A Feedback Matrix Control Method for Speed ​​Sensorless Induction Motor

Abstract

The present invention discloses a speed sensorless induction motor feedback matrix control method, including: establishing an induction motor model through motor stator current, rotor flux and input voltage, and then obtaining a full-order observer model with a feedback matrix; obtaining a state error equation based on the induction motor model and the full-order observer model, and obtaining a speed observation error; obtaining a speed observation instability interval based on the speed observation error, and obtaining a feedback matrix constraint that satisfies the speed observation stability; determining the central symmetric point of the observer pole according to the full-order observer model, and designing the observer's feedback matrix coefficient in combination with the feedback matrix parameter constraint, so that the central symmetric point of the observer pole moves to the left as the speed increases; and using the full-order observer to control the motor. The method disclosed by the present invention not only solves the system stability problem under low-speed power generation conditions, but also takes into account the dynamic performance of the observer under medium and high speed conditions compared with other methods.

Description

Technical Field

[0001] The invention relates to a speed sensorless induction motor feedback matrix control method, belonging to the technical field of motor control. Background Art

[0002] The full-order observer is a typical method in speed sensorless vector control and has been widely studied and used. However, this method has low-speed performance in high-performance asynchronous drive systems, especially the problem of low-speed power generation instability.

[0003] In the prior art, an improved feedback gain matrix is ​​generally used to improve the stability of the full-order observer under low-speed conditions. Although the prior art has disclosed a variety of improved feedback gain matrix design methods, such as the Chinese invention patent with publication number CN110492815A, these methods generally have a defect, that is, the dynamic performance of the observer is abandoned in order to pursue absolute stability of speed observation.

[0004] The feedback matrix designed for the low-speed stability problem can theoretically achieve global stability of speed observation. In practice, it is difficult to ensure stable operation at medium and high speeds. At medium and high speeds, the observer poles or extremely large real and imaginary parts make it difficult to ensure stability after discretization, or the observer is too close to the origin, resulting in non-convergence of the observed state variables.

[0005] Therefore, it is necessary to further study the methods to improve the stability of the full-order observer in order to solve the problem of ensuring the stability of the speed observation system while making the observer itself have good dynamic performance. Summary of the invention

[0006] In order to overcome the above problems, the inventors have conducted in-depth research and proposed a speed sensorless induction motor feedback matrix control method, which is characterized by comprising the following steps:

[0007] S1, establishing an induction motor model through the motor stator current, rotor flux and input voltage, and then obtaining a full-order observer model with a feedback matrix;

[0008] S2, obtaining a state error equation based on an induction motor model and a full-order observer model, and obtaining a speed observation error;

[0009] S3, obtaining the speed observation instability interval based on the speed observation error, and obtaining the feedback matrix constraint that satisfies the speed observation stability;

[0010] S4. Determine the central symmetric point of the observer pole according to the full-order observer model, and design the observer feedback matrix coefficient in combination with the feedback matrix parameter constraint, so that the central symmetric point of the observer pole moves to the left as the speed increases;

[0011] S5. Use the full-order observer to control the motor.

[0012] In a preferred embodiment, in S1, the induction motor model is expressed as:

[0013]

[0014] Where x = [i s ψ r ] T is the state variable, i s =[i sd i sq ] T is the stator current, ψ r =[ψ rd ψ rq ] T is the rotor flux, u=[u sd u sq ] T is the stator voltage; i sd is the d-axis component of the stator current, i sq is the q-axis component of the stator current; ψ rd is the d-axis component of the rotor flux, ψ rq is the q-axis component of the rotor flux; u sd is the d-axis component of the stator voltage, u sq is the q-axis component of the stator voltage, is the derivative operator, A, B, C are coefficient matrices.

[0015] In a preferred embodiment, the coefficient matrix is:

[0016]

[0017] Where σ is the magnetic leakage coefficient, T r is the rotor time constant, R s , R r are stator resistance and rotor resistance respectively; L s , L r , L m They are stator inductance, rotor inductance and mutual inductance; ω e is the synchronous angular velocity, ω r is the rotor electrical angular velocity, ω s is the slip electrical angular velocity, A 11 , A 12 , A 21 , A 22 , I, J, a1, and a2 are all intermediate quantities.

[0018] In a preferred embodiment, the full-order observer model is expressed as:

[0019]

[0020] Among them, the superscript “^” represents the observed value corresponding to the actual value of the motor, G is the feedback matrix, and g1, g2, g3, and g4 are the feedback matrix coefficients.

[0021] In a preferred embodiment, in S2, the state error equation is expressed as:

[0022]

[0023] ΔA 12 =-a2Δω r J, ΔA 22 =Δω r J,

[0024]

[0025] Among them, e is is the stator current error, e ψr is the rotor flux error, ΔA 12 , ΔA 22 is the coefficient matrix error, Δω r is the speed observation error.

[0026] In a preferred embodiment, the speed observation error is expressed as:

[0027]

[0028] Among them, e ωr 、a 51 、a 52 、a 53 、a 54 、a 55 All are intermediate variables.

[0029] In a preferred embodiment, the speed observation unstable interval boundary is:

[0030]

[0031] Among them, x, y, and z are intermediate variables.

[0032] In a preferred embodiment, the feedback matrix parameter constraint satisfying the speed observation stability is expressed as:

[0033]

[0034] In a preferred embodiment, the central symmetric point s0 of the observer pole is expressed as

[0035] in,

[0036]

[0037] In a preferred embodiment, the feedback matrix coefficients are:

[0038]

[0039] Among them, k1 and k2 are configurable parameters.

[0040] The beneficial effects of the present invention include:

[0041] (1) It not only solves the system stability problem under low-speed power generation conditions, but also takes into account the dynamic performance of the observer under medium and high-speed conditions compared with other methods;

[0042] (2) It contains two freely adjustable coefficients. By adjusting these two coefficients, the position of the observer pole can be arbitrarily configured to a certain extent, thereby achieving the effect of improving the dynamic performance of the observer itself. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 A schematic flow chart of a speed sensorless induction motor feedback matrix control method according to a preferred embodiment of the present invention is shown;

[0044] Figure 2 A schematic diagram showing an unstable region of low-speed power generation when the feedback matrix coefficient is zero in a speed sensorless induction motor feedback matrix control method according to a preferred embodiment of the present invention is shown;

[0045] Figure 3 A graph showing the change of observer poles and their symmetric points with motor speed when the feedback matrix coefficient is zero in a speed sensorless induction motor feedback matrix control method according to a preferred embodiment of the present invention;

[0046] Figure 4 The diagram shows the observer pole position diagram when k1 and k2 in the feedback matrix take different values ​​in the speed sensorless induction motor feedback matrix control method according to a preferred embodiment of the present invention;

[0047] Figure 5 It shows that when the feedback matrix coefficient is zero in the feedback matrix control method of the speed sensorless induction motor according to a preferred embodiment of the present invention, f(ω e ,ω r ) value changes with speed and slip;

[0048] Figure 6 The feedback matrix f(ω) in the speed sensorless induction motor feedback matrix control method according to a preferred embodiment of the present invention is shown. e,ω r ) value changes with speed and slip;

[0049] Figure 7 The graph shows the experimental results of 20Hz full-load regenerative braking in Example 1;

[0050] Figure 8 The graph shows the experimental results of switching between the 20Hz full-load motoring and generating modes in Example 1;

[0051] Fig. 9 The graph shows the experimental results of the motor speed of Example 2 increasing from 10 Hz to 30 Hz at half load operation;

[0052] Fig.10 The graph shows the experimental results of half-load operation of the motor in comparative example 1 when the motor speed increases from 10 Hz to 30 Hz. DETAILED DESCRIPTION

[0053] The present invention will be further described in detail below through the accompanying drawings and embodiments. Through these descriptions, the characteristics and advantages of the present invention will become more clear and distinct.

[0054] The word "exemplary" is used exclusively herein to mean "serving as an example, embodiment, or illustration." Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings are not necessarily drawn to scale unless otherwise noted.

[0055] According to a speed sensorless induction motor feedback matrix control method provided by the present invention, Figure 1 As shown, the following steps are included:

[0056] S1, establishing an induction motor model through the motor stator current, rotor flux and input voltage, and then obtaining a full-order observer model with a feedback matrix;

[0057] S2, obtaining a state error equation based on an induction motor model and a full-order observer model, and obtaining a speed observation error;

[0058] S3, obtaining the speed observation instability interval based on the speed observation error, and obtaining the feedback matrix constraint that satisfies the speed observation stability;

[0059] S4. Determine the central symmetric point of the observer pole according to the full-order observer model, and design the observer feedback matrix coefficient in combination with the feedback matrix parameter constraint, so that the central symmetric point of the observer pole moves to the left as the speed increases;

[0060] S5. Use the full-order observer to control the motor.

[0061] In S1, the induction motor model is expressed as:

[0062]

[0063] Where x = [i s ψ r ] T is the state variable, i s =[i sd i sq ] T is the stator current, ψ r =[ψ rd ψ rq ] T is the rotor flux, u=[u sd u sq ] T is the stator voltage; i sd is the d-axis component of the stator current, i sq is the q-axis component of the stator current; ψ rd is the d-axis component of the rotor flux, ψ rq is the q-axis component of the rotor flux; u sd is the d-axis component of the stator voltage, u sq is the q-axis component of the stator voltage, is the derivative operator, A, B, C are coefficient matrices.

[0064] Preferably, the coefficient matrix is:

[0065]

[0066] Where σ is the magnetic leakage coefficient, T r is the rotor time constant, R s , R r are stator resistance and rotor resistance respectively; L s , L r , L m They are stator inductance, rotor inductance and mutual inductance; ω e is the synchronous angular velocity, ω r is the rotor electrical angular velocity, ω s is the slip electrical angular velocity, A 11 , A 12 , A 21 , A 22 , I, J, a1, and a2 are all intermediate quantities.

[0067] According to the induction motor model, the full-order observer model is expressed as:

[0068]

[0069] Among them, the superscript “^” represents the observed value corresponding to the actual value of the motor, G is the feedback matrix, and g1, g2, g3, and g4 are the feedback matrix coefficients.

[0070] In S2, the state error equation is obtained by interpolating the induction motor model and the full-order observer model through Laplace transform, which is expressed as:

[0071]

[0072] ΔA 12 =-a2Δω r J, ΔA 22 =Δω r J,

[0073]

[0074] Among them, e is is the stator current error, e ψr is the rotor flux error, ΔA 12 , ΔA 22 is the coefficient matrix error, Δω r is the speed observation error.

[0075] Based on the speed adaptation rate derived from Lyapunov stability theory, in the speed sensorless vector control system oriented according to the rotor magnetic field, the observed speed is expressed as:

[0076]

[0077] Among them, s is the Laplace operator, k p is the proportionality coefficient, k i is the integration coefficient, is the d-axis component of the estimated rotor flux

[0078] And the following constraints are met:

[0079]

[0080] Substitute the q-axis component of the current error differential equation into the observed speed and combine the constraints to obtain the speed observation error, which is expressed as:

[0081]

[0082] Among them, e ωr 、a 51 、a 52 、a 53 、a 54 、a 55 All are intermediate variables.

[0083] In S3, according to the state error equation and the speed observation error, the linearized error equation is obtained, which is expressed as:

[0084]

[0085] Where, e=[e isd e isq e ψrd e ψrq e ωr ] T ,

[0086]

[0087] Among them, A5 is the coefficient matrix.

[0088] According to the linearized error equation, the necessary condition for the stability of the error system is det|A5|<0, where det is the matrix determinant value function, which is a commonly used calculation function.

[0089] Furthermore, the determinant of the coefficient matrix det|A5| is expressed as:

[0090]

[0091] Among them, x, y, z are intermediate variables, f(ω e ,ω r ) is a parabola about synchronous speed. The two intersection points of the parabola and the horizontal axis are the two boundary points when the error system is unstable. The part above the horizontal axis is the unstable area of ​​low-speed power generation. The parabola is drawn under the load condition with rated power generation properties. Figure 2 As shown in the figure, the shaded part is the unstable area of ​​low-speed power generation when the gain matrix coefficients are all zero.

[0092] Furthermore, in the present invention, the stability of the error system in the power generation area is judged by the sign of det|A5|, that is, the instability boundary of low-speed power generation can be obtained by setting det|A5|=0.

[0093] The obtained low-speed power generation instability boundary is:

[0094]

[0095] The strategy to eliminate the unstable region of low-speed power generation can be considered as shrinking the unstable boundary points other than zero to zero, thereby reducing or even eliminating the unstable interval. The following restrictions can be imposed on the equation to make the equation have only ω e =0, this unstable point:

[0096]

[0097] After applying the restrictions, the feedback matrix parameter constraints that satisfy the speed observation stability can be obtained:

[0098]

[0099] In S4, the inventors found that when the feedback matrix is ​​zero, the observer poles s1, s2 and their symmetric point s0 are distributed as follows: Figure 3 As shown, the motor speed ω r Set to -50Hz to 50Hz, at which point the observer poles coincide with the motor poles.

[0100] At medium and high speeds, the real part of the pole s2 remains basically unchanged, and the imaginary part increases with the increase of speed. The pole damping ratio of the observer gradually decreases, and there is oscillation in the convergence process of the state variable, which is not good for the dynamic performance of the observer. To increase the pole damping ratio of the observer in the medium and high speed area, you only need to increase the distance between the center point s0 and the imaginary axis. In order to make the observer converge faster, it is also necessary to make the observer pole located to the left of the motor pole position, which can also be achieved by increasing the distance between the center point s0 and the imaginary axis. At medium and high speeds, the imaginary part of the pole s1 is smaller than the real part, and the damping ratio of the pole s1 is close to 1. Although the oscillation is reduced, the convergence speed is not fast enough. At this time, the damping ratio of s1 can be appropriately reduced to speed up the convergence speed of the observer.

[0101] In S4, according to the full-order observer model, the observer state equation is expressed in complex coefficient form in a two-phase stationary coordinate system as follows:

[0102]

[0103] in, is an intermediate variable and j is an imaginary unit.

[0104] Furthermore, the observer characteristic root can be obtained through the determinant of the coefficient matrix:

[0105]

[0106] The roots of the characteristic equation are obtained by the root-finding formula, which can be expressed as:

[0107]

[0108] Taking the square root of the above equation and separating the real and imaginary parts, we can get the two root coordinates of the observer characteristic equation. Regardless of whether the speed is positive or negative, the two roots s1 and s2 of the observer characteristic equation are related to the coordinates. It is centrally symmetric, that is, the central symmetric point s0 of the observer pole is expressed as

[0109] in,

[0110]

[0111] It can be seen from the above formula that the horizontal coordinate position of the central symmetric point s0 is controlled by g1, and the vertical coordinate position is controlled by g2. The position of the observer pole can be indirectly affected by controlling the horizontal and vertical coordinates of the central symmetric point s0.

[0112] To improve the observer damping ratio, the center point should move to the left as the speed increases, while not generating too large an imaginary part. Based on this design idea and combined with the feedback matrix constraint, g2=k2T r ω r (k2>0), the position of the horizontal coordinate of the center point s0 can be adjusted by changing the coefficient k1, and the position of the vertical coordinate of s0 can be adjusted by changing the coefficient k2. The value of g4 will not affect the stability of the system, so let g4=0 and obtain the feedback matrix coefficient expression:

[0113]

[0114] Among them, k1 and k2 are configurable parameters.

[0115] In the present invention, the feedback matrix is ​​designed from the perspective of improving the observer pole damping ratio. Through the observer pole distribution diagram, the coefficients k1 and k2 in the feedback matrix are preferably selected to place the observer pole in a position more favorable to the system dynamic performance.

[0116] Furthermore, the observer and motor pole trajectories when k1 and k2 take different values ​​are as follows: Figure 4 As shown in the figure. As the value of k1 increases, the observer pole moves away from the imaginary axis. Although the pole damping ratio of the observer at medium and high speeds is improved, it is also more susceptible to interference from measurement noise. If the value of k1 is too small, the effect of improving the observer pole damping ratio is not obvious; k2 mainly plays a role in scaling the two pole trajectories. If the value of k2 is small, the imaginary part of the pole s2 is also small. If the value of k2 is large, the imaginary part of the pole s2 will also be magnified.

[0117] According to the present invention, the formula f(ω e ,ω r ) is used as the evaluation standard of speed observability, which concretely reflects the improvement of speed observability by using the improved feedback matrix. If f(ω e ,ω r ) is greater than zero, which means that the speed observation is unstable. The smaller the value is, the farther away from the unstable area. Specifically:

[0118] When the feedback matrix is ​​0, the feedback matrix of the present invention is set to be compared, such as Figure 5-6 As shown, Figure 5 When the feedback matrix is ​​0, f(ωe ,ω r ) and the three-dimensional relationship between speed and slip, Figure 6 After setting the feedback matrix of the present invention, f(ω e ,ω r ) and the three-dimensional relationship diagram of the speed and slip. It can be seen from the figure that after setting the feedback matrix of the present invention, f(ω e ,ω r ) are all less than zero, the unstable region of low-speed power generation is eliminated, and f(ω e ,ω r ) still has a large margin from zero.

[0119] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps described in the disclosure of the present invention can be performed in parallel, sequentially or in different orders, as long as the desired results of the technical solution disclosed in the present invention can be achieved, and this document does not limit this.

[0120] Example

[0121] Example 1

[0122] The speed sensorless induction motor feedback matrix control experiment was carried out. The induction motor parameters used in the experiment were: rated power 11kW, rated voltage 380V, rated current 23.6A, rated speed 1460rpm, rated frequency 50Hz, and rated torque 70N·m;

[0123] The experiment includes the following steps:

[0124] S1, establishing an induction motor model through the motor stator current, rotor flux and input voltage, and then obtaining a full-order observer model with a feedback matrix;

[0125] S2, obtaining a state error equation based on an induction motor model and a full-order observer model, and obtaining a speed observation error;

[0126] S3, obtaining the speed observation instability interval based on the speed observation error, and obtaining the feedback matrix constraint that satisfies the speed observation stability;

[0127] S4. Determine the central symmetric point of the observer pole according to the full-order observer model, and design the observer feedback matrix coefficient in combination with the feedback matrix parameter constraint, so that the central symmetric point of the observer pole moves to the left as the speed increases;

[0128] S5. Use the full-order observer to control the motor.

[0129] In S1, the induction motor model is expressed as:

[0130]

[0131] The coefficient matrix is:

[0132]

[0133] The full-order observer model is expressed as:

[0134]

[0135] The state error equation is expressed as:

[0136]

[0137] ΔA 12 =-a2Δω r J, ΔA 22 =Δω r J,

[0138]

[0139] The speed observation error is expressed as:

[0140]

[0141] The feedback matrix parameter constraints satisfying the speed observation stability are expressed as:

[0142]

[0143] The central symmetric point s0 of the observer is expressed as

[0144] in,

[0145]

[0146] The feedback matrix coefficients are:

[0147]

[0148] In the experiment, the motor was braked at a speed of 20 Hz, the braking time was set to 5 s, and the corresponding braking torque was -60 N·m. The experimental waveform is as follows Figure 7 As shown in the figure, it can be seen that the maximum error between the observed speed and the speed command is 2.2rad / s, and the motor speed remains stable during the braking process, indicating that the set full-order observer can ensure the stable operation of the speed observation system under low-speed power generation conditions.

[0149] In the experiment, the motor speed was switched between forward and reverse at 20Hz, that is, the motor switched between forward power generation and reverse motoring, and the switching time was set to 10s. The experimental results are shown in Figure 8 As shown in the figure, it can be seen that the maximum error between the observed speed and the speed command is 2.1rad / s, indicating that the set full-order observer can achieve stable switching between motoring and generating conditions under rated load.

[0150] Example 2

[0151] The motor and control method in Example 1 were used to conduct a dynamic response experiment of motor speed and torque. In the experiment, the motor speed increased from 10 Hz to 30 Hz, and the rise time was 10 s corresponding to the half-load condition. The experimental waveform is as follows: Fig. 9 shown.

[0152] Comparative Example 1

[0153] The same experiment as in Example 2 was conducted, except that the method in the Chinese invention patent with publication number CN 110492815A was used. The experimental waveform is as follows: Fig.10 shown.

[0154] Comparing the results of Example 2 with those of Comparative Example 1, Fig. 9 , Fig.10 As can be seen from the figure, the speed observation method in comparative example 1 has a tendency of non-convergence, the motor starts to oscillate at 25Hz, and completely loses control when the speed exceeds 30Hz. The method in embodiment 2 accelerates the convergence speed of the observer and solves the problem of motor speed and torque oscillation or even non-convergence in the medium and high speed area.

[0155] The present invention has been described above in conjunction with preferred embodiments, but these embodiments are only exemplary and serve only as an illustration. On this basis, the present invention may be subjected to a variety of substitutions and improvements, all of which fall within the scope of protection of the present invention.

Claims

1. A speed sensorless induction motor feedback matrix control method, characterized in that: The following steps are involved: S1, establishing an induction motor model through the motor stator current, rotor flux and input voltage, and then obtaining a full-order observer model with a feedback matrix; S2, obtaining a state error equation based on an induction motor model and a full-order observer model, and obtaining a speed observation error; S3, obtaining the speed observation instability interval based on the speed observation error, and obtaining the feedback matrix constraint that satisfies the speed observation stability; S4. Determine the central symmetric point of the observer pole according to the full-order observer model, and design the observer feedback matrix coefficient in combination with the feedback matrix parameter constraint, so that the central symmetric point of the observer pole moves to the left as the speed increases; S5, using the full-order observer to control the motor; In S1, the induction motor model is expressed as: Where x = [i s ψ r ] T is the state variable, i s =[i sd i sq ] T is the stator current, ψ r =[ψ rd ψ rq ] T is the rotor flux, u=[u sd u sq ] T is the stator voltage; i sd is the d-axis component of the stator current, i sq is the q-axis component of the stator current; ψ rd is the d-axis component of the rotor flux, ψ rq is the q-axis component of the rotor flux; u sd is the d-axis component of the stator voltage, u sq is the q-axis component of the stator voltage, is the derivative operator, A, B, C are coefficient matrices; The coefficient matrix is: C=[I] HAS 11 =a1I-ω e I, Where σ is the magnetic leakage coefficient, T r is the rotor time constant, R s , R r are stator resistance and rotor resistance respectively; L s , L r , L m They are stator inductance, rotor inductance and mutual inductance; ω e is the synchronous angular velocity, ω r is the rotor electrical angular velocity, ω s is the slip electrical angular velocity, A 11 , A 12 , A 21 , A 22 , I, J, a1, and a2 are all intermediate quantities; The full-order observer model is expressed as: Wherein, the superscript "^" indicates the observed value corresponding to the actual value of the motor, G is the feedback matrix, and g1, g2, g3, and g4 are the feedback matrix coefficients; The central symmetric point s0 of the observer pole is expressed as in, The feedback matrix coefficients are: Among them, k1 and k2 are configurable parameters.

2. The speed sensorless induction motor feedback matrix control method according to claim 1, characterized in that: In S2, the state error equation is expressed as: A 12 =-a2Show r J, ΔA 22 =Here r J, Among them, e is is the stator current error, e ψr is the rotor flux error, ΔA 12 , ΔA 22 is the coefficient matrix error, Δω r is the speed observation error.

3. The speed sensorless induction motor feedback matrix control method according to claim 2, characterized in that: The speed observation error is expressed as: Among them, e ωr 、a 51 、a 52 、a 53 、a 54 、a 55 All are intermediate variables.

4. The speed sensorless induction motor feedback matrix control method according to claim 1, characterized in that: The speed observation unstable interval boundary is: z=g2+a2g4 Among them, x, y, and z are intermediate variables.

5. The speed sensorless induction motor feedback matrix control method according to claim 4, characterized in that: The feedback matrix parameter constraints satisfying the speed observation stability are expressed as:

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