CN113541545A - Fractional order vector control method and system for permanent magnet synchronous motor - Google Patents
Fractional order vector control method and system for permanent magnet synchronous motor Download PDFInfo
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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
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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
- H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
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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
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
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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
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
- H02P21/18—Estimation of position or speed
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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
- H02P21/22—Current control, e.g. using a current control loop
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Abstract
The invention provides a fractional order vector control method for a permanent magnet synchronous motor, which comprises the following steps: collecting armature three-phase current input to a permanent magnet synchronous motor and rotor angular speed output by the permanent magnet synchronous motor; feeding the rotor angular speed back to a disturbance observer for observation to obtain a rotor angular speed observed value; inputting the rotor angular speed observed value and the rotor angular speed reference value into a speed loop fractional order PID controller together for regulation to generate an outer loop control quantity, wherein the outer loop control quantity corresponds to a q-axis current reference value; the present current is fed back into a current loop fractional order PID controller and regulated based on a q-axis current reference to produce an inner loop control quantity corresponding to the q-axis, d-axis control voltage, the inner loop control quantity being modulated for producing drive pulses for controlling the operation of the motor. The controller has better speed regulation control performance, and has good dynamic and static control performance and anti-interference capability.
Description
Technical Field
The invention relates to the technical field of synchronous motors, in particular to a fractional order vector control method and a fractional order vector control system for a permanent magnet synchronous motor.
Background
The permanent magnet synchronous motor has the advantages of high efficiency, high power density and large torque inertia ratio, is very wide in application range, and plays a significant role in the field of practical industrial application. Therefore, the realization of the high-performance control of the permanent magnet synchronous motor plays an important role.
Fractional calculus has been proposed since, due to its complex solving process, it has not been gradually applied to solving practical engineering problems until the end of the last century. In 1999, Podlubny applied fractional order to control systems, suggesting the use of PIλDμThe controller can obtain better control effect than the traditional PID.
Compared to classical PID controllers, PIλDμThe controller adds two adjustable parameters, so that more parameter choices can be obtained to improve the control performance. In one prior art, fractional order PI is usedλDμThe controller is applied to speed control of the permanent magnet synchronous motor, and obtains better control effect than an integer-order PI controller. Still another prior art technique applies a fractional order controller to the control of an unmanned aircraft, which demonstrates that better control results can be obtained using a fractional order controller than using an integer order controller.
However, the control system may also have various interference noises from the field environment when it is actually operated. The sum of these factors constitutes uncertainties and disturbances in the system, the presence of which necessarily affects the performance of the system, making control complex and difficult.
Therefore, it is also highly desirable to provide a method for eliminating the adverse effects of system performance caused by uncertainty due to various interference noises in these field environments.
Disclosure of Invention
In order to solve the above problems, the present invention provides a method for fractional order vector control of a permanent magnet synchronous motor, which comprises the following steps:
collecting armature three-phase current input to the permanent magnet synchronous motor and rotor angular speed output by the permanent magnet synchronous motor;
feeding the rotor angular speed back to a disturbance observer for observation to obtain a rotor angular speed observed value;
inputting the rotor angular speed observed value and a rotor angular speed reference value into a speed ring fractional order PID controller together for regulation so as to generate an outer ring control quantity, wherein the outer ring control quantity corresponds to a q-axis current reference value;
feeding the current back into a current loop fractional order PID controller and adjusting based on the q-axis current reference value to generate an inner loop control quantity corresponding to q-axis and d-axis control voltage, wherein the inner loop control quantity is modulated to generate a driving pulse for controlling the operation of the permanent magnet synchronous motor.
According to an embodiment of the present invention, it is preferable to establish an ideal mathematical model of the permanent magnet synchronous motor under a rotating coordinate system d-q as follows:
in the formula [ theta ]eIs an electrical angle; omega is the angular speed of the rotor; i.e. idAnd iqD-axis and q-axis stator currents, respectively; u. ofdAnd uqD-axis and q-axis stator voltages, respectively; l isdAnd LqD-axis and q-axis stator inductances, respectively; psifIs a magnetic linkage; and R is the stator resistance. n ispIs the number of pole pairs; j is the total moment of inertia of the motor and load; t iseIs an electromagnetic torque 3/2np[ψfiq+(Ld-Lq)idiq](ii) a B is the damping coefficient; t isfIs the load torqueBω；TLIs the load torque.
According to one embodiment of the invention, it is preferred to consider the external load torque as a disturbance and estimate the disturbance using a non-linear disturbance observer, wherein the disturbance observer equation is as follows:
wherein z is a construction quantity, L is an observer gain, x is a system state, and estimation errors are as follows:
According to one embodiment of the present invention, it is preferable that the load pattern of the permanent magnet synchronous motor includes a constant load disturbance, a slowly varying load disturbance, and a square waveform disturbance, wherein the disturbance is bounded such that the gain L of the observer is selected to accurately estimate the disturbance.
According to an embodiment of the present invention, it is preferable that the vector control voltage in the stationary coordinate system is obtained by inverse park transformation of the decoupled q-axis and d-axis voltages.
According to an embodiment of the present invention, it is preferable that the driving pulse supplied to the motor is generated by performing SVPWM modulation based on the vector control voltage.
According to another aspect of the present invention, there is also provided a fractional order vector control system for a permanent magnet synchronous machine, the system comprising:
the acquisition unit is used for acquiring armature three-phase current input into the permanent magnet synchronous motor and rotor angular speed output by the permanent magnet synchronous motor;
a disturbance observer for observing the rotor angular velocity of the feedback input to obtain a rotor angular velocity observed value;
a speed loop fractional order PID controller for receiving the rotor angular velocity observation value and the rotor angular velocity reference value and adjusting to generate an outer loop control quantity, wherein the outer loop control quantity corresponds to the q-axis current reference value;
a current loop fractional order PID controller for receiving the present current and adjusting based on the q-axis current reference value to generate an inner loop control quantity corresponding to a q-axis, d-axis control voltage, the inner loop control quantity being modulated for generating drive pulses for controlling operation of the permanent magnet synchronous motor.
The invention has the beneficial technical effects that: according to the invention, a simulation model of the permanent magnet synchronous motor is established in a Matlab/Simulink simulation environment, the correctness of the proposed control strategy is verified by a simulation result, and compared with the traditional PID regulation controller, the controller based on the fractional order and the interference observer has better speed regulation control performance, and has good dynamic and static control performance and anti-interference capability.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
fig. 1 shows the basic principle of a disturbance observer;
FIG. 2 shows a block diagram of a disturbance observer based fractional order control for a permanent magnet synchronous machine according to an embodiment of the present invention;
FIG. 3 shows a step response plot for control under conventional control and in accordance with the principles of the present invention; and
fig. 4 shows a graph of the load dynamic response under conventional control and under control in accordance with the principles of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention are described in further detail below with reference to the accompanying drawings.
The ideal mathematical model of the permanent magnet synchronous motor model under the synchronous rotating coordinate system d-q is as follows
In the formula is thetaeElectrical angle; omega is the angular speed of the rotor; i.e. idAnd iqD-axis and q-axis stator currents, respectively; u. ofdAnd uqD-axis and q-axis stator voltages, respectively; l isdAnd LqD-axis and q-axis stator inductances, respectively; psifIs a magnetic linkage; and R is the stator resistance. n ispIs the number of pole pairs; j is total moment of inertia (motor and load); t iseIs an electromagnetic torque 3/2np[ψfiq+(Ld-Lq)idiq](ii) a B is the damping coefficient; t isfIs the load torque B ω; t isLIs the load torque.
Fractional calculus is the generalization of integration and differentiation into non-integer order domains, with the primary operator defined as
In the formula, a and t are integral lower limit and integral upper limit of an operator; α ∈ R is the operator order.
The transfer function of the fractional order controller can be expressed by
Wherein KP，KIAnd KDProportional gain, integral gain and differential gain, respectively. In addition, μ and λ (between 0 and 2) represent the order of fractional integration and the order of fractional differentiation, respectively. The introduction of these two parameters can suitably adjust the dynamic performance of many control systems.
Fractional calculus is currently defined by Grunwald-Letnikov, Riemann-Liouville, and Caputo.
(1) Grunwald-Letnikov fractional order micro-product definition
For any real number c, the largest integer less than c is denoted as [ c ], and for any alpha, GL of the alpha order calculus of the function f (t) is defined as
Wherein
(2) Riemann-Liouville fractional calculus definition
For any alpha, RL satisfying m-1< alpha < m, m is a natural number and fractional order differential is defined as
Riemann-Liouville with fractional order integration is defined as
Wherein t >0 and α is a positive real number.
(3) Caputo fractional calculus definition
Caputo fractional order differential is defined as
Where m ═ α ], m is an integer, γ ═ α -m.
Caputo fractional order integral is defined as
Caputo fractional calculus is defined uniformly as
Wherein m-1< alpha < m, m being a natural number.
The concept of Disturbance Observer (DOB) was proposed by k.ohnisi, japan in 1987. The basic idea is to design a disturbance observer to estimate the external disturbance, and based on the output of the disturbance observer, the purpose of canceling the disturbance is achieved by combining a feedforward compensator with a traditional feedback controller. Some studies apply the disturbance observer to the control of the permanent magnet synchronous motor, and excellent anti-interference capability is obtained.
In order to further improve the accuracy of anti-interference control and the robustness of a system, a DOBC method is combined with other anti-interference control methods to process multi-source interference, so that the method becomes a reasonable choice. The DOBC method has been widely used in the industry, ranging from traditional motion control systems to aerospace systems, as a few commercial and industrial algorithms.
In a real system, no matter how the model is obtained, the real model is different from the nominal model, unmodeled dynamic characteristics exist, and disturbance exists in the system. The Disturbance Observer (DOB) estimates the equivalent disturbance, which is the difference between the actual output and the nominal model output and is viewed as the equivalent disturbance acting on the nominal model, and adds the equivalent disturbance to the control end to counteract the influence of the external disturbance, which is the basic idea of the structure of the disturbance observer.
Fig. 1 shows the basic principle of a disturbance observer. GP(s) is a transfer function of the control system,
is the equivalent interference, d is the observed interference, and u is the control input. The estimated value of the equivalent interference can be obtained from the graph
Comprises the following steps:
nonlinear systems have uncertainties of the general form
Wherein, c ═ x1，x2，…，xn]T∈RnIs a state variable vector; u e R and u e R are respectively control input and system output; a (x) and b (x) are unknown functions representing non-linearity, parameter uncertainty and unmodeled dynamics; and d (t) represents time-varying external interference. The state matrix a and the state matrix B have the canonical form as follows:
the total disturbance of the system is expressed as
ψ(x,u,t)＝a(x)+(b(x)-b0)u+d(t) (14)
Wherein b is0Is the constant gain of the system. For a nominal system, the last state is overwritten in the presence of external disturbances, i.e.
Defining a virtual state to represent the disturbance, then the system can be expanded to
In a permanent magnet synchronous motor, the external load torque is considered as a kind of disturbance, and the disturbance is estimated using a non-linear disturbance observer. And (3) designing a nonlinear differential equation by using the permanent magnet synchronous motor model equation given in the step (1).
Let the rotor angular velocity omega be the state x,
is interference d;
i.e. state x ═ ω, interference
Let us order
Therefore, the formula (17) can be written as
The disturbance observer equation is
Where z is the construction quantity, L is the observer gain, x is the system state, the estimation error is as follows
Then
In a permanent magnet synchronous motor, typical load modes are generally constant load disturbance, slowly-changing load disturbance and square waveform disturbance
Are bounded and therefore an appropriate observer gain L can be selected to accurately estimate the disturbance.
According to the vector control principle of the permanent magnet synchronous motor and the combination of the fractional order PID and the disturbance observer, the fractional order vector control structure block diagram of the permanent magnet synchronous motor based on the disturbance observer shown in FIG. 2 can be obtained.
And establishing a simulation model of the fractional order vector control system of the permanent magnet synchronous motor based on the disturbance observer on a Matlab/Simulink simulation platform. The improved Oustaloup filter can well fit a fractional order differential operator, so a Simulink module is packaged to show that for comparative study, controllers of a current loop and a rotating speed loop are designed according to a traditional method, and open loop cut-off frequency and phase margin after respective correction are obtained. And finally, adding a disturbance observer on the basis, giving the same input or disturbance, and obtaining a waveform for comparison.
The motor parameters in the simulation are set as follows: number of pole pairs np4, stator Ld＝5.35mH,Lq13mH, stator resistance R0.965 omega, flux linkage psif0.1827Wb, moment of inertia J0.003 kg m2The damping coefficient B is 0.008N · M · s.
The step response curves of the two control systems are shown in fig. 3, and it can be seen that the full fractional order controller based on the disturbance observer has a faster settling time and a smaller overshoot. FIG. 4 shows a rotational speed dynamic curve when the rotational speed is 1000rad/s and the rated load is increased by 20 N.m.
According to the invention, a simulation model of the permanent magnet synchronous motor is established in a Matlab/Simulink simulation environment, a fractional order vector control method of the permanent magnet synchronous motor based on the interference observer is provided, the correctness of the proposed control strategy is verified by a simulation result, and compared with a traditional PID (proportion integration differentiation) regulation controller, the controller based on the fractional order and the interference observer has better speed regulation control performance and good dynamic and static control performance and anti-interference capability.
It is to be understood that the disclosed embodiments of the invention are not limited to the particular structures, process steps, or materials disclosed herein but are extended to equivalents thereof as would be understood by those ordinarily skilled in the relevant arts. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting.
Reference in the specification to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. Thus, the appearances of the phrase "one embodiment" or "an embodiment" in various places throughout this specification are not necessarily all referring to the same embodiment.
Although the embodiments of the present invention have been described above, the above description is only for the convenience of understanding the present invention, and is not intended to limit the present invention. It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (10)
1. A fractional order vector control method for a permanent magnet synchronous motor, the method comprising the steps of:
collecting armature three-phase current input to the permanent magnet synchronous motor and rotor angular speed output by the permanent magnet synchronous motor;
feeding the rotor angular speed back to a disturbance observer for observation to obtain a rotor angular speed observed value;
inputting the rotor angular speed observed value and a rotor angular speed reference value into a speed ring fractional order PID controller together for regulation so as to generate an outer ring control quantity, wherein the outer ring control quantity corresponds to a q-axis current reference value;
feeding the current back into a current loop fractional order PID controller and adjusting based on the q-axis current reference value to generate an inner loop control quantity corresponding to q-axis and d-axis control voltage, wherein the inner loop control quantity is modulated to generate a driving pulse for controlling the operation of the permanent magnet synchronous motor.
2. The fractional order vector control method for a permanent magnet synchronous motor according to claim 1, wherein an ideal mathematical model of the permanent magnet synchronous motor under a rotating coordinate system d-q is established as follows:
in the formula [ theta ]eIs an electrical angle; omega is the angular speed of the rotor; i.e. idAnd iqD-axis and q-axis stator currents, respectively; u. ofdAnd uqD-axis and q-axis stator voltages, respectively; l isdAnd LqD-axis and q-axis stator inductances, respectively; psifIs a magnetic linkage; and R is the stator resistance. n ispIs the number of pole pairs; j is the total moment of inertia of the motor and load; t iseIs an electromagnetic torque 3/2np[ψfiq+(Ld-Lq)idiq](ii) a B is the damping coefficient; t isfIs the load torque B ω; t isLIs the load torque.
3. The fractional order vector control method for a permanent magnet synchronous machine according to claim 2, wherein an external load torque is taken as a disturbance and the disturbance is estimated using a non-linear disturbance observer, wherein the disturbance observer equation is as follows:
wherein z is a construction quantity, L is an observer gain, x is a system state, and estimation errors are as follows:
4. The fractional order vector control method for a permanent magnet synchronous machine according to claim 3, wherein the load pattern of the permanent magnet synchronous machine includes constant load disturbances, slowly varying load disturbances, and square waveform disturbances, wherein the disturbance is bounded such that the observer gain L is selected to accurately estimate the disturbance.
5. Method for controlling a permanent magnet synchronous machine according to any of claims 1-4, characterized in that the de-coupled q, d axis voltages are inverse park transformed to vector control voltages in a stationary coordinate system.
6. The method for controlling a permanent magnet synchronous motor according to claim 5, wherein SVPWM modulation based on the vector control voltage generates drive pulses to be supplied to the motor.
7. A fractional order vector control system for a permanent magnet synchronous motor, the system comprising:
the acquisition unit is used for acquiring armature three-phase current input into the permanent magnet synchronous motor and rotor angular speed output by the permanent magnet synchronous motor;
a disturbance observer for observing the rotor angular velocity of the feedback input to obtain a rotor angular velocity observed value;
a speed loop fractional order PID controller for receiving the rotor angular velocity observation value and the rotor angular velocity reference value and adjusting to generate an outer loop control quantity, wherein the outer loop control quantity corresponds to the q-axis current reference value;
a current loop fractional order PID controller for receiving the present current and adjusting based on the q-axis current reference value to generate an inner loop control quantity corresponding to a q-axis, d-axis control voltage, the inner loop control quantity being modulated for generating drive pulses for controlling operation of the permanent magnet synchronous motor.
8. The fractional order vector control system for a permanent magnet synchronous machine according to claim 7, wherein an ideal mathematical model of the permanent magnet synchronous machine under a rotating coordinate system d-q is established as follows:
in the formula [ theta ]eIs an electrical angle; omega is the angular speed of the rotor; i.e. idAnd iqD-axis and q-axis stator currents, respectively; u. ofdAnd uqD-axis and q-axis stator voltages, respectively; l isdAnd LqD-axis and q-axis stator inductances, respectively; psifIs a magnetic linkage; and R is the stator resistance. n ispIs the number of pole pairs; j is the total moment of inertia of the motor and load; t iseIs an electromagnetic torque 3/2np[ψfiq+(Ld-Lq)idiq](ii) a B is the damping coefficient; t isfIs the load torque B ω; t isLIs the load torque.
9. The fractional order vector control system for a permanent magnet synchronous machine of claim 8, wherein the external load torque is taken as a disturbance and the disturbance is estimated using a non-linear disturbance observer, wherein the equation of the disturbance observer is as follows:
wherein z is a construction quantity, L is an observer gain, x is a system state, and estimation errors are as follows:
10. The fractional order vector control system for a permanent magnet synchronous machine of claim 9, wherein the load pattern of the permanent magnet synchronous machine comprises constant load disturbances, slowly varying load disturbances, and square waveform disturbances, wherein the disturbance is bounded such that the observer gain L is selected to accurately estimate the disturbance.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113992088A (en) * | 2021-11-08 | 2022-01-28 | 南京航空航天大学 | Permanent magnet synchronous motor control method based on double fractional order disturbance observer |
| CN117826580A (en) * | 2024-03-05 | 2024-04-05 | 南京航空航天大学 | Valve control hydraulic cylinder reinforcement learning fractional order control method and system based on TD3 algorithm |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113992088A (en) * | 2021-11-08 | 2022-01-28 | 南京航空航天大学 | Permanent magnet synchronous motor control method based on double fractional order disturbance observer |
| CN113992088B (en) * | 2021-11-08 | 2023-10-24 | 南京航空航天大学 | Permanent magnet synchronous motor control method based on double fractional order interference observer |
| CN117826580A (en) * | 2024-03-05 | 2024-04-05 | 南京航空航天大学 | Valve control hydraulic cylinder reinforcement learning fractional order control method and system based on TD3 algorithm |
| CN117826580B (en) * | 2024-03-05 | 2024-06-07 | 南京航空航天大学 | Valve control hydraulic cylinder reinforcement learning fractional order control method and system based on TD3 algorithm |
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