阅读说明：本技术 一种基于固定时间的变幂次指数趋近律的永磁同步电机滑模控制方法 (Permanent magnet synchronous motor sliding mode control method based on variable power exponent approach law of fixed time ) 是由 姜长泓 王其铭 张袅娜 于 2021-09-07 设计创作，主要内容包括：本发明属于永磁同步电机控制技术领域,公开了一种永磁同步电机、滑模控制方法、控制系统、终端、介质,在转子同步坐标系下,将时变参数量将转化为非时变量参数,并根据电机基本特性建立永磁同步电机模型；基于固定时间的变幂次指数趋近律的永磁同步电机滑模控制策略,该控制策略包含一种可变指数系数的滑模面；设计合适趋近律,使得状态变量在固定时间收敛到滑模面；基于建立的永磁同步电机模型确定永磁同步电机控制模型,根据基于确定的控制策略以及永磁同步电机控制模型进行永磁同步电机控制。本发明的固定时间稳定性确保建立时间不依赖于初始条件,提供预定义时间达到平衡；本发明采用以加快电机速度响应和提高鲁棒性为目的的变指数幂次趋近律滑模控制策略,实现复杂工况下的永磁同步电机速度准确控制。(The invention belongs to the technical field of permanent magnet synchronous motor control, and discloses a permanent magnet synchronous motor, a sliding mode control method, a control system, a terminal and a medium, wherein under a rotor synchronous coordinate system, time-varying parameters are converted into non-time-varying parameters, and a permanent magnet synchronous motor model is established according to basic characteristics of the motor; the permanent magnet synchronous motor sliding mode control strategy based on the variable power exponent approach law of fixed time comprises a sliding mode surface with a variable exponent coefficient; designing a proper approach law to make the state variable converge to the sliding mode surface at a fixed time; and determining a permanent magnet synchronous motor control model based on the established permanent magnet synchronous motor model, and controlling the permanent magnet synchronous motor according to the determined control strategy and the permanent magnet synchronous motor control model. The fixed time stability of the invention ensures that the establishment time does not depend on the initial condition, and provides the predefined time to reach the balance; the invention adopts a variable exponential power approach law sliding mode control strategy aiming at accelerating the speed response of the motor and improving the robustness, and realizes the accurate control of the speed of the permanent magnet synchronous motor under the complex working condition.)

1. The permanent magnet synchronous motor sliding mode control strategy based on the variable power exponent approach law of the fixed time is characterized in that the permanent magnet synchronous motor sliding mode control method based on the fixed time comprises the following steps:

converting time-varying parameter quantity into non-time-varying parameter under a rotor synchronous coordinate system, and establishing a permanent magnet synchronous motor model according to basic characteristics of a motor;

step two, a permanent magnet synchronous motor rotating speed control strategy based on a variable power exponent approach law of fixed time;

and step three, determining a permanent magnet synchronous motor control model based on the established permanent magnet synchronous motor model, and controlling the permanent magnet synchronous motor according to the determined control strategy and the permanent magnet synchronous motor control model.

2. The fixed-time-based sliding-mode control method for the permanent magnet synchronous motor according to claim 1, wherein the time-varying parameters comprise: voltage, permanent magnet flux linkage.

3. The fixed-time-based sliding mode control method for the permanent magnet synchronous motor according to claim 1, wherein in the first step, the model of the permanent magnet synchronous motor is as follows:

by using i_dVector control method 0:

PMSM torque equation:

PMSM equation of motion:

wherein L is_d、L_qRespectively representing d-axis stator inductance (mH) and q-axis stator inductance (mH); p represents the number of pole pairs of the motor; w denotes an electric machineAn angular velocity; t is_eRepresenting an electromagnetic torque of the electrical machine; t is_LRepresenting the external torque applied by the motor; psi_fRepresenting the rotor flux linkage; j is moment of inertia.

4. The sliding-mode control method of the permanent magnet synchronous motor based on the variable power exponent approach law of the fixed time as claimed in claim 1, wherein in the second step, the sliding-mode control strategy of the permanent magnet synchronous motor based on the variable power exponent approach law of the fixed time comprises:

(1) defining a system state equation and a fixed time sliding mode surface:

(2) determining a variable power exponent approach law:

whereinEta is a small normal number, lambda is more than 0, mu is more than 0, beta is more than 0, alpha is more than 0, c is more than 1, and b is more than 0 and less than 1; w is a_rRepresenting a given revolution; w is a_mRepresenting the actual rotational speed; s represents the sliding mode surface, and epsilon and k are controller parameters.

5. The sliding mode control strategy of the permanent magnet synchronous motor based on the fixed-time variable power exponent approach law as claimed in claim 1, wherein the fixed time is as follows: the invention designs a fixed time sliding mode surface, and selects a control law, so that the system state x is₁，x₂The equilibrium point can be reached within a fixed time, the convergence time having an upper bound related only to the design parameters:

T＜T_max＝T₁+t₁+t₂

wherein

6. The sliding mode control strategy of the permanent magnet synchronous motor based on the fixed-time variable power exponent approach law as claimed in claim 1, wherein in step three, the permanent magnet synchronous motor control model comprises:

wherein the content of the first and second substances,

7. the permanent magnet synchronous motor sliding mode control system based on the variable power exponent approach law of the fixed time is characterized by comprising the following steps of:

the permanent magnet synchronous motor model building module is used for converting the time-varying parameter quantity into a non-time-varying parameter under a rotor synchronous coordinate system and building a permanent magnet synchronous motor model according to the basic characteristics of the motor;

and the permanent magnet synchronous motor control module is used for determining a permanent magnet synchronous motor control model based on the established permanent magnet synchronous motor model and controlling the permanent magnet synchronous motor according to the control strategy and the permanent magnet synchronous motor control model based on the determination.

8. A computer device, characterized in that the computer device comprises a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to carry out the steps of:

converting the time-varying parameter quantity into a non-time-varying parameter under a rotor synchronous coordinate system, and establishing a permanent magnet synchronous motor model according to the basic characteristics of the motor;

determining a permanent magnet synchronous motor rotating speed control strategy based on a variable index approach law and weighted integral composite method;

and determining a permanent magnet synchronous motor control model based on the established permanent magnet synchronous motor model, and controlling the permanent magnet synchronous motor according to the determined control strategy and the permanent magnet synchronous motor control model.

Technical Field

The invention belongs to the technical field of permanent magnet synchronous motor control, particularly relates to a permanent magnet synchronous motor, a sliding mode control method and a control system, and particularly relates to a permanent magnet synchronous motor sliding mode control method based on a variable power exponent approach law of fixed time.

Background

At present, the traditional motor driving mode is 'motor + reducer', and the existence of the reducer not only increases the overall energy consumption of the transmission system, but also reduces the stability and reliability of the transmission system. The permanent magnet synchronous motor has the advantages of small torque pulsation, high efficiency, simple structure, small volume and the like, thereby being widely applied to a direct drive system. The direct drive system can reduce intermediate links (such as a speed reducer and a coupling) of the transmission system and realize near-zero transmission. However, since the direct drive system has no transmission mechanism, the disturbance on the load side can seriously affect the stability of the PMSM speed regulating system. In addition, the permanent magnet synchronous motor is a complex system with nonlinearity, strong coupling and multivariable system, and has the problems of modeling error, complex working condition, uncertainty factors and the like. Particularly, when the motor runs at a low speed, the inverter can output discontinuous current to generate torque pulsation; when the motor runs at a high speed, a large amount of stator harmonic current is generated, and the rotating speed following capability and the torque stability are influenced. The control performance and reliability of the motor control system directly influence the stable operation of the whole system, so that a control strategy with strong robustness is required, and the disturbance resistance of the motor is improved.

At present, scholars at home and abroad use different methods to research a permanent magnet synchronous motor speed regulating system, such as fuzzy control, predictive control, self-adaptive control, sliding mode control and the like. The technology 1 designs a fuzzy logic speed controller, which not only improves the torque pulsation restraining capability, but also improves the dynamic quality of a speed regulating system. The technology 2 provides a continuous control set sliding mode predictive control system for a permanent magnet synchronous motor speed regulating system. The technology 3 provides a model prediction method applied to a permanent magnet synchronous motor to overcome the limitation of motion control of an unconstrained state variable. Technique 4 employs adaptive fault-tolerant control to ensure normal operation when the actuator fails. Technique 5 proposes the use of a neural network in combination with adaptive control to improve speed following. The sliding mode control is commonly used: integral sliding mode control, fuzzy sliding mode control, terminal sliding mode control, inversion sliding mode control and the like are used for controlling the rotating speed of the permanent magnet synchronous motor. Technique 6 proposes a memory-less and memory-based integral sliding mode control and applies to motor control. Technology 7 proposes a robust fuzzy neural network sliding mode control method for controlling a permanent magnet linear motor. Technology 8 originally proposes that terminal sliding mode control is applied to an uncertain dynamic system, but the system has a singular problem. Therefore, the non-singular terminal sliding mode is designed in the technology 9 to solve the problem of system singularity, and the system singularity is analyzed, reasoned and proved in detail. The technology 10 provides a self-adaptive second-order nonsingular terminal sliding mode scheme, and the scheme is used for the aspect of track tracking of an autonomous underwater vehicle. Compared with other control methods, the sliding mode control method has the advantages that the sliding mode control concrete sliding mode type is independently designed, and the influence of parameter perturbation and external disturbance is avoided. The nonsingular sliding mode has the advantages of fast dynamic response, limited time convergence, high steady-state precision and the like, and is widely applied to the field of high-precision control.

However, the sliding mode control has the advantages that high-frequency buffeting is used for replacing the high-frequency buffeting, and the buffeting phenomenon is directly related to a switching function contained in an approach law. At present, a common method for solving buffeting is as follows: high-order sliding mode, self-adaptive algorithm, interference observer, approach law method and the like. Technique 11 proposes a high-order sliding mode control strategy and provides a detailed overview. Discontinuous control in high-order sliding mode control is hidden in a high-order derivative of the discontinuous control, buffeting is effectively weakened, and the control structure of the discontinuous control is complex. The technique 12 proposes an adaptive algorithm acting on the sliding surface parameter estimation and provides a parametric fitting mechanism to learn the dynamic characteristics of the system, so that the system converges fast. The technology 13 is to solve the problem that the constant speed approach law cannot meet the requirements of rapidity and low buffeting simultaneously in the sliding mode observer, the proposed control method can effectively improve the problem of incompatibility of rapidity and stability, and the technology 14 is to propose an extended state observer to observe lumped disturbance and introduce the estimated disturbance into a feedforward compensation technology, so that the robustness of the system is improved. External disturbances and uncertainties are the main sources of buffeting in sliding mode control, and the problem can be solved by using an observer. The approach law method is simple and convenient in design, easy to implement and widely applied. The theory of approach was proposed by Ogaku et al and analyzed from three modes, sliding, arrival and steady state. The most applied exponential approach law not only shortens the approach time, but also reduces the speed when the moving point reaches the switching surface. The novel approach law proposed by the technology 15 takes a sliding mode surface as a research mechanism, and different functions are designed to enable the index term to adapt to the sliding mode surface and the change of the state. Technique 16 proposes a power approach law for automotive electronic throttle control. The power sliding mode approach law design idea utilizes the property of an exponential function to pertinently accelerate the approach rate to different stages of the approach process. In addition, methods are used for suppressing system buffeting, such as a neural network is used for on-line approximation interference, so that the gain of a switching project is reduced, a sliding mode is optimized in multiple targets, and the like.

Through the above analysis, the problems and defects of the prior art are as follows: the buffeting phenomenon in the traditional sliding mode approach law, the convergence speed and the like are low. The fixed time has slow convergence speed and has a singular problem.

The difficulty in solving the above problems and defects is: the sliding mode surface with fixed time is provided, and the rapid approach is realized. The approach law of the self-adaptive adjusting function can be designed according to different stages.

The significance of solving the problems and the defects is as follows: the convergence time of the finite time is determined again by the initial condition of the system, which may be difficult to accurately obtain in advance due to the initial condition of the actual system. The fixed time convergence theory does not depend on the convergence time upper bound of the initial condition of the system, and the actual requirements of engineering are further met.

Disclosure of Invention

Aiming at the problems in the prior art, the invention provides a fixed-time permanent magnet synchronous motor, a sliding mode control method and a control system.

The invention is realized in such a way that a permanent magnet synchronous motor sliding mode control method based on a variable power exponent approach law of fixed time comprises the following steps:

converting time-varying parameter quantity into non-time-varying parameter under rotor synchronous coordinate system, establishing permanent magnet synchronous motor model according to basic characteristics of motor, and simplifying mathematical model of permanent magnet synchronous motor by vector control method. The torque and the motion equation of the permanent magnet synchronous motor are written in L_d＝L_qThe equation continues to be simplified under the condition of the surface-mounted motor;

and step two, a permanent magnet synchronous motor rotating speed control strategy based on a variable power exponent approach law of fixed time. Substituting the torque equation of the permanent magnet synchronous motor into the motion equation to obtain a rotating speed state equation, and setting a rotating speed error as a system state variable. Selecting a fixed time sliding mode surface, and determining an equation of a variable power exponent approach law;

and step three, determining a permanent magnet synchronous motor control model based on the established permanent magnet synchronous motor model. And (3) carrying out derivation on the selected sliding mode surface, combining the derivation with a designed approach law, and substituting a rotating speed state equation to obtain a system q-axis current equation, namely the output variable of the system. Further, the time-varying parameter quantity includes: voltage, permanent magnet flux linkage.

Further, in the step one, the permanent magnet synchronous motor model is as follows:

by using i_dVector control method 0:

PMSM torque equation:

PMSM equation of motion:

wherein L is_d、L_qRespectively representing d-axis stator inductance (mH) and q-axis stator inductance (mH); p represents the number of pole pairs of the motor; w represents the angular velocity of the motor; t is_eRepresenting an electromagnetic torque of the electrical machine; t is_LRepresenting the external torque applied by the motor; psi_fRepresenting the rotor flux linkage; j is moment of inertia.

Further, in the second step, the permanent magnet synchronous motor rotation speed control strategy based on the variable power exponent approach law of the fixed time includes:

(1) defining a system state equation and a sliding mode surface:

(2) determining a variable power exponent approach law:

whereinEta is a small normal number, lambda is more than 0, mu is more than 0, beta is more than 0, alpha is more than 0, c is more than 1, and b is more than 0 and less than 1; w is a_rRepresenting a given revolution; w is a_mRepresenting the actual rotational speed; s represents the sliding mode surface, and epsilon and k are controller parameters.

Further, in step three, the permanent magnet synchronous motor control model includes:

wherein the content of the first and second substances,

(3) determining a fixed time:

the designed fixed time sliding mode surface is selected, and the system state x is obtained by selecting the control law₁，x₂The equilibrium point can be reached within a fixed time, the convergence time having an upper bound related only to the design parameters:

T＜T_max＝T₁+t₁+t₂

wherein

Another object of the present invention is to provide a system for controlling a rotating speed of a permanent magnet synchronous motor based on a variable power exponent approach law with fixed time, the system comprising:

the permanent magnet synchronous motor model building module is used for converting the time-varying parameter quantity into a non-time-varying parameter under a rotor synchronous coordinate system and building a permanent magnet synchronous motor model according to the basic characteristics of the motor;

the permanent magnet synchronous motor rotating speed control strategy determining module is used for determining a permanent magnet synchronous motor rotating speed control strategy based on a variable power exponent approach law method of fixed time;

and the permanent magnet synchronous motor control module is used for determining a permanent magnet synchronous motor control model based on the established permanent magnet synchronous motor model and controlling the permanent magnet synchronous motor according to the control strategy and the permanent magnet synchronous motor control model based on the determination.

By combining all the technical schemes, the invention has the advantages and positive effects that: the invention is improved on the basis of the traditional fixed time, and the sliding mode surface is designed by adopting a variable exponential coefficient. When the system state variable reaches the sliding mode surface s from any place to 0, the state variable moves to a tiny neighborhood of the balance point. The design not only solves the singular phenomenon, but also accelerates the convergence speed.

The invention also provides a variable power exponent approach law which can realize the function of self-adaptive adjustment according to different stages. A balance is struck between damping buffeting and increasing approach speed.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required to be used in the embodiments of the present application will be briefly described below.

Fig. 1 is a schematic diagram of a sliding-mode control method of a permanent magnet synchronous motor based on a fixed-time variable power exponent approach law according to an embodiment of the present invention.

Fig. 2 is a flowchart of a sliding mode control method of a permanent magnet synchronous motor based on a fixed-time variable power exponent approach law according to an embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

Aiming at the problems in the prior art, the invention provides a permanent magnet synchronous motor sliding mode control method based on a variable power exponent approach law of fixed time, and the invention is described in detail below by combining with the attached drawings.

As shown in fig. 1-2, a sliding-mode control method for a permanent magnet synchronous motor based on a fixed-time variable power exponent approach law according to an embodiment of the present invention includes:

s101, converting the time-varying parameter quantity into a non-time-varying parameter under a rotor synchronous coordinate system, and establishing a permanent magnet synchronous motor model according to basic characteristics of a motor;

s102, determining a rotating speed control strategy of the permanent magnet synchronous motor based on a control method of a variable power exponent approach law of fixed time;

s103, determining a permanent magnet synchronous motor control model based on the established permanent magnet synchronous motor model, and controlling the permanent magnet synchronous motor according to the determined control strategy and the permanent magnet synchronous motor control model.

The time-varying parameter provided by the embodiment of the invention comprises the following components: voltage, permanent magnet flux linkage.

In step S101, the permanent magnet synchronous motor model provided in the embodiment of the present invention is as follows:

by using i_dVector control method 0:

PMSM torque equation:

PMSM equation of motion:

wherein L is_d、L_qRespectively representing d-axis stator inductance (mH) and q-axis stator inductance (mH); p represents the number of pole pairs of the motor; w represents the angular velocity of the motor; t is_eRepresenting an electromagnetic torque of the electrical machine; t is_LRepresenting the external torque applied by the motor; psi_fRepresenting the rotor flux linkage; j is moment of inertia.

In step S102, the determining a control strategy for a rotating speed of a permanent magnet synchronous motor by using a control method based on a fixed-time variable power exponent approach law according to an embodiment of the present invention includes:

(1) defining a system state equation and a sliding mode surface:

(2) determining a variable power exponent approach law:

whereinEta is a small normal number, lambda is more than 0, mu is more than 0, beta is more than 0, alpha is more than 0, c is more than 1, and b is more than 0 and less than 1; w is a_rRepresenting a given revolution; w is a_mRepresenting the actual rotational speed; s represents the sliding mode surface, and epsilon and k are controller parameters.

Further, in step three, the permanent magnet synchronous motor control model includes:

wherein the content of the first and second substances,

(3) determining a fixed time:

the designed fixed time sliding mode surface is selected, and the system state x is obtained by selecting the control law₁，x₂The equilibrium point can be reached within a fixed time, the convergence time having an upper bound related only to the design parameters:

T＜T_max＝T₁+t₁+t₂

wherein

The technical solution of the present invention is further described with reference to the following specific examples.

The permanent magnet synchronous motor control method based on the variable power exponent approach law of the fixed time comprises the following steps:

step one, under a rotor synchronous coordinate system, the time-varying parameters such as voltage, permanent magnet flux linkage and the like are converted into non-time-varying parameters, so that the analysis is more convenient, in addition, in order to simplify the operation, the following assumptions are made for the alternating current permanent magnet synchronous motor:

(1) three phases of the stator windings are symmetrically distributed and are completely the same, and the axes of the windings are mutually different by 120 degrees in space;

(2) neglecting the influence of magnetic circuit saturation, magnetic hysteresis and eddy current, and having no damping on the rotor;

(3) when the stator winding current is three-phase symmetrical sinusoidal current, only magnetomotive force with sine wave distribution is generated in the air gap space, and no higher harmonic wave distribution exists;

(4) when the motor is in no load, the electromotive force of the stator is sine wave.

The following equation can be established again from the basic characteristics of the motor:

PMSM torque formula:

for surface-mounted motors, i is adopted_dTorque formula under control strategy of 0:

PMSM equation of motion:

wherein L is_d、L_qThe stator inductances (mH) of the d and q axes are respectively, p is the pole pair number of the motor, w is the angular velocity (r/min) of the motor, and T is_eIs the electromagnetic torque (N.m), T of the motor_LExternal torque (N m), psi applied to the motor_fIs rotor flux linkage (Wb), and J is moment of inertia (kg. m)²)。

For surface-mounted motors, i is adopted_dUnder a control strategy of 0, and rewriting formula (1):

taking a system state variable:

wherein w_rFor a given rotational speed, w_mIs the actual rotational speed. Due to w_rIs a slow varying function, satisfiesEquation (6)This is true.

The combination formula (5) is as follows:

and is defined thereinEquation (7) can be rewritten as:

step two, designing a composite variable index approach law controller:

defining a slip form surface:

the derivation of equation (9) yields:

the approximation law of the variable power exponent is substituted into the formula (10) to obtain:

thus, the q-axis current:

step three, aiming at a permanent magnet synchronous motor control system (7), adopting a sliding mode surface (9) and a composite variable index approach law control strategy, gradually converging the speed of the permanent magnet synchronous motor to an ideal rotating speed, giving a speed stability certificate, and solving fixed time:

choosing a Lyapunov function as:

derivation of the formula (13)

Firstly, whenWhen the temperature of the water is higher than the set temperature,

② whenWhen the temperature of the water is higher than the set temperature,

the fixed-time sliding mode surface meets the Lyapunov stability theory. The system state can be at a fixed time T₁The inner reach sliding mode surface s is equal to 0, then the sliding mode surface is moved to a minimal neighborhood of the balance point along the sliding mode surface, and the ideal sliding mode satisfies the following equation:

consider the following Lyapunov function

Taking into account | x₁| is not less than 1 and is in | x₁When | > eta, the sliding form can be obtainedThe noodle is as follows:

to V₂And (5) obtaining a derivative:

due to the fact that

When considering | x₁< 1 and at | x₁When | < eta, a slip form surface can be obtained:

due to 1+ mux₁Is not less than 1 and | x₁If | is less than 1, then there is

To functionDerivation:

therefore, whenTaking the minimum value

Thus the fixed time is

In the description of the present invention, "a plurality" means two or more unless otherwise specified; the terms "upper", "lower", "left", "right", "inner", "outer", "front", "rear", "head", "tail", and the like, indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, are only for convenience in describing and simplifying the description, and do not indicate or imply that the device or element referred to must have a particular orientation, be constructed in a particular orientation, and be operated, and thus, should not be construed as limiting the invention. Furthermore, the terms "first," "second," "third," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.

The above description is only for the purpose of illustrating the present invention and the appended claims are not to be construed as limiting the scope of the invention, which is intended to cover all modifications, equivalents and improvements that are within the spirit and scope of the invention as defined by the appended claims.