Sliding Mode Variable Structure Control Method Based on a New Reaching Law

Abstract

The present invention discloses a sliding mode variable structure control method based on a new reaching law, which is applied to a permanent magnet synchronous motor speed control system. The method includes: differentiating the state variables of the system according to the motion equation of the permanent magnet synchronous motor to obtain the derivative function of the state variables of the system; differentiating the sliding surface formula to obtain the derivative function of the sliding mode variable; combining the variable function of the new reaching law, the derivative function of the state variables of the system and the derivative function of the sliding mode variable to determine the q-axis current output by the sliding mode controller. The technical solution of this embodiment uses the mode surface as an independent variable and designs a new variable function based on the hyperbolic tangent function, which improves the convergence speed when far away from the sliding surface and greatly weakens the inherent jitter when close to the sliding surface; in addition, a new disturbance observer is designed to further enhance the robustness of the system.

Description

Technical Field

[0001] The embodiments of the present invention relate to the technical field of electric vehicle electric drive control, and in particular to a permanent magnet synchronous motor speed regulation system control based on a sliding mode variable structure. Background Art

[0002] For electric vehicles, there are three key technologies: battery technology, electric drive technology and vehicle control technology. The energy of electric vehicles mainly comes from batteries. At present, when there has been no major breakthrough in vehicle-mounted battery technology, it is particularly important to efficiently control the electric drive system. The control of the electric drive system is the key to electric drive, which determines whether electric vehicles can travel safely and efficiently. The complex and variable road conditions cause cars to frequently accelerate and decelerate, climb slopes, brake, etc., requiring the motor to meet different speed and torque requirements and have good dynamic and static response capabilities. Permanent magnet synchronous motors have become the preferred drive motors for most electric vehicle companies due to their high power density, high efficiency, and simple structure. However, there are also problems such as insufficient control accuracy and weak anti-interference ability.

[0003] Traditional PI control is widely used in permanent magnet synchronous motor speed control systems due to its simple algorithm, easy implementation and convenient parameter adjustment. However, traditional PI control can only meet the accuracy within a certain range, and is highly dependent on the accuracy of the system model and is easily affected by external interference and internal parameter perturbations. Summary of the invention

[0004] The present invention provides a sliding mode variable structure control method based on a new convergence law. The mode surface is used as an independent variable, and a new variable function is designed based on the hyperbolic tangent function to improve the traditional saturation function. While improving the convergence speed when far away from the sliding surface, the inherent jitter when close to the sliding surface is greatly weakened. In view of the disturbance problem caused by changes in system parameters and load torque, a composite function composed of the hyperbolic tangent function and the Fal function is introduced, and a new disturbance observer is designed to further enhance the robustness of the system.

[0005] The solution of the embodiment of the present invention is: a sliding mode variable structure control method based on a new reaching law, applied to a permanent magnet synchronous motor speed control system, comprising:

[0006] Derivative the state variable of the system according to the motion equation of the permanent magnet synchronous motor to obtain the derivative function of the state variable of the system; the state variable of the system is the speed error of the permanent magnet synchronous motor;

[0007] Derivative the sliding surface formula to obtain the derivative function of the sliding variable;

[0008] Determine the q-axis current output by the sliding mode controller by combining the variable function of the new reaching law, the derivative function of the state variable of the system and the derivative function of the sliding mode variable;

[0009] The variable function of the novel reaching law takes the module surface as the independent variable and is constructed based on the hyperbolic tangent function.

[0010] Optionally, the variable function of the new reaching law is:

[0011]

[0012] in:

[0013]

[0014] α, γ, k 1 , k 2 is a constant, and 0<α<2, 0<γ<1, k 1 >0,k 2 >0, X is the state variable of the system.

[0015] Optionally, the motion equation of the permanent magnet synchronous motor is:

[0016]

[0017] Among them, T e =1.5pψ f i q , is the moment of inertia; T e is the electromagnetic torque; T L is the load torque; B is the viscous friction factor, p is the pole pair number, ψ f is the permanent magnet flux.

[0018] Optionally, the sliding surface formula is as follows:

[0019] S=x+c∫ 0 t xdτ;

[0020] Among them, c is a constant, τ is a time variable, and t is the time it takes for the speed error x to converge to zero.

[0021] Optionally, the method further comprises setting a disturbance observer, wherein the disturbance observer is:

[0022]

[0023] Among them, ε is the error, w m is the actual motor speed, z 1 is the estimated value of the rotation speed, z 2 is the disturbance estimate, ψf is the permanent magnet flux, p is the number of pole pairs, i q is the q-axis current output by the sliding mode controller, β 1 , β 2 is the observer gain coefficient, is the filtering factor, and δ is a constant that affects the filtering effect.

[0024] Beneficial effects of the present invention:

[0025] The technical solution of this embodiment combines the sliding mode control theory, and makes improvements in the design of new sliding mode surface and optimization of reaching law to design a sliding mode speed controller for a permanent magnet synchronous motor; a disturbance observer is designed to address the problem of slow response of the speed loop to load disturbances, accurately observe the load torque, and compensate the observed value to the controller, thereby further improving the stability of the system and enhancing the adaptability of electric vehicles to changes in road conditions; compared with traditional PI control, the new sliding mode speed controller can improve the control accuracy of the drive system and enhance the dynamic response capability of the system; the observer overcomes interference by reducing the switching gain in the sliding mode control, thereby further enhancing the stability of the drive motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 A flow chart of a sliding mode variable structure control method based on a novel reaching law provided in an embodiment of the present invention;

[0027] Figure 2 A simulation model of a permanent magnet synchronous motor speed control system provided in an embodiment of the present invention;

[0028] Figure 3 A schematic diagram of the structure of a sliding mode controller provided by an embodiment of the present invention;

[0029] Figure 4 A schematic diagram of a Fal function filter provided by an embodiment of the present invention;

[0030] Figure 5 A schematic diagram of the structure of a disturbance observer provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0031] The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It is to be understood that the specific embodiments described herein are only used to explain the present invention, rather than to limit the present invention. It should also be noted that, for ease of description, only parts related to the present invention, rather than all structures, are shown in the accompanying drawings.

[0032] Example

[0033] Figure 1The flowchart of the sliding mode variable structure control method based on the novel reaching law provided in the embodiment of the present invention is applied to the permanent magnet synchronous motor (PMSM) speed control system. The simulation model of the permanent magnet synchronous motor speed control system provided in this embodiment is shown in FIG. Figure 2 Among them, the new reaching law sliding mode control (NRLSMC) and the observer are the contents disclosed by the present invention and will be described in detail later. The rest are the existing technologies and will not be described in detail.

[0034] The method specifically comprises the following steps:

[0035] S110. Deriving a state variable of a system according to a motion equation of the permanent magnet synchronous motor to obtain a derivative function of the state variable of the system; the state variable of the system is a speed error of the permanent magnet synchronous motor.

[0036] In this embodiment, in order to facilitate the establishment of a mathematical model of the permanent magnet synchronous motor in the dq axis coordinate system, the following assumptions are made: the magnetic field is sinusoidally distributed along the circumference of the air gap; the influence of the tooth slots of the stator winding on the air gap magnetic field distribution is ignored; the eddy current loss and hysteresis loss of the stator core and the rotor core are ignored; the changes in parameters such as the winding resistance and winding inductance are ignored. Then the voltage equation of the PMSM in the dq axis is:

[0037]

[0038] In the formula, u d 、u q are d and q axis voltages respectively; i d 、i q are d-axis and q-axis currents respectively; L d , L q are the d-axis and q-axis inductances respectively; R s is the stator inductance; p is the number of pole pairs; w is the rotor mechanical angular velocity; ψ f is the permanent magnet flux.

[0039] The torque equation and motion equation of PMSM are: e =1.5pψ f i q and Where, J is the moment of inertia; T e is the electromagnetic torque; T L is the load torque; B is the viscous friction coefficient.

[0040] Among them, the variable function of the new approach law in this embodiment takes the die surface as the independent variable and is constructed based on the hyperbolic tangent function. The variable function of the new approach law is:

[0041]

[0042] in:

[0043]

[0044] α, γ, k 1 , k 2 is a constant, and 0<α<2, 0<γ<1, k 1 >0,k 2 >0, X is the state variable of the system.

[0045] The new reaching law provided in this embodiment is associated with the exponent of the reaching law by adding the system state variable. When far away from the sliding surface, X is larger, which is equivalent to multiplying a gain on the basis of the original exponential term, increasing the convergence speed when far away from the sliding surface, and the speed decreases as the distance from the sliding surface decreases. When approaching the sliding surface, the first term on the right side of the equal sign of the variable function of the new reaching law plays a leading role, which solves the problem of discontinuous terms in the traditional reaching law, and solves the problem that the boundary layer caused by the fixed boundary layer saturation function is too large, causing the originally stable system to generate chatter again, and the boundary layer is too small, causing the system to move too short in the boundary layer, resulting in limited effect of the saturation function.

[0046] Optionally, in this implementation, the speed error x of the permanent magnet synchronous motor is defined as a state variable of the system, and the formula is as follows:

[0047] x=w r -w m

[0048] In the formula, w r is the given speed of the motor; w m is the actual motor speed.

[0049] Furthermore, according to the motion equation of PMSM The state variables of the system can be obtained:

[0050]

[0051] S120. Deriving the sliding surface to obtain a derivative function of the sliding variable.

[0052] Next, the sliding film surface formula is derived. Since the sliding mode variable structure control adopts a nonlinear control method, jitter will occur when approaching the sliding film surface. Therefore, in order to reduce jitter, this implementation selects the integral sliding film surface. The formula is:

[0053] s=x+c∫ 0 t xd

[0054] Where τ is the time variable; t is the moment when the speed error x converges to zero.

[0055] After taking the derivative of s, we have:

[0056]

[0057] S130, determining the q-axis current output by the sliding mode controller by combining the variable function of the new reaching law, the derivative function of the state variable of the system, and the derivative function of the sliding mode variable.

[0058] Further, according to the formula as well as We can get:

[0059]

[0060] In the formula, i q * is the q-axis current output by the sliding mode controller.

[0061] Considering the system internal parameter perturbation and external load disturbance, the above formula can be written as:

[0062]

[0063] The sliding mode controller structure corresponding to the above method is shown in Figure 3 .

[0064] On the basis of the above embodiment, in order to further improve the control performance of the system, this embodiment also designs a disturbance observer. In the PMSM vector control system, the control cycle is small, and compared with the current and speed signals, the load disturbance torque changes slowly. Therefore, the change of the load torque within the control cycle can be regarded as a constant value, that is:

[0065]

[0066] It can be further seen that the first-order derivative of the disturbance is zero:

[0067]

[0068] Selecting PMSM mechanical angular velocity and system total disturbance d as state variables, the state equation of the system is:

[0069]

[0070] In the formula, C = [1 0]; u = T e ;x 1 =[w m d(t)] T .

[0071] The Fal function has filtering characteristics and is a special nonlinear structure that is often used in the extended state observer in the active disturbance rejection controller. The function filter of the Fal function can be found in Figure 4 When the Fal function is combined with ESO, the interference in the system measurement link can be effectively observed. The Fal function expression is as follows:

[0072]

[0073] Where ε is the error, μ is the filter factor, and δ is a constant that affects the filtering effect.

[0074] In summary, the expression of the disturbance observer in this embodiment is as follows:

[0075]

[0076] In the formula, z 1 is the estimated value of the rotation speed, z 2 is the disturbance estimate, β 1 , β 2 is the observer gain coefficient. Further, the structure of the above disturbance observer can be found in Figure 5 .

[0077] The technical solution of this embodiment combines the sliding mode control theory, and makes improvements in the design of new sliding mode surface and optimization of reaching law to design a sliding mode speed controller for a permanent magnet synchronous motor; a disturbance observer is designed to address the problem of slow response of the speed loop to load disturbances, accurately observe the load torque, and compensate the observed value to the controller, thereby further improving the stability of the system and enhancing the adaptability of electric vehicles to changes in road conditions; compared with traditional PI control, the new sliding mode speed controller can improve the control accuracy of the drive system and enhance the dynamic response capability of the system; the observer overcomes interference by reducing the switching gain in the sliding mode control, thereby further enhancing the stability of the drive motor.

[0078] Note that the above are only preferred embodiments of the present invention and the technical principles used. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and that various obvious changes, readjustments and substitutions can be made by those skilled in the art without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in more detail through the above embodiments, the present invention is not limited to the above embodiments, and may include more other equivalent embodiments without departing from the concept of the present invention, and the scope of the present invention is determined by the scope of the appended claims.

Claims

1. A sliding mode variable structure control method based on a new reaching law, applied to a permanent magnet synchronous motor speed control system, characterized in that: include: Deriving the state variables of the system according to the motion equation of the permanent magnet synchronous motor to obtain the derivative function of the state variables of the system; The state variable of the system is the speed error of the permanent magnet synchronous motor; Derivative the sliding surface formula to obtain the derivative function of the sliding variable; Determine the q-axis current output by the sliding mode controller by combining the variable function of the new reaching law, the derivative function of the state variable of the system and the derivative function of the sliding mode variable; The variable function of the novel reaching law is constructed based on the hyperbolic tangent function, taking the module surface as the independent variable; The variable function of the new reaching law is: in: α, γ, k1, k2 are constants, and 0<α<2, 0<γ<1, k1>0, k2>0, and X is the state variable of the system.

2. The method according to claim 1, characterized in that The motion equation of the permanent magnet synchronous motor is: Among them, T e =1.5pψ f i q , J is the moment of inertia; T e is the electromagnetic torque; T L is the load torque; B is the viscous friction factor, p is the pole pair number, ψ f is the permanent magnet flux.

3. The method according to claim 1, characterized in that The sliding surface formula is as follows: Among them, c is a constant, τ is a time variable, and t is the time it takes for the speed error x to converge to zero.

4. The method according to claim 1, characterized in that: The method further comprises setting a disturbance observer, wherein the disturbance observer is: Among them, ε is the error, w m is the actual motor speed, z1 is the estimated speed, z2 is the disturbance estimated value, ψ f is the permanent magnet flux, p is the number of pole pairs, i q is the q-axis current output by the sliding mode controller, β1 and β2 are the observer gain coefficients, μ is the filter factor, δ is a constant that affects the filtering effect, J is the moment of inertia, and Fal() is a function with a nonlinear structure.

Images