A PMSM speed sensorless control method based on improved sliding mode observer

Abstract

The present invention relates to a PMSM speed sensorless control method based on an improved sliding mode observer, comprising the following steps: Step 1: Establish a mathematical model of a three-phase permanent magnet synchronous motor, design a traditional sliding mode observer according to the mathematical model, and estimate the stator current and back electromotive force based on the traditional sliding mode observer; Step 2: Establish an improved sliding mode observer based on a saturation function, and improve the reaching law of the traditional sliding mode observer; Step 3: Use a low-pass filter and a Kalman filter to perform secondary filtering on the results observed by the improved sliding mode observer to obtain rotor angle information. The present invention solves the switching jitter problem of the traditional sliding mode observer through a smoothly switched saturation function; and solves the output noise problem of the traditional sliding mode observer through secondary filtering composed of a low-pass filter and a Kalman filter. The estimation accuracy obtained by the control method proposed by the present invention is higher and the robustness is better.

Description

Technical Field

[0001] The invention relates to the field of AC servo motor control, and in particular to a PMSM speed sensorless control method based on an improved sliding mode observer. Background Art

[0002] Permanent Magnet Synchronous Motor (PMSM) has been widely used in the field of AC servo due to its advantages of small size, light weight, high efficiency, etc. The rotor position and speed signals are very important in the PMSM system, but the traditional mechanical sensors are easily affected by temperature, magnetic field and other external interferences, and are increasingly unable to meet the requirements of system accuracy, so speed sensorless control has begun to appear.

[0003] There are two main types of speed sensorless control methods. One is the high-frequency signal injection method suitable for low speed, including the rotating high-frequency voltage signal method and the pulse high-frequency voltage signal method; the other is the motor fundamental frequency model method suitable for high speed, including the stator flux estimation method, the model reference adaptive method, the state observer estimation method, the artificial intelligence estimation method, etc. The sliding mode observer is a type of state observer. Its principle is to estimate the back electromotive force through the input voltage and current, and then calculate the position and speed information of the stator from the back electromotive force. Its advantages are simple structure, no reliance on the precise mathematical model of the system, no influence from internal parameters and external interference, and strong robustness. The disadvantage is also the commonality of sliding mode control, that is, the jitter is difficult to eliminate. Moreover, the sliding mode observer itself cannot solve the problem of rotor position estimation under different speed conditions. Summary of the invention

[0004] The present invention provides a PMSM speed sensorless control method based on an improved sliding mode observer to solve the above technical problems.

[0005] In order to solve the above technical problems, the present invention provides a PMSM speed sensorless control method based on an improved sliding mode observer, comprising the following steps:

[0006] Step 1: establishing a mathematical model of a three-phase permanent magnet synchronous motor, designing a traditional sliding mode observer according to the mathematical model, and estimating a stator current and a back electromotive force based on the traditional sliding mode observer;

[0007] Step 2: Establish an improved sliding mode observer based on the saturation function to improve the reaching law of the traditional sliding mode observer Make improvements;

[0008] Step 3: Use a low-pass filter and a Kalman filter to perform secondary filtering on the results observed by the improved sliding mode observer to obtain rotor angle information

[0009] Preferably, the reaching law for:

[0010]

[0011]

[0012] ε=kω ref ,

[0013] Where S is the sliding surface, a is the boundary layer thickness, ω ref is the given speed, k is the adjustable coefficient, sgn is the switching function, and ε is the switching gain.

[0014] Preferably, step 2 further comprises constructing a Lyapunov function to perform stability analysis on the improved sliding mode observer.

[0015]

[0016] Among them, L s is the stator inductance, R s is the stator resistance, i α 、i β are the α-axis and β-axis components of the stator current in the two-phase stationary coordinate system, are the estimated values ​​of stator currents of α and β axes, E α 、E β are the α and β axis electromotive force components respectively, ε is the gain,

[0017] When ε>max(E α , E β ), satisfying the conditions of reachability and stability.

[0018] Preferably, in step 3, the rotor angle information is obtained by calculating the inverse tangent function after secondary filtering.

[0019]

[0020] and are the estimated values ​​of the α and β axis electromotive force components respectively.

[0021] Preferably, the step 3 further comprises compensating the rotor angle information:

[0022]

[0023] in, is the compensated rotor angle information, is the estimated value of the angular velocity after secondary filtering, is an estimate of the cutoff frequency of the low-pass filter.

[0024] Preferably, the angular velocity expression obtained after compensation is:

[0025]

[0026] ψ f is the permanent magnet flux.

[0027] Preferably, the low-pass filter adopts a variable cut-off frequency:

[0028]

[0029] h and g are variable parameters.

[0030] Compared with the prior art, the PMSM speed sensorless control method based on the improved sliding mode observer provided by the present invention has the following advantages:

[0031] The present invention first designs a traditional sliding mode observer to estimate the stator current and back electromotive force based on the permanent magnet motor model; then designs a new saturation function to replace the switching function, and improves the control law of the sliding mode observer; finally, through the two-stage filtering of the low-pass filter with variable cutoff frequency and the Kalman filter, more accurate rotor position information is obtained. The speed error of the improved sliding mode observer is smaller and the estimation result is more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a flow chart of a PMSM speed sensorless control method based on an improved sliding mode observer in a specific embodiment of the present invention;

[0033] Figure 2 It is a schematic diagram of the principle of a traditional sliding mode observer in a specific implementation mode of the present invention;

[0034] Figure 3 It is a schematic diagram of the principle of a low-pass filter in a specific implementation manner of the present invention;

[0035] Figure 4 It is a schematic diagram of the principle of two-stage filtering in a specific implementation manner of the present invention;

[0036] Figure 5 A simulation structure diagram of a permanent magnet synchronous motor in a specific implementation manner of the present invention;

[0037] Figure 6 A comparison diagram of back electromotive force between a specific implementation of the present invention and a traditional sliding mode observer;

[0038] Figure 7 A comparison diagram of the speed observation error at rated speed between a specific embodiment of the present invention and a traditional sliding mode observer;

[0039] Figure 8 A load torque speed diagram of a specific embodiment of the present invention;

[0040] Fig. 9 This is a torque waveform diagram of a specific implementation mode of the present invention. DETAILED DESCRIPTION

[0041] In order to describe the technical solution of the above invention in more detail, specific embodiments are listed below to demonstrate the technical effect; it should be emphasized that these embodiments are used to illustrate the present invention but are not limited to the scope of the present invention.

[0042] The PMSM speed sensorless control method based on the improved sliding mode observer provided by the present invention is as follows: Figure 1 As shown, the following steps are included:

[0043] Step 1: establishing a mathematical model of a three-phase permanent magnet synchronous motor, designing a traditional sliding mode observer according to the mathematical model, and estimating a stator current and a back electromotive force based on the traditional sliding mode observer;

[0044] Step 2: Establish an improved sliding mode observer based on the saturation function to improve the reaching law of the traditional sliding mode observer Make improvements;

[0045] Step 3: Use a low-pass filter and a Kalman filter to perform secondary filtering on the results observed by the improved sliding mode observer to obtain rotor angle information

[0046] The present invention first designs a traditional sliding mode observer to estimate the stator current and back electromotive force based on the permanent magnet motor model; then designs a new saturation function to replace the switching function, and improves the control law of the sliding mode observer; finally, through the two-stage filtering of the low-pass filter with variable cutoff frequency and the Kalman filter, more accurate rotor position information is obtained. The speed error of the improved sliding mode observer is smaller and the estimation result is more accurate.

[0047] Specifically, it is first assumed that the permanent magnet synchronous motor is in an ideal state, and the following assumptions are made:

[0048] (1) The magnetomotive force of a permanent magnet is fixed;

[0049] (2) The back EMF of the motor is sinusoidal;

[0050] (3) There is no damping winding on the motor rotor;

[0051] (4) The induced electromotive force and air gap magnetic field of the motor are sinusoidal, and all harmonics of the magnetic field are not considered;

[0052] (5) The three-phase stator windings are symmetrically distributed in the stator space, the armature resistance in the three-phase windings is equal, and the inductance in the three-phase windings is also equal;

[0053] (6) Eddy current losses in permanent magnet saturation motors with no consideration of motor core;

[0054] (7) The influence of the ambient temperature of the motor on the motor is not considered.

[0055] Under the above conditions, the state equations of voltage and flux in the natural coordinate system are established. The study is converted to the dq coordinate system. The model of the permanent magnet synchronous motor in the dq coordinate system is:

[0056]

[0057] λ q =L q i q (2)

[0058] λ d =L d i d +L md i df (3)

[0059] ω e =n p ω r (4)

[0060] Where: i d 、i q are the d-axis and q-axis components of the stator current respectively; U d , U q are the d-axis and q-axis components of the stator voltage respectively; R s is the stator resistance; L d , L q are the stator d-axis and q-axis inductances respectively; ω e is the rotor electrical angular velocity; ω r is the rotor mechanical angular velocity; d , q is the stator flux of d and q axes; L md is the mutual inductance of the d-axis; i df is the d-axis equivalent magnetizing current; n p is the pole pair number.

[0061] The electromagnetic torque and mechanical torque equations of permanent magnet synchronous motor are:

[0062] T e =3n p [L md I df i q +(L d-L q )i d i q ] / 2 (5)

[0063] Where: T e is the electromagnetic torque.

[0064] Due to λ d =λ q , the electromagnetic torque equation of the motor can be simplified as:

[0065]

[0066] The mathematical model of the permanent magnet synchronous motor in the α-β stationary coordinate system is as follows:

[0067] The voltage equation is:

[0068]

[0069] The magnetic flux equation is:

[0070]

[0071]

[0072] The torque equation is:

[0073]

[0074] In the formula, i α and i β is the stator current of α and β axes; θ is the angle between the rotor N pole and the a-phase axis; and is the magnetic flux component of α and β axes, ψ f is the permanent magnet flux.

[0075] The sliding mode observer (SMO) is developed from the sliding mode control, which inherits the advantages of sliding mode variable structure control. Its structural principle is as follows: Figure 2 shown.

[0076] From equations (7), (8) and (9), we can get:

[0077]

[0078] The sliding mode observer constructs a mathematical model based on the error between the reference current and the feedback current:

[0079]

[0080] in are the estimated values ​​of the stator current of the α and β axes; K is a constant, and sgn is the switching function.

[0081] Subtracting equation (11) from (12) yields:

[0082]

[0083] in

[0084] When the sliding mode enters the arrival stage, that is, moves on the sliding surface:

[0085]

[0086] E α 、E β They are the α and β axis electromotive force components respectively.

[0087] From the principle of traditional sliding mode observer (SMO) Figure 2 According to the control law formula, there are the following problems:

[0088] (1) Traditional SMO uses the sign function as the switching function, which is a discontinuous step function. When the system performs high-frequency switching, severe system jitter will occur, greatly reducing the accuracy and stability of the control system.

[0089] (2) In traditional SMO, low-pass filters are used to filter out high-frequency harmonics in the back-EMF signal. The use of low-pass filters will cause delay problems in the control system, which is particularly evident in high-speed motor control systems. In addition, the existence of phase delay requires the control system to compensate for the delay, which makes the amount of calculation in the system large, increases the system burden, reduces the system response speed, and affects the timeliness of the control system.

[0090] (3) Traditional SMO uses the inverse tangent function to calculate the speed and position of the rotor, which has a large error.

[0091] Therefore, it is necessary to improve the traditional SMO on the basis of the above.

[0092] The reaching law of the sliding mode observer determines the observer's ability to suppress chattering. The sign function has the problem of discontinuous switching process, which can easily cause system instability. The switching gain of the reaching law determines both the approaching speed and the magnitude of the chattering after the arrival stage. To address these two problems, the following new reaching law is proposed:

[0093]

[0094]

[0095] ε=kω ref ,

[0096] Where S is the sliding surface, a is the boundary layer thickness, ω ref is the given speed, k is the adjustable coefficient, sgn is the switching function, and ε is the switching gain.

[0097] The new saturation function is a continuous function, and the appropriate boundary layer thickness can reduce and improve the overall jitter, but it will affect the accuracy of the system. Therefore, the switching gain ε is introduced into the speed, and the adaptive effect is achieved by adjusting the adjustable coefficient k.

[0098] Then, the Lyapunov function is constructed to analyze the stability of the improved sliding mode observer.

[0099]

[0100] Among them, L s is the stator inductance, R s is the stator resistance, i α 、i β are the α-axis and β-axis components of the stator current in the two-phase stationary coordinate system, are the estimated values ​​of stator currents of α and β axes, E α 、E β are the α and β axis electromotive force components respectively, ε is the gain,

[0101] It can be seen that as long as ε>max(E α , E β ), the reachability and stability conditions can be met.

[0102] The results observed by the improved sliding mode observer still contain a large number of high-frequency harmonic components and noise, which will affect the estimation of the rotor position, so filters are often used for processing. Ordinary filters directly filter the input signal, and then obtain the rotor position and speed information through rotor position estimation, such as Figure 3 shown.

[0103] The transfer function of the low pass filter (LPF) is:

[0104]

[0105] Among them, ω c is the cut-off frequency.

[0106] The expanded back EMF after LPF filters out high-frequency harmonics is:

[0107]

[0108] and are the estimated values ​​of the α and β axis electromotive force components respectively.

[0109] Since the speed of the motor will change due to external interference during operation, the high-frequency harmonic components will also change. At this time, the fixed cutoff frequency cannot meet the system requirements, so a variable cutoff frequency is used instead of a fixed cutoff frequency low-pass filter.

[0110]

[0111] in It is the estimated value of the angular velocity after two-stage filtering. h and g are variable parameters, the purpose of which is to adjust the optimal cutoff frequency for different speed occasions.

[0112] Although it has passed through a low-pass filter, the system output still has ripple components. The common back-EMF observer uses the inverse tangent function to estimate the rotor position error, which is still too large and cannot solve the problem of ripple components. Therefore, a Kalman filter is used for secondary filtering. The schematic diagram is shown below. Figure 4 shown.

[0113] The Kalman filter state equation is:

[0114]

[0115] Where M is the Kalman filter gain. The size of M will affect the response speed and vibration of the system, so selecting appropriate parameters will help ensure the stability of the system.

[0116] In some embodiments, in step 3, the rotor angle information is obtained by calculating the inverse tangent function after the secondary filtering.

[0117]

[0118] and are the estimated values ​​of the α and β axis electromotive force components respectively.

[0119] Since the characteristics of the secondary filter will inevitably cause the signal to have a phase delay, the rotor position must be compensated for the angle. Therefore, step 3 of the present invention also includes compensating the rotor angle information:

[0120]

[0121] in, is the compensated rotor angle information, is the estimated value of the angular velocity after secondary filtering, is an estimate of the low-pass filter cutoff frequency.

[0122] Formula 21 can be rewritten as

[0123]

[0124] Substituting equation 23 into equation 9, the angular velocity expression after compensation is:

[0125]

[0126] In order to verify the correctness of the control method proposed in this application, a permanent magnet synchronous motor simulation structure diagram is built in simulink, as shown in Figure 5 shown.

[0127] Specifically, the specific parameters of the motor are: stator resistance R = 2.46Ω; d, q axis inductance L d =L q =6.35mH; permanent magnet flux Moment of inertia J = 1.02 g·m 2 ; Viscous friction coefficient B = 0.0001; pole pair number P = 4; rated speed 3000r / min, inverter switching frequency is 15kHz.

[0128] Given that the motor speed is 1000r / min, the PMSM sliding mode observer back electromotive force simulation waveform is as follows: Figure 6 As shown. Figure 5 It can be seen that the traditional sliding mode observer is the shaded part, and the improved sliding mode observer proposed in this application is the solid line part. The shaded part has larger jitter and more high-frequency components, so the improved sliding mode observer has higher observation accuracy. Figure 7 The figure shows the speed observation error of the two sliding mode observers at the rated speed. It can be seen that the speed error of the traditional sliding mode observer is within 20r / min, and the improved sliding mode observer is within 10r / min, which has higher accuracy. From the speed error and back-EMF observation diagram, it can be seen that the traditional sliding mode observer has delays and errors due to the filter and inverse tangent function, but the improved sliding mode observer uses secondary filtering to improve the phase delay, and the position error is also greatly improved.

[0129] In order to verify the anti-interference performance of the permanent magnet system, the load torque of 10N·m is increased 0.5 seconds after the permanent magnet system is started without load, and the result is Figure 8 and Fig. 9 It can be seen from this that the present invention has a good anti-interference ability, and a sudden change in load will not have a great impact on the system, and it can return to a steady state within 0.02s.

[0130] In summary, the PMSM speed sensorless control method based on the improved sliding mode observer provided by the present invention solves the switching jitter problem of the traditional sliding mode observer by smoothing the switching function and introducing an adaptive switching gain; the noise output by the sliding mode observer is better filtered by a low-pass filter with a variable cutoff frequency, and then the ripple component is further removed by adding a Kalman filter; and angular velocity compensation is performed to obtain a more accurate observation result. The simulation results show that the control method proposed by the present invention has higher estimation accuracy and better robustness.

[0131] Obviously, those skilled in the art can make various changes and modifications to the invention without departing from the spirit and scope of the invention. Thus, if these modifications and variations of the invention fall within the scope of the claims of the invention and their equivalents, the invention is also intended to include these modifications and variations.

Claims

1. A PMSM speed sensorless control method based on an improved sliding mode observer, characterized in that: The steps include: Step 1: Establish a mathematical model of a three-phase permanent magnet synchronous motor, design a sliding mode observer according to the mathematical model, and estimate the stator current and back electromotive force based on the sliding mode observer; Step 2: Establish an improved sliding mode observer based on the saturation function and improve the reaching law S of the sliding mode observer: Step 3: Use a low-pass filter and a Kalman filter to perform secondary filtering on the results observed by the improved sliding mode observer to obtain rotor angle information The reaching law for: e=kω ref , Where S is the sliding surface, a is the boundary layer thickness, ω ref is the given speed, k is the adjustable coefficient, sgn is the switching function, and ε is the switching gain.

2. The PMSM speed sensorless control method based on the improved sliding mode observer as claimed in claim 1 is characterized in that: Step 2 also includes constructing a Lyapunov function to perform stability analysis on the improved sliding mode observer. Among them, L s is the stator inductance, R s is the stator resistance, i α 、i β are the α-axis and β-axis components of the stator current in the two-phase stationary coordinate system, are the estimated values ​​of stator currents of α and β axes, E α 、E β are the α and β axis electromotive force components respectively, ε is the gain, When ε>max(E α , E β ), satisfying the conditions of reachability and stability.

3. The PMSM speed sensorless control method based on the improved sliding mode observer according to claim 1 is characterized in that: In step 3, the rotor angle information is obtained by calculating the inverse tangent function after secondary filtering. and They are the estimated values ​​of the α and β axis electromotive force components respectively.

4. The PMSM speed sensorless control method based on the improved sliding mode observer as claimed in claim 3 is characterized in that: The step 3 also includes compensating the rotor angle information: in, is the compensated rotor angle information, is the estimated value of the angular velocity after secondary filtering, is an estimate of the cutoff frequency of the low-pass filter.

5. The PMSM speed sensorless control method based on the improved sliding mode observer as claimed in claim 4 is characterized in that: The angular velocity expression after compensation is: ψ f is the permanent magnet flux.

6. The PMSM speed sensorless control method based on the improved sliding mode observer as claimed in claim 1 is characterized in that: The low-pass filter adopts a variable cut-off frequency: h and g are variable parameters.

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