CN112491319B - Vector control current compensation algorithm and vector control model of direct-current brushless motor - Google Patents
Vector control current compensation algorithm and vector control model of direct-current brushless motor Download PDFInfo
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Abstract
The utility model provides a brushless DC motor vector control current compensation algorithm and vector control model, relates to brushless DC motor's control field, and the current compensation algorithm is: I.C. A de =I dt ,I qe =K c I qt ,Wherein, I dt For stator currents of a brushless DC motor on the d-axis of a two-phase rotating coordinate system, I qt The stator current of the brushless DC motor on the q axis of the two-phase rotating coordinate system is shown. The control model is as follows:wherein the content of the first and second substances,the invention has the advantages of convenient realization, easy programming, the same hardware control structure as the traditional vector control structure of the permanent magnet synchronous motor, no need of additional hardware support, easy popularization in factories and enterprises and small rotation speed fluctuation.
Description
Technical Field
The invention relates to the field of control of direct current brushless motors, in particular to a vector control current compensation algorithm and a vector control model of a direct current brushless motor, which are convenient to implement and easy to program, have the same hardware control structure as the vector control structure of a traditional permanent magnet synchronous motor, do not need additional hardware support, are easy to popularize in factories and enterprises, and have small rotation speed fluctuation.
Background
As is known, the dc brushless motor is widely used in household appliances, servers, electric vehicles, etc. due to its advantages of high efficiency, etc. However, the disadvantages of torque and rotation speed oscillation in the dc brushless motor limit its popularization in high precision applications. The traditional commutation mode of a brushless dc motor is 2-2 commutation or 3-3 commutation, which is discrete and discontinuous.
The documents t.tarczewski, and l.m.grzesiak, "Constrained State Feedback Speed Control of PMSM Based on Model Predictive application," IEEE Transactions on Industrial Electronics, vol.63, No.6, pp.3867-3875,2016 describe the motor differential equation of a sine wave permanent magnet synchronous motor under vector Control.
The motor classical book document b.k.bose, "Modern Power Electronics and AC drives," 1987 specifies 2-2 commutation or 3-3 commutation and proposes the classical dynamic model of a dc brushless motor when vector control is not considered:
although the direct current brushless motor model is accurate, the direct current brushless motor model is relatively complex and has large rotation speed oscillation. The discontinuity of commutation is one of the reasons for the Torque and Speed oscillation of the dc brushless Motor, so there are many documents in which efforts are made to improve commutation, and reference may be made to the journal of Design of Speed Control and Reduction of Torque Ripple Factor in BLdc Motor Using spacer Based Controller in the IEEE database.
Due to the shortcomings of conventional commutation of dc brushless motors, technicians have attempted to apply vector control to dc brushless motors. Vector control has a decoupling characteristic in motor control. The decoupling characteristic means that independent control of electromagnetic torque and excitation of the motor can be realized by controlling torque current and excitation current respectively. Meanwhile, vector control can improve the efficiency of the motor, promote energy conservation and emission reduction, reduce the complexity of a motor model and reduce the torque and rotation speed fluctuation of the motor, so the vector control method is widely used in induction motors (asynchronous motors) and sine wave permanent magnet synchronous motors. Document a.v. sant, and k.r. rajagopal, "PM Synchronous Motor Speed Control Using Hybrid Fuzzy-PI With Novel Switching Functions," IEEE Transactions on Magnetics, vol.45, No.10, pp.4672-4675,2009, and document k.d. card, n. Zimmerman, and c.ababei, "Hybrid field oriented and direct torque Control for sensorless BLDC motors used in analog loops," IET Power Electronics, vol.12, No.3, pp.438-449,2019, and li jingke, wu, song, "brushless Motor vector Control system based on 32", electronic and packaging, 2020, 09, pp.29-29, and brushless Motor vector Control directly under the brushless Motor vector Control equation (brushless vector Control equation) are described:
documents a.g.d.castro, w.c.a.pereira, t.e.p.d.almeida, c.m.r.d.oliveira, j.r.b.d.a. monteiiro, and a.a.d.oliveira, "Improved fine Control-Set Model-Based Direct Power Control of BLDC Motor With Reduced Torque Ripple," IEEE Transactions on Industry Applications, vol.54, No.5, pp.4476-4484,2018, are improvements to the conventional dc brushless Motor vector Control Model over the structure of vector Control, which employs a method Based on active and reactive Power, which models the mechanical equations of a dc brushless Motor in a two-phase stationary coordinate system. However, the method needs to collect the back electromotive force of the brushless direct current motor, so that the structure is more complex than the traditional structure, the cost is high, and the method is not suitable for application.
Disclosure of Invention
The invention aims to solve the defects of the prior art, and provides a vector control current compensation algorithm and a vector control model of a direct current brushless motor, which are convenient to implement, easy to program, the hardware control structure of which is the same as that of the traditional permanent magnet synchronous motor, do not need additional hardware support, are easy to popularize in factories and enterprises, and have small rotation speed fluctuation.
The technical scheme adopted by the invention for solving the defects of the prior art is as follows:
the vector control current compensation algorithm of the direct current brushless motor is characterized in that equivalent stator current I of the direct current brushless motor on a two-phase rotating coordinate system d axis de =I dt In a two-phase rotating coordinate system of a brushless DC motorEquivalent stator current I on q-axis qe =K c I qt ,
Wherein, I dt For stator currents of brushless DC motors on the d-axis of a two-phase rotating coordinate system, I qt The stator current of the brushless DC motor on the q axis of the two-phase rotating coordinate system is shown. I.e. I dt Is the stator current, I, of the DC brushless motor on the d axis of a two-phase rotating coordinate system in the traditional vector control method of the DC brushless motor qt The method is a stator current of a brushless direct current motor on a q axis of a two-phase rotating coordinate system in a traditional brushless direct current motor vector control method.
A vector control model of a brushless DC motor is characterized in that the model is as follows:
in the above formula, I de Equivalent stator current I of the improved DC brushless motor on the d axis of a two-phase rotating coordinate system qe The equivalent stator current, omega, of the improved DC brushless motor in the q axis of the two-phase rotating coordinate system e Synchronous electrical angular velocity, R, for a brushless DC motor s Is the stator resistance of the brushless DC motor, L is the equivalent phase inductance of the stator of the brushless DC motor, psi r Is the rotor flux linkage of the DC brushless motor, p is the pole pair number of the DC brushless motor, J is the rotational inertia of the DC countless motor, U d For the stator voltage, U, of the brushless DC motor on the d-axis of a two-phase rotating coordinate system q For the stator voltage, T, of a brushless DC motor on the q-axis of a two-phase rotating coordinate system L For loading torque of DC brushless motor, I dt For stator currents of a conventional DC brushless motor on the d-axis of a two-phase rotating coordinate system, I qt The stator current of a traditional DC brushless motor on the q axis of a two-phase rotating coordinate system is shown.
A vector control model of a brushless DC motor is characterized in that the model is as follows:
wherein
In the above formula, I dt For stator currents of a conventional DC brushless motor on the d-axis of a two-phase rotating coordinate system, I qt For the stator current, omega, of the traditional DC brushless motor on the q axis of a two-phase rotating coordinate system e Synchronous electrical angular velocity, R, for a brushless DC motor s Is stator resistance of the brushless DC motor, L is equivalent phase inductance of the brushless DC motor stator, psi r Is the rotor flux linkage of the DC brushless motor, p is the pole pair number of the DC brushless motor, J is the rotational inertia of the DC countless motors, U d For the stator voltage, U, of the brushless DC motor on the d-axis of a two-phase rotating coordinate system q For the stator voltage, T, of a brushless DC motor on the q-axis of a two-phase rotating coordinate system L For the purpose of loading the torque of the dc brushless motor,
after the current obtained in the traditional vector control method of the direct current brushless motor is compensated, the direct current brushless motor can reduce the rotating speed oscillation under the condition that the difference between the output torque and the target torque is smaller, and the method is more suitable for being applied to the industries with higher requirements on the rotating speed oscillation, such as robot control, electric vehicles and the like. The method has the advantages of simple algorithm, convenient realization and easy programming, the hardware control structure is the same as the vector control structure of the traditional permanent magnet synchronous motor, no additional hardware support is needed, and the method is easy to popularize in factories and enterprises.
Drawings
Fig. 1 is a diagram illustrating four different motor models for controlling the same dc brushless motor, which outputs electromagnetic torque.
Fig. 2 is an enlarged view of a period from 0 to 0.0432s in fig. 1, and is an enlarged view of a start interval of each dc brushless motor.
Fig. 3 is an enlarged view of the period from 0.4742 s to 0.4939s in fig. 1, and is an enlarged view of the electromagnetic torque when the load of each dc brushless motor is stable.
Fig. 4 is a diagram illustrating an error between an actual output rotation speed and a predetermined rotation speed of each dc brushless motor in three different model-based dc brushless motor control methods.
Fig. 5 is a diagram of actual output speeds of three dc brushless motors based on different models of dc brushless motor control methods.
Detailed Description
The theory of the invention is as follows:
the dynamic model of the dc brushless motor obeys the assumption that the core loss and magnetic saturation are negligible; the stator windings are centralized, symmetrical and wye connected.
In addition, it is assumed that the back electromotive force of the dc brushless motor is a trapezoidal wave with respect to the rotor position:
equation (1) shows that A is the counter electromotive force, and B and C are similarly derived from equation (1), except that the phase shifts are respectivelyAndfrom M.P.Maharajan, and S.A.E.Xavier, "Designof Speed Control and Reduction of Torque Ripple Factor in BLdc Motor Using Spider Based Controller,”IEEE Transactions on Power Electronics,vol.34,no.8,pp.7826-7837,2019。
Theoretically, the stator current of the direct current brushless motor is trapezoidal wave; the a-phase stator current should therefore conform to equation (2):
the stator currents of the B-phase and the C-phase can be derived from the equation (2), and the difference between them is that the phase offsets are respectivelyAnd
if the trapezoidal wave Ta (θ) in the formula (2) can be converted into the sine wave sa (t), the vector control can be applied to the dc brushless motor. First, the square wave and sine wave can be viewed as two separate subspaces of the Hilbert space. Then, the connection between them can be established by L2 norm [0,2 π ] isomorphism:
substituting the formula (2, 3) into the formula (4), I trp And I sin The relationship between can be deduced:
considering that the back electromotive force and the stator current of the dc brushless motor are both trapezoidal waves, we can obtain formula (6) according to the classical mechanical equation of the dc brushless motor and formula (5):
equation (6) illustrates I that we can obtain on the vector control of the conventional DC brushless motor qt Multiplied by a compensation factorA novel vector control of the dc brushless motor can be realized. Since the conversion from trapezoidal waves to sine waves is performed in the L2 space, the conversion between them is reversible. In other words, the transformation between them is a linear transformation, which ensures that the trapezoidal wave contains the same power as the sinusoidal wave. Considering that the electromagnetic torque of the motor is the derivative of the electromagnetic power to the electrical angle theta, the power and the electromagnetic torque contained in the novel transformation of the trapezoidal wave and the sine wave are the same, which is the meaning of the transformation proposed by the invention.
By combining the derivation of the formula, a current compensation algorithm in vector control of a brushless DC motor is disclosed, wherein the equivalent stator current I of the brushless DC motor on the d axis of a two-phase rotating coordinate system de =I dt Equivalent stator current I of the DC brushless motor on the q axis of the two-phase rotating coordinate system qe =K c I qt ,
Wherein, I dt For stator currents of a brushless DC motor on the d-axis of a two-phase rotating coordinate system, I qt The stator current of the brushless DC motor on the q axis of the two-phase rotating coordinate system is shown. I.e. I dt Is the stator current, I, of the DC brushless motor on the d axis of a two-phase rotating coordinate system in the traditional vector control method of the DC brushless motor qt The method is the fixation of the DC brushless motor on the q axis of a two-phase rotating coordinate system in the traditional vector control method of the DC brushless motorThe sub-currents.
The Clarke and Park transformation equations in classical vector control are as follows:
when the compensation coefficient is adjustedIn conjunction with equation (8), the compensated Park is transformed into:
the motor differential equation of the traditional direct current brushless motor under the vector control is as follows:
according to the formula (9), the d-q axis equivalent current in the dc brushless motor is:
wherein I d And I q Representing d-q axis current of the dc brushless motor before compensation.
The compensation method in formula (11) of the present invention is very simple, practical and easy to implement.
Obtaining the vector control model of the brushless direct current motor according to the formula (10) and the formula (11):
and the vector control model of the traditional direct current brushless motor is as follows:
from equations (11) and (13), equation (12) can be rewritten as:
wherein
When K is c When 1, equation (14) is the same as equation (13). Considering that the counter electromotive force and the current of the DC brushless motor are both trapezoidal waves, and the counter electromotive force and the current of the permanent magnet synchronous motor are both sine waves, the formula (13) which is obtained by directly applying vector control to the DC brushless motor and is the same as the motor equation applied to the permanent magnet synchronous motor by the vector control is obviously inaccurate, and the new DC brushless motor vector control motor equation (14) provided by the invention considers the relation between the trapezoidal waves and the sine waves on the basis of the motor equation (13) (the motor equation is embodied by increasing delta 1 And Δ 2 ) Therefore, the new vector control model of the DC brushless motor is comparedThe vector control model of the traditional direct current brushless motor is more accurate.
The method for the vector control current compensation algorithm of the direct current brushless motor, which is provided by the invention, is specifically applied to the vector control of the direct current brushless motor, and comprises the following steps:
for speed servo, the vector control system of the DC brushless motor is a double closed-loop structure comprising a rotating speed loop and an exciting current I de Ring and an electromagnetic torque current I qe A ring; although there are three closed loops in total, the overall structure can be divided into a rotation speed loop and a current loop, so the control structure is also called a double closed loop structure; the controllers in the dual closed loop configuration are typically PID controllers.
In the vector control system of the brushless direct current motor, the given rotating speed of the rotating speed ring is an external given rotating speed which is related to actual needs and can be manually changed; the exciting current of the exciting current loop is also given externally, the given value is 0 under the normal condition, and if weak magnetism is needed, a negative value can be given; i of electromagnetic torque current loop qe The given is connected with the output of the rotating speed ring; the regulation of PID controller parameters is well known.
The rotating speed of the rotating speed loop and the current of the current loop in the vector control system of the direct current brushless motor need feedback quantity besides the given numerical values; the feedback of the rotating speed loop requires a rotating speed sensor to measure the rotating speed of the direct current brushless motor, or the position information of the rotor is derived according to the encoder to obtain the rotating speed of the direct current brushless motor, or the position information obtained according to the non-inductive technology is derived to obtain the rotating speed; the feedback steps of the two current loops are as follows: firstly, a current sensor is used for measuring three-phase current I of a stator of the direct current brushless motor a ,I b And I c Then, Clarke transformation and Park transformation are carried out on the I and the I is obtained dt And I qt Finally, the I of the equivalent stator current on the d-q axis of the improved two-phase rotating coordinate system is calculated by using the vector control current compensation algorithm of the brushless DC motor provided by the invention de And I qe ,Handle I de And I qe Respectively fed back to an excitation current loop and an electromagnetic torque current loop for feedback.
The outputs of the three controllers in the double closed loop in the vector control system of the brushless DC motor are introduced as follows: the output of the rotating speed ring is connected to the electromagnetic torque current ring as I qe A given value of (d); the output of the exciting current loop is U d The output of the electromagnetic torque current loop is U q 。U d And U q After coordinate transformation and SVPWM processing, a PWM signal is sent out to drive an inverter to obtain a three-phase voltage signal U a ,U b And U c They are respectively connected into three phases of the stator of the brushless DC motor, and the process is known.
The vector control model of the brushless direct current motor can be applied to the design of some brushless direct current motor controllers, for example, the design of a prediction controller needs to use the brushless direct current motor model, but the traditional brushless direct current motor model is difficult to use in the design of the controller, and at the moment, the vector control model of the brushless direct current motor provided by the invention can be used for designing the controller.
The vector control model of the direct current brushless motor can be applied to direct current brushless motor simulation and used as a mathematical model of the direct current brushless motor, and if the traditional model is inconvenient to build, the vector control model of the direct current brushless motor can be used for simulating the direct current brushless motor and used as a control object.
When using vector control, the classical dynamic model of a dc brushless motor is:
wherein E is a ,E b ,E c Is counter electromotive force of trapezoidal wave, and they have mutualThe angle difference of (a).
Comparing equation (12) with equation (15), equation (12) is more concise and clearer, and we proceed further comparisons below in MATLAB/Simulink simulations for better comparison of them and some other approaches to dc brushless motor modeling.
MATLAB/SIMULINK simulation analysis
The parameters of the brushless DC motor in the simulation are as follows:
table 1: parameters of a DC brushless motor
In order to avoid the influence of a closed-loop controller on the validity of a verification motor model, different direct current brushless motor models are verified in an open-loop mode. From these models, we need to consider not only their accuracy but also complexity, and then choose the optimal motor model from them.
At 0.3 seconds, a load of 10N.M was applied to the dc brushless motor.
As shown in fig. 1 to 3, the electromagnetic torque Te1 of the standard dc brushless motor is obtained according to equation (15), which is used to simulate the actual torque of the dc brushless motor.
Documents a.g.d.castro, w.c.a.pereira, t.e.p.d.almeida, c.m.r.d.oliveira, j.r.b.d.a.monteiro, and a.a.d.oliveira, "Improved fine Control-Set Model-Based Direct Power Control of BLDC Motor With Reduced Torque Ripple," IEEE Transactions on Industry Applications, vol.54, No.5, pp.4476-4484,2018, propose a method Based on active Power P and reactive Power Q to perform and Control of a dc brushless Motor, the equivalent electromagnetic Torque of the brushless Motor calculated by this method being Te 2.
The electromagnetic torque Te3 is calculated by the formula (13), and is an electromagnetic torque obtained by a conventional dc brushless motor vector control model.
The electromagnetic torque Te4 is calculated by the formula (12), and is the electromagnetic torque obtained by using the vector control model of the dc brushless motor according to the present invention.
Comparative diagrams of Te1, Te2, Te3 and Te4 are shown in fig. 1-3.
As can be seen by comparing Te3 and Te1 in fig. 1-3, the difference between them is relatively large, which means that the motor model obtained by using vector control directly for the dc brushless motor cannot accurately reflect the actual dc brushless motor operation performance (dynamic time and loading time). The difference between Te2 and Te1 is minimal, but this approach adds cost in practical applications in view of the additional sensors and peripheral circuitry required and the complex calculations required. The difference between Te4 and Te1 is small.
The specific control mode is different for different models of the dc brushless motor. Taking the rotation speed control as an example, for a traditional direct current brushless motor model, the rotation speed current double closed-loop control based on 2-2 phase commutation or 3-3 phase commutation is a known control mode, and is marked as C1; for a model obtained by directly using vector control to a direct current brushless motor, the control mode is the same as the known vector control double closed-loop control structure of the permanent magnet synchronous motor and is marked as C2; for the dc brushless motor vector control model of the present invention, the control method may refer to the aforementioned "method in which the dc brushless motor vector control current compensation algorithm is specifically applied in the dc brushless motor vector control", which is denoted as C3.
Fig. 4 and 5 are graphs comparing the effects of the three different dc brushless motor speed controls, and are graphs of the output speed data of the dc brushless motor and the error data between the output speed and the predetermined speed.
It can be seen from fig. 4 and fig. 5 that when the C2 control mode is used, there is a large error between the stable rotation speed of the motor and the given rotation speed of 600rpm, and when the improved C3 mode and the conventional C1 mode are used to control the dc brushless motor, the errors between the stable rotation speed and the given rotation speed are both small, but after amplification, it can be seen that when the C3 mode is used, the rotation speed oscillation is obviously smaller than that of the conventional C1 mode.
Description of the symbols
Claims (3)
1. The vector control current compensation algorithm of the DC brushless motor is characterized in that equivalent stator current of the DC brushless motor on a d axis of a two-phase rotating coordinate system
I de =I dt Equivalent stator current I of the DC brushless motor on the q axis of the two-phase rotating coordinate system qe =K c I qt ,
Wherein, I dt For stator currents of brushless DC motors on the d-axis of a two-phase rotating coordinate system, I qt The stator current of the DC brushless motor on the q axis of the two-phase rotating coordinate system is obtained;
the method for the vector control current compensation algorithm of the direct current brushless motor specifically applied to the vector control of the direct current brushless motor comprises the following steps:
the vector control system of the direct current brushless motor is a double closed loop structure, and a controller in the double closed loop structure is a PID controller; wherein, the rotation speed of the rotation speed loop is given as external given, the exciting current of the exciting current loop is given as external given, and I of the electromagnetic torque current loop qe The given is connected with the output of the rotating speed ring; the rotating speed of the rotating speed loop and the exciting current of the exciting current loop need feedback quantity besides the given numerical values; the feedback of the rotating speed loop requires a rotating speed sensor to measure the rotating speed of the direct current brushless motor, or derives the position information of the rotor obtained according to an encoder to obtain the rotating speed of the direct current brushless motor, or derives the position information obtained according to a non-inductive technology to obtain the rotating speed; the feedback steps of the two current loops are as follows: firstly, a current sensor is used for measuring three-phase current I of a stator of the direct current brushless motor a ,I b And I c Then, Clarke transformation and Park transformation are carried out on the I and the I is obtained dt And I qt Finally, calculating the I of the equivalent stator current on the d-q axis of the improved two-phase rotating coordinate system by using the vector control current compensation algorithm of the brushless DC motor de And I qe ,Handle I de And I qe Respectively feeding back to an excitation current loop and an electromagnetic torque current loop for feedback;
the outputs of the three controllers in the double closed loop in the vector control system of the brushless DC motor are as follows: the output of the rotating speed ring is connected to the electromagnetic torque current ring as I qe A given value of (d); the output of the exciting current loop is U d The output of the electromagnetic torque current loop is U q ;U d And U q After coordinate transformation and SVPWM processing, a PWM signal is sent out to drive an inverter to obtain a three-phase voltage signal U a ,U b And U c And the three phases are respectively connected into three phases of a stator of the direct current brushless motor.
2. A vector control model of a brushless DC motor is characterized in that the model is as follows:
in the above formula, I de Equivalent stator current I on d-axis of two-phase rotating coordinate system for improved DC brushless motor qe Equivalent stator current, omega, on the q axis of a two-phase rotating coordinate system for the improved DC brushless motor e Synchronous electrical angular velocity, R, for a brushless DC motor s Is the stator resistance of the brushless DC motor, L is the equivalent phase inductance of the stator of the brushless DC motor, psi r Is the rotor flux linkage of the DC brushless motor, p is the pole pair number of the DC brushless motor, J is the rotational inertia of the DC brushless motor, U d For the stator voltage, U, of the brushless DC motor on the d-axis of a two-phase rotating coordinate system q For the stator voltage, T, of a brushless DC motor on the q-axis of a two-phase rotating coordinate system L For loading torque on brushless DC motor,I dt For stator currents of a brushless DC motor on the d-axis of a two-phase rotating coordinate system, I qt The stator current of the DC brushless motor on the q axis of the two-phase rotating coordinate system is obtained; said I dt And I qt The acquisition method comprises the following steps: method for measuring three-phase current I of stator of direct current brushless motor by using current sensor a ,I b And I c Then, Clarke transformation and Park transformation are carried out on the I and the I is obtained dt And I qt 。
3. A vector control model of a brushless DC motor is characterized in that the model is as follows:
wherein
In the above formula, I dt For stator currents of brushless DC motors on the d-axis of a two-phase rotating coordinate system, I qt For stator currents, omega, of brushless DC motors on the q-axis of a two-phase rotating coordinate system e Synchronous electrical angular velocity, R, for a brushless DC motor s Is the stator resistance of the brushless DC motor, L is the equivalent phase inductance of the stator of the brushless DC motor, psi r Is the rotor flux linkage of the DC brushless motor, p is the pole pair number of the DC brushless motor, J is the rotational inertia of the DC brushless motor, U d For the stator voltage, U, of the brushless DC motor on the d-axis of a two-phase rotating coordinate system q For stator voltages, T, of a brushless DC motor on the q-axis of a two-phase rotating coordinate system L Loading torque for the DC brushless motor; said I dt And I qt The acquisition method comprises the following steps: method for measuring three-phase current I of stator of direct current brushless motor by using current sensor a ,I b And I c Then, Clarke transformation and Park transformation are carried out on the I and the I is obtained dt And I qt 。
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