Position sensorless control method based on improved full-order sliding mode observer

Abstract

The invention discloses a position-sensorless control method based on an improved full-order sliding-mode observer, and relates to the technical field of motor control. Three-phase current is sampled and subjected to 3 / 2 conversion, and stator voltage is input into the observer; constructing a full-order sliding mode observer by taking the two-phase current and the two-phase counter electromotive force of the stator as state variables; designing a sliding mode surface based on the stator two-phase current error; designing a current control law and a back electromotive force control law; the convergence proof of the full-order sliding mode observer is improved; on the premise that convergence is met, the two opposite electromotive forces are observed and input into a phase-locked loop, and the estimated electrical angle and the estimated electrical angular speed of the rotor can be obtained. For a surface-mounted permanent magnet synchronous motor, on the basis of a full-order sliding mode observer, high-order terminal sliding mode control is introduced, so that the control precision of a position sensorless can be effectively improved.

Description

Technical Field

[0001] The invention relates to the technical field of motor control, in particular to a position sensorless control method based on an improved full-order sliding mode observer. Background Art

[0002] Surface mounted permanent magnet synchronous motor (SPMSM) has gradually become a research hotspot in the motor field due to its simple structure, excellent dynamic performance, high power density, and reliable operation. The control method of permanent magnet synchronous motor is simple, and the realization of its control effect depends on the accurate acquisition of rotor position information. The conventional practice is to install a mechanical position sensor on the motor shaft end, such as an incremental or absolute digital encoder, or a rotary transformer. However, installing a position sensor not only increases the system cost, but also affects the performance of the mechanical sensor in some special environments (such as high temperature). Therefore, in order to reduce costs and improve system reliability, position sensorless technology is widely used.

[0003] Sliding mode is highly robust to changes in internal parameters and external disturbances. Applying sliding mode variable structure control to observer design can retain the advantages of sliding mode variable structure, so sliding mode observers are widely used in medium and high speed position sensorless control. The essence of sliding mode control is a type of nonlinear control, and the nonlinearity is manifested in the discontinuity of control, so the jitter problem it brings will have a greater impact on control accuracy.

[0004] The back EMF observed by the traditional sliding mode observer method contains many high-frequency harmonics, and the estimated position accuracy obtained by direct demodulation is very low. Usually, a first-order low-pass filter is used to filter the observed back EMF to obtain a smooth back EMF, but this brings about a phase delay problem and requires position compensation. The full-order sliding mode observer adds the back EMF as a state variable to the state equation. The high-frequency harmonics in the observed back EMF are significantly reduced, and the estimated position accuracy is significantly improved. However, the observed back EMF still contains discontinuous terms, which still has an adverse effect on improving the estimated position accuracy. Summary of the invention

[0005] In order to address the shortcomings of the background technology, the present invention provides a position sensorless control method based on an improved full-order sliding mode observer. For a surface-mounted permanent magnet synchronous motor, it can effectively improve the control accuracy of the position sensorless control by introducing a high-order terminal sliding mode control based on a full-order sliding mode observer.

[0006] To achieve the above object, the present invention adopts the following technical solution: a position sensorless control method based on an improved full-order sliding mode observer, comprising the following steps:

[0007] Step 1: Current and voltage input

[0008] Sample the three-phase current and perform a 3 / 2 transformation, consider the stator voltage to be equal to the actual voltage, and input the stator voltage into the observer;

[0009] Step 2: Construct a full-order sliding mode observer

[0010] Taking the two-phase current of the stator and the two-phase back electromotive force as state variables, the full-order state equation of the surface-mounted permanent magnet synchronous motor is constructed as follows:

[0011]

[0012] In the formula, R s and L s are the phase resistance and phase inductance of the two-phase windings respectively, i α 、i β and e α 、e β are the two-phase current and two-phase back electromotive force of the stator, ω e is the rotor electrical angular velocity, u α and u β is the stator two-phase voltage;

[0013] Then the full-order sliding mode observer is established as follows:

[0014]

[0015] In the formula, and They are respectively used to observe the two-phase current of the stator and the two-phase back electromotive force. To estimate the electrical angular velocity, z i (s) and z e (s) are the current control law and back-EMF control law in the observer respectively;

[0016] Step 3: Design the sliding surface

[0017] The sliding surface designed based on the stator two-phase current error is expressed as follows:

[0018]

[0019] In the formula, s α and β are the two-phase sliding surfaces, and are the stator two-phase current errors, sgn() represents the sign function, α>0, β>0, 0<γ<1, all of which are constants;

[0020] Step 4: Design current control law and back EMF control law

[0021] Design the current control law i(s) means as follows:

[0022]

[0023] In the formula, z iα and z iβ They are the two-phase current control laws, ω f is the equivalent cutoff frequency, which is a constant greater than 0, z iαn and z iβn is the intermediate variable, k is the current convergence coefficient;

[0024] Design of back-EMF control law e (s) means as follows:

[0025]

[0026] Where m is the back electromotive force convergence coefficient;

[0027] Step 5: Convergence proof of improved full-order sliding mode observer

[0028] Substituting formula (4)-(6) into formula (2) and subtracting them from formula (1), we can obtain the following expressions for the stator two-phase current and two-phase back electromotive force errors:

[0029]

[0030] Substituting formula (7) into formula (3) we can further obtain:

[0031]

[0032] By taking the derivative of formula (8), we can obtain:

[0033]

[0034] The Lyapunov function is:

[0035]

[0036] The expression of the derivative of the Lyapunov function is as follows:

[0037]

[0038] To satisfy The stable range of k and m can be obtained as:

[0039]

[0040] In the formula, and are the two-phase back electromotive force errors respectively, and M is the differential maximum value of the two-phase stator current error;

[0041] Step 6: Demodulate and estimate position and speed

[0042] Under the premise of satisfying formula (12), the two back electromotive forces are observed. and Input into the phase-locked loop to get the estimated electrical angle of the rotor and the estimated electrical angular velocity

[0043] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention is for a surface-mounted permanent magnet synchronous motor, and by introducing a high-order terminal sliding mode control in a full-order sliding mode observer, the discontinuous term of the observed back electromotive force will be hidden in the high-order derivative, effectively reducing the back electromotive force jitter observed when the motor is running under position-free conditions, improving the sinusoidality of the observed back electromotive force, and obtaining smaller estimated speed and estimated position errors, effectively improving the control accuracy of the position sensorless, and meeting the high-precision control requirements of the position sensorless permanent magnet synchronous motor in the industrial production field. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is a structural block diagram of the position sensorless control method of the present invention;

[0045] Figure 2 is the experimental result obtained using the traditional sliding mode observer in the embodiment;

[0046] Figure 3 is the experimental result obtained using the full-order sliding mode observer in the embodiment;

[0047] Figure 4 This is the experimental result obtained by using the improved full-order sliding mode observer of the present invention in the embodiment. DETAILED DESCRIPTION

[0048] The technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0049] like Figure 1 As shown, a position sensorless control method based on an improved full-order sliding mode observer comprises the following steps:

[0050] Step 1: Current and voltage input

[0051] The three-phase current is sampled and converted into 3 / 2, and the nonlinear links such as the inverter in the control system are ignored. The stator voltage is considered to be equal to the actual voltage, and the stator voltage is input into the designed full-order sliding mode observer based on SPMSM.

[0052] Step 2: Construct a full-order sliding mode observer

[0053] Taking the two-phase current of the stator and the two-phase back electromotive force as state variables, the full-order state equation of the surface-mounted permanent magnet synchronous motor is constructed as follows:

[0054]

[0055] In the formula, R s and L s are the phase resistance and phase inductance of the two-phase windings respectively, i α 、i β and e α 、e β are the two-phase current and two-phase back electromotive force of the stator, ω e is the rotor electrical angular velocity, u α and u β is the stator two-phase voltage.

[0056] According to the full-order state equation, the full-order sliding mode observer with the stator two-phase current and two-phase back electromotive force as state variables is established as follows:

[0057]

[0058] In the formula, and They are respectively used to observe the two-phase current of the stator and the two-phase back electromotive force. To estimate the electrical angular velocity, z i (s) and z e (s) are the current control law and back-EMF control law in the observer respectively.

[0059] Step 3: Design the sliding surface

[0060] The sliding surface designed based on the stator two-phase current error is expressed as follows:

[0061]

[0062] In the formula, s α and β are the two-phase sliding surfaces, and are the stator two-phase current errors, sgn() represents the sign function, α>0, β>0, 0<γ<1, all of which are constants.

[0063] When the stator two-phase current error is far away from the equilibrium point, the linear term plays a major role in the system state convergence rate, and the convergence time of the system can be changed by adjusting the value of α; when the stator two-phase current error is close to the equilibrium point, the nonlinear term plays a major role in the system state convergence rate, and it decays exponentially after reaching the sliding mode region. Therefore, introducing a high-order terminal sliding mode in the sliding mode control can reduce chattering.

[0064] Step 4: Design current control law and back EMF control law

[0065] Design of current control law based on stator two-phase current error i (s) means as follows:

[0066]

[0067] In the formula, z iα and z iβ They are the two-phase current control laws, ω f is the equivalent cutoff frequency, which is a constant greater than 0, z iαn and z iβn is the intermediate variable, and k is the current convergence coefficient.

[0068] Design of back-EMF control law e (s) means as follows:

[0069]

[0070] Where m is the back electromotive force convergence coefficient.

[0071] Step 5: Convergence proof of improved full-order sliding mode observer

[0072] Substituting formula (4)-(6) into formula (2) and subtracting them from formula (1), we can obtain the following expressions for the stator two-phase current and two-phase back electromotive force errors:

[0073]

[0074] Substituting formula (7) into formula (3) we can further obtain:

[0075]

[0076] By taking the derivative of formula (8), we can obtain:

[0077]

[0078] The Lyapunov function is:

[0079]

[0080] The expression of the derivative of the Lyapunov function is as follows:

[0081]

[0082] To satisfy The stable range of k and m can be obtained as:

[0083]

[0084] In the formula, and are the two-phase back electromotive force errors respectively, and M is the differential maximum value of the two-phase stator current error.

[0085] Step 6: Demodulate and estimate position and speed

[0086] Under the premise of satisfying formula (12), the improved full-order sliding mode observer can be guaranteed to converge. and Input into the phase-locked loop to get the estimated electrical angle of the rotor and the estimated electrical angular velocity This completes the position sensorless control of the surface-mounted permanent magnet synchronous motor.

[0087] Example

[0088] The parameters of the surface-mounted permanent magnet synchronous motor used in the experiment are as follows: the rated speed of the motor is 1500r / min, the rated power is 0.75kW, the number of pole pairs is 5, the phase inductance is 4mH, the phase resistance is 0.8Ω, and the permanent magnet flux is 0.06wb. In the sliding mode surface, α is 200, β is 0.1, and γ is 0.5; in the current control law, ω f Take 1, k take 1000; m in the back electromotive force control law take 1500.

[0089] An experimental comparison of three methods, namely, a traditional sliding mode observer, a full-order sliding mode observer and an improved full-order sliding mode observer of the present invention, was performed on the motor, and the motor ran at a speed of 1000 r / min.

[0090] Combination Figure 2 As shown in the figure, parts a), b), and c) are the back electromotive force, estimated speed and estimated position, and speed and position errors observed by the traditional sliding mode observer. From part a), it can be seen that the back electromotive force observed by the traditional sliding mode observer has obvious phase lag and obvious high-frequency harmonics; from parts b) and c), it can be seen that the estimated speed and position errors calculated by the traditional sliding mode observer are large.

[0091] Combination Figure 3As shown in the figure, parts a), b), and c) are the back electromotive force, estimated speed and estimated position, and speed and position errors observed by the full-order sliding mode observer. From part a), it can be seen that the sinusoidality and hysteresis of the back electromotive force observed by the full-order sliding mode observer are significantly improved; from parts b) and c), it can be seen that the accuracy of the estimated speed and position calculated by the full-order sliding mode observer is improved, the speed error peak-to-peak is 18.95r / min, the angle error average is 2.20°, and the error peak-to-peak is 2.84°.

[0092] Combination Figure 4 As shown, parts a), b), and c) are the back electromotive force, estimated speed and estimated position, and speed and position errors observed by the improved full-order sliding mode observer. From part a), it can be seen that the sinusoidality and hysteresis of the back electromotive force observed by the improved full-order sliding mode observer are significantly improved; from parts b) and c), it can be seen that the estimated speed and position accuracy calculated by the improved full-order sliding mode observer are further improved compared with the full-order sliding mode observer, the speed error peak-to-peak value is 16.40r / min, the angle error average value is 1.71°, the error peak-to-peak value is 1.96°, and the steady-state error is further reduced.

[0093] In summary, compared with the traditional sliding mode observer and the full-order sliding mode observer, the improved full-order sliding mode observer proposed in the present invention has better steady-state accuracy, higher speed and position observation accuracy, and significantly improved position-free control effect.

[0094] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other forms of assembly without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-restrictive, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all changes within the meaning and range of equivalents of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0095] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A position sensorless control method based on an improved full-order sliding mode observer, characterized in that: The following steps are involved: Step 1: Current and voltage input Sample the three-phase current and perform a 3 / 2 transformation, consider the stator voltage to be equal to the actual voltage, and input the stator voltage into the observer; Step 2: Construct a full-order sliding mode observer Taking the two-phase current of the stator and the two-phase back electromotive force as state variables, the full-order state equation of the surface-mounted permanent magnet synchronous motor is constructed as follows: In the formula, R s and L s are the phase resistance and phase inductance of the two-phase windings respectively, i α 、i β and e α 、e β are the two-phase current and two-phase back electromotive force of the stator, ω e is the rotor electrical angular velocity, u α and u β is the stator two-phase voltage; Then the full-order sliding mode observer is established as follows: In the formula, and They are respectively used to observe the two-phase current of the stator and the two-phase back electromotive force. To estimate the electrical angular velocity, z i (s) and z e (s) are the current control law and back-EMF control law in the observer respectively; Step 3: Design the sliding surface The sliding surface designed based on the stator two-phase current error is expressed as follows: In the formula, s α and β are the two-phase sliding surfaces, and are the stator two-phase current errors, sgn() represents the sign function, α>0, β>0, 0<γ<1, all of which are constants; Step 4: Design current control law and back EMF control law Design the current control law i (s) is represented as follows: In the formula, z iα and z iβ They are the two-phase current control laws, ω f is the equivalent cutoff frequency, which is a constant greater than 0, z iαn and z iβn is the intermediate variable, k is the current convergence coefficient; Design of back-EMF control law e (s) is represented as follows: Where m is the back electromotive force convergence coefficient; Step 5: Convergence proof of improved full-order sliding mode observer Substituting formula (4)-(6) into formula (2) and subtracting them from formula (1), we can obtain the following expressions for the stator two-phase current and two-phase back electromotive force errors: Substituting formula (7) into formula (3) we can further obtain: By taking the derivative of formula (8), we can obtain: The Lyapunov function is: The expression of the derivative of the Lyapunov function is as follows: To satisfy The stable range of k and m can be obtained as: In the formula, and are the two-phase back electromotive force errors respectively, and M is the differential maximum value of the two-phase stator current error; Step 6: Demodulate and estimate position and speed Under the premise of satisfying formula (12), the two back electromotive forces are observed. and Input into the phase-locked loop to get the estimated electrical angle of the rotor and the estimated electrical angular velocity

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