Improved sliding mode based back-emf observation method for permanent magnet synchronous motor
By improving the composite sliding mode reaching law and the design of the resonant term, a sliding mode back EMF observer was constructed, which solved the dynamic convergence performance and phase compensation problems of traditional observers and realized high-precision sensorless control.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHANGCHUN INST OF OPTICS FINE MECHANICS & PHYSICS CHINESE ACAD OF SCI
- Filing Date
- 2026-05-14
- Publication Date
- 2026-07-21
AI Technical Summary
In traditional sensorless control of permanent magnet synchronous motors, sliding mode back EMF observers based on exponential sliding mode approaching laws suffer from poor dynamic convergence performance and lack back EMF phase compensation capability at the operating frequency, resulting in rotor position observation amplitude attenuation and phase lag, which affects control accuracy.
A second-order back EMF observer is designed using a composite sliding mode reaching law based on improved sliding mode. A resonance term is introduced on this basis, and the transfer function is dynamically adjusted by adjusting the system bandwidth and the resonance bandwidth to construct a sliding mode back EMF observer to achieve sensorless control.
It improves the dynamic convergence quality and steady-state observation accuracy of back EMF, solves the phase delay and amplitude attenuation problems of traditional observers, enhances the ability to suppress low-frequency disturbances, and provides a sensorless control method with high dynamic convergence quality.
Smart Images
Figure CN122203904B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of motor control technology, and particularly relates to a method for observing the back electromotive force of a permanent magnet synchronous motor based on an improved sliding mode. Background Technology
[0002] Due to their high efficiency and high power density, permanent magnet synchronous motors (PMSMs) have been widely used in electric ships, electric equipment, and railway transportation. Traditional control strategies for PMSMs heavily rely on mechanical position sensors to obtain rotor information. However, the introduction of these physical sensors not only increases hardware costs and installation complexity, but their inherent characteristics such as temperature drift, vibration sensitivity, and signal delay also make them a weak link in the entire control system, severely affecting control accuracy and stability. In traditional sensorless control, sliding mode back-EMF observers using exponential sliding mode reaching laws suffer from two major problems: firstly, poor dynamic convergence performance; and secondly, a lack of phase compensation capability for the back-EMF at the operating frequency, resulting in amplitude attenuation and phase lag in the observed rotor position. These factors collectively limit the control accuracy under sensorless operating conditions. Summary of the Invention
[0003] In view of this, the present invention aims to provide a back-EMF observation method for permanent magnet synchronous motors based on improved sliding mode, to solve the problems in traditional sensorless control of permanent magnet synchronous motors. These problems include insufficient dynamic convergence quality and lack of back-EMF phase compensation capability at the operating frequency, leading to amplitude attenuation and phase lag in the observed rotor position, thus limiting the control accuracy of sensorless systems. The method provided by this invention enhances the back-EMF convergence quality and consistency while maintaining speed, contributing a new approach to developing sensorless control methods with high dynamic convergence quality and precise steady-state observation performance.
[0004] To achieve the above objectives, the technical solution created by this invention is implemented as follows: A method for observing the back electromotive force of a permanent magnet synchronous motor based on improved sliding mode includes the following steps: S1: Design a composite sliding mode reaching law based on the voltage model of a permanent magnet synchronous motor, and construct a second-order back EMF observer based on the composite sliding mode reaching law. S2: A resonant term is introduced into the second-order back EMF observer to obtain a sliding mode back EMF observer. The frequency domain properties of the transfer function of the sliding mode back EMF observer are dynamically adjusted by adjusting the system bandwidth and the resonant bandwidth to realize back EMF observation under sensorless control.
[0005] Furthermore, in step S1, the voltage model of the permanent magnet synchronous motor is: ; in, For differential operators, This is the actual value of the stator resistance. This is the actual value of the stator inductance. for Stator voltage in a stationary coordinate system for Stator current in a stationary coordinate system for The back electromotive force of a stationary coordinate system.
[0006] Furthermore, in step S1, the compound sliding mode reaching law is: ; ; in, For numbers with a base greater than 1, For symbolic operations, The exponent of the nonlinear term in the compound sliding mode reaching law is... , The gain coefficient of the linear term in the composite sliding mode reaching law. For the compound sliding mode reaching law, For sliding surface, for Stator current in a stationary coordinate system for Estimating stator current in a stationary coordinate system.
[0007] Furthermore, in step S1, the second-order back potential observer is: ; in, For the compound sliding mode reaching law, For sliding surface, for Stator current in a stationary coordinate system for Estimating stator current in a stationary coordinate system For numbers with a base greater than 1, For symbolic operations, The exponent of the nonlinear term in the compound sliding mode reaching law is... , The gain coefficient of the linear term in the composite sliding mode reaching law. For differential operators, It is the first-order gain coefficient. It is the second-order gain coefficient. for Estimating the back electromotive force in a stationary coordinate system. for , for , This is the actual value of the stator resistance. This is the actual value of the stator inductance. It is an estimate of the first-order unmodeled perturbation.
[0008] Furthermore, in step S2, the sliding mode back EMF observer is: ; in, For the compound sliding mode reaching law, For sliding surface, for Stator current in a stationary coordinate system for Estimating stator current in a stationary coordinate system For numbers with a base greater than 1, For symbolic operations, The exponent of the nonlinear term in the compound sliding mode reaching law is... , The gain coefficient of the linear term in the composite sliding mode reaching law. For differential operators, It is the first-order gain coefficient. It is the second-order gain coefficient. for , for , This is the actual value of the stator resistance. This is the actual value of the stator inductance. It is an estimate of the first-order unmodeled perturbation. This is an estimate of the second-order unmodeled perturbation. It is the third-order gain coefficient. To adjust the amplitude gain of the back EMF observed by the sliding mode back EMF observer.
[0009] Furthermore, the transfer function of the sliding mode back EMF observer is: ; Where s is the Laplace operator, for The back electromotive force in a stationary coordinate system. for Estimating the back electromotive force in a stationary coordinate system. For the resonant bandwidth, The system bandwidth of the sliding mode back EMF observer is... This is the estimated operating frequency of the permanent magnet synchronous motor.
[0010] Compared with the prior art, the present invention can achieve the following beneficial effects: This invention presents a back-EMF observation method for permanent magnet synchronous motors based on improved sliding mode. Compared to the traditional exponential sliding mode reaching law, this invention proposes a composite reaching law with a boundary layer. Outside the boundary layer, higher-order nonlinear dynamics are used to accelerate convergence, while inside the boundary layer, it degenerates into a linear kernel to eliminate chattering. By introducing a resonant term to configure the transfer function of the linear kernel, this invention fundamentally solves the phase delay and amplitude attenuation problems of traditional linear observers, while also exhibiting good DC bias and low-frequency disturbance suppression capabilities. Furthermore, by introducing system bandwidth and resonant bandwidth with explicit physical meaning, the parameter tuning process is simplified. In summary, this invention provides a new approach for developing sensorless control methods with high dynamic convergence quality and precise steady-state observation performance. Attached Figure Description
[0011] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 A schematic flowchart illustrating the back EMF observation method for a permanent magnet synchronous motor based on an improved sliding mode, which is an embodiment of the present invention. Figure 2 An overall architecture diagram of the back EMF observation method for a permanent magnet synchronous motor based on improved sliding mode, which is an embodiment of the present invention; Figure 3 Bode plots of a conventional observer based on the exponential sliding mode reaching law and a sliding mode back potential observer configured in this invention under different system bandwidths; Figure 3 (a) Bode plots of a conventional observer based on the exponential sliding mode reaching law in an embodiment of the present invention under different system bandwidths; Figure 3 (b) Bode plots of the sliding mode back EMF observer configured according to an embodiment of the present invention under different system bandwidths; Figure 4 Simulation results of sliding surface convergence before and after introducing nonlinear extrinsic terms in embodiments of the present invention; Figure 5 Simulation results of a conventional observer based on the exponential sliding mode approach law and a configured sliding mode back EMF observer, which are embodiments of the present invention. Detailed Implementation
[0012] 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 specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.
[0013] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.
[0014] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.
[0015] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.
[0016] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.
[0017] like Figure 1 As shown, this invention proposes a back EMF observation method for a permanent magnet synchronous motor based on an improved sliding mode, which specifically includes the following steps: S1: Design a composite sliding mode reaching law based on the voltage model of a permanent magnet synchronous motor, and construct a second-order back EMF observer based on the composite sliding mode reaching law. S2: A resonant term is introduced into the second-order back EMF observer to obtain a sliding mode back EMF observer. The frequency domain properties of the transfer function of the sliding mode back EMF observer are dynamically adjusted by adjusting the system bandwidth and the resonant bandwidth to realize back EMF observation under sensorless control.
[0018] It should be noted that this invention, based on the voltage model of a permanent magnet synchronous motor, designs a composite sliding mode reaching law to construct a second-order back EMF observer. A phase-locked loop (PLL) is used to extract the rotor's operating frequency and position information from the observed back EMF obtained from the second-order back EMF observer. Based on the second-order back EMF observer, a resonant term is introduced to configure the transfer function of the linear kernel, enabling the estimated back EMF to achieve zero phase lag and unity amplitude gain. The frequency domain properties of the back EMF observation transfer function are dynamically adjusted by regulating the system bandwidth and resonant bandwidth, giving each adjustment parameter of the transfer function a clear physical meaning during the configuration process.
[0019] Furthermore, the objective of this invention is to achieve zero-phase lag and unit-amplitude gain in back potential observation while improving dynamic convergence quality. This invention constructs a sliding mode back potential observer by designing a composite sliding mode reaching law. Nonlinear dynamics are used to accelerate convergence outside the boundary layer, while a linear kernel is degenerated inside the boundary layer to reduce chattering. By configuring the transfer function of the linear kernel, zero-phase lag and unit-amplitude gain in back potential estimation are effectively guaranteed.
[0020] In step S1, to construct a second-order back EMF observer, the permanent magnet synchronous motor is first established in... Voltage model in stationary coordinate system: (1); In the formula: It is a differential operator. and These are the actual values of the stator resistance and the actual values of the stator inductance, respectively. yes Stator voltage in a stationary coordinate system yes Stator current in a stationary coordinate system yes The back electromotive force in the stationary coordinate system. Let the estimated stator current be... Constructing the sliding surface for: (2); Based on sliding surface Design a composite convergence law : (3); In the formula: It represents a base greater than 1; || is the absolute value operator. Represents symbolic operations, It is the exponent of the nonlinear term of the composite reaching law, satisfying , This is the gain coefficient of the linear term in the composite reaching law. It's important to note that the fractional part of the nonlinear term... When the value is greater than the boundary layer, it approaches 1. When the voltage drops below the boundary layer, it rapidly decays to zero. This design effectively prevents nonlinear dynamics from entering the inner layer and causing chattering. Combining equations (1), (2), and (3), a second-order back potential observer can be constructed as follows: (4); In the formula: represent , represent , It is an estimate of the first-order unmodeled perturbation. It is the first-order gain coefficient. It is the second-order gain coefficient. It is to estimate the back electromotive force. Based on equation (4), the estimated back electromotive force can be obtained in real time. Considering that the back EMF is a sinusoidal signal and the fundamental frequency is equal to the rotor operating frequency, the estimated rotor operating frequency and position information can be obtained through a phase-locked loop and fed back to the other control loops (that is, control loops without sensors) in real time.
[0021] In step S2, the nonlinear term only operates outside the boundary layer, enhancing the drive and accelerating the convergence of the back EMF to the boundary layer through nonlinear dynamics. Once inside the boundary layer, it directly degenerates into a linear kernel, effectively reducing high-frequency chattering. However, the linear kernel causes the transfer function from the estimated back EMF to the reference back EMF to exhibit low-pass filtering characteristics, which can cause phase lag and amplitude attenuation at the motor's operating frequency. To address this issue, this invention further introduces a resonance term to configure the transfer function of the linear kernel. After introducing the resonance term, the sliding mode back EMF observer is: (5); In the formula: It is an estimate of the second-order unmodeled perturbation. It is the third-order gain coefficient. This involves adjusting the amplitude gain of the observed back EMF. By neglecting the nonlinear terms in the composite reaching law within the boundary layer, the transfer function from the estimated back EMF to the actual back EMF can be obtained based on a linear kernel. : (6); In the formula, s represents the Laplace operator. Configuration of the transfer function. To achieve zero phase hysteresis and unity-amplitude gain at the resonant frequency. When the Laplace operator s is assigned a specific pure resonant frequency value, even ( It is the imaginary unit. (This is the estimated operating frequency of the motor). The parameter relationships in equation (5) need to be adjusted to make the transfer function of equation (6) more accurate. Satisfying precise unit complex gain This invention will and Treating them as adjustable parameters, the remaining parameters in equation (5) are introduced into the following relationship: (7); In the formula: It is system bandwidth. It is the resonant bandwidth. Substituting equation (7) into equation (6), the transfer function of the sliding mode back EMF observer is... Rewritten as form: (8); For transfer function The estimation accuracy at the fundamental operating frequency of the permanent magnet synchronous motor is verified. Substituting into equation (8), the molecule is The denominator is N() refers to the numerator of the transfer function, and D() refers to the denominator of the transfer function. Based on the unit property of imaginary numbers, the above equation can be further simplified to... That is, the amplitude at the fundamental operating frequency of the permanent magnet synchronous motor is Phase is This characteristic ensures that the sliding mode back EMF observer can perfectly track the actual back EMF in real time under steady-state operation, fundamentally solving the phase delay and amplitude attenuation problems of traditional linear observers, and greatly improving the static accuracy of position estimation.
[0022] It should be noted that the sliding mode back EMF observer provided by this invention also has considerable suppression capability for low-frequency disturbances and DC components, making the Laplace operator... Substituting into equation (8), we get: This indicates that the sliding mode back EMF observer core possesses inherent bandpass filtering characteristics, which can completely block constant value offsets in the back EMF estimation path, thereby effectively suppressing DC bias interference caused by zero-point drift of the current and voltage sensors of the permanent magnet synchronous motor or asymmetry of the sampling circuit.
[0023] Furthermore, since the sliding mode back EMF observer constructed in this invention is a third-order dynamic system containing internal mode terms, its closed-loop transfer function has a higher system order compared to traditional sliding mode back EMF observers based on exponential sliding mode reaching laws. In practical applications, this invention can not only eliminate constant disturbances but also completely suppress ramp disturbances, significantly enhancing robustness under complex variable operating conditions. Finally, this invention additionally introduces system bandwidth and resonant bandwidth. It primarily determines the global convergence speed of the sliding mode back EMF observer, as well as its suppression depth for high-frequency measurement noise and resonant bandwidth. This determines the bandpass characteristics of the sliding mode back EMF observer near the fundamental frequency. This gives the adjustment parameters in the transfer function configuration process a clear physical meaning.
[0024] From the perspective of frequency domain properties: the larger the system bandwidth, the faster the frequency response speed of the sliding mode back EMF observer, but the higher the sensitivity to high frequency measurement noise. It can generally be set to 5-20 times the estimated operating frequency of the motor. The larger the resonant bandwidth, the lower the sensitivity of the sliding mode back EMF observer to frequency shift, but the weaker the selectivity for back EMF extraction. The resonant bandwidth can be set to 1%-5% of the estimated operating frequency of the motor.
[0025] Based on the above description, using the estimated operating frequency of the motor as a reference, the tuning ranges for the system bandwidth and resonant bandwidth are calculated: the system bandwidth range is 5 to 20 times the estimated operating frequency of the motor, and the resonant bandwidth range is 1% to 5% of the estimated operating frequency of the motor. A first step size for adjusting the system bandwidth and a second step size for adjusting the resonant bandwidth are set. First, the system bandwidth is adjusted incrementally according to the first step size. Under each fixed system bandwidth condition, the resonant bandwidth is then adjusted incrementally according to the second step size. Under a test condition with a given speed command step of ±20%, when the root mean square value of the observed back EMF tracking error is less than 5% of the rated back EMF amplitude, and the overshoot of the back EMF waveform does not exceed 5%, parameter traversal tuning is stopped. The currently matched system bandwidth and resonant bandwidth are taken as the optimal tuning parameters for back EMF observation under sensorless control.
[0026] like Figure 2 As shown, It is a reference frequency. yes Rotating coordinate system reference current, The symbol represents the integral, and PI stands for Proportional-Integral Controller. The sliding mode back EMF observer provided by this invention obtains the estimated operating frequency from the estimated back EMF through a phase-locked loop. and estimated location .
[0027] like Figure 3 As shown, traditional observers based on the exponential sliding mode reaching law exhibit low-pass filtering characteristics, inevitably causing amplitude attenuation and phase lag in the estimated back EMF. Although increasing the bandwidth can reduce phase lag, it cannot fundamentally eliminate it. In contrast, this invention... All of them can achieve effective unit amplitude attenuation and zero phase hysteresis at the operating frequency, and the higher the value... The stronger the suppression effect on low-frequency disturbances, the better it is without affecting the high-frequency suppression characteristics, which shows a clear physical significance.
[0028] like Figure 4 As shown, the initial rotational speed increases from 0 r / min to 500 r / min under operating conditions. It can be seen that after introducing the nonlinear term in this invention, the dynamic convergence performance of the sliding surface is significantly improved. It can enhance the back EMF driving effect when the rotational speed error is large, accelerate the convergence speed and enter the boundary layer.
[0029] like Figure 5 As shown, the operating condition is set with the initial speed increasing from 0 r / min to 500 r / min. From top to bottom, the comparisons are: back EMF estimation comparison, back EMF estimation error comparison, rotor position estimation comparison, and position estimation error comparison. It can be seen that the traditional observer based on the exponential sliding mode reaching law has a large back EMF estimation error, and the position estimation error exhibits a significant non-zero mean systematic deviation across the entire operating range. In contrast, the method proposed in this invention effectively reduces the back EMF estimation error while achieving good unit amplitude attenuation and zero phase lag characteristics, ensuring that the rotor position estimation error has excellent zero-mean estimation performance throughout the entire speed change process.
[0030] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.
[0031] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.
Claims
1. A method for observing the back electromotive force of a permanent magnet synchronous motor based on an improved sliding mode, characterized in that: Specifically, the steps include the following: S1: Design a composite sliding mode reaching law based on the voltage model of a permanent magnet synchronous motor, and construct a second-order back EMF observer based on the composite sliding mode reaching law. S2: A resonant term is introduced into the second-order back EMF observer to obtain a sliding mode back EMF observer. The frequency domain properties of the transfer function of the sliding mode back EMF observer are dynamically adjusted by adjusting the system bandwidth and the resonant bandwidth to realize back EMF observation under sensorless control. In step S2, the sliding mode back EMF observer is: ； in, For sliding surface, for Stator current in a stationary coordinate system for Estimating stator current in a stationary coordinate system For the compound sliding mode reaching law, For numbers with a base greater than 1, For symbolic operations, The exponent of the nonlinear term in the compound sliding mode reaching law is... , The gain coefficient of the linear term in the composite sliding mode reaching law. For differential operators, It is the first-order gain coefficient. It is the second-order gain coefficient. for , for , This is the actual value of the stator resistance. This is the actual value of the stator inductance. It is an estimate of the first-order unmodeled perturbation. This is an estimate of the second-order unmodeled perturbation. It is the third-order gain coefficient. To adjust the amplitude gain of the back EMF observed by the sliding mode back EMF observer, for Estimating the back electromotive force in a stationary coordinate system.
2. The back EMF observation method for a permanent magnet synchronous motor based on improved sliding mode according to claim 1, characterized in that: In step S1, the voltage model of the permanent magnet synchronous motor is: ； in, For differential operators, This is the actual value of the stator resistance. This is the actual value of the stator inductance. for Stator voltage in a stationary coordinate system for Stator current in a stationary coordinate system for The back electromotive force of a stationary coordinate system.
3. The back EMF observation method for a permanent magnet synchronous motor based on improved sliding mode according to claim 1, characterized in that: In step S1, the compound sliding mode reaching law is: ； ； in, For numbers with a base greater than 1, For symbolic operations, The exponent of the nonlinear term in the compound sliding mode reaching law is... , The gain coefficient of the linear term in the composite sliding mode reaching law. For the compound sliding mode reaching law, For sliding surface, for Stator current in a stationary coordinate system for Estimating stator current in a stationary coordinate system.
4. The back EMF observation method for a permanent magnet synchronous motor based on improved sliding mode according to claim 2, characterized in that: In step S1, the second-order back potential observer is: ； in, For the compound sliding mode reaching law, For sliding surface, for Stator current in a stationary coordinate system for Estimating stator current in a stationary coordinate system For numbers with a base greater than 1, For symbolic operations, The exponent of the nonlinear term in the compound sliding mode reaching law is... , The gain coefficient of the linear term in the composite sliding mode reaching law. For differential operators, It is the first-order gain coefficient. It is the second-order gain coefficient. To estimate the back potential, for , for , This is the actual value of the stator resistance. This is the actual value of the stator inductance. It is an estimate of the first-order unmodeled perturbation.
5. The back EMF observation method for a permanent magnet synchronous motor based on improved sliding mode according to claim 1, characterized in that: The transfer function of the sliding mode back EMF observer is: ； Where s is the Laplace operator, for The back electromotive force in a stationary coordinate system. for Estimating the back electromotive force in a stationary coordinate system. For the resonant bandwidth, The system bandwidth of the sliding mode back EMF observer is... This is the estimated operating frequency of the permanent magnet synchronous motor.