PMSM position sensorless control system with improved SMO

Abstract

The invention relates to the technical field of permanent magnet synchronous motor control, and discloses a PMSM position sensorless control system with an improved SMO. An SMO module is improved; a second-order low-pass filter module; a position / rotating speed extraction module; a PI controller module; and an inverter module. According to the invention, a novel approach rate is designed, the approach gain can be dynamically adjusted according to system errors, and adaptive balance of acceleration approach in case of large errors and chattering suppression in case of small errors is realized; a saturation function easy to realize is adopted as a control switching function, buffeting during system control is reduced, and the control precision is improved; an integral sliding mode surface is adopted to replace a traditional sliding mode surface, the influence of stator resistance is eliminated, and the convergence speed and parameter disturbance resistance of a control system are improved; and a second-order low-pass filter is adopted, so that useless high-frequency interference signals can be attenuated more quickly, high-frequency noise can be filtered more thoroughly, and the estimation precision is improved.

Description

A sensorless control system for PMSM with improved SMO Technical Field

[0001] This invention relates to the field of permanent magnet synchronous motor control technology, and more specifically, to an improved SMO-based PMSM sensorless control system. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) rely on sensors such as encoders or resolvers mounted on the motor shaft to obtain precise rotor position information, which brings several drawbacks. The installation of sensors increases the axial dimension and size of the motor, and requires the design of additional auxiliary circuitry and interfaces, increasing system complexity and cost. The sensor signal wiring is highly susceptible to external electromagnetic interference in complex industrial environments, leading to unstable data transmission and reduced reliability of the entire control system. In extreme environments, the performance and lifespan of mechanical sensors can be severely affected, limiting the motor's application range.

[0003] Sensorless control solutions can be broadly categorized into two technical approaches based on their applicable speed range: one is the high-frequency injection method, suitable for the zero-speed and low-speed range; the other is the back-EMF estimation method, suitable for the medium-speed and high-speed range. Back-EMF estimation methods mainly include the sliding mode observer method, the model reference adaptive method, and the extended Kalman filter method.

[0004] Among these, the sliding mode observer (SMO) is relatively simple, insensitive to motor parameter disturbances, and exhibits excellent dynamic performance. However, its traditional form suffers from significant chattering. Common methods to address chattering include the boundary layer method, which uses a continuous function to approximate the sign function; or higher-order sliding mode methods, which are complex to design and difficult to tune the gain. Another approach is disturbance compensation, which estimates and compensates for disturbances to reduce switching gain, but this method is structurally complex and computationally intensive.

[0005] Therefore, improvements to the SMO are needed to enhance the control performance of the PMSM control system. Summary of the Invention

[0006] To achieve the above objectives, this application provides a sensorless control system for a PMSM with an improved SMO (Slip Mode Optimization) architecture, comprising: a current sampling module for acquiring three-phase current and converting it into a stationary coordinate system current; an improved SMO module for constructing an integral sliding mode surface based on the stationary coordinate system current and calculating an adaptive approach rate; a second-order low-pass filter module for filtering the adaptive approach rate and obtaining the back electromotive force (EMF); a position / speed extraction module for estimating the rotor position and speed based on the back EMF, and obtaining the estimated speed; a PI controller module for generating a q-axis voltage based on the estimated speed; and an inverter module for performing sensorless vector control based on the q-axis voltage.

[0007] Furthermore, the improved SMO module includes: a current error calculation unit: calculating the current error based on the current in the stationary coordinate system; an adaptive approach rate unit: used to achieve an adaptive balance by dynamically adjusting the approach gain based on the current error, accelerating the approach when the error is large and suppressing chattering when the error is small; a control switching function unit: used to reduce chattering and improve control accuracy; and an integral sliding surface unit: used to construct an integral sliding surface based on the current error to eliminate the influence of the stator resistance.

[0008] Furthermore, the expression for the adaptive approach rate unit is: In the formula: For adaptive approach rate; It is a symbolic function; The gain function varies with time; Basic gain; This is the error adaptive term; This refers to system state error; The smoothness coefficient; It is a differential operator in time-domain computation.

[0009] Furthermore, the control switching function unit supports easily implemented saturation functions, specifically: In the formula: It is a symbolic function; This is the gain coefficient; For boundary layer.

[0010] Furthermore, the expression for the integral sliding surface element is: In the formula: , They are respectively , Sliding surface on the shaft; , These are the observed values ​​of the stator current. , This is the actual value of the stator current; Stator resistance; It is the stator inductor.

[0011] Furthermore, the control rate of the improved SMO module is: In the formula: , For the control input of the observer; Basic gain; This is the error adaptive term; This refers to system state error; The smoothness coefficient; This is the switching function; , They are respectively , Sliding surface on the shaft.

[0012] Furthermore, the overall transfer function of the second-order low-pass filter module is: In the formula: The total transfer function; This is the transfer function of the previous low-pass filter; This is the transfer function of the next low-pass filter; This is the cutoff frequency of the previous low-pass filter; This is the cutoff frequency of the next low-pass filter; It is a differential operator in time-domain computation.

[0013] Furthermore, the method for constructing the improved SMO module includes the following steps: S101, establishing a mathematical model of the permanent magnet synchronous motor; S102, designing the approach rate and control switching function; S103, defining the integral sliding surface; S104, constructing the improved SMO module based on the mathematical model of the permanent magnet synchronous motor, the approach rate, the control switching function, and the integral sliding surface.

[0014] Furthermore, the acquisition of back EMF includes the following steps: S201, the current sampling module collects the three-phase current and converts the three-phase current into a stationary coordinate system current; S202, the improved SMO module calculates the adaptive approach rate based on the stationary coordinate system current; S203, the second-order low-pass filter module filters the back EMF to obtain a smoothed back EMF.

[0015] Furthermore, the sensorless vector control includes the following steps: S301, the position / speed extraction module estimates the position and speed based on the smoothed back electromotive force, and obtains the estimated speed; S302, the PI controller module generates the q-axis voltage based on the estimated speed, and the inverter module inversely transforms the q-axis voltage to complete the sensorless vector control.

[0016] The beneficial effects of this invention are as follows: a novel approach rate is designed, which can dynamically adjust the approach gain according to the system error, achieving an adaptive balance of accelerating approach under large errors and suppressing chattering under small errors; an easily implemented saturation function is used as the control switching function to reduce chattering and improve control accuracy during system control; an integral sliding surface is used instead of the traditional sliding surface to eliminate the influence of stator resistance and improve the convergence speed and anti-parameter disturbance capability of the control system; a second-order low-pass filter is used to attenuate useless high-frequency interference signals faster, filter out high-frequency noise more thoroughly, and improve estimation accuracy. Attached Figure Description

[0017] Figure 1 is a schematic diagram of the system structure provided in an embodiment of the present invention; Figure 2 is a schematic diagram of the saturation function provided in an embodiment of the present invention; Figure 3 is a flowchart of constructing the improved SMO module provided in an embodiment of the present invention; Figure 4 is a schematic diagram of the system operation principle provided in an embodiment of the present invention; Figure 5 is a schematic diagram of the speed change of the traditional SMO provided in an embodiment of the present invention; Figure 6 is a schematic diagram of the speed change of the improved SMO provided in an embodiment of the present invention; Figure 7 is a schematic diagram of the speed error of the traditional SMO provided in an embodiment of the present invention; Figure 8 is a schematic diagram of the speed error of the improved SMO provided in an embodiment of the present invention. Detailed Implementation

[0018] The specific implementation of the present invention will now be described in detail with reference to the accompanying drawings.

[0019] As shown in Figure 1, the present invention provides an improved SMO (Stationary Motion Module) PMSM (Position-Based Module) sensorless control system, comprising: a current sampling module for acquiring three-phase current and converting the three-phase current into a stationary coordinate system current; the current sampling module acquires three-phase current. , , The current is converted to a stationary coordinate system using Clark transformation, and its specific expression is as follows: In the formula: , , It is a three-phase current. , This is the stator current.

[0020] Improved SMO module: used to construct an integral sliding mode surface based on the current in the stationary coordinate system and calculate the adaptive approach rate; the improved SMO module includes: a current error calculation unit: calculating the current error based on the current in the stationary coordinate system; the expression for calculating the current error based on the current in the stationary coordinate system is: In the formula: , These are the observed values ​​of the stator current. , This is the actual value of the stator current.

[0021] Adaptive approach rate unit: used to achieve adaptive balance by dynamically adjusting the approach gain according to the current error, accelerating the approach when the error is large and suppressing chattering when the error is small; the traditional SMO control algorithm uses a constant speed approach rate for the switching function. Since there is a sign function in the system, this will reduce the system stability and produce obvious chattering.

[0022] This system designs a novel approach rate that can dynamically adjust the approach gain according to the system error, achieving an adaptive balance of accelerating approach when there is a large error and suppressing chattering when there is a small error.

[0023] Specifically, the expression for the adaptive approach rate unit is: In the formula: For adaptive approach rate; It is a symbolic function; The gain function varies with time; Basic gain; This is the error adaptive term; This refers to system state error; The smoothness coefficient; It is a differential operator in time-domain computation.

[0024] When the system is far from the sliding surface, i.e., the state error at this point... Larger, increase At this point, the system gain increases, causing the control system to converge to the sliding surface more quickly. When the system is close to the sliding surface, i.e., at this point, the error... Smaller, decrease At this point, the gain of the control system decreases, which can suppress the attenuation of chattering; when the system is near the sliding surface, i.e. This can maintain the system's stable operation and suppress high-frequency switching.

[0025] Control switching function unit: used to reduce chattering and improve control accuracy; in practical applications, the sliding mode switching function of traditional sliding mode observers often adopts a sign function; however, due to the limitations of system inertia and switching characteristics, this method has a delay in position and velocity estimation, which leads to increased estimation error and chattering phenomenon.

[0026] As shown in Figure 2, in order to reduce chattering and improve control accuracy, this system uses an easily implemented saturation function as the control switching function, specifically: In the formula: It is a symbolic function; This is the gain coefficient; For boundary layer.

[0027] If the boundary layer is too small, the chattering reduction effect is not significant; if the boundary layer is too large, the discrete structure of the observer will be destroyed. Only by reasonably selecting the boundary layer can a better reduction effect be achieved.

[0028] Integral sliding surface element: used to construct an integral sliding surface based on current error to eliminate the influence of stator resistance.

[0029] Traditional SMOs typically use the difference between the observed and actual values ​​of the stator current as the sliding surface, which cannot eliminate the influence of stator resistance on the sliding surface observer.

[0030] To eliminate the influence of stator resistance, this system uses an integral sliding surface instead of a traditional sliding surface.

[0031] Specifically, the expression for the integral sliding surface element is: In the formula: , They are respectively , Sliding surface on the shaft; , These are the observed values ​​of the stator current. , This is the actual value of the stator current; Stator resistance; It is the stator inductor.

[0032] The control rate of the improved SMO module can be obtained as follows: In the formula: , For the control input of the observer; Basic gain; This is the error adaptive term; This refers to system state error; The smoothness coefficient; This is the switching function; , They are respectively , Sliding surface on the shaft.

[0033] When the observer's state variables reach the sliding surface At this time, the control quantity can be regarded as the equivalent control quantity, and the estimated value of the back electromotive force can be obtained as follows: In the formula: , They are respectively , Estimated back electromotive force of the shaft; Basic gain; This is the error adaptive term; This refers to system state error; The smoothness coefficient; , They are respectively , Sliding surface on the shaft.

[0034] Among them, the basic gain Used to ensure basic robustness, smoothness coefficient The value range is from 0.1 to 1.

[0035] The stator current state error equation is: In the formula: , These are the observed values ​​of the stator current; Stator resistance; For stator inductance; , To extend the back electromotive force; Basic gain; This is the error adaptive term; This refers to system state error; The smoothness coefficient; , They are respectively , Sliding surface on the shaft; This is the switching function.

[0036] Similarly, base gain Used to ensure basic robustness, smoothness coefficient The value range is from 0.1 to 1.

[0037] The second-order low-pass filter module is used to filter the adaptive approach rate to obtain the back electromotive force (EMF). In traditional SMOs, the back EMF is obtained by filtering out higher harmonics using a first-order low-pass filter. However, in reality, a single low-pass filter can only remove some higher harmonics, and the final result still cannot accurately estimate the rotor position information, leaving residual errors. Moreover, compared to the first-order low-pass filter, the second-order low-pass filter has a narrower transition band, allowing useless high-frequency interference signals to attenuate faster and filtering out high-frequency noise more thoroughly. When calculating rotor position and speed, the second-order low-pass filter significantly improves the estimation accuracy compared to the traditional first-order filter.

[0038] Specifically, the overall transfer function of the second-order low-pass filter module is: In the formula: The total transfer function; This is the transfer function of the previous low-pass filter; This is the transfer function of the next low-pass filter; This is the cutoff frequency of the previous low-pass filter; This is the cutoff frequency of the next low-pass filter; It is a differential operator in time-domain computation.

[0039] The filtered back electromotive force can be obtained. , The equation is: In the formula: , This is the filtered back electromotive force; This is the cutoff frequency of the previous low-pass filter; This is the cutoff frequency of the next low-pass filter; For differential operators in time-domain computation; , This is the control input for the observer.

[0040] Position / Speed ​​Extraction Module: Used to estimate the rotor position and speed based on the back electromotive force, and obtain the estimated speed; PI Controller Module: Used to generate q-axis voltage based on the estimated speed; Inverter Module: Used to complete sensorless vector control based on the q-axis voltage.

[0041] As shown in Figure 3, the method for constructing the improved SMO module includes the following steps: S101, establishing a mathematical model of the permanent magnet synchronous motor; In the process of analyzing the PMSM, in order to simplify the analysis, the following assumptions are made: 1. The induced electromotive force generated by the armature winding changes sinusoidally; 2. The stator core magnetic circuit does not experience saturation; 3. The inductance and resistance of the stator winding remain basically unchanged during the operation of the motor; 4. Core eddy currents and hysteresis losses are neglected.

[0042] In this embodiment, a surface-mounted PMSM is taken as the research object, and a mathematical model in a two-phase stationary coordinate system is established: In the formula: , The stator voltage is respectively at , The components of the axis; , For stator current in , The amount; Stator resistance; For stator inductance; , To extend the back electromotive force.

[0043] In the formula: Electric angular velocity; It is an electrical angle; For use of permanent magnet magnetic flux.

[0044] As can be seen from the above formula, the back electromotive force of the PMSM includes information on the motor speed and rotor position.

[0045] S102, Design the approach rate and control switching function; In the traditional SMO control algorithm, the switching function uses the constant velocity approach rate. Since there is a sign function in the system, this will reduce the system stability and produce obvious chattering.

[0046] By designing a novel approach rate, the approach gain can be dynamically adjusted according to the system error, achieving an adaptive balance that accelerates approach when there is a large error and suppresses chattering when there is a small error.

[0047] In this embodiment, the expression for the convergence rate is: In the formula: For adaptive approach rate; It is a symbolic function; The gain function varies with time; Basic gain; This is the error adaptive term; This refers to system state error; The smoothness coefficient; It is a differential operator in time-domain computation.

[0048] When the system is far from the sliding surface, i.e., the state error at this point... Larger, increase At this point, the system gain increases, causing the control system to converge to the sliding surface more quickly. When the system is close to the sliding surface, i.e., at this point, the error... Smaller, decrease At this point, the gain of the control system decreases, which can suppress the attenuation of chattering; when the system is near the sliding surface, i.e. This can maintain the system's stable operation and suppress high-frequency switching.

[0049] In practical applications, traditional sliding mode observers often use sign functions for their sliding mode switching functions; however, due to limitations in system inertia and switching characteristics, this method suffers from delays in position and velocity estimation, leading to increased estimation errors and chattering.

[0050] In this embodiment, to reduce chattering and improve control accuracy, an easily implemented saturation function is used as the control switching function, specifically: In the formula: It is a symbolic function; This is the gain coefficient; For boundary layer.

[0051] If the boundary layer is too small, the chattering reduction effect is not significant; if the boundary layer is too large, the discrete structure of the observer will be destroyed. Only by reasonably selecting the boundary layer can a better reduction effect be achieved.

[0052] S103. Define the integral sliding surface; Traditional SMOs generally use the difference between the observed and actual values ​​of the stator current as the sliding surface, which cannot eliminate the influence of the stator resistance on the sliding observer.

[0053] In this embodiment, to eliminate the influence of stator resistance, an integral sliding surface is used instead of a traditional sliding surface.

[0054] Specifically, the expression for the integral sliding surface element is: In the formula: , They are respectively , Sliding surface on the shaft; , These are the observed values ​​of the stator current. , This is the actual value of the stator current; Stator resistance; It is the stator inductor.

[0055] S104. Based on the mathematical model of permanent magnet synchronous motor, the approach rate, the control switching function, and the integral sliding surface, an improved SMO module is constructed.

[0056] Based on steps S1 to S3, the control rate of the improved SMO module in this embodiment is: In the formula: , For the control input of the observer; Basic gain; This is the error adaptive term; This refers to system state error; The smoothness coefficient; This is the switching function; , They are respectively , Sliding surface on the shaft.

[0057] Figure 4 illustrates the principle of sensorless vector control achieved by improving the SMO module.

[0058] Specifically, the sensorless vector control includes the following steps: S201, the current sampling module collects the three-phase current and converts the three-phase current into a stationary coordinate system current; in this embodiment, converting the three-phase current into a stationary coordinate system current yields: In the formula: , , It is a three-phase current. , This is the stator current.

[0059] S202, the improved SMO module calculates the adaptive approach rate based on the current in the stationary coordinate system; the current error can be calculated based on the current in the stationary coordinate system. In the formula: , These are the observed values ​​of the stator current. , This is the actual value of the stator current.

[0060] Then, the integral sliding surface is calculated to obtain , Thus, the back electromotive force can be estimated. .

[0061] The S203 second-order low-pass filter module filters the back EMF to obtain a smoothed back EMF.

[0062] Estimating the back electromotive force The input is processed by a second-order low-pass filter module, and the output is a smooth back electromotive force. .

[0063] The operation of the position / speed extraction module, PI controller module, and inverter module includes: S301, the position / speed extraction module estimates the position and speed based on the smoothed back electromotive force to obtain the estimated speed; the position / speed extraction module then estimates the rotor position at this time to obtain the estimated angle. ,in This is the phase compensation angle, used to correct filter delay.

[0064] Then through the The rotational speed is estimated by performing differentiation and filtering. The S302 PI controller module generates the q-axis voltage based on the estimated rotational speed, and the inverter module inversely transforms the q-axis voltage to complete sensorless vector control.

[0065] Will With reference speed The comparison is performed, and the q-axis voltage is generated by the PI controller module. Then, after passing through the Park inverse converter and the SVPWM module to drive the inverter, sensorless vector control is completed.

[0066] This invention provides an improved sensorless control system for a permanent magnet synchronous motor (PMSM) based on a SMO (Self-Modulating Motor). It constructs an adaptive approach rate, enabling intelligent adjustment to achieve rapid convergence when errors are large and suppress chattering when errors are small. Simultaneously, it softens the control signal by replacing the sign function with a saturation function and introduces an integral sliding surface to enhance convergence speed and resistance to parameter disturbances. This improves the dynamic response speed, tracking accuracy, and anti-interference capability of the sensorless control system for permanent magnet synchronous motors in speed and position estimation.

[0067] In this embodiment, a simulation experiment of a sensorless control system for a modified SMO PMSM was conducted using MATLAB / Simulink. The motor was started under no-load conditions, and the reference speed was set to 600 rpm. At a simulation time of 0.05s, the rotational speed was increased to 1200. Add 7 at 0.15s The load torque was measured, and the simulation time was 0.2s.

[0068] The corresponding motor parameters are shown in the table below:

[0069] The simulation results are shown in Figures 5 to 8. It can be seen that the control system proposed in this application has a faster response speed and converges to the target speed more quickly when the motor is starting at low speed, and the overshoot is small.

[0070] It can return to its original speed and stabilize at the target speed more quickly after a load is applied, even within 0.1 seconds. Compared to other control systems, it exhibits less fluctuation.

[0071] The comparison charts from the simulation experiments show that the improved SMO PMSM sensorless control system proposed in this application has better speed tracking, faster system response, lower speed error, better suppression of chattering, and can quickly react to and approach stability in the face of external disturbances.

[0072] Compared to other control systems or methods, it converges faster and has better control performance.

[0073] This invention uses a more effective switching function, which improves the chatter suppression effect and robustness of the control system; the adaptive approach rate can dynamically adjust the approach gain according to the system error, achieving an adaptive balance of accelerating the approach when the error is large and suppressing chatter when the error is small; at the same time, the entire control system has a simple structure and strong robustness.

[0074] The above-disclosed embodiments are merely a few specific examples of the present invention. However, the present invention is not limited thereto, and any variations that can be conceived by those skilled in the art should fall within the protection scope of the present invention.

Claims

1. An improved SMO-based PMSM sensorless control system, characterized in that, include: Current sampling module: used to collect three-phase current and convert the three-phase current into current in a stationary coordinate system; Improved SMO module: used to construct an integral sliding mode surface based on the current in the stationary coordinate system and calculate the adaptive approach rate; Second-order low-pass filter module: used to filter the adaptive approach rate and obtain the back electromotive force; Position / speed extraction module: used to estimate the rotor position and speed based on the back electromotive force and obtain the estimated speed; PI controller module: used to generate the q-axis voltage based on the estimated speed; Inverter module: used to complete sensorless vector control based on the q-axis voltage.

2. The PMSM sensorless control system according to claim 1, characterized in that, The improved SMO module includes: a current error calculation unit: calculating the current error based on the current in the stationary coordinate system; an adaptive approach rate unit: used to dynamically adjust the approach gain based on the current error, accelerating the approach when the error is large and suppressing chattering when the error is small; a control switching function unit: used to reduce chattering and improve control accuracy; and an integral sliding surface unit: used to construct an integral sliding surface based on the current error to eliminate the influence of stator resistance.

3. The PMSM sensorless control system according to claim 2, characterized in that, The expression for the adaptive approach rate unit is: In the formula: For adaptive approach rate; It is a symbolic function; The gain function varies with time; Basic gain; This is the error adaptive term; This refers to system state error; The smoothness coefficient; It is a differential operator in time-domain computation.

4. The PMSM sensorless control system according to claim 2, characterized in that, The control switching function unit supports easily implemented saturation functions, specifically: In the formula: It is a symbolic function; This is the gain coefficient; For boundary layer.

5. The PMSM sensorless control system according to claim 2, characterized in that, The expression for the integral sliding surface element is: In the formula: 、 They are respectively 、 Sliding surface on the shaft; 、 These are the observed values ​​of the stator current. 、 This is the actual value of the stator current; Stator resistance; It is the stator inductor.

6. The PMSM sensorless control system according to claim 1, characterized in that, The control rate of the improved SMO module is: In the formula: 、 For the control input of the observer; Basic gain; This is the error adaptive term; This refers to system state error; The smoothness coefficient; This is the switching function; 、 They are respectively 、 Sliding surface on the shaft.

7. The PMSM sensorless control system according to claim 1, characterized in that, The overall transfer function of the second-order low-pass filter module is: In the formula: The total transfer function; This is the transfer function of the previous low-pass filter; This is the transfer function of the next low-pass filter; This is the cutoff frequency of the previous low-pass filter; This is the cutoff frequency of the next low-pass filter; It is a differential operator in time-domain computation.

8. The PMSM sensorless control system according to claim 1, characterized in that, The method for constructing the improved SMO module includes the following steps: S101, establishing a mathematical model of a permanent magnet synchronous motor; S102, designing the approach rate and control switching function; S103, defining the integral sliding surface; S104, constructing the improved SMO module based on the mathematical model of the permanent magnet synchronous motor, the approach rate, the control switching function, and the integral sliding surface.

9. The PMSM sensorless control system according to claim 1, characterized in that, The process of obtaining the back EMF includes the following steps: S201, the current sampling module collects the three-phase current and converts the three-phase current into a stationary coordinate system current; S202, the improved SMO module calculates the adaptive approach rate based on the stationary coordinate system current; S203, the second-order low-pass filter module filters the back EMF to obtain a smoothed back EMF.

10. The PMSM sensorless control system according to claim 1, characterized in that, The sensorless vector control process includes the following steps: S301, the position / speed extraction module estimates the position and speed based on the smoothed back electromotive force, and obtains the estimated speed; S302, the PI controller module generates the q-axis voltage based on the estimated speed, and the inverter module inversely transforms the q-axis voltage to complete the sensorless vector control.

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