Sliding mode control method of PMSM speed regulation system with variable reaching law considering iron loss

Abstract

The application considers a PMSM speed regulation system iron loss variable reaching law sliding mode control method and relates to the minimum loss speed regulation technology field of a permanent magnet synchronous motor, which takes the iron loss torque as a link and designs a PMSM sliding mode speed controller under the minimum loss target; firstly, a minimum loss point d-axis current compensation method based on virtual loss power Taylor series expansion is proposed to realize the minimum loss control of the motor under different working conditions; secondly, in order to eliminate the influence of the iron loss on the speed regulation performance, a PMSM speed tracking model containing the iron loss is established, the minimum loss control is linked with the speed control, an adaptive sliding mode reaching law based on disturbance estimation is proposed to avoid the system energy consumption and the sliding mode chattering caused by the too high sliding mode gain, and the chattering is weakened by adjusting the system state to reach the sliding mode surface. In addition, the chattering is effectively reduced by adding the switching function to the derivative of the control quantity, and the set speed is quickly followed under the uncertain environment.

Description

TECHNICAL FIELD

[0001] The application relates to the field of permanent magnet synchronous motor speed control considering iron loss, and particularly relates to a variable reaching law sliding mode control method for a permanent magnet synchronous motor speed regulation system under consideration of iron loss. BACKGROUND

[0002] The permanent magnet synchronous motor (PMSM) has the characteristics of high efficiency, simple structure, strong overload capacity and easy maintenance, and is widely applied in the fields of robots, electric vehicles, medical devices, aerospace, etc. Generally, in order to obtain the maximum power density and the minimum copper loss, the pole pair number of the PMSM is usually more than that of the asynchronous motor. Therefore, at the same rotor speed, the working frequency of the PMSM is high, and the iron loss is also large, which will lead to the increase of the motor temperature, and the high motor temperature will demagnetize the permanent magnet of the PMSM. Usually, in order to simplify the mathematical model of the PMSM, it is assumed that the iron loss is ignored. However, in a certain sense, the assumption is also the root of hindering the further improvement of the control performance and the further improvement of the control accuracy of various control strategies, especially under the condition of limited energy supply of the PMSM (such as in the application field of electric vehicles, etc.). Because the mathematical model ignoring the iron loss cannot reflect the actual operation condition of the motor, the control strategy derived on the basis of the mathematical model will inevitably show its limitations in the actual application. In addition, there are various uncertain disturbances in the speed control of the PMSM, which affect the improvement of the speed regulation performance of the PMSM. Therefore, the application proposes a PMSM speed control method considering iron loss. The method combines the minimum loss control of the PMSM with the speed control, and realizes the speed control under the minimum loss target. SUMMARY

[0003] The application takes the permanent magnet synchronous motor under the condition of limited energy supply as the research object, and proposes a variable reaching law sliding mode control method for the PMSM speed regulation system considering iron loss, in order to fundamentally solve the problem that the existence of the iron loss is usually ignored in the modeling and control of the PMSM, which restricts the improvement of the control performance and the control accuracy. In the d-axis, a minimum loss control method of the PMSM based on virtual loss power is proposed, which will not cause additional loss of the motor, avoids the speed fluctuation caused by the discontinuous change of the control quantity in the traditional search method, and greatly shortens the time of converging to the minimum loss working point. In the q-axis, the influence of the iron loss is considered, a PMSM speed tracking model containing the iron loss is established, and an adaptive sliding mode reaching law speed control method based on disturbance estimation is proposed, which improves the dynamic response and the anti-disturbance ability of the system.

[0004] The technical scheme adopted by the application to solve the technical problems is as follows:

[0005] This invention relates to a variable approach law sliding mode control method for a PMSM speed regulation system considering iron loss, the method comprising the following steps:

[0006] Step 1: Obtain the real-time speed ω of the permanent magnet synchronous motor using a data acquisition module. m Real-time position θ, real-time three-phase stator voltage u a u b u c and real-time three-phase stator current i a i b i c The aforementioned data acquisition module includes a speed sensor, a position sensor, a voltage sensor, and a current sensor.

[0007] Step 2: Convert the real-time three-phase stator voltage u obtained in Step 1 into... a u b u c and real-time three-phase stator current i a i b i c The three-phase / two-phase transformation and synchronous rotation transformation are equivalent to the DC voltage u in the synchronous rotating coordinate system. d u q and DC current i d i q ;

[0008] Step 3: Convert the DC voltage u obtained in Step 2 into a DC voltage value. d u q The electric angular velocity ω of PMSM e And a minimum loss algorithm for the applied small DC signal ε input is used to obtain the optimal d-axis current setpoint.

[0009] Step 4: Calculate the real-time velocity ω obtained in Step 1. m With a given velocity ω * Perform the difference calculation to obtain the speed tracking error e. m =ω m -ω * ; the speed tracking error e m DC voltage u d u q and DC current i d i q Input the speed controller to obtain the optimal q-axis current setpoint.

[0010] Step 5: Apply the optimal d-axis current setpoint obtained in Step 3. The optimal q-axis current setpoint obtained in step four The measured DC current i d iq The difference is made, and the difference value is input to the PI controller, and then the control signal for driving the PMSM movement is generated through coordinate transformation and space vector modulation technology.

[0011] The beneficial effects of the present application are as follows:

[0012] 1) A minimum loss point d-axis current compensation method based on virtual loss power Taylor series expansion is proposed to realize minimum loss control of the motor under different working conditions.

[0013] 2) A PMSM speed tracking model containing iron loss is established, which connects the minimum loss control with the speed control.

[0014] 3) An adaptive sliding mode reaching law based on disturbance estimation is proposed, which avoids the system energy consumption caused by too high sliding mode gain, and weakens the chattering by adjusting the system state to reach the sliding mode surface.

[0015] 4) The chattering is effectively reduced by adding the switching function to the derivative of the control quantity, and the set speed is quickly followed under uncertain environment.

[0016] 5) The method of the present application is simple and easy to implement, has wide application, and is suitable for wide application and popularization. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 It is the structure principle diagram of the PMSM speed regulation system variable reaching law sliding mode control method considering iron loss of the present application.

[0018] Figure 2 It is the principle diagram of the minimum loss algorithm of the present application.

[0019] Figure 3 It is the relationship between the controllable loss of the PMSM of the present application and i dt .

[0020] Figure 4 It is the structure principle diagram of the speed controller of the present application. DETAILED DESCRIPTION

[0021] The present application will be further described in detail below in combination with the drawings and specific embodiments.

[0022] Figure 1is the structure principle diagram of the PMSM speed regulation system variable reaching law sliding mode control method considering iron loss. Firstly, the voltage and current sensors are used to obtain the voltage and current signals in the three-phase static coordinate system; then the voltage and current signals in the three-phase static coordinate system are converted into the voltage and current signals in the synchronous rotating coordinate system through the coordinate transformation link; then the voltage and current signals in the synchronous rotating coordinate system and the speed information measured by the sensor are input into the minimum loss algorithm module to obtain the d-axis current given value under the minimum loss control target; at the same time, the measured voltage and current signals in the synchronous rotating coordinate system and the speed error signal are input into the speed controller to obtain the q-axis current given value of the motor. Thus, the d-axis and q-axis given values are obtained, and the speed control of the PMSM under the minimum loss target considering iron loss is realized.

[0023] Figure 2 is the principle diagram of the minimum loss algorithm module in Figure 1 . The input quantity of the minimum loss algorithm module is the voltage, current and speed information detected by the voltage, current and speed sensors, and the d-axis current given value is obtained after the intermediate minimum loss algorithm processing.

[0024] Figure 3 is the relationship between the controllable loss of the PMSM and i dt , the controllable loss of the PMSM is a concave function about the d-axis current component, and there is only one minimum point.

[0025] Figure 4 is the principle diagram of the speed controller in Figure 1 . The input quantity of the speed controller is the voltage, current information detected by the voltage and current sensors and the error e m between the actual speed and the given speed, and the q-axis current given value is obtained after the sliding mode control algorithm processing based on the disturbance estimation sliding mode reaching law.

[0026] The PMSM speed regulation system variable reaching law sliding mode control method considering iron loss comprises the following steps:

[0027] Step one: the real-time speed ω m , real-time position θ, real-time three-phase stator voltage u a , u b , u c and real-time three-phase stator current i a , i b , i c of the permanent magnet synchronous motor are obtained by using a data acquisition module; the data acquisition module comprises a speed sensor, a position sensor, a voltage sensor and a current sensor;

[0028] Step two: the real-time three-phase stator voltage u a , u bu c and real-time three-phase stator current i a i b i c The three-phase / two-phase transformation and synchronous rotation transformation are equivalent to the DC voltage u in the synchronous rotating coordinate system. d u q and DC current i d i q ;

[0029] Step 3: Convert the DC voltage u obtained in Step 2 into a DC voltage value. d u q The electric angular velocity ω of PMSM e And a minimum loss algorithm for the applied small DC signal ε input is used to obtain the optimal d-axis current setpoint.

[0030] Step 4: Calculate the real-time velocity ω obtained in Step 1. m With a given velocity ω * Perform the difference calculation to obtain the speed tracking error e. m =ω m -ω * ; the speed tracking error e m DC voltage u d u q and DC current i d i q Input the speed controller to obtain the optimal q-axis current setpoint.

[0031] Step 5: Apply the optimal d-axis current setpoint obtained in Step 3. The optimal q-axis current setpoint obtained in step four The measured DC current i d i q The difference is calculated and input into the PI controller. Then, through coordinate transformation and space vector modulation technology, a control signal is generated to drive the PMSM motion.

[0032] The specific implementation steps are as follows:

[0033] 1. Minimum Loss Algorithm

[0034] (1) Establish a mathematical model of PMSM that considers iron loss.

[0035] The voltage equation in the dq coordinate system of a permanent magnet synchronous motor is:

[0036]

[0037] The torque equation is

[0038]

[0039] In the formula: u d u q These are the d-axis voltage and q-axis voltage, respectively; R s R is the stator resistance. Fe For iron loss resistance; i dt i is the d-axis magnetic weakening current; qt ψ is the q-axis torque current; f For magnetic flux; L d L q These are the d-q axis inductances; ω e T is the electric angular velocity; e is the electromagnetic torque; P is the number of pole pairs.

[0040] The equation of motion of the permanent magnet synchronous motor is

[0041]

[0042] In the formula: B is the coefficient of viscous friction, ω m Let J be the velocity, J be the moment of inertia, and T be the moment of inertia. L This represents the load torque.

[0043] When the motor is running stably, the iron loss current of the dq axis can be expressed as:

[0044]

[0045] In the formula: i df i qf These are the d-axis iron loss current and the q-axis iron loss current, respectively.

[0046] (2) Establish a loss model for minimum loss control of PMSM.

[0047] Copper loss P of permanent magnet synchronous motor Cu for

[0048]

[0049] In the formula: i d Let i be the d-axis current. q This is the q-axis current.

[0050] Iron loss P of permanent magnet synchronous motor Fe for

[0051]

[0052] Controllable losses P of permanent magnet synchronous motor E (i dt P represents copper loss. Cu And iron loss P Fe sum

[0053] P E (i dt )=P Fe +P Cu (9)

[0054] Substituting formula (7) and formula (8) into formula (9) can obtain the controllable loss P E (i dt )

[0055]

[0056] From formula (3), i qt can be obtained as 2T e / [3P(ψ f +(L d -L q )i dt )], and i qt is substituted into formula (10), so that the controllable loss P E (i dt ) of the PMSM can be rewritten as

[0057]

[0058] (3) d-axis current given value calculation of the minimum loss target

[0059] The relationship between the PMSM loss power and i dt is shown in the schematic diagram of Figure 3 . The curve is obtained by scanning test under different i dt given values when the motor is in no-load operation at 2000 rpm. As can be seen from Figure 3 , with the change of i dt from 1A to-8A, the controllable loss power first decreases and then increases (similar curves can be obtained under other working conditions), and there is only one minimum loss working point, and the minimum loss working point satisfies dP E / di dt =0. For the traditional model-based minimum loss algorithm, it is not easy to obtain the optimal i dt of the built-in PMSM, and the present application proposes a method based on virtual loss power current compensation to obtain the optimal i dt .

[0060] A small direct current signal with an intensity of ε is superimposed on i dt . The small direct current signal ε and i dtAfter superposition, the motor's power loss after superimposing the small signals is reconstructed online. Since this signal is not injected into the motor drive system but is superimposed mathematically, the change in motor power loss caused by this signal is virtual. Therefore, the motor's power loss after superimposing the signals is called virtual power loss. Virtual power loss is a function of the superimposed signal ε, and can be expressed as... Using Taylor series Expanding at zero point, we can obtain

[0061]

[0062] In the formula: To avoid the loss from the superposition of a small DC signal ε, and

[0063] Because the intensity of the superimposed signal is very small, the first-order component in equation (12) dominates the change in the power loss of the permanent magnet synchronous motor, and the higher-order components can be ignored. Thus, the virtual power loss is obtained. The first-order Taylor series expansion at zero is:

[0064]

[0065] After superimposing the signals, the virtual power loss of the permanent magnet synchronous motor is

[0066]

[0067] In the formula:

[0068] By combining equations (9), (13), and (14), we can obtain (dP) E / di dt The expression for ε is

[0069]

[0070] Depend on Figure 3 It can be seen that when i dt When the value is to the right of the minimum loss operating point, equation (15) is greater than zero, and i should be reduced. dt Move it to the left; when i dt When the operating point is to the left of the minimum loss operating point, equation (15) is less than zero, and i should be increased. dt This caused it to move to the right. This led to the design of... Figure 2 The current compensation strategy based on the virtual loss power method is shown. The compensation current Δi is obtained using the minimum loss algorithm. dt like Figure 2 As shown, the d-axis current setpoint is finally obtained.

[0071] 2. Speed controller

[0072] (1) PMSM speed control model considering iron loss

[0073] According to formula (3), the electromagnetic torque is rewritten as

[0074]

[0075] In the formula: T Fe = (3P / 2) [ψ f i qf + (L d -L q )i d i qf + (L d -L q )i df (i q -i qf )], T Fe is the iron loss torque generated by the iron loss.

[0076] Let the speed tracking error e m = ω * - ω m . From formula (4) and (16), we have:

[0077]

[0078] Considering the measurement noise of the current sensor and the speed sensor, formula (17) is rewritten as

[0079]

[0080] In the formula: is the given value of the q-axis current, d represents the measurement noise of the current sensor and the speed sensor, the current tracking error, and the load disturbance, etc. uncertain factors, d = d1 + d2 + d3. Among them:

[0081]

[0082] In the formula: Δω is the speed measurement error, Δi d and Δi q are the measurement errors of the d-axis and q-axis currents respectively.

[0083] (2) PMSM speed control based on disturbance estimation sliding mode reaching law

[0084] The following sliding mode surface is selected

[0085]

[0086] In the formula: c, β, and α are the design parameters of the sliding surface, representing the sliding surface s m China e m , and γ(e) m The weights of ) are c > 0, β > 0, α > 0, and γ(e m ) represents

[0087]

[0088] In the formula: In the exponent p / g, g is a positive odd number, p = 1, and 0 < p / g < 1, l1 is e. m The weight of the term, l2 is The weight of the term, l1=(2-p / g)δ p / g-1 l2=(p / g-1)δ p / g-2 δ is |e m | is the dividing point, where δ is a positive integer. p, g, l1, l2, and δ are all design parameters of the sliding surface.

[0089] make Since the load is a slow-disturbance signal and the current and speed measurement noise is very small, it meets the requirements. This is an estimate of D. Adaptive estimation rate The design is as follows:

[0090]

[0091] In the formula: λ is the adaptive estimation rate. The design parameters are given, where λ is a positive integer.

[0092] The sliding mode convergence law is designed in the following form:

[0093]

[0094] In the formula: k1 is the design parameter of the sliding mode reaching law, representing the sliding mode reaching law. Chinese m The weight of the item, k1 is a positive integer.

[0095] The PMSM speed control law considering iron loss is as follows:

[0096]

[0097] Design a speed controller based on equation (22) as follows: Figure 4 As shown. ω m With ω * Perform the difference calculation to obtain the speed tracking error e. m =ω m -ω *; the speed tracking error e m , the DC voltage u d , u q , and the DC current i d , i q is input to the speed controller to obtain the q-axis current given value

[0098] The obtained d-axis current given value q-axis current given value is subtracted from the measured DC current i d , i q , and the difference is input to the PI controller, and then through coordinate transformation, space vector modulation technology to generate control signals to drive the PMSM movement.

Claims

1. A PMSM speed regulation system variable reaching law sliding mode control method considering iron loss, characterized in that, The method comprises the following steps: Step one: obtaining real-time speed ω of permanent magnet synchronous motor, real-time position θ, real-time three-phase stator voltage u m , u a , u b , and real-time three-phase stator current i c , i a , i b , i c of permanent magnet synchronous motor by using data acquisition module; the data acquisition module comprises a speed sensor, a position sensor, a voltage sensor and a current sensor; Step two: the real-time three-phase stator voltage u a , u b , u c and the real-time three-phase stator current i a , i b , i c are equivalent into the direct current voltage u d , u q and the direct current i d , i q in the synchronous rotating coordinate system through the three-phase / two-phase conversion and the synchronous rotating conversion. Step three: the direct voltage u d , u q , the electrical angular velocity ω e of the PMSM and the applied small direct signal ε input the minimum loss algorithm to obtain the optimal d-axis current given value Step 4: Calculate the real-time velocity ω obtained in Step 1. m With a given velocity ω * Perform the difference calculation to obtain the speed tracking error e. m =ω m -ω * ; the speed tracking error e m DC voltage u d u q and DC current i d i q Input the speed controller to obtain the optimal q-axis current setpoint. Step five: the optimal d-axis current given value obtained in step three Step four: the optimal q-axis current given value obtained in step three Subtracting the measured direct current i d , i q respectively, and inputting the difference into a PI controller, then through coordinate transformation, space vector modulation technology to generate control signals to drive PMSM movement. The minimum loss algorithm in step three comprises the following steps: (1) Establish a PMSM mathematical model considering iron loss The voltage equation in the d-q coordinate system of the PMSM is The torque equation is wherein: u d , u q are d-axis voltage, q-axis voltage, respectively; R s is stator resistance; R Fe is iron loss resistance; i dt is d-axis field-weakening current; i qt is q-axis torque current; ψ f is flux linkage; L d , L q are d-q axis inductances, respectively; ω e is electrical angular velocity; T e is electromagnetic torque; P is number of pole pairs; The motion equation of the PMSM is where B is the viscous friction coefficient, ω m is the velocity, J is the moment of inertia, T L is the load torque; When the motor is in stable operation, the d-q axis iron loss current can be expressed as wherein: i df , i qf are the d-axis and q-axis iron loss currents, respectively; (2) Establish a loss model of the PMSM minimum loss control Copper losses P of a permanent magnet synchronous motor Cu For where: i d is the d-axis current, i q is the q-axis current; Permanent magnet synchronous machine iron loss P Fe For Controllable losses P of a permanent magnet synchronous machine E (i dt ) is the sum of copper losses P Cu and iron losses P Fe ​ P E (i dt )=P Fe +P Cu (9) Substituting formula (7) and formula (8) into formula (9) can obtain the controllable loss P of the permanent magnet synchronous motor E (i dt ) From equation (3), we have i qt = 2T e / 3P(ψ f + L d -L q )i dt , substituting i qt into equation (10), the controllable loss P E (i dt ) of PMSM can be rewritten as (3) d-axis current given value calculation of the minimum loss target A small DC signal of strength ε is superimposed to i dt Above, the small DC signal ε is superimposed to i dt After superimposition, the virtual loss power of the motor after superimposition of the small signal is reconstructed online Using Taylor series to expand At zero point, get In the formula: P is the loss when no small direct current signal ε is superimposed, and Neglecting the higher order components in equation (12), the virtual loss power is The first order Taylor series expansion at zero is After superimposing the signal, the virtual loss power of the PMSM is In the formulae: Simultaneous equations (9), (13) and (14) give an expression for (dP E / di dt )ε When i dt Located on the right side of the minimum loss operating point, formula (15) is greater than zero, i dt should be reduced to move it to the left; when i dt Located on the left side of the minimum loss operating point, formula (15) is less than zero, i dt should be increased to move it to the right; the compensation current Δi dt is obtained by the minimum loss algorithm, and finally the d-axis current given value id* is obtained.

2. The PMSM speed regulation system variable nearing law sliding mode control method considering iron loss according to claim 1, characterized in that, The step four comprises the following steps: (1) Establish a PMSM speed control model considering iron loss According to formula (3), the electromagnetic torque is rewritten as where: T Fe = (3P / 2) [ψ f i qf + (L d -L q ) i d i qf + (L d -L q ) i df (i q -i qf ), T Fe is the iron loss torque resulting from the iron loss Let the velocity tracking error e m = ω * - ω m ; from equations (4) and (16) we have: Considering the measurement noise of the current sensor and the speed sensor, formula (17) is rewritten as In the formula: The q-axis current is given a value, d represents the measurement noise of the current sensor, the speed sensor, the current tracking error, and the load disturbance uncertainty factor, d=d1+d2+d3. Wherein: where: Δω is the speed measurement error, Δi d and Δi q are the measurement errors of the d-axis and q-axis currents, respectively; (2) PMSM speed control based on disturbance estimation sliding mode reaching law The following sliding mode surface is selected wherein: c, β, α are design parameters of the sliding surface s m m , and γ(e m ) are weight values of c, β, α, respectively, c > 0, β > 0, α > 0, and γ(e m ) is given by​ In the formula: g is a positive odd number in the index p / g, p = 1, and 0 < p / g < 1, l1 is e m the weight of the term, l2 is the weight of the term, l1 = (2-p / g)δ p / g-1 , l2 = (p / g-1)δ p / g-2 , δ is the boundary point of |e m |; δ is a positive integer; p, g, l1, l2 and δ are all design parameters of the sliding mode surface; Let Since the load is a slow disturbance signal and the current and speed measurement noise is small, the following holds The estimate of D is designed as follows The adaptive estimation rate of D is designed as follows where λ is the adaptive estimation rate design parameters, λ is a positive integer; The sliding mode reaching law is designed as the following form: In the formula, k1 is a design parameter of the sliding mode reaching law, and represents the sliding mode reaching law In the formula, k1 is a design parameter of the sliding mode reaching law, and represents the sliding mode reaching law m The weight of the term, k1 is a positive integer; The PMSM speed control law considering iron loss is designed as: The speed controller is designed according to formula (22), ω m is subtracted from ω * to obtain the speed tracking error e m = ω m - ω * ; the speed tracking error e m , the direct current u d , u q and the direct current i d , i q are input into the speed controller to obtain the q-axis current given value The acquired d-axis current is given a value The q-axis current is given a value The measured direct current i d , i q The difference is input to a PI controller, and the difference is input to a PI controller, and the difference is input to a PI controller, and the difference is input to a PI controller, and the difference is input to a PI controller, and the difference is input to a PI controller, and the difference is input to a PI controller, and the difference is input to a PI controller, and the difference is input to a PI controller, and the difference is input to a PI controller, and the difference is input to a PI controller, and the difference is input to a PI controller, and the difference is input to a PI controller, and the difference is input

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