Sensorless permanent magnet synchronous motor control method based on adaptive phase-locked loop and anti-windup controller

Abstract

This invention discloses a sensorless permanent magnet synchronous motor (PMSM) control method based on an adaptive phase-locked loop (PLL) and an anti-saturation controller, comprising the following steps: S1, injecting a high-frequency square wave voltage signal into the estimated synchronous rotating coordinate system; acquiring the stator current of the PMSM to obtain a high-frequency current deviation signal in a two-phase stationary coordinate system; S2, using an improved anti-integral saturation controller as the speed loop controller to receive the speed command and feedback speed error signal; simultaneously, calculating the rotor position error signal based on the high-frequency current signal; S3, inputting the rotor position error signal to the adaptive PLL, which adaptively adjusts its undamped oscillation frequency according to the motor's operating state to achieve dynamic adjustment of the observation bandwidth, and outputs rotor position and speed estimates; sensorless vector control of the PMSM is achieved through the estimates. This invention exhibits excellent stability and adaptability during low-speed motor operation.

Description

Technical Field

[0001] This invention relates to the field of permanent magnet synchronous motor technology, and more specifically to a sensorless permanent magnet synchronous motor control method based on an adaptive phase-locked loop and an anti-saturation controller. Background Technology

[0002] Compared to traditional built-in permanent magnet synchronous motor control strategies, sensorless control eliminates the need for mechanical position and speed sensors, better meeting the requirements of high reliability, low cost, and operation in harsh environments such as high temperature and humidity. Due to its promising development prospects, it has become a hot topic in the field of motor control research.

[0003] Sensorless control is generally classified into two categories based on the method of acquiring rotor position: back-EMF-based methods and reluctance-based methods. At high speeds, the motor generates an observable extended back-EMF, which can be used for rotor position estimation and control. Back-EMF-based methods are widely used in this field and mainly include sliding mode observers, model reference adaptive systems, and extended Kalman filters. This approach has proven effective for achieving sensorless control at medium to high speeds.

[0004] However, at low speeds, extracting and analyzing useful signals from the motor becomes quite challenging due to the low signal-to-noise ratio. In such cases, injecting high-frequency signals into the motor has proven to be an effective solution. The basic principle of sensorless control is to superimpose a high-frequency voltage or current signal onto the fundamental signal and apply the synthesized signal to the motor windings. The effects of these injected signals are reflected in the high-frequency response, from which rotor position information can be extracted by filtering and processing the response signal. Currently, sensorless low-speed operation control algorithms for permanent magnet synchronous motors mainly rely on high-frequency signal injection detection methods. This method is unaffected by motor parameters and is suitable for sensorless low-speed operation. In traditional high-frequency signal injection methods, a high-frequency sinusoidal signal is injected into the stator windings of the motor, and rotor position information is obtained by detecting the high-frequency components in the stator current. High-frequency voltage types can be divided into high-frequency sinusoidal voltage injection and high-frequency square wave voltage injection.

[0005] In the context of low-speed motor operation, this invention addresses the weaknesses in dynamic performance and low estimation accuracy of traditional phase-locked loops (PLLs) for sensorless control of permanent magnet synchronous motors (PMSMs) in the zero-to-low speed range. A novel PLL is designed to address these issues. This PLL features an adaptive improvement upon the traditional PLL structure, utilizing d-axis and q-axis current responses for rotor position estimation. This improvement enhances the sensorless control performance of PMSMs in the zero-to-low speed range.

[0006] Permanent magnet synchronous motors (PMSMs) are widely used in high-performance speed control and servo systems due to their advantages such as low harmonic distortion and high torque accuracy. Traditional speed control systems typically employ PI controllers, which are prone to integral saturation under sudden speed changes or load disturbances, leading to a decline in dynamic performance. To mitigate this problem, anti-integral saturation control strategies have been introduced, with the back-integration method and conditional integration method being classic approaches. Furthermore, novel anti-integral saturation structures are constantly emerging to enhance control effectiveness. Meanwhile, fractional-order PID controllers are increasingly used in motor control due to their superior dynamic and robust characteristics. However, their integral part also carries the risk of integral saturation. Research indicates that combining fractional-order control with anti-integral saturation mechanisms can effectively balance the system's responsiveness, stability, and anti-integral saturation capability, providing a promising research direction for optimizing PMSM speed control systems. Summary of the Invention

[0007] To address the aforementioned issues, this invention proposes a sensorless permanent magnet synchronous motor (PMSM) control method based on an adaptive phase-locked loop (PLL) and an anti-saturation controller. First, the speed loop employs an anti-saturation controller, effectively resolving the integrator saturation problem during motor acceleration / deceleration through conditional integration and feedback compensation mechanisms, further improving the system's dynamic response and steady-state performance. Second, to address the high-frequency oscillations and fixed gain issues inherent in traditional PLLs over a wide speed range, which reduce estimation accuracy, the designed APLL uses an adaptive algorithm to suppress high-frequency oscillations, significantly improving the observation accuracy of rotor position and speed. Finally, a series of experiments compare the performance of the proposed scheme with traditional control methods. Experimental results on an embedded permanent magnet synchronous motor (IPMSM) verify the superiority and feasibility of the proposed scheme in sensorless control systems.

[0008] The specific plan is as follows:

[0009] A sensorless permanent magnet synchronous motor control method based on adaptive phase-locked loop and anti-saturation controller includes the following steps:

[0010] S1. Inject a high-frequency square wave voltage signal into the estimated synchronous rotating coordinate system; collect the stator current of the permanent magnet synchronous motor, establish a high-frequency voltage equation, and obtain the high-frequency current deviation signal in the two-phase stationary coordinate system based on the transformation relationship between the actual and estimated rotating coordinate systems.

[0011] S2. An improved anti-integral saturation controller is used as the speed loop controller to receive speed commands and feedback speed error signals. The controller includes a proportional channel and an integral channel, and is equipped with a hard limiting module. When the controller output is limited, the integral compensation amount is calculated and fed back to the integral channel to suppress integral saturation. At the same time, the rotor position error signal is calculated based on the high-frequency current signal.

[0012] S3. The rotor position error signal is input to the adaptive phase-locked loop (APLL). The APLL adaptively adjusts its undamped oscillation frequency according to the motor's operating state to achieve dynamic adjustment of the observation bandwidth, and outputs rotor position and speed estimates. Sensorless vector control of the permanent magnet synchronous motor is achieved through the estimates.

[0013] Further, step S1 includes:

[0014] The relationship between the actual synchronous rotating coordinate system and the estimated synchronous rotating coordinate system of the built-in permanent magnet synchronous motor (IPMSM) is established; α-β represents the two-phase stationary coordinate system, and dq represents the actual synchronous rotating coordinate system. - This represents the estimated synchronous rotating coordinate system; the voltage and current relationships between these coordinate systems are as follows:

[0015] (1)

[0016] (2)

[0017] Among them, u d ,u q i d , and i q These represent the stator voltage and current in the dq coordinate system, respectively. d , q , d ,and q They represent - Stator voltage and current in the coordinate system; θ err It is the actual rotor position angle θ and the estimated rotor position angle θ e The difference between them;

[0018] (3)

[0019] Since the frequency of high-frequency signals is much higher than that of fundamental signals, a high-frequency square wave voltage signal can be injected into the synchronous rotating coordinate system to establish a high-frequency model of the permanent magnet synchronous motor.

[0020] exist - In the coordinate system, the injected voltage signal is:

[0021] (4)

[0022] Where n is the sampling sequence number, and the sampling frequency is twice the PWM carrier frequency; Vh The amplitude of the injected voltage signal;

[0023] Therefore, the high-frequency voltage equation becomes:

[0024] (5)

[0025] Substituting equations (2) and (4) into equation (5) yields:

[0026] (6)

[0027] Among them, L dh ,L qh ,u dh ,u qh i dh and i qh Let represent the stator inductance, high-frequency voltage signal, and high-frequency current signal in the dq coordinate system, respectively; therefore, in the αβ coordinate system, we have:

[0028] (7)

[0029] Where, Δi αh and Δi βh These are the high-frequency current deviation signals along the α and β axes of adjacent sampling points in the α-β coordinate system on the stator side of the permanent magnet synchronous motor (PMSM); ΔT is the sampling period, which is the PWM period T. s Half of, i.e., ΔT = T s / 2.

[0030] Further, step S2 includes:

[0031] S21, Traditional Anti-Integral Saturation Controller

[0032] The vector control system for permanent magnet synchronous motors suffers from problems such as excessive overshoot and low control accuracy. The root cause lies in the integral saturation phenomenon caused by the integral element in the proportional-integral (PI) module of the speed loop. An anti-integral saturation controller is employed to suppress the saturation effect and improve the system's control performance.

[0033] The traditional anti-integral saturation controller is a linear feedback controller. Its principle is to estimate the difference between the output before and after the PI loop saturation, and feed this error back to the integral term through the gain, thereby achieving double integral compensation and eliminating the error caused by integral saturation.

[0034] when i n =i s :

[0035] (8)

[0036] when i n ≠is :

[0037] (9)

[0038] Among them, i sat i represents the maximum output of the controller when the system is saturated. n and i s K represents the current value before and after the constraint, respectively. p , K i , K c All are coefficients greater than zero;

[0039] S22, Improved anti-integral saturation controller

[0040] Since traditional anti-integral saturation controller algorithms suffer from low control accuracy and difficulty in designing feedback coefficients, it is necessary to introduce a new algorithm that retains the simple and easy-to-implement structure of traditional anti-integral saturation controllers while employing new output and integral limiting methods.

[0041] The improved anti-integral saturation controller consists of two channels: a proportional channel that responds quickly to the received error signal with a fixed coefficient, and an integral channel that eliminates steady-state error through integral gain and discrete integral elements; a limiting module that limits the total pre-output within the set value and simultaneously calculates the deviation as a compensation amount fed back to the integral channel to prevent integral saturation; in the output limiting mechanism, to ensure that the control quantity does not exceed the physical limits of the actuator, the following hard limiting rule is designed:

[0042] (10)

[0043] It ensures that the actual output out is strictly within the effective range by directly truncating any pre-output pre_out that exceeds the effective range [−lmt,lmt]; pre_out represents the preliminary controller output synthesized by adding the proportional and integral parts.

[0044] When the pre-output is truncated by the limiting module (i.e., pre_out ≠ out), the controller's integral term may experience integral saturation due to continuous error accumulation. To address this issue, an anti-integral saturation compensation variable is designed:

[0045] (11)

[0046] It acts on the integral channel through a feedback loop to perform real-time correction on the integral output:

[0047] (12)

[0048] Among them ki outThis represents the integral output, where ki*out is the corrected integral output. When the system is not saturated, ki_down=0, and the integral circuit works normally. When saturation occurs, ki_down precisely cancels out the excessive integral quantity, keeping the integral output consistent with the actual output and effectively suppressing the integral saturation phenomenon.

[0049] Substituting the average inductance L and the half-difference inductance ΔL into the above equation, we get:

[0050] (13)

[0051] If θ e =θ, that is, θ err =0, then:

[0052] (14)

[0053] (15)

[0054] Rotor position information is obtained through (10).

[0055] Rotor position error signal:

[0056] (16)

[0057] Among them, K err Represents the coefficients of the high-frequency rotor position error signal;

[0058] S23, Improved high-frequency square wave signal injection

[0059] For high-frequency signal injection, low-pass filters are required for extracting the fundamental current signal, while band-pass filters are required for extracting the high-frequency current signal. To address this issue, an improved algorithm is proposed that completely eliminates the need for these filters, significantly improving system bandwidth and dynamic performance.

[0060] Since the actual rotor position is unknown, it needs to be studied in the estimated dq coordinate system. Therefore, equation (6) is rewritten in dq coordinate system form as follows:

[0061] (17)

[0062] In the voltage equations of a permanent magnet synchronous motor, the basic voltage equation is given by the following formula:

[0063] (18)

[0064] (19)

[0065] Within each pulse width modulation (PWM) cycle, idh It alternates between positive and negative values, while i df There are two possibilities: either the fundamental current remains unchanged, or it changes.

[0066] During steady-state operation, the fundamental voltage will not change suddenly within one PWM cycle. df Reaching a stable value, i.e., L d ·d df / dt=0; Under this condition, the fluctuation of the total current can be considered as being caused only by high-frequency square wave voltage excitation; however, during acceleration / deceleration or load disturbances (dynamic response of the current loop), L d ·di df / dt≠0, which means that the current change within a PWM cycle is caused by the combined effect of the fundamental wave and the high-frequency response current;

[0067] When k−1 is the peak sampling time, and k and k−2 are the valley sampling times, we have:

[0068] (20)

[0069] (twenty one)

[0070] Subtracting equation (16) from equation (15) gives:

[0071] (twenty two)

[0072] Meanwhile, according to (15)-(17), when k−1 is the valley sampling time, and k and k−2 are the peak sampling times, we have:

[0073] (twenty three)

[0074] In short, at any given moment, there is:

[0075] (twenty four)

[0076] Meanwhile, the extraction of the fundamental frequency component is given by the following formula:

[0077] (25)

[0078] This method also effectively separates the fundamental frequency component from the high-frequency component through subtraction.

[0079] Similarly, the high-frequency response current at any given moment is expressed as:

[0080] (26)

[0081] In this formula, i α,βh (k),i α,β (k), and i α,βf (k) represent the high-frequency response current vector, the sampling current vector, and the fundamental current vector at the k-th sampling time, respectively; according to equation (26), the expressions for the high-frequency response current vector and the fundamental current vector at the k-th sampling time are derived as follows:

[0082] (27)

[0083] Traditional carrier signal separation requires low-pass or notch filters, while extraction requires band-pass filters. However, using filters, especially high-order filters, inevitably degrades the system's dynamic performance and consumes more system resources. This method can extract the high-frequency response current vector and the fundamental current vector through simple algebraic operations.

[0084] To obtain rotor position and speed signals, the separated high-frequency response current signal needs to be converted into an envelope signal.

[0085] Further, step S3 includes:

[0086] In modern control theory, the description and representation of the state space is a direct reflection of the system. However, for various reasons, some states cannot be directly measured, thus hindering the resolution of control engineering-related problems. Therefore, researchers have proposed the goal of reconstructing the state of dynamic systems by designing observers.

[0087] After demodulating the position error signal, a position observer is needed to track the rotor's position and velocity. From the perspective of classical control theory, introducing an integrator element can improve the system's steady-state accuracy. Then, by introducing the integral part into the observer, the observer can estimate the state using the ratio of past and current values ​​and integral state information. This type of observer is called a PI observer.

[0088] Due to their versatility and ease of implementation, PI-type rotor position observers have been widely used. In sensorless control processes, the switching of different loads places very high demands on phase-locked loop (PLL)-based position observers. The constant bandwidth of the PLL cannot adapt to changing conditions. Therefore, an adaptive PLL bandwidth strategy is proposed to address this problem. This method is based on adaptively adjusting the PLL gain during transient speed and load changes; that is, the PLL bandwidth increases during transients and decreases during steady-state conditions.

[0089] First, a traditional phase-locked loop (PLL) is a typical second-order system; therefore, when the motor is in a dynamic process, zero dynamic position tracking error cannot be achieved due to the limited tracking bandwidth of the PI controller. The error transfer function of a traditional PLL is as follows:

[0090] (28)

[0091] To balance faster response speed and better stability, the damping coefficient ξ of the second-order system is designed as follows: / 2; In this way, the control parameters of the phase-locked loop (PLL) are designed as follows:

[0092] (29)

[0093] Where ρ is the oscillation frequency of the phase-locked loop;

[0094] Combining equations (28) and (29), the relationship between the observer bandwidth and the undamped oscillation frequency ρ is obtained:

[0095] (30)

[0096] It can be seen that the larger the undamped oscillation frequency ρ, the higher the bandwidth of the observer, the faster the convergence speed of the system, and thus the stronger the position tracking capability of the algorithm. However, due to the presence of signal noise in the actual system, the bandwidth cannot be designed to be too high. This is to suppress high-frequency HF noise and improve the stability of the system.

[0097] Traditional quadrature phase-locked loops (PLLs), as typical second-order systems, can achieve steady-state tracking with zero error at both low and high speeds. However, under variable speed conditions, the rotor position tracking speed is not fast enough, resulting in poor position estimation performance. If the speed changes suddenly, the position estimation error will increase sharply, even leading to tracking failure. To address this issue, an adaptive phase-locked loop (APLL) is proposed to suppress steady-state position tracking deviations under variable speed conditions and also helps reduce harmonic position errors.

[0098] ψ f It is magnetic flux, ω c It is the cutoff frequency; as ω c As ω increases, the amplitude of the phase-locked loop decreases across the entire frequency band; when ω c When the amplitude is 0, the APLL is equivalent to the traditional quadrature phase-locked loop; the APLL has a smaller bandwidth and a lower amplitude, especially in the low-frequency band, where its filtering performance is better.

[0099] (31)

[0100] Where, ρ n It is the undamped oscillation frequency, ρ sIt is the steady-state undamped oscillation frequency, ρ d It is the adaptive undamped oscillation frequency gain under transient changes, ρ sd It is the gain of the undamped oscillation frequency attenuation; Equation (31) is divided into three states: (I) in steady state, the bandwidth is a certain value; (II) in transient state, the bandwidth of the phase-locked loop is linearly related to the rate of change of the q-axis current; (III) in the process from transient to steady state, due to the current decay, the current bandwidth of the phase-locked loop should be linearly related to the bandwidth of the previous cycle. The proposed adaptive adjustment ensures strong adaptability to various operating conditions such as variable speed and variable load.

[0101] The beneficial effects of this invention are: it innovatively integrates an adaptive phase-locked loop and an anti-integral saturation controller into a sensorless control system for a three-phase permanent magnet synchronous motor. This method exhibits excellent stability and adaptability during low-speed motor operation. The main contributions are as follows:

[0102] 1. The innovation of the adaptive phase-locked loop lies in the introduction of a mechanism on the basis of the traditional structure, which can dynamically adjust the bandwidth or parameters according to the large changes in motor speed and load, thereby achieving fast and accurate tracking of rotor position.

[0103] 2. The innovation of the anti-saturation controller lies in its effective suppression of excessive accumulation of errors in the integrator when errors persist, through the introduction of intelligent limiting or feedback compensation mechanisms. This significantly enhances control stability and anti-interference capabilities while ensuring the system's dynamic response. Attached Figure Description

[0104] Figure 1 It is the relationship between the actual rotor and the estimated rotor's synchronously rotating coordinate system.

[0105] Figure 2 This is the control block diagram for the anti-integral saturation method.

[0106] Figure 3 This is a structural diagram of an improved anti-integral saturation controller.

[0107] Figure 4 This is a decoupling diagram of the position error signal.

[0108] Figure 5 This is a current change graph within a PWM cycle. (a) The fundamental current is constant, and (b) The fundamental current changes.

[0109] Figure 6 This is an extraction diagram of the fundamental frequency and high frequency signals.

[0110] Figure 7 This is a schematic diagram of a filterless carrier separation principle.

[0111] Figure 8 This is a schematic diagram of position error acquisition.

[0112] Figure 9 This is a block diagram of a traditional phase-locked loop (PLL) position observer.

[0113] Figure 10 It is an adaptive phase-locked loop diagram.

[0114] Figure 11 This is a block diagram of the control structure of a permanent magnet synchronous motor.

[0115] Figure 12 The figures show the experimental results of rotational speed under different controllers: (a) PI controller, (b) anti-integral saturation controller.

[0116] Figure 13 The figures show the experimental results under stable conditions: (a) traditional method, (b) the method of this invention.

[0117] Figure 14 The figures show the experimental results under different load conditions: (a) traditional method, (b) the method of the present invention.

[0118] Figure 15 The figures show the experimental results under different load conditions: (a) traditional method, (b) the method of the present invention. Detailed Implementation

[0119] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0120] This invention provides a sensorless permanent magnet synchronous motor control method based on an adaptive phase-locked loop and an anti-saturation controller, comprising the following steps:

[0121] S1. Inject a high-frequency square wave voltage signal into the estimated synchronous rotating coordinate system; collect the stator current of the permanent magnet synchronous motor, establish a high-frequency voltage equation, and obtain the high-frequency current deviation signal in the two-phase stationary coordinate system based on the transformation relationship between the actual and estimated rotating coordinate systems.

[0122] S2. An improved anti-integral saturation controller is used as the speed loop controller to receive speed commands and feedback speed error signals. The controller includes a proportional channel and an integral channel, and is equipped with a hard limiting module. When the controller output is limited, the integral compensation amount is calculated and fed back to the integral channel to suppress integral saturation. At the same time, the rotor position error signal is calculated based on the high-frequency current signal.

[0123] S3. The rotor position error signal is input to the adaptive phase-locked loop (APLL). The APLL adaptively adjusts its undamped oscillation frequency according to the motor's operating state to achieve dynamic adjustment of the observation bandwidth, and outputs rotor position and speed estimates. Sensorless vector control of the permanent magnet synchronous motor is achieved through the estimates.

[0124] Further, step S1 includes:

[0125] Establish the relationship between the actual synchronous rotating coordinate system and the estimated synchronous rotating coordinate system of the built-in permanent magnet synchronous motor (IPMSM), such as... Figure 1 As shown; α-β represents the two-phase stationary coordinate system, and dq represents the actual synchronous rotating coordinate system. - This represents the estimated synchronous rotating coordinate system; the voltage and current relationships between these coordinate systems are as follows:

[0126] (1)

[0127] (2)

[0128] Among them, u d ,u q i d , and i q These represent the stator voltage and current in the dq coordinate system, respectively. d , q , d ,and q They represent - Stator voltage and current in the coordinate system; θ err It is the actual rotor position angle θ and the estimated rotor position angle θ e The difference between them;

[0129] (3)

[0130] Since the frequency of high-frequency signals is much higher than that of fundamental signals, a high-frequency square wave voltage signal can be injected into the synchronous rotating coordinate system to establish a high-frequency model of the permanent magnet synchronous motor.

[0131] exist - In the coordinate system, the injected voltage signal is:

[0132] (4)

[0133] Where n is the sampling sequence number, and the sampling frequency is twice the PWM carrier frequency; V h The amplitude of the injected voltage signal;

[0134] Therefore, the high-frequency voltage equation becomes:

[0135] (5)

[0136] Substituting equations (2) and (4) into equation (5) yields:

[0137] (6)

[0138] Among them, L dh ,L qh ,u dh ,u qh i dh and i qh Let represent the stator inductance, high-frequency voltage signal, and high-frequency current signal in the dq coordinate system, respectively; therefore, in the αβ coordinate system, we have:

[0139] (7)

[0140] Where, Δi αh and Δi βh These are the high-frequency current deviation signals along the α and β axes of adjacent sampling points in the α-β coordinate system on the stator side of the permanent magnet synchronous motor (PMSM); ΔT is the sampling period, which is the PWM period T. s Half of, i.e., ΔT = T s / 2.

[0141] Further, step S2 includes:

[0142] S21, Traditional Anti-Integral Saturation Controller

[0143] The vector control system for permanent magnet synchronous motors suffers from problems such as excessive overshoot and low control accuracy. The root cause lies in the integral saturation phenomenon caused by the integral element in the proportional-integral (PI) module of the speed loop. An anti-integral saturation controller is employed to suppress the saturation effect and improve the system's control performance.

[0144] like Figure 2 As shown, the traditional anti-integral saturation controller is a linear feedback controller. Its principle is to estimate the difference between the output before and after the PI loop saturation, and feed this error back to the integral term through the gain, thereby achieving secondary integral compensation and eliminating the error caused by integral saturation.

[0145] when i n =i s :

[0146] (8)

[0147] when i n ≠i s :

[0148] (9)

[0149] Among them, i sat i represents the maximum output of the controller when the system is saturated. n and i s K represents the current value before and after the constraint, respectively. p , K i , K c All are coefficients greater than zero;

[0150] S22, Improved anti-integral saturation controller

[0151] Since traditional anti-integral saturation controller algorithms suffer from low control accuracy and difficulty in designing feedback coefficients, it is necessary to introduce a new algorithm that retains the simple and easy-to-implement structure of traditional anti-integral saturation controllers while employing new output and integral limiting methods.

[0152] The improved anti-integral saturation controller consists of two channels: a proportional channel that responds quickly to the received error signal with a fixed coefficient, and an integral channel that eliminates steady-state error through integral gain and discrete integrator circuitry; a limiting module that limits the total pre-output within a set value and simultaneously calculates the deviation as a compensation amount fed back to the integral channel to prevent integral saturation; the specific block diagram is shown below. Figure 3 As shown; in the output limiting mechanism, to ensure that the control quantity does not exceed the physical limits of the actuator, the following hard limiting rule is designed:

[0153] (10)

[0154] It ensures that the actual output out is strictly within the effective range by directly truncating any pre-output pre_out that exceeds the effective range [−lmt,lmt]; pre_out represents the preliminary controller output synthesized by adding the proportional and integral parts.

[0155] When the pre-output is truncated by the limiting module (i.e., pre_out ≠ out), the controller's integral term may experience integral saturation due to continuous error accumulation. To address this issue, an anti-integral saturation compensation variable is designed:

[0156] (11)

[0157] It acts on the integral channel through a feedback loop to perform real-time correction on the integral output:

[0158] (12)

[0159] Among them ki out This represents the integral output, where `ki*out` is the corrected integral output. When the system is not saturated, `ki_down` = 0, and the integral circuit works normally. When saturation occurs, `ki_down` precisely cancels out the excessive integral quantity, ensuring that the integral output matches the actual output and effectively suppressing integral saturation. Figure 3 As shown;

[0160] Substituting the average inductance L and the half-difference inductance ΔL into the above equation, we get:

[0161] (13)

[0162] If θ e =θ, that is, θ err =0, then:

[0163] (14)

[0164] (15)

[0165] The rotor position information is obtained through (10), and the rotor position error signal f(θ) is obtained. err The implementation principle of ) is as follows Figure 4 As shown.

[0166] from Figure 4 It can be seen that the rotor position error signal is:

[0167] (16)

[0168] Among them, K err Represents the coefficients of the high-frequency rotor position error signal;

[0169] S23, Improved high-frequency square wave signal injection

[0170] For high-frequency signal injection, low-pass filters are required for extracting the fundamental current signal, while band-pass filters are required for extracting the high-frequency current signal. To address this issue, an improved algorithm is proposed that completely eliminates the need for these filters, significantly improving system bandwidth and dynamic performance.

[0171] Since the actual rotor position is unknown, it needs to be studied in the estimated dq coordinate system. Therefore, equation (6) is rewritten in dq coordinate system form as follows:

[0172] (17)

[0173] In the voltage equations of a permanent magnet synchronous motor, the basic voltage equation is given by the following formula:

[0174] (18)

[0175] (19)

[0176] Within each pulse width modulation (PWM) cycle, i dh It alternates between positive and negative values, while i df There are two possibilities: either the fundamental current remains unchanged, or it changes.

[0177] During steady-state operation, the fundamental voltage will not change suddenly within one PWM cycle. df Reaching a stable value, i.e., L d ·d df / dt=0; Under this condition, the fluctuation of the total current can be considered as being caused only by high-frequency square wave voltage excitation; however, during acceleration / deceleration or load disturbances (dynamic response of the current loop), L d ·di df / dt≠0, which means that the current change within a PWM cycle is caused by the combined effect of the fundamental frequency and the high-frequency response current, such as Figure 5 As shown;

[0178] When k−1 is the peak sampling time, and k and k−2 are the valley sampling times, we have:

[0179] (20)

[0180] (twenty one)

[0181] Subtracting equation (16) from equation (15) gives:

[0182] (twenty two)

[0183] Meanwhile, according to (15)-(17), when k−1 is the valley sampling time, and k and k−2 are the peak sampling times, we have:

[0184] (twenty three)

[0185] In short, at any given moment, there is:

[0186] (twenty four)

[0187] Meanwhile, the extraction of the fundamental frequency component is given by the following formula:

[0188] (25)

[0189] This method also effectively separates the fundamental frequency component from the high-frequency component through subtraction, such as... Figure 6 As shown.

[0190] Similarly, the high-frequency response current at any given moment is expressed as:

[0191] (26)

[0192] In this formula, i α,βh (k),i α,β (k), and i α,βf (k) represent the high-frequency response current vector, the sampling current vector, and the fundamental current vector at the k-th sampling time, respectively; according to equation (26), the expressions for the high-frequency response current vector and the fundamental current vector at the k-th sampling time are derived as follows:

[0193] (27)

[0194] Traditional carrier signal separation requires low-pass or notch filters, while extraction requires band-pass filters. However, using filters, especially high-order filters, inevitably degrades the system's dynamic performance and consumes more system resources. The principle of filterless carrier separation is as follows... Figure 7 As shown. This method can extract the high-frequency response current vector and the fundamental current vector through simple algebraic operations.

[0195] To obtain the rotor position and speed signals, the separated high-frequency response current signal needs to be converted into an envelope signal, such as... Figure 8 As shown.

[0196] Further, step S3 includes:

[0197] In modern control theory, the description and representation of the state space is a direct reflection of the system. However, for various reasons, some states cannot be directly measured, thus hindering the resolution of control engineering-related problems. Therefore, researchers have proposed the goal of reconstructing the state of dynamic systems by designing observers.

[0198] After demodulating the position error signal, a position observer is needed to track the rotor's position and velocity. From the perspective of classical control theory, introducing an integrator element can improve the system's steady-state accuracy. Then, by introducing the integral part into the observer, the observer can estimate the state using the ratio of past and current values ​​and integral state information. This type of observer is called a PI observer.

[0199] Due to their versatility and ease of implementation, PI-type rotor position observers have been widely used. In sensorless control processes, the switching of different loads places very high demands on phase-locked loop (PLL)-based position observers. The constant bandwidth of the PLL cannot adapt to changing conditions. Therefore, an adaptive PLL bandwidth strategy is proposed to address this problem. This method is based on adaptively adjusting the PLL gain during transient speed and load changes; that is, the PLL bandwidth increases during transients and decreases during steady-state conditions.

[0200] First, the block diagram of a traditional phase-locked loop position observer, as follows: Figure 9 As shown.

[0201] A traditional phase-locked loop (PLL) is a typical second-order system; therefore, when the motor is in a dynamic process, zero dynamic position tracking error cannot be achieved due to the limited tracking bandwidth of the PI controller. The error transfer function of a traditional PLL is as follows:

[0202] (28)

[0203] To balance faster response speed and better stability, the damping coefficient ξ of the second-order system is designed as follows: / 2; In this way, the control parameters of the phase-locked loop (PLL) are designed as follows:

[0204] (29)

[0205] Where ρ is the oscillation frequency of the phase-locked loop;

[0206] Combining equations (28) and (29), the relationship between the observer bandwidth and the undamped oscillation frequency ρ is obtained:

[0207] (30)

[0208] It can be seen that the larger the undamped oscillation frequency ρ, the higher the bandwidth of the observer, the faster the convergence speed of the system, and thus the stronger the position tracking capability of the algorithm. However, due to the presence of signal noise in the actual system, the bandwidth cannot be designed to be too high. This is to suppress high-frequency HF noise and improve the stability of the system.

[0209] Traditional quadrature phase-locked loops (PLLs), as typical second-order systems, can achieve steady-state tracking with zero error at both low and high speeds. However, under variable speed conditions, the rotor position tracking speed is not fast enough, resulting in poor position estimation performance. If the speed changes suddenly, the position estimation error increases sharply, even leading to tracking failure. To address this issue... Figure 10 The paper proposes an adaptive phase-locked loop (APLL) to suppress steady-state position tracking deviation under variable speed conditions and also helps to reduce harmonic position errors.

[0210] exist Figure 10 In the middle, ψ f It is magnetic flux, ω c It is the cutoff frequency; as ω c As ω increases, the amplitude of the phase-locked loop decreases across the entire frequency band; when ω c When the amplitude is 0, the APLL is equivalent to the traditional quadrature phase-locked loop; the APLL has a smaller bandwidth and a lower amplitude, especially in the low-frequency band, where its filtering performance is better.

[0211] (31)

[0212] Where, ρ n It is the undamped oscillation frequency, ρ s It is the steady-state undamped oscillation frequency, ρ d It is the adaptive undamped oscillation frequency gain under transient changes, ρ sd It is the gain of the undamped oscillation frequency attenuation; Equation (31) is divided into three states: (I) in steady state, the bandwidth is a certain value; (II) in transient state, the bandwidth of the phase-locked loop is linearly related to the rate of change of the q-axis current; (III) in the process from transient to steady state, due to the current decay, the current bandwidth of the phase-locked loop should be linearly related to the bandwidth of the previous cycle. The proposed adaptive adjustment ensures strong adaptability to various operating conditions such as variable speed and variable load. The overall block diagram of the control system is as follows Figure 11 As shown.

[0213] Example:

[0214] The sensorless permanent magnet synchronous motor experimental platform built according to the proposed method mainly consists of a test motor, torque sensor, current sensor, DC power supply, voltage inverter, and power drive module. The test motor is driven by dSPACE, which can transmit experimental results to a computer. The DC voltage is 320 volts. In this experiment, the parameters of the controller and observer are described using a vector control method. Table I also lists the relevant parameters of the permanent magnet synchronous motor.

[0215] Table I. Parameters of Permanent Magnet Synchronous Motor

[0216]

[0217] A. Comparison under stable conditions

[0218] Under the same conditions, a comparison between a traditional PI controller and an anti-integral saturation controller is as follows: Figure 12 As shown.

[0219] from Figure 12It can be seen that, under the same conditions, when the speed controllers are inconsistent, the proposed novel anti-saturation controller is significantly better than the traditional PI controller in terms of speed error and rapid recovery capability when the load changes.

[0220] Under low-speed conditions, the speed, rotor error, rotor position, and q-axis current of the traditional sensorless control scheme and the proposed sensorless control scheme were compared under the same load and speed. Experimental results are as follows: Figure 13 As shown. The traditional solution is a phase-locked loop (PLL), while the proposed solution is an adaptive phase-locked loop (APLL). The speed controller in both solutions is the anti-saturation controller designed in this invention.

[0221] like Figure 13 As shown, under given conditions, both control schemes achieved the target speed of 300 rpm. The experimental results clearly demonstrate that the speed fluctuation range of the traditional control method is within ±5 rpm, while the proposed control scheme reduces the speed error range to ±2 rpm, improving accuracy by nearly 71%. Furthermore, in terms of rotor position error estimation, the traditional scheme's estimation error range is between -0.04 radians and 0.04 radians, while the proposed scheme's error range is limited to -0.02 radians to 0.02 radians, significantly narrower than the former. Moreover, this scheme also exhibits superior performance in controlling the q-axis current compared to the traditional scheme.

[0222] B. Comparison under variable speed conditions

[0223] Figure 14 The comparison of dynamic performance between the traditional solution and the proposed solution is shown. After the motor reaches steady state, the reference speed drops to 200 rpm in 1 second, and the load torque remains at 2 N·m throughout the entire motor speed regulation process.

[0224] according to Figure 14 The load change test results shown indicate that when the load changes suddenly, the maximum speed error of the traditional method reaches 15 rpm, while the proposed method only reaches 9 rpm, demonstrating significantly better performance. Regarding rotor position tracking, the maximum position error of the traditional method is -0.05 radians, while the proposed method maintains higher accuracy, with the error limited to -0.02 radians. This comparison clearly demonstrates that the proposed method has better tracking performance and dynamic response. Experimental results show that, compared to the traditional method, this method reduces the error by 71% in terms of disturbance amplitude and the smoothness of disturbance recovery during load changes.

[0225] C. Comparison under inversion conditions

[0226] After analyzing the forward rotation of the motor, a reverse rotation test and analysis were conducted, and the experimental results are as follows: Figure 15 As shown.

[0227] from Figure 15 It can be seen that even when the motor is running in reverse, the proposed method is still superior to the traditional method in terms of speed error.

[0228] In summary, this invention proposes an advanced control scheme for driving embedded permanent magnet synchronous motors, combining an adaptive phase-locked loop (APLL) and an anti-saturation controller to improve dynamic performance and operational stability. The proposed APLL improves upon traditional APLLs through an adaptive algorithm, reducing jitter under different speeds and load disturbances while maintaining high-accuracy estimation. Its adaptive mechanism ensures optimal performance in different operating cycles, thereby improving the reliability of the sensorless control system.

[0229] In terms of speed regulation, the anti-saturation controller addresses the integrator saturation problem under large transients or sudden reference changes. When the control signal saturates, it clamps the integrator output to prevent performance degradation, accelerate dynamic response, and reduce overshoot, which is crucial for high-performance drives requiring rapid acceleration. Experimental results demonstrate that the proposed strategy excels in position estimation, speed tracking, and interference immunity. By combining an adaptive phase-locked loop (APLL) with the anti-saturation controller, a robust sensorless solution is provided for embedded permanent magnet synchronous motor (IPMSM) drive systems.

[0230] The technical means disclosed in this invention are not limited to those disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications are also considered within the scope of protection of this invention.

Claims

1. A sensorless permanent magnet synchronous motor control method based on an adaptive phase-locked loop and an anti-saturation controller, comprising the following steps: S1. Inject a high-frequency square wave voltage signal into the estimated synchronous rotating coordinate system; collect the stator current of the permanent magnet synchronous motor, establish a high-frequency voltage equation, and obtain the high-frequency current deviation signal in the two-phase stationary coordinate system based on the transformation relationship between the actual and estimated rotating coordinate systems. S2. An improved anti-integral saturation controller is used as the speed loop controller to receive the speed command and the error signal of the feedback speed; the controller includes a proportional channel and an integral channel, and is equipped with a hard limiting module; When the controller output is limited, the integral compensation amount is calculated and fed back to the integral channel to suppress integral saturation; at the same time, the rotor position error signal is calculated based on the high-frequency current signal. S3. The rotor position error signal is input to the adaptive phase-locked loop (APLL). The APLL adaptively adjusts its undamped oscillation frequency according to the motor's operating state to achieve dynamic adjustment of the observation bandwidth, and outputs rotor position and speed estimates. Sensorless vector control of the permanent magnet synchronous motor is achieved through the estimates.

2. The sensorless permanent magnet synchronous motor control method based on adaptive phase-locked loop and anti-saturation controller according to claim 1, characterized in that: Step S1 includes: Establish the relationship between the actual synchronous rotating coordinate system and the estimated synchronous rotating coordinate system; α-β represents the two-phase stationary coordinate system, and dq represents the actual synchronous rotating coordinate system. - This represents the estimated synchronous rotating coordinate system; the voltage and current relationships between these coordinate systems are as follows: (1) (2) Among them, u d ,u q i d , and i q These represent the stator voltage and current in the dq coordinate system, respectively. d , q , d ,and q They represent - Stator voltage and current in the coordinate system; θ err It is the actual rotor position angle θ and the estimated rotor position angle θ e The difference between them; (3) A high-frequency square wave voltage signal is injected into a synchronous rotating coordinate system to establish a high-frequency model of the permanent magnet synchronous motor; exist - In the coordinate system, the injected voltage signal is: (4) Where n is the sampling sequence number, and the sampling frequency is twice the PWM carrier frequency; V h The amplitude of the injected voltage signal; Therefore, the high-frequency voltage equation becomes: (5) Substituting equations (2) and (4) into equation (5) yields: (6) Among them, L dh ,L qh ,u dh ,u qh i dh and i qh Let represent the stator inductance, high-frequency voltage signal, and high-frequency current signal in the dq coordinate system, respectively; therefore, in the αβ coordinate system, we have: (7) Where, Δi αh and Δi βh These are the high-frequency current deviation signals along the α and β axes of adjacent sampling points in the α-β coordinate system on the stator side of the permanent magnet synchronous motor (PMSM); ΔT is the sampling period, which is the PWM period T. s Half of, i.e., ΔT = T s / 2.

3. The sensorless permanent magnet synchronous motor control method based on adaptive phase-locked loop and anti-saturation controller according to claim 2, characterized in that: Step S2 includes: S21. The traditional anti-integral saturation controller is a linear feedback controller. Its principle is to estimate the difference between the output before and after the PI loop saturation, and feed this error back to the integral term through the gain, thereby achieving secondary integral compensation and eliminating the error caused by integral saturation. This i n =i s : (8) This i n ≠i s : (9) Among them, i sat i represents the maximum output of the controller when the system is saturated. n and i s K represents the current value before and after the constraint, respectively. p , K i , K c All are coefficients greater than zero; S22. The improved anti-integral saturation controller consists of two channels: a proportional channel that responds quickly to the received error signal with a fixed coefficient, and an integral channel that eliminates steady-state error through integral gain and discrete integral elements; a limiting module that limits the total pre-output within the set value and simultaneously calculates the deviation as a compensation amount fed back to the integral channel to prevent integral saturation; in the output limiting mechanism, to ensure that the control quantity does not exceed the physical limits of the actuator, the following hard limiting rule is designed: (10) It ensures that the actual output out is strictly within the effective range by directly truncating any pre-output pre_out that exceeds the effective range [−lmt,lmt]; pre_out represents the preliminary controller output synthesized by adding the proportional and integral parts. When the pre-output is truncated by the limiting module (i.e., pre_out ≠ out), the controller's integral term may experience integral saturation due to continuous error accumulation. To address this issue, an anti-integral saturation compensation variable is designed: (11) It acts on the integral channel through a feedback loop to perform real-time correction on the integral output: (12) Among them ki out This represents the integral output, where ki*out is the corrected integral output. When the system is not saturated, ki_down=0, and the integral circuit works normally. When saturation occurs, ki_down precisely cancels out the excessive integral quantity, keeping the integral output consistent with the actual output and effectively suppressing the integral saturation phenomenon. Substituting the average inductance L and the half-difference inductance ΔL into the above equation, we get: (13) If θ e =θ, that is, θ err =0, then: (14) (15) The rotor position information and rotor position error signal are obtained through (10): (16) Among them, K err Represents the coefficients of the high-frequency rotor position error signal; S23. Rewrite equation (6) in dq coordinate system form as follows: (17) In the voltage equations of a permanent magnet synchronous motor, the basic voltage equation is given by the following formula: (18) (19) Within each pulse width modulation (PWM) cycle, i dh It alternates between positive and negative values, while i df There are two possibilities: either the fundamental current remains unchanged, or it changes. During steady-state operation, the fundamental voltage will not change suddenly within one PWM cycle. df Once a stable value is reached, the fluctuation of the total current can be considered as being caused solely by the high-frequency square wave voltage excitation; however, during acceleration / deceleration or load disturbance, the current variation within a PWM cycle is caused by the combined effect of the fundamental wave and the high-frequency response current. When k−1 is the peak sampling time, and k and k−2 are the valley sampling times, we have: (20) (21) Subtracting equation (16) from equation (15) gives: (22) Meanwhile, according to (15)-(17), when k−1 is the valley sampling time, and k and k−2 are the peak sampling times, we have: (23) In short, at any given moment, there is: (24) Meanwhile, the extraction of the fundamental frequency component is given by the following formula: (25) Similarly, the high-frequency response current at any given moment is expressed as: (26) In this formula, i α,βh (k),i α,β (k), and i α,βf (k) represent the high-frequency response current vector, the sampling current vector, and the fundamental current vector at the k-th sampling time, respectively; according to equation (26), the expressions for the high-frequency response current vector and the fundamental current vector at the k-th sampling time are derived as follows: (27)。 4. The sensorless permanent magnet synchronous motor control method based on adaptive phase-locked loop and anti-saturation controller according to claim 3, characterized in that: Step S3 includes: First, a traditional phase-locked loop (PLL) is a typical second-order system; therefore, when the motor is in a dynamic process, zero dynamic position tracking error cannot be achieved due to the limited tracking bandwidth of the PI controller. The error transfer function of a traditional PLL is as follows: (28) To balance faster response speed and better stability, the damping coefficient ξ of the second-order system is designed as follows: / 2; In this way, the control parameters of the phase-locked loop (PLL) are designed as follows: (29) Where ρ is the oscillation frequency of the phase-locked loop; Combining equations (28) and (29), the relationship between the observer bandwidth and the undamped oscillation frequency ρ is obtained: (30) The larger the undamped oscillation frequency ρ, the higher the bandwidth of the observer, the faster the convergence speed of the system, and thus the stronger the position tracking capability of the algorithm. An adaptive phase-locked loop (APLL) is proposed to suppress steady-state position tracking deviation under variable speed conditions and also helps to reduce harmonic position error. ψ f It is magnetic flux, ω c It is the cutoff frequency; as ω c As ω increases, the amplitude of the phase-locked loop decreases across the entire frequency band; when ω c When the amplitude is 0, the APLL is equivalent to the traditional quadrature phase-locked loop; the APLL has a smaller bandwidth and a lower amplitude, especially in the low-frequency band, where its filtering performance is better. (31) Where, ρ n It is the undamped oscillation frequency, ρ s It is the steady-state undamped oscillation frequency, ρ d It is the adaptive undamped oscillation frequency gain under transient changes, ρ sd It is the gain of the undamped oscillation frequency attenuation; Equation (31) is divided into three states: (I) In steady state, the bandwidth is a certain value; (II) In transient state, the bandwidth of the phase-locked loop is linearly related to the rate of change of the q-axis current; (III) In the process from transient to steady state, due to the current decay, the current bandwidth of the phase-locked loop should be linearly related to the bandwidth of the previous cycle.

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