CN112187130A - Method and system for controlling a permanent magnet synchronous machine - Google Patents

Abstract

The present invention provides a method for controlling a permanent magnet synchronous motor, which comprises the following steps: collecting the armature three-phase current input to the permanent magnet synchronous motor and the rotational speed output by the permanent magnet synchronous motor; feeding back the rotational speed to a speed loop Adjustment is performed in the controller Fo-ISMC to generate an outer-loop control amount corresponding to the q-axis current reference value; the current current is fed back into the current loop fractional-order PI (Fo-PI) controller and Adjusting based on the q-axis current reference value to generate an inner-loop control quantity corresponding to the q-axis, d-axis control voltage, the inner-loop control quantity being modulated for generating drive pulses for controlling the operation of the permanent magnet synchronous motor .

Description

Method and system for controlling a permanent magnet synchronous motor

technical field

The present invention relates to the field of motor control, in particular to a method and system for controlling a permanent magnet synchronous motor.

Background technique

Permanent Magnet Synchronous Motor (PMSM) has the advantages of high efficiency, high power density, large torque-to-inertia ratio, low noise, high reliability, and maintenance-free. Compared with other motors, it has the highest comprehensive performance and the most developed Advantage of the motor. PMSMs have been widely used in various industrial sectors such as robotics, machine tools, electric vehicles, generators, and aerospace.

Traditionally, motor control typically employs dual closed-loop control—an inner current loop and an outer speed loop. In the current loop, the PID controller is simple, easy to adjust, and has high reliability. After introducing the system error, the system can run stably by adjusting the control amount in real time. However, the high-precision control of the PMSM driver of the current technology is not ideal, because its motion characteristics are strongly coupled, nonlinear, and easily affected by various interference sources and uncertainties. These factors make PMSM control more difficult. .

Therefore, in order to achieve higher precision control of PMSMs, improvements to conventional controllers are required.

SUMMARY OF THE INVENTION

In order to solve the above problems, the present invention provides a method for controlling a permanent magnet synchronous motor, which includes the following steps:

Collect the armature three-phase current input to the permanent magnet synchronous motor and the output speed of the permanent magnet synchronous motor;

Feeding back the rotational speed to the speed loop controller for adjustment to generate an outer loop control amount, the outer loop control amount corresponding to the q-axis current reference value;

The current current is fed back into a current loop fractional-order PI (Fo-PI) controller and adjusted based on the q-axis current reference value to generate an inner-loop control amount corresponding to the q-axis and d-axis control voltages, the The inner loop control quantity is modulated for generating drive pulses that control the operation of the permanent magnet synchronous motor.

According to an embodiment of the present invention, preferably, the speed loop controller includes a nominal control part and a sliding mode control part, wherein, in the sliding mode control part, a fractional order integral is introduced to make the system reach the sliding mode faster In order to reduce or eliminate the unknown interference of the system.

According to an embodiment of the present invention, preferably, the control law of the current loop fractional-order PI (Fo-PI) controller is:

和

分别是控制器d轴和q轴的分数阶算子，取值在0到1之间；e_d和e_q分别是d轴和q轴的电流误差；ω是电机角转速；L_q和L_d为定子电感分量；i_q和i_d分别是定子电流的d-q轴分量；ψ_f是永磁体磁链。Among them, _ud and u _q are the voltage components output to the following d-axis and q-axis respectively; K _pd and K _pq are the proportional gains of the controller d-axis and q-axis respectively; Ki _d and Ki _q are the controller d-axis respectively and the proportional integral of the q-axis;

and

are the fractional operators of the d-axis and q-axis of the controller, with values between 0 and 1; ed and e _q are the current errors of the _d -axis and q-axis, respectively; ω is the angular speed of the motor; L _q and L _d is the stator inductance component; i _q and _id are the dq-axis components of the stator current, respectively; ψ _f is the permanent magnet flux linkage.

According to an embodiment of the present invention, preferably, the control law of the speed loop:

为控制器输出电流量；ω_r是期望转速；T_L是负载转矩；

是给定转速的导数；e_ω是转速误差；J^λ为分数阶算子；sgn(S_ω)是关于滑模滑模面S_ω的符号函数；η是控制器增益；

和

其中np为极对数；J为转动惯量；B为阻尼系数；TL为负载转矩；ψ_f是永磁体磁链。in,

is the output current of the controller; ω _r is the desired speed; _TL is the load torque;

is the derivative of the given speed; e _ω is the speed error; J ^λ is the fractional operator; sgn(S _ω ) is the sign function of the sliding mode surface S _ω ; η is the controller gain;

and

Where np is the number of pole pairs; J is the moment of inertia; B is the damping coefficient; TL is the load torque; ψ _f is the permanent magnet flux linkage.

According to an embodiment of the present invention, it is preferable to perform inverse Parker transformation on the decoupled q and d axis voltages to obtain the vector control voltage in the static coordinate system.

According to an embodiment of the present invention, it is preferable to perform SVPWM modulation based on the vector control voltage to generate driving pulses provided to the motor.

According to another aspect of the present invention, a permanent magnet synchronous motor control system is also provided, which includes:

a detection unit, which is connected with the synchronous motor to detect in real time the three-phase current and rotational speed of the armature when the motor is running;

a speed loop adjustment unit, which is used for feeding back the rotational speed to the Fo-ISMC controller for adjustment to generate an outer loop control amount, the outer loop control amount corresponding to the q-axis current reference value;

Design a current loop fractional-order PI (Fo-PI) controller for feeding back the armature three-phase currents into the current loop Fo-PI controller and making adjustments based on the q-axis current reference to generate a corresponding The q-axis and the d-axis control the inner-loop control quantity of the voltage, and the inner-loop control quantity is modulated to generate the driving pulse for controlling the operation of the permanent magnet synchronous motor.

According to an embodiment of the present invention, preferably, the speed loop controller includes a nominal control part and a sliding mode control part, wherein, in the sliding mode control part, a fractional order integral is introduced to make the system reach the sliding mode faster In order to reduce or eliminate the unknown interference of the system.

Beneficial technical effects of the present invention: Through the implementation of the present invention, in the current loop, fractional-order PI is adopted to improve the response speed of the system. In the speed loop, compared with the traditional PID control, the sliding mode control has the advantages of simple algorithm, strong robustness and high reliability, and has obvious effect on improving the dynamic performance. In view of the problems existing in sliding mode control, fractional and integral sliding mode are introduced into the sliding mode control algorithm. This makes the steady-state error of the motor small, and controls the entire sliding process of the system to be "undisturbed by the matching uncertainty", and both reduce the impact of chattering on the system.

Other features and advantages of the present invention will be set forth in the description which follows, and in part will be apparent from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention may be realized and attained by the structure particularly pointed out in the description, claims and drawings.

Description of drawings

The accompanying drawings are used to provide a further understanding of the present invention, and constitute a part of the specification, and together with the embodiments of the present invention, are used to explain the present invention, and do not constitute a limitation to the present invention. In the attached image:

Fig. 1 shows the conventional control block diagram of PMSM in the prior art;

2 shows a block diagram of fractional-order PI control according to an embodiment of the present invention;

Fig. 3 shows the block diagram based on fractional order and sliding mode control of PMSM according to the present invention;

Fig. 4 shows the variation curve diagram of the motor speed that is simulated according to an embodiment of the present invention;

Figure 5 shows a plot of the q-axis current simulated according to one embodiment of the present invention; and

Figure 6 shows a d-axis current plot simulated according to one embodiment of the present invention.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

In order to further improve the performance of the PID controller, the fractional order PID (Fractional Order PID, FoPID) control method can be used, and additional parameters—fractional integrator and fractional differentiator are introduced. This can significantly improve the robustness and dynamic performance of the system. In the speed loop control of the motor, in order to obtain the ideal control performance, in addition to the classical proportional-integral-derivative (PID) controller, many advanced control algorithms for AC mechanical transmission are proposed. For example: Sliding Mode Variable Structure Control (SMC), Model Predictive Control, Robust and Adaptive Control, Internal Model Control (IMC), Disturbance Observer Based Control (DOBC) and Active Disturbance Rejection Control (ADRC).

Among them, sliding mode control is widely used because of its simple implementation and invariance to external disturbances, model uncertainty and unmodeled dynamics that meet matching conditions. in PMSM control. As a robust control scheme, sliding mode control can make the motor achieve the desired motion characteristics through the design of the sliding mode.

However, an obvious disadvantage of the sliding mode control method is the chattering phenomenon caused by discontinuous control law and frequent switching actions near the sliding mode surface. The performance of the system is as follows: when the trajectory of the system reaches the sliding surface, it is difficult to strictly slide along the equilibrium point of the sliding surface, but traverses back and forth on both sides of the sliding surface. There are many different methods to suppress and eliminate chattering. One way is to replace the sign function with a saturation function to reduce chattering. However, this sacrifices disturbance immunity to some extent. Another method is to choose an appropriate sliding mode gain for the sliding mode control law, because an inappropriate sliding mode gain can lead to large chattering. If the selected switch control gain is greater than the upper limit of the disturbance, the disturbance can be completely suppressed. However, since it is difficult to obtain an upper bound for the perturbation, this often results in a chosen control law with a large switching gain. In the case where the upper bound of the disturbance is accurately obtained, the control gain must also be selected as a high gain when a large disturbance is encountered. In general, chattering has limited the application of sliding mode control.

In addition, the motion characteristics of the system under sliding mode control have two processes: (1) under the action of the control law, the system reaches the sliding mode surface within a limited time, which is the approach segment; (2) the system performs sliding mode on the sliding mode surface. Movement and movement towards the equilibrium point, the sliding phase. However, the system does not have high robustness in the first stage, and it will be disturbed by the uncertainty of the model. It is necessary to ensure that the system has sufficient robustness in this stage. The system movement in the second stage only needs to ensure that the system does not leave the sliding surface.

Considering the working characteristics of permanent magnet synchronous motor, the application of sliding mode control in permanent magnet synchronous motor is studied. In order to suppress the chattering problem of sliding mode control and ensure the robustness of the approach segment, the fractional-order operator is placed before the sign function, and the designed control law should satisfy the differential of the rotor error and the zero error of the rotor speed. conditions to reduce the steady-state error of the system. In this paper, a system-based nominal model and fractional-order integral sliding-mode controller are designed to make the system meet the design requirements in the two motion stages under the sliding-mode control, so that the permanent magnet synchronous motor has better performance.

Fractional calculus theory was initially studied only in the purely mathematical neighborhood. It was later discovered that fractional calculus theory could solve many engineering problems. The fractional order theory is introduced into the control domain algorithm, which can be used in complex controllers. The combination of fractional order and sliding mode can make the control parameters have more degrees of freedom and achieve better control performance.

Permanent magnet synchronous motor is a strongly coupled and complex nonlinear system, and there are inevitable and unmeasurable disturbances and parameter changes. Therefore, it is more convenient to design an advanced control algorithm by establishing an appropriate mathematical model.

To simplify the analysis, a three-phase PMSM is assumed to be an ideal motor. Thus, the model of PMSM can be obtained as

Among them, u _d0 and u _q0 are the fully decoupled d-axis and q-axis voltages.

After Laplace transform, we can get

The mechanical motion equation of the three-phase permanent magnet synchronous motor is

Among them, ω is the mechanical angular velocity of the motor; J is the moment of inertia; B is the damping coefficient; T _L is the load torque.

Considering the disturbance situation, parameter change problem and convenient controller design, the equation of motion of permanent magnet synchronous motor ^[17] is:

in

In the formula, n _p is the number of pole pairs; Δa, Δb, and Δc are the parameter changes of the motor, respectively. And all parameters and their changing values are bounded values.

Equation (4) can be rewritten as

where D = Δai _q - Δbω - _ΔcTL represents the lumped disturbance.

The controller design according to the present invention is as follows:

When converting integer order to fractional order, it can be seen as a special case of fractional calculus. From the theory of fractional calculus, it can be obtained: Caputo fractional specific operation formula is

where λ∈R ⁺ , n∈N, n-1≤λ≤n. Γ(·) is a Gamma function.

Similarly, it can be obtained

where f(t) is a continuous function.

When f(0 ⁺ )=0 is satisfied, equation (7) can be rewritten as

J ^λ sgn(f(t))=J ⁿ D ^n-λ sgn(f(t)) (8)

可以提取函数f(t)的符号。由式(7)和式(8)可同理得出结论，既

也能提取函数f(t)的符号。It can be proved that

The sign of the function f(t) can be extracted. From equations (7) and (8), the same conclusion can be drawn, both

The sign of the function f(t) can also be extracted.

so

The current loop design according to the present invention is as follows:

The design of the traditional motor current loop generally adopts PID control. In a system with an input of e(t) and an output of u(t), the time-domain and frequency-domain formulas of the integer-order PID controller are:

Among them, Kp is proportional gain, Ki is integral gain, Kd is differential gain.

The derivation process of the fractional-order control block diagram and transfer function is given below.

Figure 2 shows a block diagram of a fractional PI control according to the present invention.

Frequency Domain Model of PIμ Controller

When the order is not an integer, it is a fractional order PID, and more parameters need to be adjusted to increase the degree of freedom. This paper adopts fractional-order PI control. When μ is equal to 1, the controller is an integer-order controller, so the fractional-order controller has great flexibility and adaptability to the control object. Fractional controllers are not sensitive to changes in plant parameters. Therefore, the fractional-order controller has good robustness.

结合式(1)、式(2)和式(11)可得电流环控制律Error in the induced current

Combining Equation (1), Equation (2) and Equation (11), the current loop control law can be obtained

The speed loop design according to the present invention is as follows:

Sliding mode control is a type of variable structure control, and variable structure control is a discontinuous control, that is, the controller will change purposefully in the process of system motion, so sliding mode control has strong robustness. . But discontinuous control leads to chattering. This limits the application of sliding mode control.

The key to designing a sliding mode controller is to suppress chattering, for which it is necessary to properly design the sliding mode control law. Make the system reach the sliding surface in a limited time and keep moving on the sliding surface.

Introducing the rotor speed error e _ω =ω-ω _r , combined with equation (4), we can get

The goal of the controller design is to make the speed of the motor track the given value. Even if e _ω = 0,

The integral sliding mode surface can reduce the static error, and the second derivative of the speed error will not appear in the control, so the integral sliding mode surface can be designed as

Where k is the sliding mode coefficient, and the value of k should be less than b in order to satisfy the switching condition, and the choice of this value determines the speed at which the speed error converges to zero on the sliding mode surface.

Combined with equation (14), the controller can be designed as

是标称控制部分，

为滑模控制器。in

is the nominal control part,

is a sliding mode controller.

So the design of the controller is composed of both the nominal model part and the sliding mode control part. In practical engineering, the real physical parameters and interference cannot be obtained accurately, and a model needs to be established to obtain a real model whose parameters can be obtained through measurement and state feedback. The design nominal control law is

The sliding mode control part is mainly to reduce or eliminate the unknown disturbance of the system. Combined with equation (15), the sliding mode control law is designed as

Where η>0 is the sliding mode gain; sgn(·) is the sign function; Jλ is the fractional integral.

The introduction of fractional integration can realize the characteristics of "small error and small gain, large error and large gain". This feature allows the system to reach the sliding surface faster while reducing chattering.

Combining equations (17) and (18), the system control law can be obtained as

As shown in FIG. 3, there is shown a control block diagram for PMSM control in accordance with the principles of the present invention.

作为李雅普诺夫函数。有Demonstration of the stability of the control system of the present invention is carried out below. Pick

as a Lyapunov function. Have

When η≥|D|, then dV/dt≤0. In order to satisfy the accessibility condition, the gain of the sliding mode controller needs to be greater than the upper bound of the uncertain factors in the system, then the motion of the system can reach the sliding mode surface in a limited time.

According to the Lyapunov stability criterion, it can be concluded that the system is asymptotically stable. Even if there is uncertainty in the external disturbance model of the matching conditions, by selecting an appropriate value of η, the global asymptotic stability of the system can be ensured, thereby obtaining ideal characteristics.

Simulation and experimental results according to the present invention are shown in Figures 4-6. The speed loop and current loop double closed-loop control mode adopted by the present invention, the motor parameters used in the simulation are set as: stator resistance R=2.875Ω; Ld=0.0085H; Lq=0.0085H; number of pole pairs np=4; flux linkage ψf =0.175Wb; moment of inertia J=0.001kg·m2. Damping coefficient B=0.008N·m·s.

The designed sliding mode control law is verified below. The simulation conditions are set as follows: the reference speed is 400r/min, and the parameters of the controller are: k=6, λ=-0.1, η=500. The simulation results are shown in Fig.

From the above figure is obtained in the simulation of MATLAB, and the effect of traditional PID algorithm is compared with the effect of the algorithm discussed in this paper. It can be seen that after a given 400r/min, the actual speed of the motor can quickly track the reference speed, and the d-q axis current also has a faster response speed, which verifies the correctness of the design.

In the current loop, the use of fractional PI improves the response speed of the system. In the speed loop, compared with the traditional PID control, the sliding mode control has the advantages of simple algorithm, strong robustness and high reliability, and has obvious effect on improving the dynamic performance. But in the two stages of sliding mode control, the approaching segment will be affected by disturbance, and it needs to ensure that it reaches the sliding mode surface within a limited time. Moreover, there is an inherent chattering problem in sliding mode control. These factors limit the use of sliding mode control in various industrial sectors.

In view of the problems existing in sliding mode control, fractional and integral sliding mode are introduced into the sliding mode control algorithm. This makes the steady-state error of the motor small, and controls the entire sliding process of the system to be "undisturbed by the matching uncertainty", and both reduce the impact of chattering on the system.

It is to be understood that the disclosed embodiments of the present invention are not limited to the specific structures, process steps or materials disclosed herein, but extend to equivalents of these features as understood by those of ordinary skill in the relevant art. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not meant 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 present invention. Thus, appearances of the phrases "one embodiment" or "an embodiment" in various places throughout the specification are not necessarily all referring to the same embodiment.

Although the disclosed embodiments of the present invention are as above, the content described is only an embodiment adopted to facilitate understanding of the present invention, and is not intended to limit the present invention. Any person skilled in the art to which the present invention belongs, without departing from the spirit and scope disclosed by the present invention, can make any modifications and changes in the form and details of the implementation, but the scope of patent protection of the present invention, The scope as defined by the appended claims shall still prevail.

Claims (8)

1. a method for controlling a permanent magnet synchronous motor, wherein the method comprises the following steps: Collect the armature three-phase current input to the permanent magnet synchronous motor and the output speed of the permanent magnet synchronous motor; Feeding back the rotational speed to the speed loop controller Fo-ISMC for adjustment to generate an outer loop control amount, the outer loop control amount corresponding to the q-axis current reference value; The current current is fed back into a current loop fractional-order PI (Fo-PI) controller and adjusted based on the q-axis current reference value to generate an inner-loop control amount corresponding to the q-axis and d-axis control voltages, the The inner loop control quantity is modulated for generating drive pulses that control the operation of the permanent magnet synchronous motor. 2. The method for controlling a permanent magnet synchronous motor according to claim 1, wherein the speed loop controller comprises a nominal control part and a sliding mode control part, wherein, in the sliding mode control part, the introduction of Fractional integration can make the system reach the sliding surface faster, thereby reducing or eliminating the unknown disturbance of the system. 3. the method for controlling permanent magnet synchronous motor as claimed in claim 1 is characterized in that, the control law of described current loop fractional order PI (Fo-PI) controller is:

Among them, _ud and u _q are the voltage components output to the following d-axis and q-axis respectively; K _pd and K _pq are the proportional gains of the controller d-axis and q-axis respectively; Ki _d and Ki _q are the controller d-axis respectively and the proportional integral of the q-axis;

and

are the fractional operators of the d-axis and q-axis of the controller, with values between 0 and 1; ed and e _q are the current errors of the _d -axis and q-axis, respectively; ω is the angular speed of the motor; L _q and L _d is the stator inductance component; i _q and _id are the dq-axis components of the stator current, respectively; ψ _f is the permanent magnet flux linkage. 4. The method for controlling a permanent magnet synchronous motor as claimed in claim 2, wherein the control law of the speed loop:

in,

is the output current of the controller; ω _r is the desired speed; _TL is the load torque;

is the derivative of the given speed; e _ω is the speed error; J ^λ is the fractional operator; sgn(S _ω ) is the sign function of the sliding mode surface S _ω ; η is the controller gain;

and

Where n _p is the number of pole pairs; J is the moment of inertia; B is the damping coefficient; T _L is the load torque; ψ _f is the permanent magnet flux linkage. 5. The method for controlling a permanent magnet synchronous motor according to any one of claims 1 to 4, wherein the decoupled q and d axis voltages are subjected to inverse Parker transformation to obtain vector control in a stationary coordinate system Voltage. 6. The method for controlling a permanent magnet synchronous motor according to claim 5, wherein SVPWM modulation is performed based on the vector control voltage to generate drive pulses provided to the motor. 7. A permanent magnet synchronous motor control system, wherein the system comprises: a detection unit, which is connected to the synchronous motor to detect in real time the three-phase current and rotational speed of the armature when the motor is running; a speed loop adjustment unit, which is used for feeding back the rotational speed to the Fo-ISMC controller for adjustment to generate an outer loop control amount, the outer loop control amount corresponding to the q-axis current reference value; Design a current loop fractional-order PI (Fo-PI) controller for feeding back the armature three-phase currents into the current loop Fo-PI controller and making adjustments based on the q-axis current reference to generate a corresponding The q-axis and the d-axis control the inner-loop control quantity of the voltage, and the inner-loop control quantity is modulated to generate a drive pulse for controlling the operation of the permanent magnet synchronous motor. 8. The permanent magnet synchronous motor control system according to claim 7, wherein, The speed loop controller includes a nominal control part and a sliding mode control part, wherein, in the sliding mode control part, fractional integral is introduced to make the system reach the sliding mode surface faster and reduce or eliminate the unknown disturbance of the system.

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