller is required to perform electronic phase change on the motor, the low-voltage servo motor is a complex controlled object with multivariable, strong coupling, nonlinearity and variable parameters, and in order to make the low-voltage servo motor have high working accuracy, strong external interference resistance and better dynamic performance, some specific algorithms must be adopted to control the low-voltage servo motor.
The control strategy of the low-voltage servo motor mainly comprises square wave control and vector control, and the square wave control has the influences of large torque fluctuation, low control precision and the like due to the control scheme of the square wave control. Therefore, vector control is generally used under the high-precision control working condition. The control scheme of the low-voltage servo motor mainly comprises the following steps: current loop (torque control), speed loop control and position loop. Wherein a current loop is generally nested in the speed loop and the position loop for control. Control algorithms for three loops have been extensively studied. The control algorithms that are currently in common use: traditional PID control, sliding mode variable structure control, model-based adaptive control, model predictive control, fuzzy control, active disturbance rejection control and the like. In the industrial field, the PID control is widely used by application engineers because the content of the information amount required by the model is small. The active disturbance rejection control is control which is not based on a model and is proposed by a research staff in Konjin and Qing of Chinese academy of sciences, can be regarded as continuation and development of traditional PID control, regards internal parameter disturbance and external environment disturbance of a system as the concept of total disturbance together through the concept of an observer, and observes and compensates the total disturbance through the observer. But since the proposed active disturbance rejection controller is a non-linear controller, the tuning of the non-linear function and the tuning of the controller parameters is not understood by most application engineers. In 2003, the senior has proposed to convert the nonlinear active disturbance rejection controller into a linear active disturbance rejection controller through the concept of bandwidth, the tuning parameters of the controller are reduced to 4 parameters by combining the concept of bandwidth with the tuning parameters of the controller, and the bandwidth of the controller and the bandwidth of the observer are connected in a proportional manner. This method can be understood by application engineers and achieves better control than PID.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a low-voltage servo discrete linear active-disturbance-rejection control method, a discrete linear active-disturbance-rejection controller is designed on a current loop and a speed loop to replace the traditional PID control to control a motor, the parameters of the speed loop and the controller of the current loop are adjusted, the parameters obtained by parameter identification are fused into the parameters of the controller to determine the approximate range of a compensation factor, and therefore, the control precision of the discrete linear active-disturbance-rejection controller is improved.
In order to solve the above technical problem, the present invention is implemented as follows:
a low-voltage servo discrete linear active-disturbance-rejection control method, the method comprising the steps of:
step 1) determining the order of a controlled object of a current loop and a speed loop, wherein the determined order is determined by a differential equation of current and a motion equation, and the differential equation of quadrature-direct axis current is as follows:
Figure BDA0003116814310000031
Figure BDA0003116814310000032
in the above formula id、iqIs a quadrature-direct axis current value, RsIs the motor resistance value, Ld、LqIs a quadrature-direct axis inductance value, omegaeFor motor speed value, #fIs the flux linkage value of the permanent magnet;
the equation of motion is:
Figure BDA0003116814310000033
in the above formula npIs the number of pole pairs, T, of the motoreIs the electromagnetic torque of the machine, TLIs the load torque of the motor, J is the moment of inertia of the motor, Lmd、LmqThe armature reaction inductor is a quadrature-direct axis armature reaction inductor;
as can be seen from (1.1) to (1.3), the order of the passive object of the current loop and the speed loop is 1, and according to the design rule of the active disturbance rejection controller, the order of the extended observer needs to be increased by 1 on the basis of the order of the controlled object, so the order of the extended observer is 2 orders;
step 2) the differential equation of the current loop and the motion equation of the motor are rewritten into a form of input plus disturbance, because the adopted form is idThe control strategy is 0, so that only the quadrature axis current is analyzed when the current loop is analyzed, the direct axis current is not analyzed any more, and the differential equation of the quadrature axis current is rewritten as follows:
Figure BDA0003116814310000034
in the above formula
Figure BDA0003116814310000035
Can be regarded as the total disturbance of quadrature axis current loop, which is composed of resistance, inductance, and permanent magnetFlux linkage change and external disturbance;
the equation of motion is rewritten as:
Figure BDA0003116814310000041
in the above formula fωTotal disturbance of the speed loop, caused by internal parameter changes and external load torque changes;
step 3) designing a current loop continuous linear active disturbance rejection controller, firstly analyzing the current loop, inputting the current loop as a cross-axis current reference value, outputting as a cross-axis voltage control value, and recording a state variable
Figure BDA0003116814310000042
Then equation (1.4) is expressed in the form of the following equation of state:
Figure BDA0003116814310000043
a linear state observer is designed by utilizing the design principle of Luenberger to observe disturbance quantity and state variables, and the equation of the state observer is as follows:
Figure BDA0003116814310000044
in the above formula
Figure BDA0003116814310000045
Figure BDA0003116814310000046
Respectively represent state variables
Figure BDA0003116814310000047
Figure BDA0003116814310000048
Which represents the value of the gain of the observer,
Figure BDA0003116814310000049
in order to be able to observe the error of the observer,
Figure BDA00031168143100000410
the current loop linear expansion observer is written as:
Figure BDA00031168143100000411
in the above formula
Figure BDA00031168143100000412
Figure BDA00031168143100000413
Step 4) designing a continuous linear active disturbance rejection controller of a speed loop, wherein a linear extended observer of the speed loop is expressed as:
Figure BDA0003116814310000051
the state variable matrix z in the above equationω＝[z1_ω,z2_ω]TMatrix of states
Figure BDA0003116814310000052
Observer gain matrix Lω＝[l1_ω,l2_ω]TOutput matrix Cω＝[1,0]Input matrix Bω＝[bω',0]T，uc_ω＝[uo_ω,yω]T
Step 5) designing a tracking differentiator of the speed loop, wherein the current loop does not need to track the differentiator because the expected current value of the current loop is changed rapidly along with the reference value of the current; because of the inertia effect of the speed ring, if the arrangement of the transition process is carried out without using a tracking differentiator, the speed ring system can generate bad dynamic processes such as overshoot, and the arrangement of the transition process adopts a first-order inertia link, and the expression of the first-order inertia link is as follows:
Figure BDA0003116814310000053
meanwhile, the relation between the output and the input through an inertia link is obtained as follows:
Figure BDA0003116814310000054
step 6) designing a gain matrix of the linear extended observer, connecting the gain of the observer with the bandwidth commonly used in the actual control, and writing a characteristic equation of the system in the formula (1.8) as follows:
Figure BDA0003116814310000055
expanding the characteristic expression, placing the poles of the characteristic expression at the same position, wherein the position is the bandwidth value of the observer, and obtaining a gain matrix of the observer as follows:
Figure BDA0003116814310000056
and 7) designing control laws of the speed loop and the current loop continuous linear active disturbance rejection controller, and adopting single P control for a first-order controlled object, wherein the control laws of the current loop and the speed loop are as follows:
Figure BDA0003116814310000061
uω＝Kω(rω-yω) (1.15)
in the above formula
Figure BDA0003116814310000062
KωIn order to control the gain of the laws,
Figure BDA0003116814310000063
rωreference signals for the speed loop and the current loop;
step 8) discretizing the continuous linear active disturbance rejection controller, wherein the control law part in the continuous linear active disturbance rejection controller only amplifies the output signal of the linear extended observer, so the control law part does not need to carry out discretization treatment, only the continuous linear extended observer part needs to be discretized, an Euler discretization method is adopted for discretization, the discretization mode of a speed ring is similar to that of a current ring, only the discretization process of the current ring is deduced, and a state variable is subjected to state variable derivation
Figure BDA0003116814310000064
Differentiation is performed using the following equation:
Figure BDA0003116814310000065
in the above formula
Figure BDA0003116814310000066
For the delay time caused by the current loop digital controller, the above equation is rewritten as the change of the current time compared to the previous time:
Figure BDA0003116814310000067
substituting the above equation into the state equation of the continuous system to obtain:
Figure BDA0003116814310000068
in the above formula
Figure BDA0003116814310000069
Corresponding to the state matrix
Figure BDA00031168143100000610
The expression is as follows:
Figure BDA00031168143100000611
wherein I is an identity matrix, and I is an identity matrix,
Figure BDA00031168143100000612
corresponding to the input matrix
Figure BDA00031168143100000613
The expression is as follows:
Figure BDA0003116814310000071
Figure BDA0003116814310000072
equaling the output matrix in a continuous controller
Figure BDA0003116814310000073
Is a zero matrix, and simultaneously obtains an expression equation of the discrete linear extended observer as follows:
Figure BDA0003116814310000074
in the above formula
Figure BDA0003116814310000075
The expression of (a) is:
Figure BDA0003116814310000076
wherein
Figure BDA0003116814310000077
The characteristic equation is written for a discrete linear extended observer gain matrix similar to a continuous system as follows:
Figure BDA0003116814310000078
the characteristic roots are placed at the same polar point, and a gain matrix is obtained after expansion
Figure BDA0003116814310000079
Comprises the following steps:
Figure BDA00031168143100000710
simultaneously obtaining:
Figure BDA00031168143100000711
the corresponding input matrix is:
Figure BDA00031168143100000712
the corresponding output matrix is:
Figure BDA0003116814310000081
corresponding to
Figure BDA0003116814310000082
The matrix expression of (a) is:
Figure BDA0003116814310000083
the conversion expressions of the bandwidth of the continuous linear expansion observer and the bandwidth of the discrete linear expansion observer are as follows:
Figure BDA0003116814310000084
step 9) discretization of a velocity loop tracking differentiator, wherein a forward Euler method is adopted for discretization of a first-order inertia link, and a reverse Laler identification is carried out on the inertia link to obtain:
Figure BDA0003116814310000085
obtained by a forward Euler method:
Figure BDA0003116814310000086
the simultaneous expression is as follows:
Figure BDA0003116814310000087
step 10) identifying the rotational inertia and the inductance value of the low-voltage servo motor as a determination reference of a compensation factor, and obtaining the rotational inertia value and the inductance value through an identification algorithm according to a formula:
Figure BDA0003116814310000088
Figure BDA0003116814310000089
the base numbers of the compensation factors of the current loop and the speed loop are determined, because the anti-interference performance and the dynamic performance of the system can be improved by properly increasing the value of the compensation factor in the linear active-disturbance-rejection controller, the compensation factor is multiplied by a gain factor a to obtain the compensation factor in the actual controller as follows:
Figure BDA0003116814310000091
b0_ω'＝aω*b0_ω (1.36)
step 11) using a steady state diagram mode to control the control law bandwidth omega of the current loop and the speed loopcAnd observer bandwidth ωoAnd setting, and reserving enough amplitude margin and phase margin for the two systems.
The invention has the beneficial effects that: the discrete linear active-disturbance-rejection controller is designed on the current ring and the speed ring to replace the traditional PID control to control the motor, the controller parameters of the speed ring and the current ring are subjected to parameter setting, and the parameters obtained through parameter identification are fused into the parameters of the controller to be used for determining the approximate range of the compensation factor, so that the control precision of the discrete linear active-disturbance-rejection controller is improved.
Drawings
Fig. 1 is a control block diagram of a low-voltage servo controller.
Fig. 2 is a control block diagram of a current loop linear active disturbance rejection controller.
Fig. 3 is a controller block diagram of a speed loop linear active disturbance rejection controller.
FIG. 4 is a flow chart of a low-voltage servo discrete linear active disturbance rejection control method.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
Referring to fig. 1-4, a low-voltage servo discrete linear active-disturbance-rejection control method includes the steps of:
step 1) determining the order of a controlled object of a current loop and a speed loop, wherein the determined order is determined by a differential equation of current and a motion equation, and the differential equation of quadrature-direct axis current is as follows:
Figure BDA0003116814310000101
Figure BDA0003116814310000102
in the above formula id、iqIs a quadrature-direct axis current value, RsIs the motor resistance value, Ld、LqIs a quadrature-direct axis inductance value, omegaeFor motor speed value, #fIs the flux linkage value of the permanent magnet;
the equation of motion is:
Figure BDA0003116814310000103
in the above formula npIs the number of pole pairs, T, of the motoreIs the electromagnetic torque of the machine, TLIs the load torque of the motor, J is the moment of inertia of the motor, Lmd、LmqThe armature reaction inductor is a quadrature-direct axis armature reaction inductor;
as can be seen from (1.1) to (1.3), the order of the passive object of the current loop and the speed loop is 1, and according to the design rule of the active disturbance rejection controller, the order of the extended observer needs to be increased by 1 on the basis of the order of the controlled object, so the order of the extended observer is 2 orders;
step 2) the differential equation of the current loop and the motion equation of the motor are rewritten into a form of input plus disturbance, because the adopted form is idThe control strategy is 0, so that only the quadrature axis current is analyzed when the current loop is analyzed, the direct axis current is not analyzed any more, and the differential equation of the quadrature axis current is rewritten as follows:
Figure BDA0003116814310000104
in the above formula
Figure BDA0003116814310000105
The total disturbance of the quadrature axis current loop can be regarded as the total disturbance, and the total disturbance comprises resistance, inductance, permanent magnet flux linkage change and external disturbance;
the equation of motion is rewritten as:
Figure BDA0003116814310000111
in the above formula fωTotal disturbance of the speed loop, caused by internal parameter changes and external load torque changes;
step 3) designing a current loop continuous linear active disturbance rejection controller, firstly analyzing the current loop, inputting the current loop as a cross-axis current reference value, outputting as a cross-axis voltage control value, and recording a state variable
Figure BDA0003116814310000112
Then equation (1.4) is expressed in the form of the following equation of state:
Figure BDA0003116814310000113
a linear state observer is designed by utilizing the design principle of Luenberger to observe disturbance quantity and state variables, and the equation of the state observer is as follows:
Figure BDA0003116814310000114
in the above formula
Figure BDA0003116814310000115
Figure BDA0003116814310000116
Respectively represent state variables
Figure BDA0003116814310000117
Figure BDA0003116814310000118
Which represents the value of the gain of the observer,
Figure BDA0003116814310000119
in order to be able to observe the error of the observer,
Figure BDA00031168143100001110
the current loop linear expansion observer is written as:
Figure BDA00031168143100001111
in the above formula
Figure BDA00031168143100001112
Figure BDA00031168143100001113
Step 4) designing a continuous linear active disturbance rejection controller of a speed loop, wherein a linear extended observer of the speed loop is expressed as:
Figure BDA0003116814310000121
the state variable matrix z in the above equationω＝[z1_ω,z2_ω]TMatrix of states
Figure BDA0003116814310000122
Observer gain matrix Lω＝[l1_ω,l2_ω]TOutput matrix Cω＝[1,0]Input matrix Bω＝[bω',0]T，uc_ω＝[uo_ω,yω]T
Step 5) designing a tracking differentiator of the speed loop, wherein the current loop does not need to track the differentiator because the expected current value of the current loop is changed rapidly along with the reference value of the current; because of the inertia effect of the speed ring, if the arrangement of the transition process is carried out without using a tracking differentiator, the speed ring system can generate bad dynamic processes such as overshoot, and the arrangement of the transition process adopts a first-order inertia link, and the expression of the first-order inertia link is as follows:
Figure BDA0003116814310000123
meanwhile, the relation between the output and the input through an inertia link is obtained as follows:
Figure BDA0003116814310000124
step 6) designing a gain matrix of the linear extended observer, connecting the gain of the observer with the bandwidth commonly used in the actual control, and writing a characteristic equation of the system in the formula (1.8) as follows:
Figure BDA0003116814310000125
expanding the characteristic expression, placing the poles of the characteristic expression at the same position, wherein the position is the bandwidth value of the observer, and obtaining a gain matrix of the observer as follows:
Figure BDA0003116814310000126
and 7) designing control laws of the speed loop and the current loop continuous linear active disturbance rejection controller, and adopting single P control for a first-order controlled object, wherein the control laws of the current loop and the speed loop are as follows:
Figure BDA0003116814310000131
uω＝Kω(rω-yω)(1.51)
in the above formula
Figure BDA0003116814310000132
KωIn order to control the gain of the laws,
Figure BDA0003116814310000133
rωreference signals for the speed loop and the current loop;
step 8) discretizing the continuous linear active disturbance rejection controller, wherein the control law part in the continuous linear active disturbance rejection controller only carries out input on the output signal of the linear extended observerThe control law part does not need discretization processing, only needs to discretize the continuous linear extended observer part and adopt an Euler discretization method to discretize the control law part, the discretization mode of the speed loop is similar to that of the current loop, only the discretization process of the current loop is deduced, and the state variable is subjected to state variable processing
Figure BDA0003116814310000134
Differentiation is performed using the following equation:
Figure BDA0003116814310000135
in the above formula
Figure BDA0003116814310000136
For the delay time caused by the current loop digital controller, the above equation is rewritten as the change of the current time compared to the previous time:
Figure BDA0003116814310000137
substituting the above equation into the state equation of the continuous system to obtain:
Figure BDA0003116814310000138
in the above formula
Figure BDA0003116814310000139
Corresponding to the state matrix
Figure BDA00031168143100001310
The expression is as follows:
Figure BDA00031168143100001311
wherein I is an identity matrix, and I is an identity matrix,
Figure BDA00031168143100001312
corresponding to the input matrix
Figure BDA00031168143100001313
The expression is as follows:
Figure BDA00031168143100001314
Figure BDA00031168143100001315
equaling the output matrix in a continuous controller
Figure BDA00031168143100001316
Is a zero matrix, and simultaneously obtains an expression equation of the discrete linear extended observer as follows:
Figure BDA0003116814310000141
in the above formula
Figure BDA0003116814310000142
The expression of (a) is:
Figure BDA0003116814310000143
wherein
Figure BDA0003116814310000144
The characteristic equation is written for a discrete linear extended observer gain matrix similar to a continuous system as follows:
Figure BDA0003116814310000145
the characteristic roots are placed at the same polar point, and a gain matrix is obtained after expansion
Figure BDA0003116814310000146
Comprises the following steps:
Figure BDA0003116814310000147
simultaneously obtaining:
Figure BDA0003116814310000148
the corresponding input matrix is:
Figure BDA0003116814310000149
the corresponding output matrix is:
Figure BDA00031168143100001410
corresponding to
Figure BDA00031168143100001411
The matrix expression of (a) is:
Figure BDA0003116814310000151
the conversion expressions of the bandwidth of the continuous linear expansion observer and the bandwidth of the discrete linear expansion observer are as follows:
Figure BDA0003116814310000152
step 9) discretization of a velocity loop tracking differentiator, wherein a forward Euler method is adopted for discretization of a first-order inertia link, and a reverse Laler identification is carried out on the inertia link to obtain:
Figure BDA0003116814310000153
obtained by a forward Euler method:
Figure BDA0003116814310000154
the simultaneous expression is as follows:
Figure BDA0003116814310000155
step 10) identifying the rotational inertia and the inductance value of the low-voltage servo motor as a determination reference of a compensation factor, and obtaining the rotational inertia value and the inductance value through an identification algorithm according to a formula:
Figure BDA0003116814310000156
Figure BDA0003116814310000157
the base numbers of the compensation factors of the current loop and the speed loop are determined, because the anti-interference performance and the dynamic performance of the system can be improved by properly increasing the value of the compensation factor in the linear active-disturbance-rejection controller, the compensation factor is multiplied by a gain factor a to obtain the compensation factor in the actual controller as follows:
Figure BDA0003116814310000158
b0_ω'＝aω*b0_ω (1.72)
step 11) using a steady state diagram mode to control the control law bandwidth omega of the current loop and the speed loopcAnd observer bandwidth ωoAnd setting, and reserving enough amplitude margin and phase margin for the two systems.
The true bookIn the embodiment, the reference input of the speed loop is given through the software of the upper computer, the given input is introduced into a discrete first-order inertia link, the time constant tau in the inertia link is adjusted, and the sampling time is the control period of the speed loop, namely ts0.001, wherein the larger the value of the time constant, the stronger the suppression of overshoot, but at the same time the longer the adjustment time required by the system.
Firstly, a PID controller is used for enabling a low-voltage servo motor to work under the condition of constant speed, at the moment, inductance parameters and rotational inertia parameters of the motor are identified, cardinalities of compensation factors of a speed loop and a current loop are determined according to the identified parameters, and meanwhile, the cardinalities are multiplied by a scale factor to obtain the compensation factors of the controller.
The output value of the operational amplifier circuit is used for sampling the direct-quadrature axis current value of the motor and is used as the input of a discrete linear extension observer, and the output of the observer from a control law is input into a control quantity obtained by a limiting function.
And designing parameters of the discrete linear active disturbance rejection controller. Firstly, considering the transfer function of a linear active disturbance rejection device, converting the linear active disturbance rejection controller into the form of the transfer function through a state equation, simultaneously considering the time delay generated by the time delay caused by a digital controller, converting the time delay into the form of the transfer function, and simultaneously writing the transfer function of a controlled object. And writing a closed-loop transfer function of the whole system, independently writing a closed-loop characteristic equation of the system, writing an iterative program, combining different control law bandwidths and proportional factors between the control laws and the observer bandwidths, substituting the combined values into the characteristic equation, and judging whether a characteristic root of the characteristic equation is positioned on a left half plane or not.
Drawing the obtained control law bandwidth and a scale factor between the control law and the observer bandwidth into a graph, determining a stable region, and obtaining controller parameters meeting requirements in the stable region through a performance evaluation function, wherein the maximum value of the scale factor cannot exceed 10.
The bandwidth of the current loop discrete linear expansion observer is obtained through a formula (1.29), and the bandwidth is substituted into a current loop controller to look up actual working conditions and find an optimal solution.
The low-voltage servo controller generally receives output values from an incremental encoder, a rotary encoder, and an absolute value encoder, and processes the signals by the controller to determine the real-time speed of the low-voltage servo motor. The linear expansion observer is used as the input of the discrete linear expansion observer of the speed loop, and the input and the current loop adopt the control quantity after amplitude limiting as the input.
The speed ring is set by adopting a setting method, so that the low-voltage servo motor can stably run under the speed ring.
The above examples merely represent one embodiment of the present invention and are not to be construed as limiting the scope of the invention. It should be noted that a person skilled in the art could make several alternative designs without departing from the inventive concept, which falls within the scope of the invention.

Claims (1)

1. A low-voltage servo discrete linear active disturbance rejection control method, comprising the steps of:
step 1) determining the order of a controlled object of a current loop and a speed loop, wherein the determined order is determined by a differential equation of current and a motion equation, and the differential equation of quadrature-direct axis current is as follows:
Figure FDA0003116814300000011
Figure FDA0003116814300000012
in the above formula id、iqIs a quadrature-direct axis current value, RsIs the motor resistance value, Ld、LqIs a quadrature-direct axis inductance value, omegaeFor motor speed value, #fIs the flux linkage value of the permanent magnet;
the equation of motion is:
Figure FDA0003116814300000013
in the above formula npIs the number of pole pairs, T, of the motoreIs the electromagnetic torque of the machine, TLIs the load torque of the motor, J is the moment of inertia of the motor, Lmd、LmqThe armature reaction inductor is a quadrature-direct axis armature reaction inductor;
as can be seen from (1.1) to (1.3), the order of the passive object of the current loop and the speed loop is 1, and according to the design rule of the active disturbance rejection controller, the order of the extended observer needs to be increased by 1 on the basis of the order of the controlled object, so the order of the extended observer is 2 orders;
step 2) the differential equation of the current loop and the motion equation of the motor are rewritten into a form of input plus disturbance, because the adopted form is idThe control strategy is 0, so that only the quadrature axis current is analyzed when the current loop is analyzed, the direct axis current is not analyzed any more, and the differential equation of the quadrature axis current is rewritten as follows:
Figure FDA0003116814300000014
in the above formula
Figure FDA0003116814300000015
The total disturbance of the quadrature axis current loop can be regarded as the total disturbance, and the total disturbance comprises resistance, inductance, permanent magnet flux linkage change and external disturbance;
the equation of motion is rewritten as:
Figure FDA0003116814300000016
in the above formula fωIs the total disturbance of the speed loop, caused by internal parameter changes and external load torque changes;
step 3) designing a current loop continuous linear active disturbance rejection controller, firstly analyzing the current loop, inputting the current loop as a cross-axis current reference value, outputting as a cross-axis voltage control value, and recording a state variable
Figure FDA0003116814300000017
Then equation (1.4) is expressed in the form of the following equation of state:
Figure FDA0003116814300000021
a linear state observer is designed by utilizing the design principle of Luenberger to observe disturbance quantity and state variables, and the equation of the state observer is as follows:
Figure FDA0003116814300000022
in the above formula
Figure FDA0003116814300000023
Figure FDA00031168143000000216
Respectively represent state variables
Figure FDA0003116814300000024
Figure FDA0003116814300000025
Which represents the value of the gain of the observer,
Figure FDA0003116814300000026
in order to be able to observe the error of the observer,
Figure FDA0003116814300000027
the current loop linear expansion observer is written as:
Figure FDA0003116814300000028
the upper typeIn
Figure FDA0003116814300000029
Figure FDA00031168143000000210
Step 4) designing a continuous linear active disturbance rejection controller of a speed loop, wherein a linear extended observer of the speed loop is expressed as:
Figure FDA00031168143000000211
the state variable matrix z in the above equationω＝[z1_ω,z2_ω]TMatrix of states
Figure FDA00031168143000000212
Observer gain matrix Lω＝[l1_ω,l2_ω]TOutput matrix Cω＝[1,0]Input matrix Bω＝[bω',0]T，uc_ω＝[uo_ω,yω]T；
Step 5) designing a tracking differentiator of the speed loop, wherein the current loop does not need to track the differentiator because the expected current value of the current loop is changed rapidly along with the reference value of the current; because of the inertia effect of the speed ring, if the arrangement of the transition process is carried out without using a tracking differentiator, the speed ring system can generate bad dynamic processes such as overshoot, and the arrangement of the transition process adopts a first-order inertia link, and the expression of the first-order inertia link is as follows:
Figure FDA00031168143000000213
meanwhile, the relation between the output and the input through an inertia link is obtained as follows:
Figure FDA00031168143000000214
step 6) designing a gain matrix of the linear extended observer, connecting the gain of the observer with the bandwidth commonly used in the actual control, and writing a characteristic equation of the system in the formula (1.8) as follows:
Figure FDA00031168143000000215
expanding the characteristic expression, placing the poles of the characteristic expression at the same position, wherein the position is the bandwidth value of the observer, and obtaining a gain matrix of the observer as follows:
Figure FDA0003116814300000031
and 7) designing control laws of the speed loop and the current loop continuous linear active disturbance rejection controller, and adopting single P control for a first-order controlled object, wherein the control laws of the current loop and the speed loop are as follows:
Figure FDA0003116814300000032
uω＝Kω(rω-yω) (0.15)
in the above formula
Figure FDA0003116814300000033
KωIn order to control the gain of the laws,
Figure FDA0003116814300000034
rωreference signals for the speed loop and the current loop;
step 8) discretizing the continuous linear active disturbance rejection controller, wherein a control law part in the continuous linear active disturbance rejection controller only amplifies an output signal of the linear extended observer, so that the control law part does not need to carry outDiscretization only needs to be carried out on a continuous linear expansion observer part, the continuous linear expansion observer part is discretized by adopting an Euler discretization method, the discretization mode of a speed loop is similar to that of a current loop, only the discretization process of the current loop is deduced, and state variables are subjected to state variable discretization
Figure FDA0003116814300000035
Differentiation is performed using the following equation:
Figure FDA0003116814300000036
in the above formula
Figure FDA0003116814300000037
For the delay time caused by the current loop digital controller, the above equation is rewritten as the change of the current time compared to the previous time:
Figure FDA0003116814300000038
substituting the above equation into the state equation of the continuous system to obtain:
Figure FDA0003116814300000039
in the above formula
Figure FDA00031168143000000310
Corresponding to the state matrix
Figure FDA00031168143000000311
The expression is as follows:
Figure FDA00031168143000000312
wherein I is a unit momentThe number of the arrays is determined,
Figure FDA00031168143000000313
corresponding to the input matrix
Figure FDA00031168143000000314
The expression is as follows:
Figure FDA00031168143000000315
Figure FDA00031168143000000316
equaling the output matrix in a continuous controller
Figure FDA00031168143000000317
Is a zero matrix, and simultaneously obtains an expression equation of the discrete linear extended observer as follows:
Figure FDA00031168143000000318
in the above formula
Figure FDA00031168143000000319
The expression of (a) is:
Figure FDA00031168143000000320
wherein
Figure FDA0003116814300000041
The characteristic equation is written for a discrete linear extended observer gain matrix similar to a continuous system as follows:
Figure FDA0003116814300000042
the characteristic roots are placed at the same polar point, and a gain matrix is obtained after expansion
Figure FDA0003116814300000043
Comprises the following steps:
Figure FDA0003116814300000044
simultaneously obtaining:
Figure FDA0003116814300000045
the corresponding input matrix is:
Figure FDA0003116814300000046
the corresponding output matrix is:
Figure FDA0003116814300000047
corresponding to
Figure FDA0003116814300000048
The matrix expression of (a) is:
Figure FDA0003116814300000049
the conversion expressions of the bandwidth of the continuous linear expansion observer and the bandwidth of the discrete linear expansion observer are as follows:
Figure FDA00031168143000000410
step 9) discretization of a velocity loop tracking differentiator, wherein a forward Euler method is adopted for discretization of a first-order inertia link, and a reverse Laler identification is carried out on the inertia link to obtain:
Figure FDA00031168143000000411
obtained by a forward Euler method:
Figure FDA00031168143000000412
the simultaneous expression is as follows:
Figure FDA00031168143000000413
step 10) identifying the rotational inertia and the inductance value of the low-voltage servo motor as a determination reference of a compensation factor, and obtaining the rotational inertia value and the inductance value through an identification algorithm according to a formula:
Figure FDA0003116814300000051
Figure FDA0003116814300000052
the base numbers of the compensation factors of the current loop and the speed loop are determined, because the anti-interference performance and the dynamic performance of the system can be improved by properly increasing the value of the compensation factor in the linear active-disturbance-rejection controller, the compensation factor is multiplied by a gain factor a to obtain the compensation factor in the actual controller as follows:
Figure FDA0003116814300000053
b0_ω'＝aω*b0_ω (0.36)
step 11) using a steady state diagram mode to control the control law bandwidth omega of the current loop and the speed loopcAnd observer bandwidth ωoAnd setting, and reserving enough amplitude margin and phase margin for the two systems.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114265441A (en) * 2021-12-29 2022-04-01 中车大连电力牵引研发中心有限公司 Improved self-reactive control speed controller based on time delay and hysteresis compensation
CN114428457A (en) * 2021-12-15 2022-05-03 东南大学 Robust active disturbance rejection control method for time delay-containing system

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH06289917A (en) * 1993-03-30 1994-10-18 Fanuc Ltd Servo motor control method by estimated disturbance load torque
JPH07327382A (en) * 1994-05-30 1995-12-12 Fanuc Ltd Control system for ac motor
CN107592048A (en) * 2017-10-12 2018-01-16 重庆航天职业技术学院 The adaptive chaos control method of fractional order brushless DC motor system
CN112398397A (en) * 2020-11-27 2021-02-23 浙江工业大学 Linear active disturbance rejection permanent magnet synchronous motor control method based on model assistance
CN112782977A (en) * 2020-12-23 2021-05-11 中国科学院宁波材料技术与工程研究所慈溪生物医学工程研究所 Motor compliance control method based on BP neural network and extended observer

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP6289917B2 (en) * 2014-01-21 2018-03-07 住友重機械工業株式会社 Injection molding machine

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH06289917A (en) * 1993-03-30 1994-10-18 Fanuc Ltd Servo motor control method by estimated disturbance load torque
JPH07327382A (en) * 1994-05-30 1995-12-12 Fanuc Ltd Control system for ac motor
CN107592048A (en) * 2017-10-12 2018-01-16 重庆航天职业技术学院 The adaptive chaos control method of fractional order brushless DC motor system
CN112398397A (en) * 2020-11-27 2021-02-23 浙江工业大学 Linear active disturbance rejection permanent magnet synchronous motor control method based on model assistance
CN112782977A (en) * 2020-12-23 2021-05-11 中国科学院宁波材料技术与工程研究所慈溪生物医学工程研究所 Motor compliance control method based on BP neural network and extended observer

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
唐彬彬 等: "永磁同步电机自抗扰控制调速***", 《电机与控制应用》 *

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114428457A (en) * 2021-12-15 2022-05-03 东南大学 Robust active disturbance rejection control method for time delay-containing system
CN114428457B (en) * 2021-12-15 2023-09-05 东南大学 Robust active disturbance rejection control method for delay-containing system
CN114265441A (en) * 2021-12-29 2022-04-01 中车大连电力牵引研发中心有限公司 Improved self-reactive control speed controller based on time delay and hysteresis compensation

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