A low-speed sensorless control method for an induction motor

Abstract

The application is suitable for the technical field of induction motor control, and provides a low-speed speed sensorless control method for an induction motor, which comprises the following steps: step 1, establishing a traditional and estimated back electromotive force model based on an inverse Γ model; step 2, reconstructing the traditional back electromotive force and a reduced-order flux linkage observer state equation by using virtual voltage; step 3, setting the virtual voltage amplitude to ensure that the estimated rotor flux linkage angle is constant; and step 4, decoupling the reconstructed state equation to a synchronous rotating coordinate system and combining a slip estimation module to obtain the rotor speed. The method solves the speed estimation divergence defect caused by the fact that the back electromotive force tends to zero at zero frequency in the traditional method, and enhances the stability and load capacity of the speed sensorless control system in the low-speed and zero synchronous frequency range.

Description

Technical Field

[0001] This invention belongs to the field of induction motor control technology, and particularly relates to a sensorless control method for low-speed induction motors. Background Technology

[0002] Induction motors are widely used in industrial manufacturing, rail transportation, home appliances, and new energy equipment due to their advantages such as simple structure, low manufacturing cost, reliable operation, and convenient maintenance. To achieve high-performance drive of induction motors, vector control technology is typically employed, which relies on precise rotor speed and flux linkage position information. Traditionally, rotor speed is obtained by installing mechanical speed sensors such as photoelectric encoders. However, the introduction of mechanical sensors not only increases system cost and size but also makes them prone to failure in harsh operating environments, reducing the overall reliability of the system. Therefore, sensorless control technology that estimates the rotational speed using algorithms based on the motor's electrical quantities has attracted widespread attention from academia and industry.

[0003] Currently, sensorless control methods for induction motors are mainly divided into signal injection methods based on motor anisotropy and fundamental wave model methods based on motor mathematical models. Signal injection methods inject high-frequency signals into the stator side of the motor, utilizing the motor's anisotropy to extract rotor speed, performing well at low speeds. However, since general-purpose squirrel-cage induction motors typically lack significant structural anisotropy, this method has poor versatility. In contrast, the fundamental wave model method based on the motor's mathematical model requires no additional physical signal injection, is independent of motor structure, and avoids torque ripple and noise problems caused by signal injection. It has stronger versatility and engineering practicality, and has become the mainstream method for medium- and high-speed sensorless control. However, the fundamental wave model method suffers from severe performance bottlenecks in extremely low-speed and zero-synchronous-frequency operating regions. When the induction motor operates at zero or low synchronous frequencies, the induced back electromotive force in the motor approaches zero. This makes it difficult for the observer based on the basic mathematical model to obtain effective feedback information, and the system's state variables lose observability. Within this unobservable region, the lack of continuous and effective excitation amplifies parameter mismatch or inverter nonlinearity errors, preventing the observer from accurately extracting rotor speed information. This leads to speed estimation divergence, ultimately causing instability in the entire motor control system. Therefore, overcoming the observability bottleneck of the model method at zero and low synchronous frequencies, solving the speed estimation divergence problem, and achieving stable operation of induction motors across a wide speed range are critical technical issues that urgently need to be addressed. Summary of the Invention

[0004] The purpose of this invention is to provide a sensorless control method for low-speed induction motors, aiming to solve the problems mentioned in the background art.

[0005] The present invention is implemented as follows: a sensorless control method for low-speed induction motors includes the following steps:

[0006] Step 1: Establish a traditional back EMF model and estimate the back EMF model based on the inverse Γ model;

[0007] Step 2: Design a virtual voltage injection scheme, use the virtual voltage introduced into the observer to reconstruct the traditional back electromotive force, and establish the reconstructed reduced-order flux observer state equation;

[0008] Step 3: Design the virtual voltage injection coefficient based on the virtual voltage injection scheme to set the injection amplitude of the virtual voltage, thereby ensuring that the estimated rotor flux angle of the motor remains unchanged;

[0009] Step 4: Decouple the reconstructed reduced-order flux observer state equation to the synchronous rotating coordinate system to obtain the synchronous speed equation and the d-axis flux equation. Combine this with the slip estimation module to obtain the estimated rotor speed, thereby ultimately realizing sensorless control of the induction motor and improving the system's zero-frequency stability and expanding its operating range.

[0010] A further technical solution is that, in step 1, the basic dynamic equation of the induction motor based on the inverse Γ model is:

[0011]

[0012]

[0013] In the formula, u s For the stator voltage vector, i s ψ is the stator current vector. R R is the rotor flux linkage vector; s L is the stator resistance. σ For equivalent leakage inductance, ω e Synchronous electric angular velocity; It is an orthogonal rotation matrix;

[0014] e is the traditional back electromotive force model, which is expressed as:

[0015]

[0016] Based on estimated rotor flux And estimate rotor speed Established back electromotive force estimation model for:

[0017]

[0018] In the formula, R R Let α be the equivalent rotor resistance, α be the reciprocal of the rotor time constant, and I be the identity matrix.

[0019] A further technical solution is that, in step 2, the virtual voltage u inj After being superimposed onto the internal input of the observer, the reconstructed back electromotive force e' is expressed as:

[0020]

[0021] Combining the reconstructed back EMF e' and the estimated back EMF model The reconstructed reduced-order flux observer state equation is:

[0022]

[0023] In the formula, Let g1 be the observer gain matrix, where g1 and g2 are the feedback gain parameters.

[0024] A further technical solution, in step 3, to ensure that the estimated rotor flux angle is not affected by the virtual voltage, in the two-phase stationary coordinate system, the estimated rotor flux expression of the reconstructed reduced-order flux observer state equation in the complex frequency domain is constrained as follows:

[0025]

[0026]

[0027] In the formula, and These are the components of the rotor flux linkage estimated along the α-axis and β-axis of the two-phase stationary shaft system, respectively. and To reconstruct the components of the back electromotive force e' along the α and β axes of the two-phase stationary axis system;

[0028] The estimated rotor flux angle obtained from this The expression constraints are:

[0029]

[0030] Under steady-state conditions and when the stator current frequency is zero, and considering that all feedback gain parameters are zero, how can the estimated rotor flux linkage angle be ensured without the injection of virtual voltage? Equally, the injection amplitudes of the virtual voltage along the d-axis and q-axis in the synchronously rotating dq coordinate system are specifically calculated as follows:

[0031]

[0032] In the formula, u dinj and u qinj These represent the injected components of the virtual voltage along the d-axis and q-axis, respectively. sd and u sqThese are the stator voltage components on the d-axis and q-axis, respectively; k is the injection coefficient of the virtual voltage.

[0033] A further technical solution, in step 4, is to decouple the d-axis flux linkage equation and the synchronous rotational speed equation in the synchronous rotating dq coordinate system as follows:

[0034]

[0035] In the formula, each back electromotive force component is expressed as:

[0036]

[0037]

[0038]

[0039] In the formula, i sd and i sq These represent the stator current components along the d-axis and q-axis, respectively. To estimate the d-axis component of the rotor flux linkage, L M For magnetizing inductance, To estimate the d-axis components of the back electromotive force model, and These are the components of the back electromotive force along the d-axis and q-axis, respectively.

[0040] Finally, extract the estimated rotor speed. The equation for the low-pass filter is:

[0041]

[0042] In the formula, α0 is the bandwidth of the low-pass filter.

[0043] Finally, the estimated rotor speed is obtained by solving the equation.

[0044] The sensorless low-speed control method for an induction motor provided in this invention has the following advantages:

[0045] This method establishes a traditional back EMF model and an estimated back EMF model based on the inverse Γ model. A virtual voltage injection scheme is designed, utilizing a virtual voltage introduced into the observer to reconstruct the traditional back EMF and establish the reconstructed reduced-order flux observer state equation. Based on the virtual voltage injection scheme, virtual voltage injection coefficients are designed to set the injection amplitude to ensure angle invariance. Finally, the system is decoupled to a synchronous rotating coordinate system to extract the d-axis flux equation and output the estimated rotational speed. The proposed method, through local weak observability analysis, confirms that the system is observable at extremely low speeds and zero synchronization frequencies. It overcomes the inherent defect of the traditional fundamental wave model method, which causes speed estimation divergence due to the back EMF approaching zero, thereby enhancing the system stability and load-carrying capacity of the sensorless control system in the low-speed and zero-synchronization frequency range. Attached Figure Description

[0046] Figure 1 This is an overall system control block diagram of a sensorless low-speed control method for an induction motor provided in an embodiment of the present invention;

[0047] Figure 2 The experimental waveforms of the motor decelerating from 200 r / min to 0 r / min using the traditional reduced-order flux observer method when the motor is running at 32% excitation and no load;

[0048] Figure 3 The experimental waveform diagram shows the motor deceleration from 200 r / min to 0 r / min using this method when the motor is running at 32% excitation and no load.

[0049] Figure 4 The experimental waveforms show the reduction speed of the motor from 200 r / min to 80 r / min using the traditional reduced-order flux observer method when the motor is running at 100% excitation and no load.

[0050] Figure 5 The experimental waveform diagram shows the motor decelerating from 200 r / min to -120 r / min using this method when the motor is running at 100% excitation and 60% rated load. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0052] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.

[0053] like Figure 1 The image shows a sensorless control method for low-speed induction motors according to an embodiment of the present invention. Figure 1The system mainly includes a reconstructed reduced-order flux linkage observer module, a back EMF estimation module, and a slip estimation module. During execution, the system first introduces a virtual voltage signal into the internal input of the reduced-order flux linkage observer module to reconstruct the back EMF; then, it sets the injection amplitude of the virtual voltage; finally, it decouples the reconstructed reduced-order flux linkage observer state equation to a synchronous rotating coordinate system, obtaining the synchronous speed equation and the d-axis flux linkage equation, and combines this with the slip estimation module to finally obtain the estimated rotor speed. This invention integrates the advantages of signal injection and model-based approaches in sensorless control, breaking through the traditional physical motor-side injection thinking. It innovatively introduces an additional virtual voltage input signal directly into the reduced-order flux linkage observer at the software algorithm level. This virtual voltage signal acts as an excitation similar to real physical signal injection within the algorithm, greatly improving the observability and signal-to-noise ratio of the observer at zero synchronization frequency and extremely low speed conditions, while avoiding the high-frequency noise, additional losses, and dependence on motor spatial anisotropy caused by actual physical injection, thus achieving a unity of the advantages of both methods.

[0054] The sensorless low-speed control method for the induction motor specifically includes the following steps:

[0055] Step 1: Establish a traditional back EMF model and estimate the back EMF model based on the inverse Γ model.

[0056] The basic dynamic equation of an induction motor based on the inverse Γ model is:

[0057]

[0058]

[0059] In the formula, u s For the stator voltage vector, i s ψ is the stator current vector. R R is the rotor flux linkage vector; s L is the stator resistance. σ For equivalent leakage inductance, ω e Synchronous electric angular velocity; It is an orthogonal rotation matrix;

[0060] e is the traditional back electromotive force model, which is expressed as:

[0061]

[0062] Based on estimated rotor flux And estimate rotor speed Established back electromotive force estimation model for:

[0063]

[0064] In the formula, R R Let α be the equivalent rotor resistance, α be the reciprocal of the rotor time constant, and I be the identity matrix.

[0065] Step 2: Design a virtual voltage injection scheme, use the virtual voltage introduced into the observer to reconstruct the traditional back electromotive force, and establish the reconstructed reduced-order flux observer state equation.

[0066] Virtual voltage u inj After being superimposed onto the internal input of the observer, the reconstructed back electromotive force e' is expressed as:

[0067]

[0068] Combining the reconstructed back EMF e' and the estimated back EMF model The reconstructed reduced-order flux observer state equation is:

[0069]

[0070] In the formula, Let g1 be the observer gain matrix, where g1 and g2 are the feedback gain parameters.

[0071] Step 3: Design the virtual voltage injection coefficient based on the virtual voltage injection scheme to set the injection amplitude of the virtual voltage, thereby ensuring that the estimated rotor flux angle of the motor remains unchanged.

[0072] To ensure that the estimated rotor flux angle is not affected by the virtual voltage, the estimated rotor flux expression of the reconstructed reduced-order flux observer state equation in the complex frequency domain is constrained as follows:

[0073]

[0074]

[0075] In the formula, and These are the components of the rotor flux linkage estimated along the α-axis and β-axis of the two-phase stationary shaft system, respectively. and To reconstruct the components of the back electromotive force e' along the α and β axes of the two-phase stationary axis system;

[0076] The estimated rotor flux angle obtained from this The expression constraints are:

[0077]

[0078] Under steady-state conditions and when the stator current frequency is zero, and considering that all feedback gain parameters are zero, how can the estimated rotor flux linkage angle be ensured without the injection of virtual voltage? Equally, the injection amplitudes of the virtual voltage along the d-axis and q-axis in the synchronously rotating dq coordinate system are specifically calculated as follows:

[0079]

[0080] In the formula, u dinj and u qinj These represent the injected components of the virtual voltage along the d-axis and q-axis, respectively. sd and u sq These are the stator voltage components on the d-axis and q-axis, respectively; k is the injection coefficient of the virtual voltage.

[0081] Step 4: Decouple the reconstructed reduced-order flux observer state equation to the synchronous rotating coordinate system to obtain the synchronous speed equation and the d-axis flux equation. Combine this with the slip estimation module to obtain the estimated rotor speed, thereby ultimately realizing sensorless control of the induction motor and improving the system's zero-frequency stability and expanding its operating range.

[0082] The d-axis flux linkage equation and synchronous rotation speed equation decoupled to the synchronous rotating dq coordinate system are as follows:

[0083]

[0084] In the formula, each back electromotive force component is expressed as:

[0085]

[0086]

[0087]

[0088] In the formula, i sd and i sq These represent the stator current components along the d-axis and q-axis, respectively. To estimate the d-axis component of the rotor flux linkage, L M For magnetizing inductance, To estimate the d-axis components of the back electromotive force model, and These represent the components of the reconstructed back electromotive force along the d-axis and q-axis, respectively.

[0089] Finally, extract the estimated rotor speed. The equation for the low-pass filter is:

[0090]

[0091] In the formula, α0 is the bandwidth of the low-pass filter.

[0092] Finally, the estimated rotor speed is obtained by solving the equation.

[0093] To further verify the beneficial effects of the present invention, a specific embodiment is described below:

[0094] The experiment was validated on an induction motor-driven test platform. A 2.2 kW control induction motor and a load induction motor were coaxially connected, with the load induction motor providing the load torque. The main parameters of the control induction motor used were: rated voltage 380 V, rated current 5.36 A, rated torque 22.35 N∙m, rated speed 940 r / min, stator resistance 2.011 Ω, rotor resistance 1.667 Ω, magnetizing inductance 0.2450 H, stator and rotor self-inductance 0.2564 H, and number of pole pairs 3. The virtual voltage injection factor was set to 0.7.

[0095] Figure 2 The figure shows the operating results under 32% excitation and no-load conditions, using a traditional reduced-order flux observer, with the speed setpoint reduced from 200 r / min to 0 r / min. It can be observed that when the speed decreases to 10 r / min, the estimated rotor speed exhibits slight oscillations but remains stable. When the speed decreases to the critical point of 0 r / min, the observer loses observability, causing the speed estimate to completely diverge. The motor generates high-frequency current noise, and both the current and the actual speed increase rapidly, ultimately leading to system collapse and instability.

[0096] Figure 3 The figure shows the operating results of the speed setpoint being reduced from 200 r / min to 0 r / min under the condition of 32% excitation and no load using this method. Thanks to the existence of the virtual voltage inside the algorithm, the observer can operate normally at both 10 r / min and 0 r / min, successfully suppressing the zero-frequency divergence phenomenon. The estimated speed and the actual current are kept within a controllable range, and the system has achieved critical stable operation.

[0097] Figure 4 The figure shows the operating results under 100% excitation and no-load conditions, using a traditional reduced-order flux observer, with the speed setpoint reduced from 200 r / min to 80 r / min. It can be observed that due to the increased nonlinearity of the magnetic circuit, the system has already diverged violently when the speed is reduced to 80 r / min, and it is impossible to continue to reduce the speed or increase the load, otherwise it will lead to system instability.

[0098] Figure 5The results show the operating conditions under 100% excitation and 60% rated load (speed setpoint reduced from 200 r / min to -120 r / min) when using this method. Under these conditions, the speed estimation remained consistent, successfully achieving zero-frequency ride-through and avoiding the fluctuation issues present when operating at 0 r / min with 32% excitation. Although the introduction of the virtual voltage caused a slight discrepancy between the actual and estimated speeds under load, the maximum speed estimation error measured at the worst-case zero-frequency condition was only 16 r / min, with both current and speed remaining within a completely controllable and safe range. Compared to traditional reduced-order flux observers, the proposed method successfully solves the speed estimation divergence problem at zero synchronization frequency and significantly improves the load-carrying capacity in the ultra-low speed domain while ensuring system stability, achieving stable zero-frequency operation under 60% rated load.

[0099] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A sensorless control method for low-speed induction motors, characterized in that, Includes the following steps: Step 1: Establish a traditional back EMF model and estimate the back EMF model based on the inverse Γ model; Step 2: Design a virtual voltage injection scheme, use the virtual voltage introduced into the observer to reconstruct the traditional back electromotive force, and establish the reconstructed reduced-order flux observer state equation; Step 3: Design the virtual voltage injection coefficient based on the virtual voltage injection scheme to set the injection amplitude of the virtual voltage, thereby ensuring that the estimated rotor flux angle of the motor remains unchanged; Step 4: Decouple the reconstructed reduced-order flux observer state equation to the synchronous rotating coordinate system to obtain the synchronous speed equation and the d-axis flux equation. Combine this with the slip estimation module to obtain the estimated rotor speed, thereby ultimately realizing sensorless control of the induction motor and improving the system's zero-frequency stability and expanding its operating range.

2. The sensorless low-speed control method for an induction motor according to claim 1, characterized in that, In step 1, the basic dynamic equation of the induction motor based on the inverse Γ model is: ； ； In the formula, u s For the stator voltage vector, i s ψ is the stator current vector. R R is the rotor flux linkage vector; s L is the stator resistance. σ For equivalent leakage inductance, ω e Synchronous electric angular velocity; It is an orthogonal rotation matrix; e is the traditional back electromotive force model, which is expressed as: ； Based on estimated rotor flux And estimate rotor speed Established back electromotive force estimation model for: ； In the formula, R R Let α be the equivalent rotor resistance, α be the reciprocal of the rotor time constant, and I be the identity matrix.

3. The sensorless low-speed control method for an induction motor according to claim 2, characterized in that, In step 2, the virtual voltage u inj After being superimposed onto the internal input of the observer, the reconstructed back electromotive force e' is expressed as: ； Combining the reconstructed back EMF e' and the estimated back EMF model The reconstructed reduced-order flux observer state equation is: ； In the formula, Let g1 be the observer gain matrix, where g1 and g2 are the feedback gain parameters.

4. The sensorless low-speed control method for an induction motor according to claim 3, characterized in that, In step 3, to ensure that the estimated rotor flux angle is not affected by the virtual voltage, the estimated rotor flux expression of the reconstructed reduced-order flux observer state equation in the complex frequency domain is constrained as follows: ； ； In the formula, and These are the components of the rotor flux linkage estimated along the α-axis and β-axis of the two-phase stationary shaft system, respectively. and To reconstruct the components of the back electromotive force e' along the α-axis and β-axis of the two-phase stationary axis system; The estimated rotor flux angle obtained from this The expression constraints are: ； Under steady-state conditions and when the stator current frequency is zero, and considering that all feedback gain parameters are zero, how can the estimated rotor flux linkage angle be ensured without the injection of virtual voltage? Equally, the injection amplitudes of the virtual voltage along the d-axis and q-axis in the synchronously rotating dq coordinate system are specifically calculated as follows: ； In the formula, u dinj and u qinj These represent the injected components of the virtual voltage along the d-axis and q-axis, respectively. sd and u sq These are the stator voltage components on the d-axis and q-axis, respectively; k is the injection coefficient of the virtual voltage.

5. The sensorless low-speed control method for an induction motor according to claim 4, characterized in that, In step 4, the d-axis flux linkage equation and synchronous rotation speed equation decoupled to the synchronous rotating dq coordinate system are specifically as follows: ； In the formula, each back electromotive force component is expressed as: ； ； ； In the formula, i sd and i sq These represent the stator current components along the d-axis and q-axis, respectively. To estimate the d-axis component of the rotor flux linkage, L M For magnetizing inductance, To estimate the d-axis component of the back electromotive force model, and These represent the components of the reconstructed back electromotive force along the d-axis and q-axis, respectively. Finally, extract the estimated rotor speed. The equation for the low-pass filter is: ； In the formula, α0 is the bandwidth of the low-pass filter; Finally, the estimated rotor speed is obtained by solving the equation.

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