A permanent magnet synchronous motor control method

Abstract

The present invention belongs to the field of permanent magnet synchronous motor control, and specifically, is a permanent magnet synchronous motor control method, including establishing a voltage equation in a three-phase coordinate system of a permanent magnet synchronous motor PMSM; simplifying the voltage equation in the three-phase coordinate system of the permanent magnet synchronous motor into a voltage equation in an αβ two-phase stationary coordinate system through Clark transformation; simplifying the voltage equation in the αβ two-phase stationary coordinate system into another form with a current derivative as the left-hand term, and obtaining a mathematical model of the permanent magnet synchronous motor in the aβ two-phase stationary coordinate system; constructing an observer equation according to the mathematical model; constructing a sliding mode surface according to the Lyapunov theorem; calculating the sliding mode gain range, obtaining a back electromotive force, and performing noise elimination on the back electromotive force through a low-pass filter; and extracting a rotor electrical angle and speed using a phase-locked loop according to the obtained back electromotive force. The rotor angular velocity is measured by replacing a Hall sensor, saving costs and improving efficiency.

Description

Technical Field

[0001] The present invention belongs to the field of permanent magnet synchronous motor control, and specifically relates to a permanent magnet synchronous motor control method. Background Art

[0002] Permanent Magnet Synchronous Motor (PMSM) has a simple structure, high reliability, high power efficiency, strong load capacity, and is widely used in the motor field. The core of the vector control strategy of permanent magnet synchronous motor is two coordinate transformations, which decompose the three-phase current into the d-axis current and q-axis current on the rotating shaft, which requires the electrical angle of the rotor. Traditional permanent magnet synchronous motors require the installation of Hall sensors to detect the electrical angle of the motor rotor in real time. In order to save cost and volume, algorithms are used to measure the electrical angle. Which algorithm to use to make the algorithm simpler has become a research hotspot in the field of motor control. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a permanent magnet motor control method based on a sliding mode observer, which is based on a mathematical model of PMSM in the αβ coordinate system and a sliding surface designed according to the mathematical model; a sliding mode algorithm is used to ensure that the observer can accurately observe the required electrical angle and electrical speed, and the present invention proposes a method for calculating the sliding mode gain, which will replace the traditional sliding mode algorithm to calculate the sliding mode gain. The final determination of the electrical angle also increases the system robustness in the PMSM control system.

[0004] The present invention is achieved in this way.

[0005] A permanent magnet synchronous motor control method comprises the following steps:

[0006] 1) Establish the voltage equation of permanent magnet synchronous motor PMSM in three-phase coordinate system;

[0007] 2) The voltage equation of the permanent magnet synchronous motor in the three-phase coordinate system is simplified to the voltage equation in the αβ two-phase stationary coordinate system through Clark transformation;

[0008] 3) Simplify the voltage equation in the αβ two-phase stationary coordinate system into another form with the current derivative as the left-hand term, and obtain the mathematical model of the permanent magnet synchronous motor in the aβ two-phase stationary coordinate system;

[0009] 4) Constructing observer equations based on mathematical models;

[0010] 5) Construct the sliding surface according to Lyapunov's theorem;

[0011] 6) Calculate the sliding mode gain range, determine the sliding mode gain through the actual system parameters, make the current output by the observer converge to the actual current, and obtain the back electromotive force, and then use the low-pass filter to eliminate noise;

[0012] 7) Use a phase-locked loop to extract the rotor electrical angle and speed based on the obtained back electromotive force.

[0013] Furthermore, the input data of the observer is discretized, and the K of the PI controller in the phase-locked loop is determined before the phase-locked loop is used to extract the rotor electrical angle and speed. p ,K i .

[0014] Further, in step 1), the voltage equation of the permanent magnet synchronous motor in the three-phase coordinate system is established:

[0015]

[0016] Among them U a , U b , U c are the terminal voltages of the windings respectively; i a 、i b 、i c are the phase currents of the three-phase windings; E a 、E b 、E c is the back electromotive force of the three-phase winding; R s is the winding phase resistance, and L is the equivalent inductance.

[0017] Furthermore, in step 2), the voltage equation in the three-phase coordinate system is simplified to the voltage equation in the αβ two-phase stationary coordinate system:

[0018]

[0019] Where E α 、E β Back electromotive force; λ αf is the permanent magnet flux; ω r is the rotor angular velocity; θ is the rotor speed.

[0020] Furthermore, in step 3), the voltage equation in the αβ two-phase stationary coordinate system is simplified to another form:

[0021]

[0022] Furthermore, in step 4), the observer equation is constructed according to the mathematical model as follows:

[0023]

[0024] in is the current value estimated by the observer, V a , V β is the input of the observer;

[0025]

[0026] If the estimated current is larger than the actual current, the observer input is +h. If the estimated current is smaller than the actual current, the observer input is -h. h is the sliding mode gain. The input size of the observer depends on the sliding mode gain.

[0027] Furthermore, in step 5), the sliding surface is constructed according to Lyapunov's theorem as follows:

[0028]

[0029] Further, step 6) specifically includes: selecting As a Lyapunov candidate function of S1, its derivative is Derivative expansion like but Then the sliding mode gain h satisfies The same reason roll out Combining the two equations, we can deduce That is, the observation gain only needs to satisfy By formula It can be obtained that the larger h is, the greater the maximum distance that the observer deviates from the actual current is, and the greater the jitter amplitude near the sliding surface after steady state. Similarly, h satisfies these two conditions, then S1 and S2 will converge to 0, and the current observation errors will all be 0. At this time, E a =V a , E β =V β ,Right now

[0030] Further, step 7) multiply the two back electromotive forces obtained in step 6 by and The difference is used to obtain the angular velocity through the PI controller, and the angle is obtained after the angular velocity is integrated.

[0031] Furthermore, the transfer function K of the PI controller in the phase-locked loop is determined p ,K i : According to the transfer function input and output of the PI controller, we can get is the estimated angle, θ e For practical purposes, write the second-order dynamic system form ζ is the damping coefficient, ω n is the natural angular frequency, then K p ,K i The value of depends on the damping factor and the natural angular frequency.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] The present invention uses a sliding mode observer to replace the Hall sensor to measure the rotor angular velocity, thereby saving costs; uses a sliding mode algorithm to reduce algorithm computing power; calculates the value range of the sliding mode gain, thereby replacing the method of trial and error, which makes the control more efficient and improves the control efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 An equivalent circuit diagram of a permanent magnet synchronous motor provided by an embodiment of the present invention;

[0035] Figure 2 A block diagram of the control principle of a permanent magnet synchronous motor with a sliding mode observer provided in an embodiment of the present invention;

[0036] Figure 3 A synovial surface constructed according to an embodiment of the present invention;

[0037] Figure 4 The introduction 4(a) provided in the embodiment of the present invention is E when no filter is added a 4(b) is E without adding filter β , 4(c) is E when the filter is added a 4(d) is E when the filter is added β Comparison of back EMF waveforms;

[0038] Figure 5 A phase-locked loop for extracting electrical angle and angular velocity provided in an embodiment of the present invention;

[0039] Figure 6 The Hall sensor provided in the embodiment of the present invention detects the value of the electrical angle (a) and the electrical angle value (b) estimated by the observer. DETAILED DESCRIPTION

[0040] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0041] like Figure 1 As shown, a permanent magnet synchronous motor control method comprises the following steps:

[0042] 1) Establish the voltage equation of permanent magnet synchronous motor PMSM in three-phase coordinate system;

[0043] 2) The voltage equation of the permanent magnet synchronous motor in the three-phase coordinate system is simplified to the voltage equation in the αβ two-phase stationary coordinate system through Clark transformation;

[0044] 3) Simplify the voltage equation in the αβ two-phase stationary coordinate system into another form with the current derivative as the left-hand term, and obtain the mathematical model of the permanent magnet synchronous motor in the aβ two-phase stationary coordinate system;

[0045] 4) Constructing observer equations based on mathematical models;

[0046] 5) Construct the sliding surface according to Lyapunov's theorem;

[0047] 6) Calculate the sliding mode gain range, determine the sliding mode gain through the actual system parameters, make the current output by the observer converge to the actual current, and obtain the back electromotive force, and then use the low-pass filter to eliminate noise;

[0048] 7) Using a phase-locked loop to extract the rotor electrical angle and speed based on the obtained back electromotive force;

[0049] The acquired rotor electrical angle and speed are fed back to the permanent magnet synchronous motor controller.

[0050] In which, assuming that the three-phase winding of the permanent magnet synchronous motor is symmetrical, and the electromagnetic hysteresis loss and eddy current loss of the permanent magnet synchronous motor are ignored, the voltage equation is:

[0051]

[0052] Among them U a , U b , U c are the terminal voltages of the windings respectively; i a 、i b 、i c are the phase currents of the three-phase windings; E a 、E b 、E c is the back electromotive force of the three-phase winding; R s is the winding phase resistance, and L is the equivalent inductance. The three-phase current of the permanent magnet synchronous motor in the three-phase coordinate system can be transformed into the stator current i in the two-phase coordinate system through coordinate equivalent transformation. a 、i β .

[0053] The mathematical model of the permanent magnet synchronous motor in the aβ two-phase stationary coordinate system is:

[0054]

[0055]

[0056] In formula (2) and (3), ia 、i β , U α , U β 、E a 、E β is the stator current, voltage, and back electromotive force; λ αf is the permanent magnet flux; ω r is the rotor angular velocity; θ is the rotor speed.

[0057] Figure 2 As shown, the phase current and phase voltage are introduced into the observer. In order to obtain the back electromotive force, the observer equation is constructed:

[0058]

[0059] Where V a 、V β is the input of the observer; To observe the current.

[0060]

[0061] h is the sliding mode gain. When the estimated current is larger than the actual current, the observer input is +h. If the estimated current is smaller than the actual current, the observer input is -h. h is the sliding mode gain. The input size of the observer depends on the sliding mode gain.

[0062] Figure 3 As shown, construct the sliding surface

[0063] The vertical axis is the observed current and the horizontal axis is the actual current.

[0064] If the observed current is slightly larger than the actual current, according to formula (5), as long as the sliding mode gain h is large enough, the derivative of the observed current in formula (4) will be negative, and the observed current will gradually decrease, and eventually the difference with the actual current will become smaller and smaller, at which time the back electromotive force can be obtained.

[0065] According to Lyapunov's theorem, the sliding surface is constructed as:

[0066]

[0067] Introducing Lyapunov's theorem: there exists a system f(S1) represents a function of S1. U(S1) is a candidate Lyapunov function of S1 if U(S1) ≥ 0 and And this system For the equilibrium point S1 = 0, it is globally asymptotically stable. Define the sliding surface If the observed state and the actual state both stay on the sliding surface, S1 converges to 0. If a suitable sliding gain h is selected, the observer input will make the observed current converge to the actual current, so that both current quantities remain on the sliding surface.

[0068] Calculate the sliding mode gain range, determine the sliding mode gain through the actual system parameters, make the current output by the observer converge to the actual current, and obtain the back electromotive force, and then use the low-pass filter to eliminate the noise of the back electromotive force; select As a Lyapunov candidate function of S1, its derivative is Derivative expansion like but Then the sliding mode gain h satisfies The same reason roll out Combining the two equations, we can deduce That is, the observation gain only needs to satisfy By formula It can be obtained that the larger h is, the greater the maximum distance that the observer deviates from the actual current is, and the greater the jitter amplitude near the sliding surface after steady state. Similarly, h satisfies these two conditions, then S1 and S2 will converge to 0, and the current observation errors will all be 0. At this time, E a =V a , E β =V β ,Right now

[0069] See also Figure 5 As shown, a phase-locked loop is introduced into the observer, and the two back electromotive forces of the phase-locked loop are multiplied by and The difference is obtained by the PI controller to obtain the angular velocity, and the angular velocity is integrated to obtain the angle. Before the phase-locked loop calculates the angular velocity and angle, the transfer function K of the PI controller in the phase-locked loop is determined. p ,K i : According to the transfer function input and output of the PI controller, we can get To estimate the angle, θ e For practical purposes, write the second-order dynamic system form ζ is the damping coefficient, ω n is the natural angular frequency, then K p ,K i The value of depends on the damping factor and the natural angular frequency.

[0070] Figure 4As shown in Figure 4, the simulation diagrams before and after the low-pass filter is introduced before the two extended back-EMFs are introduced into the phase-locked loop. Figure 4(a) and Figure (b) are the simulation waveforms of the waveforms without the low-pass filter. It can be seen from the waveforms that the high-frequency clutter in the back-EMF is removed after the filter is introduced. a 4(b) is E without adding filter β , 4(c) is E when the filter is added a 4(d) is E when the filter is added β .

[0071] Figure 6 As shown, Figure 6(a) is the value of the electrical angle detected by the Hall sensor, and Figure 6(b) is the value of the electrical angle estimated by the observer. It can be seen from the figure that the error between the value estimated by the observer and the electrical angle value tested by the Hall sensor is within one degree, and the sliding mode observer is effective.

[0072] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A permanent magnet synchronous motor control method, characterized in that: The following steps are involved: 1) The voltage equation of the permanent magnet synchronous motor PMSM in the three-phase coordinate system is established as follows: ， in , , are the terminal voltages of the windings respectively; , , are the phase currents of the three-phase windings respectively; , , is the back electromotive force of the three-phase winding; is the winding phase resistance, L is the equivalent inductance; 2) The voltage equation of the permanent magnet synchronous motor in the three-phase coordinate system is simplified by Clark transformation to The voltage equation in the two-phase stationary coordinate system is: ， ， in , Back EMF; is the permanent magnet flux; is the rotor angular velocity; is the rotor speed; 3) The voltage equation in the two-phase stationary coordinate system is simplified to another form with the current derivative as the left term, and the permanent magnet synchronous motor is obtained. Mathematical model in two-phase stationary coordinate system; The voltage equation in the two-phase stationary coordinate system is simplified to another form: ， 4) The observer equation is constructed according to the mathematical model: ， in , is the current value estimated by the observer, , is the input of the observer; ， If the estimated current is larger than the actual current, the observer input is +h. If the estimated current is smaller than the actual current, the observer input is -h. h is the sliding mode gain. The observer input size depends on the sliding mode gain. 5) Construct sliding surface according to Lyapunov theorem: ， 6) Calculate the sliding mode gain range, determine the sliding mode gain through the actual system parameters, make the current output by the observer converge to the actual current, and obtain the back electromotive force, and then use the low-pass filter to eliminate noise; Specifically include: Select U ( )= As The Lyapunov candidate function of , then its derivative is ( )= , derivative expansion ,like 0, then , then the sliding mode gain h satisfies h + , similarly 0, launch h - , combining the two equations, we can deduce h> + , that is, the observation gain only needs to satisfy h> + , according to the formula , It can be seen that the larger h is, the greater the maximum distance that the observer deviates from the actual current is, and the greater the jitter amplitude near the sliding surface after steady state. Similarly, h> + , h satisfies these two conditions, then , will converge to 0, and the current observation errors are all 0. = , = ,Right now = , ; 7) Use a phase-locked loop to extract the rotor electrical angle and speed based on the obtained back electromotive force.

2. The permanent magnet synchronous motor control method according to claim 1, characterized in that: The input data of the observer is discretized to determine the PI controller in the phase-locked loop before using the phase-locked loop to extract the rotor electrical angle and speed. .

3. A permanent magnet synchronous motor control method according to claim 1, characterized in that: Step 7) Multiply the two back electromotive forces obtained in step 6 by cos( ) and sin( The difference is used to obtain the angular velocity through a PI controller, and the angle is obtained by integrating the angular velocity.

4. A permanent magnet synchronous motor control method according to claim 1, characterized in that: Determine the transfer function of a PI controller in a phase-locked loop : According to the transfer function input and output of the PI controller, we can get = To estimate the angle, For practical purposes, write the second-order dynamic system form , is the damping coefficient, is the natural angular frequency, then = , = ,but The value of depends on the damping factor and the natural angular frequency.

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