CN117439463A - Active disturbance rejection rotating speed current single loop control method and system for permanent magnet synchronous motor - Google Patents

Active disturbance rejection rotating speed current single loop control method and system for permanent magnet synchronous motor Download PDF

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Publication number
CN117439463A
CN117439463A CN202311169688.1A CN202311169688A CN117439463A CN 117439463 A CN117439463 A CN 117439463A CN 202311169688 A CN202311169688 A CN 202311169688A CN 117439463 A CN117439463 A CN 117439463A
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observer
permanent magnet
axis
magnet synchronous
synchronous motor
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张广明
刘小俊
史志寒
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Nanjing Tech University
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Nanjing Tech University
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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
    • H02P21/22—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
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • 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
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Control Of Ac Motors In General (AREA)

Abstract

The invention discloses an active disturbance rejection rotating speed current single loop control method and system of a permanent magnet synchronous motor, and relates to the field of permanent magnet synchronous motor control. Calculating a calibration value error and total disturbance quantity, and setting out a second-order equation form; expanding the state quantity of the second-order equation by using an extended state observer, and determining gain parameters of the extended state observer to estimate a state variable; introducing a new observer having a derivative form to estimate state variables of the extended state observer and further optimizing observer errors to correct the observer output; and calculating the control rate of the controller by comparing the corrected observer output and the given value. Compared with the traditional extended state observer, the new extended state observer solves the problem of non-derivative items of the traditional extended state observer, compensates the observed disturbance quantity of the observer, and enhances the accuracy of the observer.

Description

Active disturbance rejection rotating speed current single loop control method and system for permanent magnet synchronous motor
Technical Field
The invention relates to the field of permanent magnet synchronous motor control, in particular to an active disturbance rejection rotating speed current single loop control method and system of a permanent magnet synchronous motor.
Background
With the improvement of the manufacturing process of the rare earth permanent magnet material, the permanent magnet synchronous motor has the characteristics of high efficiency, small volume, simple structure and the like, so that the development of the permanent magnet synchronous motor is greatly improved, and the permanent magnet synchronous motor is particularly used in the fields of wind power generation, new energy automobiles, rail transit and the like. The control system of the permanent magnet synchronous motor is of great importance for the application field of the permanent magnet synchronous motor. The permanent magnet synchronous motor control system comprises a plurality of variables, and complex electromagnetic relations and coupling relations exist among the variables. At present, vector control and direct torque control are mostly adopted for controlling the permanent magnet synchronous motor, and various control means are derived on the basis of the vector control and the direct torque control. However, in essence, the control amount of the permanent magnet synchronous motor is not more than 3, namely, the rotational speed, the d-axis current and the q-axis current are respectively, namely, 3 controllers are usually required to be designed. Currently, in practical engineering applications, a proportional-integral (PI) controller is mostly adopted, however, the PI controller is deficient in terms of robustness, that is, cannot cope with external disturbances well. With the development of modern control theory, more and more advanced control means are applied to 3 controllers of the permanent magnet synchronous motor, such as sliding mode control, self-adaptive control, active disturbance rejection control and the like. In essence, the output of the speed controller is given by the q-axis current controller, and the equation of the speed and the q-axis current can be established by the equation, so that 1 speed/q-axis current controller can solve 2 speed and q-axis current controllers.
The active disturbance rejection control is Han Jing, and is a technology capable of estimating and compensating the unmodeled dynamic and out-of-position disturbance actions of the system without total disturbance of the system, and is particularly suitable for nonlinear systems with system parameter changes and external disturbance. The motor motion equation between the rotating speed and q-axis current of the permanent magnet synchronous motor is a second-order equation and is a nonlinear system of parameter change and external disturbance, so that an active disturbance rejection control technology can be used, and in a traditional second-order active disturbance rejection controller, because of the non-derivative term of the equation of the state expansion observer, a larger error exists between the system equation and the equation, and the performance of the controller is affected. Meanwhile, the disturbance quantity of the observer is not further compensated, so that the observation precision is problematic.
Disclosure of Invention
The invention is provided in view of the problem that the equation of the state expansion observer in the traditional active disturbance rejection control has a non-derivative term, so that a larger error exists between the equation and a system equation.
Therefore, the problem to be solved by the invention is how to solve the problem of non-derivative term of the equation of the state expansion observer in the traditional active disturbance rejection control, and compensate the expanded disturbance quantity, so that the performance of the observer is ensured, and the performance of the controller is further improved.
In order to solve the technical problems, the invention provides the following technical scheme:
in a first aspect, an embodiment of the present invention provides an active disturbance rejection rotational speed current single loop control method for a permanent magnet synchronous motor, which includes calculating a calibration value error and a total disturbance quantity through a permanent magnet synchronous motor shaft current equation, a motion equation and an electromagnetic torque equation of the permanent magnet synchronous motor, and setting a second order equation form; expanding the state quantity of the second-order equation by using an extended state observer, converting the second-order equation into a group of first-order equations by selecting proper state variables, and determining gain parameters of the extended state observer to estimate the state variables; introducing a new observer having a derivative form to estimate state variables of the extended state observer and further optimizing observer errors to correct the observer output; calculating the control rate of the controller by comparing the corrected observer output and the given value; according to the control rate of the controller, voltage and current are applied to the permanent magnet synchronous stator windings through power electronics to achieve the desired speed and q-axis current control rate.
As a preferable scheme of the active disturbance rejection rotational speed current single loop control method of the permanent magnet synchronous motor, the invention comprises the following steps: the specific formula of the d-q axis current equation of the permanent magnet synchronous motor is as follows:
wherein R is the stator resistance of the motor, u d And u q Voltages of d-axis and q-axis of stator, i d And i q Currents of d-axis and q-axis of stator, L d And L q Respectively the d-axis inductance and the q-axis inductance of the stator, omega e For the electrical angular velocity of the motor, ψ f Is a permanent magnet flux linkage.
The specific formula of the motion equation of the permanent magnet synchronous motor is as follows:
wherein T is e Is electromagnetic torque, T L For the load torque, J is the moment of inertia of the motor, B is the coefficient of friction of the motor, p is the pole pair number of the motor, ω e Is the electrical angular velocity of the motor.
The specific formula of the electromagnetic torque equation is as follows:
wherein T is e For electromagnetic torque, p is the pole pair number of the motor, ψ f I is a permanent magnet flux linkage d And i q Currents of d-axis and q-axis of stator, L d And L q The stator d-axis and q-axis inductances, respectively.
As a preferable scheme of the active disturbance rejection rotational speed current single loop control method of the permanent magnet synchronous motor, the invention comprises the following steps: the specific formula for determining the gain parameters of the extended state observer to estimate the state variables is as follows:
wherein u is q For the voltage of the q axis of the stator, b is the system input coefficient, d ω The specific formula is as follows:
wherein R is the stator resistance of the motor, i d And i q Currents of d-axis and q-axis of stator, L d And L q Respectively the d-axis inductance and the q-axis inductance of the stator, omega e For the electrical angular velocity of the motor, ψ f Is a permanent magnet flux linkage, T e Is electromagnetic torque, T L J is the moment of inertia of the motor, B is the coefficient of friction of the motor, and p is the pole pair number of the motor.
The specific formula listing the second order equation form is as follows:
wherein b 0 For the initial value of the system input coefficient, i.e. calculated by the relevant parameters of the motor calibration, f is the total disturbance quantity, u q For voltage of stator q-axis, x 1 ＝ω e ，ω e Is the electrical angular velocity of the motor.
As a preferable scheme of the active disturbance rejection rotational speed current single loop control method of the permanent magnet synchronous motor, the invention comprises the following steps: the specific formula for expanding the state quantity of the second-order equation by using the expanding state observer is as follows:
wherein:u q for stator q-axis current, x 3 ＝f。
As a preferable scheme of the active disturbance rejection rotational speed current single loop control method of the permanent magnet synchronous motor, the invention comprises the following steps: the specific formula of the using the extended state observer is as follows:
wherein z is e1 、z e2 And z e3 Is the observed quantity of the extended state observer, l 1 、l 2 And l 3 B is the gain of the observer 0 For initial values of system input coefficients, x 1 ＝ω e ，ω e For the electrical angular velocity of the motor u q Is the voltage of the q-axis of the stator.
As a preferable scheme of the active disturbance rejection rotational speed current single loop control method of the permanent magnet synchronous motor, the invention comprises the following steps: the specific formula for introducing a new observer with derivative form is as follows:
wherein z is 1 、z 2 And z 3 For the observed quantity of the new observer, l 1 And l 2 In order for the gain of the observer to be,observations of f, b 0 For initial values of system input coefficients, x 1 ＝ω e ，ω e For the electrical angular velocity of the motor u q For voltage of q-axis of stator e 1 ＝x 1 -z 1 ，e 2 ＝x 2 -z 2 ，/>
As a preferable scheme of the active disturbance rejection rotational speed current single loop control method of the permanent magnet synchronous motor, the invention comprises the following steps: the specific formula according to the control rate of the controller is as follows:
wherein k is p And k d Is a controller parameter to be designed, z 1 And z 2 For the observed quantity of the new observer,k d ＝2ω c ，ω c for the bandwidth of the controller, r is the rotating speed given value, b 0 For the initial value of the system input coefficient, +.>Is the observed value of f.
In a second aspect, an embodiment of the present invention provides an active disturbance rejection rotational speed current single loop control system for a permanent magnet synchronous motor, including: the calibration value error and total disturbance quantity calculation module is used for calculating the calibration value error and the total disturbance quantity based on a permanent magnet synchronous motor shaft current equation, a motion equation and an electromagnetic torque equation; the extended state observer module expands the state quantity of the second-order equation and determines gain parameters of the extended state observer so as to estimate state variables; a new extended state observer module that introduces a new observer with derivative form to estimate state variables of the extended state observer and further optimizes the observation error to correct the output of the observer; the controller module is used for calculating the control rate of the controller; and the power electronic device module is used for applying voltage to the stator winding of the permanent magnet synchronous motor through a power electronic device so as to realize the required rotation speed and q-axis current control. In a third aspect, embodiments of the present invention provide a computer apparatus comprising a memory and a processor, the memory storing a computer program, wherein: the computer program instructions, when executed by a processor, implement the steps of the active disturbance rejection rotational speed current single loop control method of the permanent magnet synchronous motor according to the first aspect of the present invention.
In a fourth aspect, embodiments of the present invention provide a computer-readable storage medium having a computer program stored thereon, wherein: the computer program instructions, when executed by a processor, implement the steps of the active disturbance rejection rotational speed current single loop control method of the permanent magnet synchronous motor according to the first aspect of the present invention.
The invention has the beneficial effects that: compared with the traditional extended state observer, the new extended state observer solves the problem of non-derivative items of the traditional extended state observer, compensates the observed disturbance quantity of the observer, enhances the accuracy of the observer, and has better robustness under the conditions of given rotation speed change and load mutation as can be seen through rotation speed response.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art. Wherein:
fig. 1 is a control block diagram of the method according to the present invention for controlling the active disturbance rejection rotational speed current single loop of the permanent magnet synchronous motor according to embodiment 1.
Fig. 2 is a block diagram of a permanent magnet synchronous motor driving system according to the active disturbance rejection rotational speed current single loop control method of the permanent magnet synchronous motor of embodiment 1.
Fig. 3 is a PI rotational speed waveform of the active disturbance rejection rotational speed current single loop control method of the permanent magnet synchronous motor of embodiment 2.
Fig. 4 is a waveform of a conventional active disturbance rejection rate of the active disturbance rejection rate current single loop control method of the permanent magnet synchronous motor according to embodiment 2.
Fig. 5 is a rotational speed waveform of the active disturbance rejection rotational speed current single loop control method of the permanent magnet synchronous motor of embodiment 2.
Detailed Description
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways other than those described herein, and persons skilled in the art will readily appreciate that the present invention is not limited to the specific embodiments disclosed below.
Further, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic can be included in at least one implementation of the invention. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.
Example 1
Referring to fig. 1-2, a first embodiment of the present invention provides an active disturbance rejection rotational speed current single loop control method for a permanent magnet synchronous motor, including,
s1: calculating a calibration value error and total disturbance quantity through a permanent magnet synchronous motor shaft current equation, a motion equation and an electromagnetic torque equation of the permanent magnet synchronous motor, and setting out a second-order equation form.
Specifically, the specific formula of the d-q axis current equation of the permanent magnet synchronous motor is as follows:
wherein R is the stator resistance of the motor, u d And u q Voltages of d-axis and q-axis of stator, i d And i q Currents of d-axis and q-axis of stator, L d And L q Respectively the d-axis inductance and the q-axis inductance of the stator, omega e For the electrical angular velocity of the motor, ψ f Is a permanent magnet flux linkage.
Further, the specific formula of the motion equation of the permanent magnet synchronous motor is as follows:
wherein T is e Is electromagnetic torque, T L For the load torque, J is the moment of inertia of the motor, B is the coefficient of friction of the motor, p is the pole pair number of the motor, ω e Is the electrical angular velocity of the motor.
Further, the specific formula of the electromagnetic torque equation is as follows:
wherein T is e For electromagnetic torque, p is the pole pair number of the motor, ψ f I is a permanent magnet flux linkage d And i q Currents of d-axis and q-axis of stator, L d And L q The stator d-axis and q-axis inductances, respectively.
Specifically, the specific formula for obtaining the derivative equation by combining the motion equation and the electromagnetic torque equation of the permanent magnet synchronous motor is as follows:
wherein R is the stator resistance of the motor, i d And i q Currents of d-axis and q-axis of stator, L d And L q For stator d-axis and q-axis inductances, ω e For the electrical angular velocity of the motor, ψ f Is a permanent magnet flux linkage, T L J is the moment of inertia of the motor, B is the coefficient of friction of the motor, and p is the pole pair number of the motor.
S2: the state quantity expansion is performed on the second-order equation by using the expansion state observer, the second-order equation is converted into the expansion state observer equation by selecting an appropriate state variable, and gain parameters of the expansion state observer are determined to estimate the state variable.
Further, substituting the q-axis current equation of the permanent magnet synchronous motor into a derivative equation obtained by combining a motion equation and an electromagnetic torque equation of the permanent magnet synchronous motor to obtain a specific formula for determining gain parameters of the extended state observer to estimate state variables, wherein the specific formula is as follows:
wherein u is q For the voltage of the q axis of the stator, b is the system input coefficient, d ω The specific formula is as follows:
wherein R is the stator resistance of the motor, i d And i q Currents of d-axis and q-axis of stator, L d And L q Is a statord-axis and q-axis inductances, ω e For the electrical angular velocity of the motor, ψ f Is a permanent magnet flux linkage, T e Is electromagnetic torque, T L J is the moment of inertia of the motor, B is the coefficient of friction of the motor, and p is the pole pair number of the motor.
Specifically, since the motor parameter changes during operation, i.e. there is an error with the calibration value, the parameter of b will change, and thus the specific formula is as follows:
f＝(Δbu q +d ω )
wherein b 0 For the initial value of the system input coefficient, namely, calculated by the related parameters of motor calibration, delta b is the variation of the parameters, f is the total disturbance quantity, u q For voltage of q-axis of stator, ω e Is the electrical angular velocity of the motor.
Further, the specific formulas listing the second order equation form are as follows:
wherein b 0 For the initial value of the system input coefficient, i.e. calculated by the relevant parameters of the motor calibration, f is the total disturbance quantity, u q For voltage of stator q-axis, x 1 ＝ω e ，ω e Is the electrical angular velocity of the motor.
S3: a new observer with derivative form is introduced to estimate the state variables of the extended state observer and the observer error is further optimized to correct the observer output.
Specifically, an extended state observer is required in active disturbance rejection control, and a second-order equation form is required to be subjected to stateThe amount of expansion is usually calculated by taking the disturbance amount as the expansion amount, let x 3 =f, the specific formula for state quantity expansion of the second order equation using the expansion state observer is obtained as follows:
wherein:u q is the voltage of the q-axis of the stator.
Further, the state quantity expansion is performed on the second-order equation by using the expansion state observer to construct the expansion state observer, namely, the specific formula of the expansion state observer is as follows:
wherein z is e1 、z e2 And z e3 Is the observed quantity of the extended state observer, l 1 、l 2 And l 3 B is the gain of the observer 0 For initial values of system input coefficients, x 1 ＝ω e ，ω e For the electrical angular velocity of the motor u q Is the voltage of the q-axis of the stator.
Further, the parameters are selected to stabilize the observer system while ensuring z e1 、z e2 And z e3 Respectively converge to x 1 、x 2 And x 3 The formula extended state observer performs state quantity extension on the second-order equation to subtract the formula extended state observer to obtain a specific formula such asThe following steps:
wherein,
specifically, to ensure system stability, it is common to 1 、l 2 And l 3 Is selected so that A 1 The root of the characteristic root equation is on the negative real axis, and the specific formula of the characteristic root equation is as follows:
α 1 (s)＝s 3 +l 1 s 2 +l 2 s+l 3 ＝(s+ω o ) 3
wherein l 1 ＝3ω o ，l 2 ＝3ω o 2 ，l 2 ＝ω o 3 ，ω o Is the bandwidth of the observer.
Preferably, by selecting ω o Is used to determine the gain parameters of the extended state observer, the bandwidth omega of the observer o Determining the tracking speed omega of the observer o The larger the observer estimates the faster the disturbance, but ω o Excessive, may cause the permanent magnet synchronous motor to cause mechanical vibration during high-speed operation, and the mechanical vibration may be converted into sound, resulting in intolerable noise and motor output oscillation.
S4: and calculating the control rate of the controller by comparing the corrected observer output and the given value.
Specifically, by comparing the state quantity expansion equation for the second-order equation with the expansion state observer, it is found that x, which performs the state quantity expansion equation for the second-order equation with the expansion state observer, is calculated 1 And x 2 Is in the form of a derivative, and z of the extended state observer formula e1 And z e2 Rather than in derivative form, it is furthermore possible to derive from the formula of state quantity expansion of the second order equation with a state of expansion observer:
wherein, indicate e e2 Not only e e1 Derivative of e e3 Nor only e e1 And is disturbed by other terms.
Specifically, to solve the problem of accumulated error, a new observer with derivative form is proposed with the following specific formula:
wherein z is 1 And z 2 For the observed quantity of the new observer, l 1 And l 2 In order for the gain of the observer to be,observations of f, b 0 For initial value, u q For voltage of q-axis of stator e 1 ＝x 1 -z 1 ，e 2 ＝x 2 -z 2 。
Further, the second order equation form equation minus the new observer equation with derivative form yields the original disturbance specific equation for the system as follows:
further, it can be seen that e 2 Is e 1 And solves the problem of accumulated error of the observer, but the estimation error in the original disturbance formula of the system still has a relation with the original disturbance estimation of the system, and in order to solve the problem, a specific formula of adding a compensation function into the new observer is as follows:
wherein z is 1 And z 2 For the observed quantity of the new observer, l 1 And l 2 In order for the gain of the observer to be,observation of f, ++>B for compensation function 0 For the initial value of system input coefficient, u q For voltage of q-axis of stator e 1 ＝x 1 -z 1 ，e 2 ＝x 2 -z 2 。
Specifically, the formula of the compensation function added to the new observer is subtracted from the formula of the second-order equation of the expansion state quantity, so that the following formula can be obtained:
further, whenWhen f is sufficiently close, the estimation error of the equation of the form of the second order equation minus the equation of the new observer to which the compensation function is added will be significantly reduced, due to +.>For the estimated value of f, a low-pass filter can be designed to obtain the specific formula of the compensation function as follows:
where λ is the filter coefficient, typically 2pi.f c ，f c Is the cut-off frequency of the filter.
Specifically, the formula for obtaining the compensation function by the low-pass filter can be obtained:
further, the specific formula for introducing a new observer with derivative form is as follows:
wherein z is 1 、z 2 And z 3 For the observed quantity of the new observer, l 1 And l 2 In order for the gain of the observer to be,observations of f, b 0 For initial values of system input coefficients, x 1 ＝ω e ，ω e For the electrical angular velocity of the motor u q For voltage of q-axis of stator e 1 ＝x 1 -z 1 ，e 2 ＝x 2 -z 2 ，/>
Specifically, the formula of the new observer with derivative form is subtracted from the formula of the second order equation of the state quantity of expansion to obtain:
wherein,
further, to ensure system stability, it is common to 1 、l 2 And selecting parameters of lambda, namely enabling the root of the characteristic root equation of A2 to be on the negative real axis, wherein the characteristic root equation is specifically as follows:
α 2 (s)＝s 3 +l 1 s 2 +(λl 1 +l 2 )s+λl 2
wherein let l 1 ＝2ξω n ，l 2 ＝ω n 2 The specific formula of the feature root equation is as follows:
α 2 (s)＝s 3 +2ξω n s 2 +(2λξω n +ω n 2 )s+λω n 2
wherein, xi is damping ratio, omega n For observer bandwidth, s is the feature root, lambda filter coefficient.
Furthermore, the damping ratio is generally selected to be about 1, λ is a filter coefficient, the cut-off frequency of the low-pass filter represented by the damping ratio is proportional to the convergence rate of the compensating disturbance function, and ω can be selected according to the maximum disturbance frequency and the minimum noise frequency n Expressed as observer bandwidth.
S5: according to the control rate of the controller, voltage and current are applied to the permanent magnet synchronous stator windings through power electronics to achieve the desired speed and q-axis current control rate.
Specifically, the core of the active disturbance rejection control is how to estimate and eliminate f in real time, so that x in the form of a second-order equation 2 A specific formula for the standard form of the linear integrator series, which is similar to the following, is presented as follows:
i.e. the specific formula of the linear state error feedback control law is as follows:
wherein u is q For the voltage of the stator q-axis, f is the total disturbance quantity, b 0 An initial amount of coefficients is input to the system.
Further, since the observer can estimate the disturbance and compensate in real time, an integrator may no longer be needed, and the linear state error feedback control law can be further simplified into the specific formula of the design of the proportional-derivative combination as follows:
u q0 ＝k p (r-z 1 )-k d z 2
wherein k is p And k d Is a controller parameter to be designed, z 1 And z 2 U is the observed quantity of the new observer q0 Is a linear state error feedback control law.
Furthermore, according to the designed output signal of the controller, the specific formula for obtaining the control rate is as follows:
wherein k is p And k d Is a controller parameter to be designed, z 1 And z 2 For the observed quantity of the new observer,k d ＝2ω c ，ω c for the bandwidth of the controller, r is the rotating speed given value, b 0 For the initial value of the system input coefficient, +.>Is the observed value of f.
It should be noted that, in the method of this embodiment, rotation speed setting and rotation speed feedback need to be obtained, by this method, a control law of q-axis voltage can be obtained, and in addition, a control law of d-axis voltage still adopts traditional proportional integral control. On the basis of obtaining the control law of d-q axis voltage, alpha-beta axis voltage is obtained through Ipak transformation, PWM signals are obtained through SVPWM pulse width modulation, PWM is given to a three-phase full-bridge inverter, and output three-phase voltage of the inverter is given to a stator winding of a permanent magnet synchronous motor for driving the motor.
Further, the embodiment also provides an active disturbance rejection rotation speed current single loop control system of the permanent magnet synchronous motor, which comprises the embodiment and a computer device, and is suitable for the situation of an active disturbance rejection rotation speed current single loop control method of the permanent magnet synchronous motor, and comprises a memory and a processor; the memory is used for storing computer executable instructions, and the processor is used for executing the computer executable instructions to realize the active disturbance rejection rotating speed current single loop control method of the permanent magnet synchronous motor, which is provided by the embodiment.
The computer device may be a terminal comprising a processor, a memory, a communication interface, a display screen and input means connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The communication interface of the computer device is used for carrying out wired or wireless communication with an external terminal, and the wireless mode can be realized through WIFI, an operator network, NFC (near field communication) or other technologies. The display screen of the computer equipment can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer equipment can be a touch layer covered on the display screen, can also be keys, a track ball or a touch pad arranged on the shell of the computer equipment, and can also be an external keyboard, a touch pad or a mouse and the like.
The present embodiment also provides a storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of: calculating a calibration value error and total disturbance quantity through a permanent magnet synchronous motor shaft current equation, a motion equation and an electromagnetic torque equation of the permanent magnet synchronous motor, and setting out a second-order equation form; expanding the state quantity of the second-order equation by using an extended state observer, converting the second-order equation into a group of first-order equations by selecting proper state variables, and determining gain parameters of the extended state observer to estimate the state variables; introducing a new observer having a derivative form to estimate the error of the extended state observer and correcting the output of the observer; calculating an output signal of the controller by comparing the corrected observer output with the target value; according to the output signal of the controller, voltage and current are applied to the permanent magnet synchronous motor through a power electronic device so as to realize the required rotating speed and q-axis current control rate.
In conclusion, compared with the traditional extended state observer, the novel extended state observer solves the problem of non-derivative items of the traditional extended state observer, compensates the observed disturbance quantity of the observer, enhances the accuracy of the observer, and has better robustness under the conditions of given rotation speed change and load abrupt change as can be seen through rotation speed response.
Example 2
Referring to fig. 3 to 5, in order to verify the beneficial effects of the present invention, a scientific demonstration is performed through economic benefit calculation and simulation experiments.
Specifically, through verification on a MATLAB/Simulink simulation platform, and comparison with a traditional expansion state observer applied to traditional rotating speed current double-loop proportional integral control and rotating speed current single-loop control, simulation conditions are set as follows: at start-up, the given speed was 600rpm, after 4s, 2400rpm. At start-up, the load torque was 0.028n.m, and after 5s, the load torque was 0.28n.m. Rotational speed waveforms in three cases.
Further, as shown in fig. 3, under the conventional speed-current double-loop proportional-integral control, when a given speed is changed, the speed response has a larger overshoot of about 60rpm, and when the load is suddenly changed, the speed has a larger pulsation of about 120rpm.
Further, using a conventional extended state observer in the speed-current single loop control, as shown in fig. 4, the overshoot of the speed response is about 40rpm for a given speed change, and the speed pulsation is about 24rpm for a sudden load change.
Preferably, as shown in fig. 5, under the proposed control method, the rotational speed response is substantially free from overshoot given the rotational speed change, and the rotational speed pulsation is about 4rpm when the load is suddenly changed.
Specifically, compared with the traditional rotating speed current double-loop proportional integral control, the method of the embodiment can replace 2 controllers of PI by 1 controller, the rotating speed response is improved greatly compared with PI, and the method has good robustness for given rotating speed change and load mutation.
Furthermore, compared with the traditional extended state observer, the method solves the problem of the non-derivative term of the traditional active disturbance rejection, compensates the observed disturbance quantity, enhances the accuracy of the observer, and has better robustness under the conditions of given rotation speed change and load abrupt change as can be seen through rotation speed response.
It should be noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solution of the present invention may be modified or substituted without departing from the spirit and scope of the technical solution of the present invention, which is intended to be covered in the scope of the claims of the present invention.

Claims (10)

1. A method for controlling an active disturbance rejection rotating speed current single loop of a permanent magnet synchronous motor is characterized by comprising the following steps of: comprising the steps of (a) a step of,
calculating a calibration value error and total disturbance quantity through a permanent magnet synchronous motor shaft current equation, a motion equation and an electromagnetic torque equation of the permanent magnet synchronous motor, and setting out a second-order equation form;
expanding the state quantity of the second-order equation by using an extended state observer, converting the second-order equation into an extended state observer equation by selecting an appropriate state variable, and determining gain parameters of the extended state observer to estimate the state variable;
introducing a new observer having a derivative form to estimate state variables of the extended state observer and further optimizing observer errors to correct the observer output;
calculating the control rate of the controller by comparing the corrected observer output and the given value;
according to the control rate of the controller, voltage and current are applied to the permanent magnet synchronous stator windings through power electronics to achieve the desired speed and q-axis current control rate.
2. The active disturbance rejection rotational speed current single loop control method of the permanent magnet synchronous motor according to claim 1, wherein: the specific formula of the d-q axis current equation of the permanent magnet synchronous motor is as follows:
wherein R is the stator resistance of the motor, u d And u q Voltages of d-axis and q-axis of stator, i d And i q Currents of d-axis and q-axis of stator, L d And L q Respectively the d-axis inductance and the q-axis inductance of the stator, omega e For the electrical angular velocity of the motor, ψ f Is a permanent magnet flux linkage;
the specific formula of the motion equation of the permanent magnet synchronous motor is as follows:
wherein T is e Is electromagnetic torque, T L For the load torque, J is the moment of inertia of the motor, B is the coefficient of friction of the motor, p is the pole pair number of the motor, ω e Is the electrical angular velocity of the motor;
the specific formula of the electromagnetic torque equation is as follows:
wherein T is e For electromagnetic torque, p is the pole pair number of the motor, ψ f I is a permanent magnet flux linkage d And i q Currents of d-axis and q-axis of stator, L d And L q The stator d-axis and q-axis inductances, respectively.
3. The active disturbance rejection rotational speed current single loop control method of the permanent magnet synchronous motor according to claim 1, wherein: the specific formula for determining the gain parameters of the extended state observer to estimate the state variables is as follows:
wherein u is q For the voltage of the q axis of the stator, b is the system input coefficient, d ω The specific formula is as follows:
wherein R is the stator resistance of the motor, i d And i q Currents of d-axis and q-axis of stator, L d And L q Respectively the d-axis inductance and the q-axis inductance of the stator, omega e For the electrical angular velocity of the motor, ψ f Is a permanent magnet flux linkage, T e Is electromagnetic torque, T L J is the moment of inertia of the motor, B is the coefficient of friction of the motor, and p is the pole pair number of the motor;
the specific formula listing the second order equation form is as follows:
wherein b 0 For the initial value of the system input coefficient, i.e. calculated by the relevant parameters of the motor calibration, f is the total disturbance quantity, u q Is the voltage of the q-axis of the stator.
4. The active disturbance rejection rotational speed current single loop control method of the permanent magnet synchronous motor according to claim 1, wherein: the specific formula for expanding the state quantity of the second-order equation by using the expanding state observer is as follows:
wherein,u q is the current of the stator q-axis.
5. The active disturbance rejection rotational speed current single loop control method of the permanent magnet synchronous motor according to claim 1, wherein: the specific formula of the using the extended state observer is as follows:
wherein z is e1 、z e2 And z e3 Is the observed quantity of the extended state observer, l 1 、l 2 And l 3 B is the gain of the observer 0 For the initial value of the system input coefficient, u q Is the voltage of the q-axis of the stator.
6. The active disturbance rejection rotational speed current single loop control method of the permanent magnet synchronous motor according to claim 1, wherein: the specific formula for introducing a new observer with derivative form is as follows:
wherein z is 1 、z 2 And z 3 For the observed quantity of the new observer, l 1 And l 2 In order for the gain of the observer to be,observations of f, b 0 For initial value, x 1 ＝ω e ，ω e For the electrical angular velocity of the motor u q Is the voltage of the q-axis of the stator.
7. The active disturbance rejection rotational speed current single loop control method of the permanent magnet synchronous motor according to claim 1, wherein: the specific formula according to the control rate of the controller is as follows:
wherein k is p And k d Is a controller parameter to be designed, z 1 And z 2 R is the rotation speed given value, b is the observed quantity of the new observer 0 For the initial value of the system input coefficient,is the observed value of f.
8. An active disturbance rejection rotational speed current single loop control system of a permanent magnet synchronous motor, based on the active disturbance rejection rotational speed current single loop control method of the permanent magnet synchronous motor of any one of claims 1 to 7, characterized in that: comprising the steps of (a) a step of,
the total disturbance quantity calculation module is used for calculating a calibration value error and total disturbance quantity based on a permanent magnet synchronous motor shaft current equation, a motion equation and an electromagnetic torque equation;
the extended state observer module expands the state quantity of the second-order equation and determines gain parameters of the extended state observer so as to estimate state variables;
a new extended state observer module that introduces a new observer with derivative form to estimate state variables of the extended state observer and further optimizes the observation error to correct the output of the observer;
the controller module is used for calculating the control rate of the controller;
and the power electronic device module is used for applying voltage to the stator winding of the permanent magnet synchronous motor through a power electronic device so as to realize the required rotation speed and q-axis current control.
9. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that: the steps of the active disturbance rejection rotational speed current single loop control method of the permanent magnet synchronous motor according to any one of claims 1 to 7 are realized when the processor executes the computer program.
10. A computer-readable storage medium having stored thereon a computer program, characterized by: the steps of the active disturbance rejection rotational speed current single loop control method of the permanent magnet synchronous motor according to any one of claims 1 to 7 are realized when the computer program is executed by a processor.
CN202311169688.1A 2023-09-12 2023-09-12 Active disturbance rejection rotating speed current single loop control method and system for permanent magnet synchronous motor Pending CN117439463A (en)

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