A speed sensorless control method for induction motor based on variable speed reaching law

Abstract

The present invention discloses a speed sensorless control method for an induction motor based on a variable speed reaching law, which belongs to the field of motor drive and control technology, and includes the following steps: step S1, constructing a full-order sliding mode observer model according to the mathematical model of the induction motor; step S2, designing a variable speed reaching law function and a feedback gain matrix; step S3, designing an induction motor speed estimation method; step S4, building an induction motor speed sensorless vector control system model; step S5, adjusting observer parameters and controller parameters so that the control system performance indicators meet actual needs. The present invention solves the problems of jitter and slow speed convergence speed of the speed sensorless control system of the induction motor under zero speed and low speed conditions, so that the system can operate stably with load under zero speed and low speed conditions, and has good steady-state performance and fast dynamic performance.

Description

Technical Field

[0001] The invention relates to the field of motor driving and control, and in particular to a speed sensorless control method of an induction motor based on a variable speed reaching law. Background Art

[0002] Induction motors are widely used in various industrial applications due to their simple structure and low cost. Vector control has the advantage of high voltage utilization, so more and more frequency converters use vector control algorithms. To achieve closed-loop speed control, it is usually necessary to install a speed sensor (such as a photoelectric encoder) to detect the speed information, but the installation of the speed sensor increases the system cost and complexity, and the speed signal is susceptible to electromagnetic interference during transmission. Speed ​​sensorless control is small in size, low in cost, and can be applied to harsh environments. Therefore, sensorless control technology for induction motors has become a research hotspot in recent years. This method requires constructing an observer based on the mathematical model of the induction motor and calculating the motor speed through easily measured physical quantities such as rotor voltage and rotor current. Due to its inherent variable structure characteristics, the sliding mode observer is less dependent on the accuracy of the motor model. The sliding mode observer has the advantages of reduced order, simple implementation, and strong robustness, but it also has problems such as jitter and slow convergence.

[0003] At present, the research on sliding mode observers mainly focuses on the stability of the observer and the reduction of chattering, so as to ensure that the state variables can smoothly reach the sliding surface within a limited time. However, how the state variables reach the sliding surface, that is, the path to the sliding surface, also has an important impact on the performance of the observer, especially the improvement of dynamic performance and the reduction of chattering, but the current research is relatively small. Based on the above analysis, it is necessary to develop a new sliding mode observer with variable speed reaching law. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide an induction motor speed sensorless control method based on a variable speed reaching law, which solves the problems of jitter and slow speed convergence of the induction motor speed sensorless control system under zero speed and low speed conditions, so that the system can operate stably with load under zero speed and low speed conditions, and has good steady-state performance and fast dynamic performance.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is: a speed sensorless control method of an induction motor based on a variable speed reaching law, comprising the following steps:

[0006] Step S1, constructing a full-order sliding mode observer model according to the mathematical model of the induction motor;

[0007] Step S2, designing a variable speed reaching law function and a feedback gain matrix;

[0008] Step S3, designing an induction motor speed estimation method;

[0009] Step S4, building an induction motor speed sensorless vector control system model;

[0010] Step S5, adjusting observer parameters and controller parameters so that the control system performance indicators meet actual requirements.

[0011] A further improvement of the technical solution of the present invention is that the specific process of step S1 is:

[0012] Step S1.1, providing a dynamic mathematical model of the induction motor in a two-phase stationary coordinate system, and deriving a state equation based on the mathematical model;

[0013] The dynamic mathematical model of the induction motor in the two-phase stationary coordinate system is as follows:

[0014] Voltage equation:

[0015]

[0016] Magnetic flux equation:

[0017]

[0018] In the formula, u sα ,u sβ ,u rα ,u rβ - are the voltage components of the stator and rotor on the corresponding axis in the αβ system; i sα ,i sβ ,i rα ,i rβ - are the current components of the stator and rotor on the corresponding axis in the αβ system; ψ sα ,ψ sβ ,ψ rα ,ψ rβ - are the magnetic flux components of the stator and rotor on the corresponding axis in the αβ system respectively; ω r - rotor electrical angular velocity; R s - stator resistance; R r - rotor resistance; L s - stator inductance; L r -Rotor inductance; L m -Motor mutual inductance;

[0019] The state equation obtained from the dynamic mathematical model of the induction motor is:

[0020]

[0021] In the formula, x=[i sα isβ ψ rα ψ rβ ] T , y=[i sα i sβ ] T ,u=[u sα u sβ 0 0] T ,

[0022] Step S1.2, construct a full-order sliding mode observer model based on the state equation of step S1.1:

[0023]

[0024] In the formula, G is the feedback gain matrix and S is the sliding surface and e isα and e isβ is the component of the stator current estimation error in each coordinate axis in the two-phase stationary coordinate system, F(S) is the sliding mode function, is the estimated value of the rotation speed, and is the component of each coordinate axis of the stator current estimate in the two-phase stationary coordinate system, and is the component of each coordinate axis of the rotor flux estimate in the two-phase stationary coordinate system.

[0025] A further improvement of the technical solution of the present invention is that the specific process of step S2 includes:

[0026] Step S2.1, design variable speed reaching law function:

[0027]

[0028] Where, D(δ)=m+(1+hm)e -ηδ , 0<m<1, h>0, η>0, δ is the stator current error term and

[0029] F(S) in formula (4) is designed as:

[0030]

[0031] From the analysis of formula (6), we can see that when the state variable is far away from the sliding surface, the absolute value of the stator current error is large, making e -ηδ→0, then D(δ)=m, at this time the full-order sliding mode observer gain becomes K / m, since 0<m<1, the system converges very quickly at this time; when the state variable is close to the sliding mode surface, the absolute value of the stator current error is very small, making e -ηδ →1, then D(δ)=1+h, at this time, the full-order sliding mode observer gain becomes K / (1+h), and 1+h>1, so the convergence speed of the system is slow at this time, and the full-order sliding mode observer gain is adaptively adjusted between K / m and K / (1+h);

[0032] Step S2.2, according to the full-order sliding mode observer model, the error equation of the full-order sliding mode observer model is obtained:

[0033]

[0034] In formula (7), e ψrα and e ψrβ is the component of the rotor flux estimation error in each coordinate axis in the two-phase stationary coordinate system;

[0035] Step S2.3, the system output is the stator current and the system output error term is used to construct the Lyapunov function:

[0036]

[0037] Step S2.4, derive equation (8) to obtain:

[0038]

[0039] Assumptions Since λ1<0, as well as Let g2 = 0, to ensure As long as formula (10) is established:

[0040]

[0041] According to the state equation in the two-phase stationary coordinate system shown in formula (3), the expression of the rotor flux is:

[0042]

[0043] When the system enters a steady state, the rotor flux expression is expressed as:

[0044]

[0045] When the system enters a steady state isα =e isβ=0, the feedback gain of the full-order sliding mode observer model is 0, and the full-order sliding mode observer model is consistent with the dynamic mathematical model of the induction motor. Therefore, the observed value of the rotor flux is expressed as:

[0046]

[0047] Subtracting equation (12) from equation (13), we can get the rotor flux observation error:

[0048]

[0049] Substituting formula (14) into formula (10), we get:

[0050]

[0051] Simplify the above formula to get the value range of g1 and g2:

[0052]

[0053] From formula (16), we can see that D(δ) is a bounded positive number, and the current error term in the inequality is also a bounded function. Therefore, as long as the absolute value of g1 is large enough and positive when g1 is selected, and g2 is 0, the derivative of V1 is negative. According to the Lyapunov stability theorem, the estimated current will converge to the actual current.

[0054] Step S2.5, when When , the error equation of the full-order sliding mode observer model in equation (7) is simplified to:

[0055]

[0056] Step S2.6, reconstruct a Lyapunov function:

[0057]

[0058] Step S2.7, derive equation (18) to obtain:

[0059]

[0060] From formula (17), we can get:

[0061]

[0062] Let g4 = 0. At the same time, substitute equation (20) into equation (19) to obtain:

[0063]

[0064] From the analysis of formula (21), we can see that as long as the following formula holds, the derivative of V2 is negative:

[0065]

[0066] From this we can get the value range of g3 and g4:

[0067]

[0068] Therefore, when g3 and g4 are given by equation (23), the derivative of V2 is negative, and according to the Lyapunov stability theorem, the system will be asymptotically stable;

[0069] Step S2.8, introducing the variable speed reaching law function and the feedback gain matrix into the full-order sliding mode observer model.

[0070] A further improvement of the technical solution of the present invention is that the specific process of step S3 includes:

[0071] Step S3.1, define a Lyapunov function:

[0072]

[0073] In the formula,

[0074] Step S3.2, derive equation (24), and substitute equation (9) and equation (19) into its derivative formula:

[0075]

[0076] According to Lyapunov theorem, the following equation holds true, and the system is stable:

[0077]

[0078] In step S3.3, the flux error term in equation (26) is ignored; in addition, the designed reaching law function is introduced into the speed estimation, and the PI controller is used to replace the gain and integral links, and finally the motor speed estimation method is obtained:

[0079]

[0080] A further improvement of the technical solution of the present invention is that the specific process of step S4 includes:

[0081] Step S4.1, sampling stator voltage u A ,u B ,u C and the stator current i A ,i B ,i C And through Clark transformation, the stator voltage and stator current are transformed to the two-phase stationary coordinate system. The transformation matrix is ​​C 3 / 2 :

[0082]

[0083] Step S4.2, the stator voltage u in the two-phase stationary coordinate system sα ,u sβ and the stator current i sα ,i sβ The estimated rotor flux is calculated by a full-order sliding mode observer and estimated speed And given the estimated rotor flux and estimated speed A closed loop is formed, and after adjustment by the PI regulator, the stator current given value in the rotating coordinate system is obtained.

[0084] Step S4.3, the stator current i in the two-phase stationary coordinate system sα ,i sβ After Park transformation, it is transformed into the rotating coordinate system and compared with the stator current given value A closed loop is formed, and the stator voltage set value in the two-phase stationary coordinate system is obtained through the PI regulator. The transformation matrix is ​​C 2s / 2r :

[0085]

[0086] In formula (29), is the angle between the stationary coordinate system and the rotating coordinate system;

[0087] Step S4.4, set the stator voltage in the rotating coordinate system to a given value After Park inverse transformation, it is transformed into a two-phase stationary coordinate system, and the stator voltage in the two-phase stationary coordinate system is Through SVPWM modulation, the control signal is output to control the opening and closing of the inverter power devices and control the stator side input of the induction motor.

[0088] Due to the adoption of the above technical solution, the technical progress achieved by the present invention is:

[0089] 1) The present invention adopts a full-order sliding mode observer to estimate the state of the induction motor, and proposes a new state estimation method based on the variable speed reaching law, which improves the reliability of the state estimation of the induction motor under zero speed and low speed load conditions;

[0090] 2) The variable speed reaching law function proposed in the present invention can enable the sliding mode observer to adaptively adjust the convergence speed as the system state changes, thereby improving the dynamic performance of the system and weakening chattering;

[0091] 3) The present invention proposes a corresponding feedback matrix design method based on the designed variable speed reaching law function, which can improve the state estimation accuracy of the system under zero-speed and low-speed conditions, and greatly enhances the practicality and portability of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 is a flow chart of the present invention;

[0093] Figure 2 It is a structural diagram of a speed sensorless vector control system of an induction motor in the present invention;

[0094] Figure 3 is a structural diagram of a full-order sliding mode observer in the present invention;

[0095] Figure 4 It is the simulation result of the traditional sliding mode observer under low speed loading and unloading conditions of speed, electromagnetic torque, stator current and rotor flux;

[0096] Figure 5 It is the simulation result of the speed, electromagnetic torque, stator current and rotor flux linkage of the new full-order sliding mode observer designed by the present invention under low-speed loading and unloading conditions;

[0097] Figure 6 It is the simulation result of the traditional sliding mode observer under the system load speed stepping condition of speed, electromagnetic torque, stator current and rotor flux;

[0098] Figure 7 It is the simulation result of the speed, electromagnetic torque, stator current and rotor flux of the new full-order sliding mode observer designed in the present invention under the system load speed stepping working condition;

[0099] Figure 8 It is the simulation result of the speed and speed error of the traditional sliding mode observer under extremely low speed conditions;

[0100] Fig. 9 It is the simulation result of the speed and speed error of the new full-order sliding mode observer designed in the present invention under extremely low speed conditions. DETAILED DESCRIPTION

[0101] The present invention is further described in detail below in conjunction with embodiments:

[0102] Working principle or usage:

[0103] like Figure 1 As shown, a speed sensorless control method of an induction motor based on a variable speed reaching law of the present invention comprises:

[0104] Step S1, constructing a full-order sliding mode observer model according to the mathematical model of the induction motor;

[0105] Step S1 specifically includes the following steps:

[0106] Step S1.1, providing a dynamic mathematical model of the induction motor in a two-phase stationary coordinate system, and deriving a state equation based on the mathematical model;

[0107] The dynamic mathematical model of the induction motor in the two-phase stationary coordinate system is as follows:

[0108] Voltage equation:

[0109]

[0110] Magnetic flux equation:

[0111]

[0112] In the formula, u sα ,u sβ ,u rα ,u rβ - are the voltage components of the stator and rotor on the corresponding axis in the αβ system; i sα ,i sβ ,i rα ,i rβ - are the current components of the stator and rotor on the corresponding axis in the αβ system; ψ sα ,ψ sβ ,ψ rα ,ψ rβ - are the magnetic flux components of the stator and rotor on the corresponding axis in the αβ system respectively; ω r - rotor electrical angular velocity; R s - stator resistance; R r - rotor resistance; L s - stator inductance; L r -Rotor inductance; L m -Motor mutual inductance;

[0113] The state equation obtained from the dynamic mathematical model of the induction motor is:

[0114]

[0115] In the formula, x=[i sα i sβ ψ rα ψ rβ ] T , y=[i sα i sβ ] T ,u=[u sα u sβ 0 0] T ,

[0116] Step S1.2, construct a full-order sliding mode observer model based on the state equation of step S1.1:

[0117]

[0118] In the formula, G is the feedback gain matrix and S is the sliding surface and e isα and e isβ is the component of the stator current estimation error in each coordinate axis in the two-phase stationary coordinate system, F(S) is the sliding mode function, is the estimated value of the rotation speed, and is the component of each coordinate axis of the stator current estimate in the two-phase stationary coordinate system, and is the component of the rotor flux estimation value in each coordinate axis in the two-phase stationary coordinate system. The structure diagram of the induction motor speed sensorless vector control system is as follows: Figure 2 shown.

[0119] Step S2, designing a variable speed reaching law function and a feedback gain matrix;

[0120] Step S2 specifically includes the following steps:

[0121] Step S2.1, design variable speed reaching law function:

[0122]

[0123] Where, D(δ)=m+(1+hm)e -ηδ , 0<m<1, h>0, η>0, δ is the stator current error term and

[0124] F(S) in formula (4) is designed as:

[0125]

[0126] From the analysis of formula (6), we can see that when the state variable is far away from the sliding surface, the absolute value of the stator current error is large, making e -ηδ →0, then D(δ)=m, at this time the full-order sliding mode observer gain becomes K / m, since 0<m<1, the system converges very quickly at this time; when the state variable is close to the sliding mode surface, the absolute value of the stator current error is very small, making e -ηδ→1, then D(δ)=1+h, at this time, the full-order sliding mode observer gain becomes K / (1+h), and 1+h>1, so the system convergence speed is slow at this time, so the system chattering can be reduced. In summary, the full-order sliding mode observer gain is adaptively adjusted between K / m and K / (1+h), which not only ensures the convergence performance of the system, but also weakens the system chattering;

[0127] Step S2.2, according to the full-order sliding mode observer model, the error equation of the full-order sliding mode observer model is obtained:

[0128]

[0129] In formula (7), e ψrα and e ψrβ is the component of the rotor flux estimation error in each coordinate axis in the two-phase stationary coordinate system;

[0130] Step S2.3, since the system output is the stator current, the output convergence is guaranteed, that is, the system convergence can be guaranteed. The system output is the stator current and the system output error term is used to construct the Lyapunov function:

[0131]

[0132] Step S2.4, derive equation (8) to obtain:

[0133]

[0134] Considering the stability and accuracy of the system and the fact that the speed is a constant within a sampling period, it is assumed that the error between the identified speed and the true speed can be ignored. Therefore, it is assumed in the above formula that Since λ1<0, as well as In order to simplify the design difficulty of the feedback gain matrix, let g2 = 0 to ensure As long as formula (10) is established:

[0135]

[0136] According to the state equation in the two-phase stationary coordinate system shown in formula (3), the expression of the rotor flux is:

[0137]

[0138] When the system enters a steady state, the rotor flux expression is expressed as:

[0139]

[0140] When the system enters a steady state isα =e isβ=0, the feedback gain of the full-order sliding mode observer model is 0, and the full-order sliding mode observer model is consistent with the dynamic mathematical model of the induction motor. Therefore, the observed value of the rotor flux is expressed as:

[0141]

[0142] Subtracting equation (12) from equation (13), we can get the rotor flux observation error:

[0143]

[0144] Substituting formula (14) into formula (10), we get:

[0145]

[0146] Simplify the above formula to get the value range of g1 and g2:

[0147]

[0148] From formula (16), we can see that D(δ) is a bounded positive number. Considering the actual operating conditions of the motor, the current error term in the inequality is also a bounded function. Therefore, as long as the absolute value of g1 is large enough and positive, and g2 is 0, the derivative of V1 is negative. According to the Lyapunov stability theorem, the estimated current will converge to the actual current.

[0149] Step S2.5, when When , the error equation of the full-order sliding mode observer model in equation (7) is simplified to:

[0150]

[0151] Step S2.6, reconstruct a Lyapunov function:

[0152]

[0153] Step S2.7, derive equation (18) to obtain:

[0154]

[0155] From formula (17), we can get:

[0156]

[0157] To simplify the design complexity of the feedback gain matrix, let g4 = 0. At the same time, substitute equation (20) into equation (19) to obtain:

[0158]

[0159] From the analysis of formula (21), we can see that as long as the following formula holds, the derivative of V2 is negative:

[0160]

[0161] From this we can get the value range of g3 and g4:

[0162]

[0163] Therefore, when g3 and g4 are given by equation (23), the derivative of V2 is negative. According to the Lyapunov stability theorem, the system will be asymptotically stable;

[0164] Step S2.8, introducing the variable speed reaching law function and the feedback gain matrix into the full-order sliding mode observer model Step S3, designing the induction motor speed estimation method;

[0165] The specific process of step S3 includes:

[0166] Step S3.1, define a Lyapunov function:

[0167]

[0168] In the formula,

[0169] Step S3.2, derive equation (24), and substitute equation (9) and equation (19) into its derivative formula:

[0170]

[0171] The previous design has ensured According to Lyapunov's theorem, the system is stable as long as the following equation holds:

[0172]

[0173] Step S3.3, such as Figure 3 As shown in Figure 2, since the flux error is very small under actual working conditions, the flux error term in equation (26) can be ignored. In addition, in order to improve the convergence performance of the system and weaken the chattering, the designed reaching law function is introduced into the speed estimation, and the PI controller is used to replace the gain and integral links. Finally, the motor speed estimation method is obtained:

[0174]

[0175] Step S4, building an induction motor speed sensorless vector control system model;

[0176] Step S4 specifically includes the following steps:

[0177] Step S4.1, sampling stator voltage u A ,u B ,u C and the stator current i A ,i B ,i C And through Clark transformation, the stator voltage and stator current are transformed to the two-phase stationary coordinate system. The transformation matrix is ​​C 3 / 2 :

[0178]

[0179] Step S4.2, the stator voltage u in the two-phase stationary coordinate system sα ,u sβ and the stator current i sα ,i sβ The estimated rotor flux is calculated by a full-order sliding mode observer and estimated speed And given the estimated rotor flux and estimated speed A closed loop is formed, and after adjustment by the PI regulator, the stator current given value in the rotating coordinate system is obtained.

[0180] Step S4.3, the stator current i in the two-phase stationary coordinate system sα ,i sβ After Park transformation, it is transformed into the rotating coordinate system and compared with the stator current given value A closed loop is formed, and the stator voltage set value in the two-phase stationary coordinate system is obtained through the PI regulator. The transformation matrix is ​​C 2s / 2r :

[0181]

[0182] In formula (29), is the angle between the stationary coordinate system and the rotating coordinate system;

[0183] Step S4.4, set the stator voltage in the rotating coordinate system to a given value After Park inverse transformation, it is transformed into a two-phase stationary coordinate system, and the stator voltage in the two-phase stationary coordinate system is Through SVPWM modulation, the control signal is output to control the opening and closing of the inverter power devices and control the stator side input of the induction motor.

[0184] Step S5, adjusting the observer parameters and the controller parameters so that the control system performance indicators meet the actual requirements.

[0185] The following examples are used to verify the beneficial effects of the present invention:

[0186] The model parameters of the induction motor speed sensorless vector control system adopted in the present invention are:

[0187]

[0188]

[0189] To verify the effectiveness of the designed full-order sliding mode observer, it is compared with the traditional sliding mode observer.

[0190] Given a speed of 20 rad / s, a load of 20 N·m is suddenly added at 1.5 s and unloaded at 3 s. Figure 4 The simulation results of the speed, electromagnetic torque, stator current and rotor flux of the traditional sliding mode observer are shown in Figure 2. Figure 5 Simulation results of speed, electromagnetic torque, stator current and rotor flux of the new full-order sliding mode observer designed for the present invention.

[0191] from Figure 4 a) to Figure 4 d) It can be seen that the estimated speed of the traditional sliding mode observer cannot track the real speed in a timely and accurate manner, and the system converges slowly. When the system is suddenly loaded, the estimated speed fluctuates greatly and jitters. It takes about 0.5s to suppress the jitter and barely track the real speed. Similarly, the electromagnetic torque of the system also fluctuates greatly when the load is suddenly added, and even after the system enters a steady state, the electromagnetic torque of the system still has a lot of jitter.

[0192] from Figure 5 a) to Figure 5 d) It can be seen that the estimated speed of the new full-order sliding mode observer designed in the present invention can track the real speed of the system in a timely and accurate manner from the beginning, and there is no deviation from the real speed even when the system is suddenly loaded or unloaded, and the estimated speed is very smooth with almost no jitter. The system torque is also smooth and stable when the system is suddenly loaded or unloaded, with only minimal jitter.

[0193] contrast Figure 4 and Figure 5 It shows that the traditional sliding mode observer has slow convergence speed and jitter problems due to the existence of sign function and fixed sliding mode approach speed. However, the full-order sliding mode observer proposed in the present invention can still work quickly and accurately when adding or removing loads due to the introduction of variable speed approach law, which improves the convergence speed of the system and greatly reduces the system jitter.

[0194] Given a speed of 20 rad / s, a 10 N·m load torque is suddenly applied at 0.5 s. From 1 s on, the speed is stepped down to a low speed, once every 1 second, with a step length of 2 rad / s. Figure 6 The simulation results of the speed, electromagnetic torque, stator current and rotor flux of the traditional sliding mode observer are shown in Figure 2. Figure 7 Simulation results of speed, electromagnetic torque, stator current and rotor flux of the new full-order sliding mode observer designed for the present invention.

[0195] from Figure 6 a) to Figure 6 d) It can be seen that the traditional sliding mode observer still has the problem of slow convergence speed. When the system is suddenly loaded, the estimated speed fluctuates greatly and deviates greatly from the actual speed. The same phenomenon occurs at each speed step. At the same time, the system torque also fluctuates greatly when the system is suddenly loaded. At each speed step, there is also a large torque drop, and the system torque has a large jitter from beginning to end.

[0196] from Figure 7 a) to Figure 7 d) It can be seen that the new full-order sliding mode observer designed in the present invention can track the real speed of the system very quickly and accurately. When the system is suddenly loaded, there is no phenomenon of inaccurate estimated speed, but the estimated speed curve is firmly "close to" the real speed. When the speed is stepped, there is no visible deviation between the estimated speed and the real speed. Similarly, the system torque also changes very smoothly when the system is suddenly loaded, without large fluctuations and jitters. When the speed is stepped, the torque drop is relatively small, and the system torque has small jitters in the whole process.

[0197] contrast Figure 6 and Figure 7 This shows that the new full-order sliding mode observer designed in the present invention still has good identification performance under the system load speed stepping condition, which also shows that the designed feedback gain matrix can operate stably under such conditions.

[0198] Given a speed of 3 rad / s, Figure 8 The simulation results of the estimated speed and the estimated speed error of the traditional sliding mode observer are: Fig. 9 Simulation results of the estimated speed and the estimated speed error of the new full-order sliding mode observer designed for the present invention.

[0199] from Figure 8 a) to Figure 8 b) It can be seen that the estimated speed of the traditional sliding mode observer under extremely low speed conditions will have large jitter, and the speed error oscillates back and forth between -0.1rad / s and 0.1rad / s, with a speed error of 0.2rad / s. This is caused by the switching function of the traditional sliding mode observer.

[0200] from Fig. 9 a) to Fig. 9b) It can be seen that even under extremely low-speed conditions, the new sliding mode observer designed in the present invention can still suppress system chattering, making the system estimated speed error extremely small, only 0.02rad / s, and the estimated speed is very smooth in the whole process. This is due to the existence of the designed new reaching law function, which enables the system state to converge in a smoother manner when it is close to the sliding mode surface.

[0201] contrast Figure 8 and Fig. 9 , which shows that the new full-order sliding mode observer designed in the present invention can operate stably under extremely low speed conditions, and has a faster convergence speed and smaller jitter.

[0202] The present invention may also have other various embodiments. Without violating the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and deformations based on the present invention, but these corresponding changes and deformations should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A speed sensorless control method for an induction motor based on a variable speed reaching law, characterized in that: The steps include: Step S1, constructing a full-order sliding mode observer model according to the mathematical model of the induction motor; the full-order sliding mode observer model is as follows: In the formula, G is the feedback gain matrix and S is the sliding surface and e isα and e isβ is the component of the stator current estimation error in each coordinate axis in the two-phase stationary coordinate system, F(S) is the sliding mode function, is the estimated value of the rotation speed, and is the component of each coordinate axis of the stator current estimate in the two-phase stationary coordinate system, and is the component of each coordinate axis of the rotor flux estimation value in the two-phase stationary coordinate system, Step S2, designing a variable speed reaching law function and a feedback gain matrix; the variable speed reaching law function is as follows: Where, D(δ)=m+(1+hm)e -η|δ| , 0<m<1, h>0, η>0, δ is the stator current error term and F(S) in formula (4) is designed as: From the analysis of formula (6), we can see that when the state variable is far away from the sliding surface, the absolute value of the stator current error is large, making e -η|δ| →0, then D(δ)=m, at this time the full-order sliding mode observer gain becomes K / m, since 0<m<1, the system converges very quickly at this time; when the state variable is close to the sliding mode surface, the absolute value of the stator current error is very small, making e -η|δ| →1, then D(δ)=1+h, at this time, the full-order sliding mode observer gain becomes K / (1+h), and 1+h>1, so the convergence speed of the system is slow at this time, and the full-order sliding mode observer gain is adaptively adjusted between K / m and K / (1+h); Step S3, designing an induction motor speed estimation method; Step S4, building an induction motor speed sensorless vector control system model; Step S5, adjusting observer parameters and controller parameters so that the control system performance indicators meet actual requirements.

2. The method for controlling an induction motor without a speed sensor based on a variable speed reaching law according to claim 1, characterized in that: In the step S1, a dynamic mathematical model of the induction motor in a two-phase stationary coordinate system is given, and a state equation is derived according to the mathematical model; The dynamic mathematical model of the induction motor in the two-phase stationary coordinate system is as follows: Voltage equation: Magnetic flux equation: In the formula, u sα ,u sβ ,u rα ,u rβ - are the voltage components of the stator and rotor on the corresponding axis in the αβ system respectively; i sα ,i sβ ,i rα ,i rβ - are the current components of the stator and rotor on the corresponding axis in the αβ system; ψ sα ,ψ sβ ,ψ rα ,ψ rβ - are the magnetic flux components of the stator and rotor on the corresponding axis in the αβ system respectively; ω r - rotor electrical angular velocity; R s - stator resistance; R r - rotor resistance; L s - stator inductance; L r -Rotor inductance; L m -Motor mutual inductance; The state equation obtained from the dynamic mathematical model of the induction motor is: In the ceremony, x = [i sα i sβ ψ rα ψ rβ ] T , y=[i sα i sβ ] T , u = [u sα u sβ 00] T , 3. The method for controlling an induction motor without a speed sensor based on a variable speed reaching law according to claim 2, characterized in that: In the step S2; According to the full-order sliding mode observer model, the error equation of the full-order sliding mode observer model is obtained: In formula (7), e ψrα and e ψrβ is the component of the rotor flux estimation error in each coordinate axis in the two-phase stationary coordinate system; The system output is the stator current, and the system output error term is used to construct the Lyapunov function: Derivation of formula (8) yields: Assumptions Since λ1<0, as well as Let g2 = 0, to ensure As long as formula (10) is established: According to the state equation in the two-phase stationary coordinate system shown in formula (3), the expression of the rotor flux is: When the system enters a steady state, the rotor flux expression is expressed as: When the system enters a steady state isα =e isβ =0, the feedback gain of the full-order sliding mode observer model is 0, and the full-order sliding mode observer model is consistent with the dynamic mathematical model of the induction motor. Therefore, the observed value of the rotor flux is expressed as: Subtracting equation (12) from equation (13), we can get the rotor flux observation error: Substituting formula (14) into formula (10), we get: Simplify the above formula to get the value range of g1 and g2: From formula (16), we can see that D(δ) is a bounded positive number, and the current error term in the inequality is also a bounded function. Therefore, as long as the absolute value of g1 is large enough and positive when g1 is selected, and g2 is 0, the derivative of V1 is negative. According to the Lyapunov stability theorem, the estimated current will converge to the actual current. when When , the error equation of the full-order sliding mode observer model in equation (7) is simplified to: Reconstruct a Lyapunov function: Derivative of formula (18) yields: From formula (17), we can get: Let g4 = 0. At the same time, substitute equation (20) into equation (19) to obtain: From the analysis of formula (21), we can see that as long as the following formula holds, the derivative of V2 is negative: From this we can get the value range of g3 and g4: Therefore, when g3 and g4 are given by equation (23), the derivative of V2 is negative, and according to the Lyapunov stability theorem, the system will be asymptotically stable; The variable speed reaching law function and feedback gain matrix are introduced into the full-order sliding mode observer model.

4. The method for controlling an induction motor without a speed sensor based on a variable speed reaching law according to claim 3, characterized in that: The specific process of step S3 includes: Step S3.1, define a Lyapunov function: In the formula, Step S3.2, derive equation (24), and substitute equation (9) and equation (19) into its derivative formula: According to Lyapunov theorem, the following equation holds true, and the system is stable: In step S3.3, the flux error term in equation (26) is ignored; in addition, the designed reaching law function is introduced into the speed estimation, and the PI controller is used to replace the gain and integral links, and finally the motor speed estimation method is obtained:

5. The method for controlling an induction motor without a speed sensor based on a variable speed reaching law according to claim 4, characterized in that: The specific process of step S4 includes: Step S4.1, sampling stator voltage u A ,u B ,u C and the stator current i A ,i B ,i C And through Clark transformation, the stator voltage and stator current are transformed to the two-phase stationary coordinate system. The transformation matrix is ​​C 3 / 2 : Step S4.2, the stator voltage u in the two-phase stationary coordinate system sα ,u sβ and the stator current i sα ,i sβ The estimated rotor flux is calculated by a full-order sliding mode observer and estimated speed Given an estimated rotor flux and estimated speed A closed loop is formed, and after adjustment by the PI regulator, the stator current given value in the rotating coordinate system is obtained. Step S4.3, the stator current i in the two-phase stationary coordinate system sα ,i sβ After Park transformation, it is transformed into the rotating coordinate system and compared with the stator current given value A closed loop is formed, and the stator voltage set value in the two-phase stationary coordinate system is obtained through the PI regulator. The transformation matrix is ​​C 2s / 2r : In formula (29), is the angle between the stationary coordinate system and the rotating coordinate system; Step S4.4, set the stator voltage in the rotating coordinate system to a given value After Park inverse transformation, it is transformed into a two-phase stationary coordinate system, and the stator voltage in the two-phase stationary coordinate system is Through SVPWM modulation, the control signal is output to control the opening and closing of the inverter power devices and control the stator side input of the induction motor.

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