A method for speed regulation of a permanent magnet synchronous motor based on a homing law

Abstract

The application discloses a permanent magnet synchronous motor speed regulation method based on a reaching law, the reaching law can adaptively adjust parameters according to the distance of system state from a sliding mode surface, and the reaching law comprehensively resolves the contradiction between chattering and rapidity in the sliding mode control, the reaching law does not introduce redundant unknown parameters compared with an exponential reaching law. In order to prove the superiority of the reaching law, phase trajectory diagrams are used for analysis, and Lyapunov functions are used for stability analysis of the new reaching law. Meanwhile, in order to avoid repeatedly trying and fitting the parameters of the reaching law, a universal gravitation algorithm is introduced to set the parameters. MATLAB / simulink is used for modeling simulation, compared with the exponential reaching law, the speed loop sliding mode control designed by using the reaching law not only improves the speed regulation performance of the system, but also weakens the chattering phenomenon of the system, and improves the dynamic characteristics and robustness of the system.

Description

Technical Field

[0001] The present invention relates to the technical field of permanent magnet synchronous motor speed regulation, and in particular to a permanent magnet synchronous motor speed regulation method based on reaching law. Background Art

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in industrial control, aerospace, electric vehicles, and medical devices due to their high power density, compact size, wide speed regulation range, and high reliability. Currently, PI control is often used for the speed loop of PMSM vector control. PI control is favored by many engineers due to its simplicity, ease of implementation, and simple parameter adjustment. However, because PMSMs are multivariable, strongly coupled, and nonlinear control targets, PI control is only suitable for simple operating conditions. External disturbances and sudden changes in operating conditions significantly impact the robustness of the system. For high-precision control applications, simple PI control can no longer meet the demands of society. With the advancement of control theory, many scholars are constantly pursuing better control methods. Currently, fuzzy control, neural network control, predictive control, active disturbance rejection control, and sliding mode control are commonly used for PMSM speed regulation.

[0003] Sliding mode control, a nonlinear variable structure control method, offers excellent interference immunity and robustness when system parameters and operating conditions change, making it widely used in permanent magnet synchronous motor speed control systems. However, when in sliding mode, sliding mode control can cause chattering as the sliding surface traverses back and forth. If applied directly to permanent magnet synchronous motor control without prior processing, this can lead to system instability and poor sliding mode quality.

[0004] Therefore, many scholars have adopted different methods to eliminate the chattering caused by the control process. In order to improve the quality of sliding mode control, Chinese scholar Gao Weibing proposed the concept of reaching law and designed an exponential reaching law as shown below:

[0005] Where ε,k are constants greater than zero, s is the sliding surface, sign() is the switching function of the sliding mode, ks is the exponential term, and -εsign(s) is the constant speed approach term.

[0006] When the initial state s(0) of the system is far away from the sliding surface, the approach mode is completed by adjusting the exponential term and the constant speed term parameters at the same time. When the system state point reaches the sliding surface, the exponential term is zero, and the sliding mode is completed by the constant speed term. Since the constant speed term contains a sign function, ε cannot be zero, so the system will always be accompanied by jitter of the size of ε. From the above, we can see that the dynamic quality of the sliding mode control can be guaranteed by adjusting the ε and k parameters. When the ε and k parameters take larger values, the system will converge to the sliding surface at a very fast speed, but will produce larger jitter. When the ε and k parameters take smaller values, the system converges slower and the jitter is smaller. At this time, by calculating the convergence time of the exponential approach law, we can clearly see the shortcomings of the approach law. The calculation is as follows:

[0007] In formula (1), when s>0

[0008]

[0009] Assuming that the initial state of the system is at s(0), the time when the system reaches the sliding surface is as follows:

[0010]

[0011] From formula (4), we can clearly see that increasing the k value can speed up the system's arrival speed to improve rapidity, but it will cause the speed of reaching the sliding surface to be too high, and the system state will traverse the sliding surface back and forth, resulting in large chattering, and vice versa.

[0012] In summary, the problem with the reaching law used in existing permanent magnet synchronous motor speed regulation is that improving speed and reducing jitter are technically contradictory and cannot be achieved simultaneously. Summary of the Invention

[0013] In order to solve the above shortcomings and deficiencies of the prior art, an object of the present invention is to provide a permanent magnet synchronous motor speed control method based on reaching law.

[0014] The technical solution of the present invention is: a permanent magnet synchronous motor speed control method based on reaching law, comprising:

[0015] Let the reference value of the direct-axis current component be

[0016] The rotor position θ m Provided for Park and Anti-Park use;

[0017] The actual rotor speed ω m and reference speed ω ref The error is sent to the sliding mode controller, and the reference value of the quadrature axis current component is obtained after adjustment by the sliding mode controller.

[0018] The three-phase stator winding current i a ,i b ,i c The quadrature axis current component i in the rotating coordinate system is obtained by Clark and Park transformation q and the direct axis current component i d ;

[0019] The actual quadrature-axis current component i q and the direct axis current component i d The reference value of the quadrature axis component after sliding mode control adjustment and the reference value of the direct-axis current component Subtract and get the error;

[0020] The error is sent to PI control and then output u q ,u d ;u q ,u d Obtain u through inverse Park transform α ,u β ;

[0021] will u α ,u β The input is sent to the space vector pulse width modulation module to generate a pulse signal to the three-phase inverter to drive the motor;

[0022] The sliding mode controller outputs the reference value of the quadrature-axis current component through the following reaching law

[0023] Wherein, 0<σ<0.1, s represents the sliding surface, k1 is a constant greater than zero, and k2 is a constant greater than zero.

[0024] Furthermore, the control expression of the sliding mode speed loop of the permanent magnet synchronous motor is as follows:

[0025] Among them, x1 represents the speed error, T L represents the load torque, J represents the motor moment of inertia, c represents the sliding surface coefficient, P n is the number of motor pole pairs, ψ f is the permanent magnet flux linkage.

[0026] Furthermore, the optimal sliding mode parameters are found by using the universal gravitation algorithm. The method is as follows:

[0027] In the gravitational algorithm, particles are assigned to k1, k2, σ, and c in sequence;

[0028] In the gravitational algorithm, the fitness function is: f = ∫t*|x1|dt;

[0029] Here, t represents time.

[0030] The beneficial effects of the present invention are as follows: compared with the prior art, the present invention introduces a reaching law for the reference value of the quadrature axis current component output by the sliding mode controller, and introduces an adaptive factor e for the constant speed term. -|s| +σ |s| , to solve the contradiction between the rapidity and chattering reduction of sliding mode control, the hyperbolic tangent function is introduced to further reduce the chattering caused by the sign function switching process. The sliding mode controller is designed by adopting the reaching law. The simulation results using MATLAB / SIMULINK show that the reaching law can solve the technical contradiction between the rapidity and chattering reduction of sliding mode control, and the problem that they cannot have both at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is the image of the switching function tanh(as) of the sliding mode of the system of the present invention;

[0032] Figure 2 is the phase trajectory of the sliding mode motion of the present invention;

[0033] Figure 3 The time diagram required for the approach process of the present invention;

[0034] Figure 4 This is a structural block diagram of the sliding mode speed loop of the present invention;

[0035] Figure 5 is the speed comparison curve of the present invention;

[0036] Figure 6 This is the comparison result of the electromagnetic torque of the present invention;

[0037] Figure 7 A comparison diagram of three-phase currents of the prior art exponential reaching law of the present invention;

[0038] Figure 8 This is a comparison diagram of the reaching law three-phase current of the present invention. DETAILED DESCRIPTION

[0039] Mathematical model of permanent magnet synchronous motor:

[0040] In order to simplify the analysis, an ideal permanent magnet synchronous motor mathematical model is established, and the following assumptions are made for the PMSM: the saturation of the permanent magnet synchronous motor core is ignored, the influence of hysteresis and eddy current is ignored, the magnetomotive force is sinusoidally distributed, and the influence caused by the irregularity of the stator slot is ignored.

[0041] The mathematical model of the permanent magnet synchronous motor under the dq axis is as follows

[0042]

[0043] The magnetic flux equation is shown below

[0044]

[0045] u d ,u q is the stator voltage under dq, i d ,i q is the stator current under dq, L d ,L q is the stator inductance under the dq axis, R is the stator resistance, ψ d ,ψ q is the magnetic flux under dq, ψ f is the permanent magnet flux, ω e is the mechanical angular velocity, ω is the electrical angular velocity, P n is the number of motor pole pairs.

[0046] The electromagnetic torque equation is shown below

[0047]

[0048] This article takes the surface-mounted permanent magnet synchronous motor as an example, so L d =L q =L, so the new electromagnetic torque equation is as follows

[0049]

[0050] The equation of motion is

[0051]

[0052] The invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0053] Implementation Example 1:

[0054] In order to solve the problem that improving speed and reducing chattering in the existing technology are technical contradictions and cannot be achieved simultaneously, the present invention adopts a permanent magnet synchronous motor speed control method based on the reaching law, including:

[0055] Let the reference value of the direct-axis current component be

[0056] The rotor position θ m Provided for Park and Anti-Park use;

[0057] The actual rotor speed ω m and reference speed ω ref The error is sent to the sliding mode controller, and the reference value of the quadrature axis current component is obtained after adjustment by the sliding mode controller.

[0058] The three-phase stator winding current i a ,i b ,i c The quadrature axis current component i in the rotating coordinate system is obtained by Clark and Park transformation q and the direct axis current component i d ;

[0059] The actual quadrature-axis current component i q and the direct axis current component i d The reference value of the quadrature axis component after sliding mode control adjustment and the reference value of the direct-axis current component Subtract and get the error;

[0060] The error is sent to PI control and then output u q ,u d ;u q ,u d Obtain u through inverse Park transform α ,u β ; will u α ,u β The input is to the space vector pulse width modulation module to generate a pulse signal to the three-phase inverter to drive the motor; the sliding mode controller outputs the reference value of the quadrature axis current component through the following reaching law Wherein, 0<σ<0.1, s represents the sliding surface, k1 is a constant greater than zero, and k2 is a constant greater than zero.

[0061] The reaching law proposed in the present invention is analyzed in terms of reaching mode and sliding mode as follows:

[0062] Approaching mode: When the system state is far away from the sliding surface, the exponential term and the constant velocity term act simultaneously. At this time, the constant velocity term is k1e |s| , which makes the system approach speed become very large, increases the speed at which the system approaches the sliding surface, and makes sliding mode control possible.

[0063] Sliding mode: When the system state is close to the sliding surface, that is, when s→0, the exponential term k2s is zero, and the constant speed term takes effect. At this time, e -|s| →1,σ |s| →1, the constant velocity term becomes k1 / 2, and the system will slide on the sliding surface at a very small number, effectively reducing chattering.

[0064] Therefore, the convergence law of this patent can solve the technical contradiction between the rapidity and the reduction of chattering in sliding mode control, while achieving both rapidity and reduced chattering.

[0065] This patent selects the hyperbolic sine function as the switching function of the system sliding mode, making its switching process smoother and further reducing the chattering. Its tanh(as) image is as follows: Figure 1 shown.

[0066] In order to analyze the stability of the reaching law proposed in this paper, the following Lyapunov function is constructed:

[0067]

[0068] By taking the derivative of the above formula, we can get the following: From the above formula (10), we can see that -s tanh(s)<0,e -s| +σ |s| >0, according to Lyapunov principle, when Therefore, when k1, k2>0, the designed reaching law satisfies the reaching condition of sliding mode control, and the system can converge within a finite time.

[0069] In order to further verify that the proposed reaching law has better performance, we compare it with the existing exponential reaching law and take a typical second-order system as an example:

[0070]

[0071] Select the sliding surface s = Cx and perform the derivative

[0072] Substituting equation (11) into the equation, we can get u=(CB) -1 (-CAx+s) (13) is the reaching law. In the above formula, x = [x1, x2] is the state variable of the system; ε = k1 = 5, k2 = k = 10, σ = 0.05.

[0073] C = [15 1], initial position x(0) = [10 10].

[0074] get Figure 2 Phase trajectory of sliding mode motion, and Figure 3 The time required for the approach process.

[0075] Furthermore, the control expression of the sliding mode speed loop of the permanent magnet synchronous motor is as follows:

[0076] Among them, x1 represents the speed error, T L represents the load torque, J represents the motor moment of inertia, c represents the sliding surface coefficient, Pn is the number of motor pole pairs, ψ f is the permanent magnet flux linkage.

[0077] The derivation process of the control expression of the sliding mode speed loop is as follows: Among them, x1 represents the velocity error, x2 represents the derivative of x1, ω ref Reference speed, ω m is the actual speed.

[0078] Combining formulas (9) and (14), we can obtain:

[0079] make The state space equation of the system can be obtained as follows:

[0080] In order to eliminate the steady-state error of the system, this paper selects the integral sliding surface as the switching function of the system, which is expressed as

[0081] The formula is as follows: s=x1+c∫x1dt (17)

[0082] By deriving formula (17) and combining it with the reaching law proposed in this paper, the control expression of the sliding mode speed loop of the permanent magnet synchronous motor can be designed as follows:

[0083] Furthermore, the optimal sliding mode parameters are found by using the universal gravitation algorithm. The method is as follows:

[0084] In the gravitational algorithm, particles are assigned to k1, k2, σ, and c in sequence;

[0085] In the gravitational algorithm, the fitness function is: f = ∫t*|x1|dt;

[0086] Here, t represents time.

[0087] The specific steps of the algorithm optimization are:

[0088] (1) First, assign values ​​to the particles. In this paper, the objective function space is 4-dimensional, the initial population is 30, and the position of the i-th particle in space is expressed as Speed ​​is expressed as

[0089] (2) The fitness function is selected as follows: f = ∫t*|x1|dt; (19)

[0090] (3) Set the maximum number of iterations to 30, and find the particle with the minimum fitness function through continuous iteration. The position of this particle in the search space is the optimal sliding mode parameter.

[0091] (4) Determine whether the algorithm meets the constraints. If so, end the optimization and output the optimal parameters.

[0092] If the end condition is not met, continue to search for the best solution.

[0093] Simulation experiment results:

[0094] Figure (4) is a structural block diagram of the sliding mode speed loop of the permanent magnet synchronous motor based on the proposed reaching law. The permanent magnet synchronous motor vector control is studied and i d =0 control strategy, the control structure mainly includes speed loop, current loop, SVPWM, and decoupling control is performed through coordinate transformation (Clarke, Park).

[0095] The PMSM model parameters used in this paper in MATLAB2014a / simulink simulation are as follows: stator resistance R = 2.875Ω, inductance Ld = Lq = 0.0085mH, magnetic flux The torque coefficient is 1.05Nm / A, and the moment of inertia J is 0.003Kg.m 2 , pole pairs = 4. In order to verify the superiority of the reaching law proposed in this paper, the proposed reaching law is compared with the exponential reaching law.

[0096] To ensure the accuracy of the simulation comparison, the current loop parameters were kept constant. The speed loop was controlled using a reaching law and an exponential reaching law, respectively. The exponential reaching law parameters were ε = 200, k = 300, and c = 60. The reaching law parameters were optimized online using the universal gravitational algorithm, resulting in k1 = 1.5, k2 = 130.2, σ = 0.01, and c = 2.23.

[0097] In order to verify the dynamic performance of the sliding mode speed loop control of the permanent magnet synchronous motor, the no-load speed is set to 1000r / min at the initial moment of system simulation. In order to compare the anti-interference performance of the system, a load of 5N.m is suddenly added to the system at 0.2s, and the speed is increased to 1200r / min at 0.3s. Figure 5 As shown, the electromagnetic torque is Figure 6 As shown, the exponential reaching law three-phase current contrast is Figure 7 As shown, the three-phase current contrast of the reaching law of this patent is Figure 8 shown.

[0098] From the speed comparison curve in Figure (5), it can be seen that the sliding mode speed loop designed with the exponential reaching law has a faster response, but the overshoot is large (31%) at the initial moment and the tracking time is long (0.06s). The sliding mode speed loop designed with the reaching law has a fast response speed (0.03s) and no speed overshoot. When the system is suddenly loaded at 0.2s, the speed fluctuation of the exponential reaching law is large (50r / min) and the recovery time is long. The speed fluctuation of the reaching law is small (15r / min) and has a faster recovery time. When the speed suddenly changes, it can respond quickly and reach a steady state. The electromagnetic torque comparison results in Figure (6) show that the torque under the exponential reaching law control fluctuates greatly at the initial moment. When the load is suddenly added at 0.2s, the electromagnetic torque takes a long time to reach stability. Under the reaching law control mode, the electromagnetic torque fluctuation is small and stable at the initial time. At the same time, when the load is suddenly added at 0.2s, the electromagnetic torque can quickly track and reach stability in a very short time. Figures (7) and (8) show the three-phase current output under the exponential reaching law and reaching law control, respectively. Under the exponential reaching law control mode, the initial time current has a large fluctuation compared to the reaching law control. When the load is suddenly added at 0.2s, the three-phase current distortion rate under the exponential reaching law is serious. Under the reaching law control mode, the three-phase current is more stable. When the speed suddenly changes, the reaching law current change is smaller than the exponential reaching law. In summary, the sliding mode speed loop control mode of the permanent magnet synchronous motor using the proposed reaching law design has better dynamic characteristics than the exponential reaching law control mode.

[0099] in conclusion:

[0100] In order to improve the dynamic quality of the speed regulation of permanent magnet synchronous motors and solve the problems of large chattering and slow response speed in the traditional sliding mode application of the speed loop, a reaching law is proposed. This reaching law improves the traditional exponential reaching law and introduces an adaptive factor e to the constant speed term. -|s| +σ |s| To resolve the contradiction between rapidity and chattering in sliding mode control, the hyperbolic tangent function is introduced to further reduce the chattering caused by the sign function switching process. The controller is designed by adopting the reaching law. The simulation results using MATLAB / SIMULINK show that the sliding mode speed loop designed with the reaching law can reduce the steady-state error of the system, eliminate speed overshoot, and further improve the dynamic quality and robustness of the permanent magnet synchronous motor.

[0101] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A permanent magnet synchronous motor speed control method based on reaching law, comprising: Let the reference value of the direct-axis current component be The rotor position θ m Provided for Park and Anti-Park use; The actual rotor speed ω m and reference speed ω ref The error is sent to the sliding mode controller, and the reference value of the quadrature axis current component is obtained after adjustment by the sliding mode controller. The three-phase stator winding current i a ,i b ,i c The quadrature axis current component i in the rotating coordinate system is obtained by Clark and Park transformation q and the direct axis current component i d ; The actual quadrature-axis current component i q and the direct axis current component i d The reference value of the quadrature axis component after sliding mode control adjustment and the reference value of the direct-axis current component Subtract and get the error; The error is sent to PI control and then output u q ,u d ; u q ,u d Obtain u through inverse Park transform α ,u β ; will u α ,u β The input is sent to the space vector pulse width modulation module to generate a pulse signal to the three-phase inverter to drive the motor; It is characterized in that the sliding mode controller outputs the reference value of the quadrature axis current component through the following reaching law Wherein, 0<σ<0.1, s represents the sliding surface, k1 is a constant greater than zero, and k2 is a constant greater than zero.

2. The permanent magnet synchronous motor speed control method based on reaching law according to claim 1, characterized in that: The control expression of the sliding mode speed loop of the permanent magnet synchronous motor is as follows: Among them, x1 represents the speed error, T L represents the load torque, J represents the motor moment of inertia, c represents the sliding surface coefficient, P n is the number of motor pole pairs, ψ f is the permanent magnet flux linkage.

3. The permanent magnet synchronous motor speed control method based on reaching law according to claim 2, characterized in that: The optimal sliding mode parameters are found by the universal gravitation algorithm. The method is as follows: In the gravitational algorithm, particles are assigned to k1, k2, σ, and c in sequence; In the gravitational algorithm, the fitness function is: f=∫t*|x1|dt; Where t represents time and x1 is the velocity error.

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