A sensorless control method based on surface-mounted permanent magnet synchronous motor

Abstract

A sensorless control method for a surface-mounted permanent magnet synchronous motor (SPMSM) is proposed. The method involves writing the current equations for the SPMSM in a synchronous rotating coordinate system, neglecting iron losses, eddy current losses, and saturation effects. A sliding mode dq observer and an improved sliding mode load torque observer are established. Stability analysis is performed on the sliding mode load torque observer. The estimated back EMF output from the sliding mode dq observer is processed by a phase-locked loop to obtain real-time rotor position information and estimated speed. The sign function of the sliding mode load torque observer is replaced with a saturation function, and an additional component is added to represent the average load. This achieves real-time rotor position estimation and accurate identification of load torque, improving the system's dynamic response and reducing sliding mode chattering in traditional sliding mode observers.

Description

Technical Field

[0001] This invention relates to the field of permanent magnet synchronous motor control, and in particular to a control method based on a combination of sliding mode load torque observer and sliding mode dq observer. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in various industrial precision control fields due to their advantages such as high efficiency, high reliability, wide speed range, and high power density. Sensorless control technology for PMSMs effectively obtains motor speed and rotor position information through algorithm processing, thus replacing traditional sensors and reducing production costs. However, traditional sensorless control methods are susceptible to position and speed estimation errors, resulting in significant speed fluctuations during sudden load changes, severely impacting system control performance. Therefore, to mitigate the effects of load changes, a control method that improves system dynamic response and enhances control system robustness is needed. Summary of the Invention

[0003] This invention provides a control method that combines a sliding mode dq observer based on a synchronous rotating coordinate reference system and a sliding mode torque observer based on an improved load torque identification algorithm. This method improves the dynamic response of the system and reduces the impact of load abrupt disturbances on the control system. The method specifically includes the following steps:

[0004] Step 1: Establish a mathematical model of the permanent magnet synchronous motor and a sliding mode dq observer based on a synchronous rotating coordinate system;

[0005] Step 2: Design an improved sliding mode load torque observer;

[0006] Step 3: Analyze the improved sliding mode load torque observer to achieve accurate identification of the load torque, thereby realizing precise control of the permanent magnet synchronous motor.

[0007] The mathematical model of the permanent magnet synchronous motor established in step 1 ignores iron loss, eddy current loss and saturation effect.

[0008]

[0009] In the formula: U d For direct-axis voltage; U q For quadrature axis voltage; i d i represents the stator current component along the direct axis; q L represents the stator current component along the quadrature axis. d The direct-axis component of inductance; L q n is the component of inductance along the quadrature axis; p λ is the number of pole pairs of the motor; mpm For permanent magnet flux linkage; ω eω is the electric angular velocity of the motor rotor. r T is the rotor's mechanical angular velocity; e For electromagnetic torque; R s B is the stator resistance; B is the friction viscosity coefficient; J is the moment of inertia; where the direct-axis and quadrature-axis inductances of the surface-mounted permanent magnet synchronous motor are equal, i.e., L d =L q Define the transformation matrix. The expression is:

[0010]

[0011] The voltage and current along the dq axis can then be expressed as:

[0012]

[0013] in: d respectively * q * Voltage components in a coordinate system;

[0014]

[0015] in: d respectively * q * Current components in the coordinate system;

[0016] The expression for the magnetic flux linkage is:

[0017]

[0018] in: d respectively * q * Magnetic flux components in the coordinate system;

[0019] The current equation in the dq coordinate system is further transformed into d * q * Current equations in coordinate system:

[0020]

[0021] The expression for the sliding surface S is defined as follows:

[0022]

[0023] In the formula: This is an estimated value for the direct-axis current; This is an estimated value for the direct-axis current; substituting it into the current equation yields:

[0024]

[0025] Where: f = Rs / L d g = 1 / L d , and is the sliding variable of the observer, and k is the sliding mode gain coefficient.

[0026] In step 2, based on the mathematical model of the permanent magnet synchronous motor, the motion state equation of the traditional sliding mode observer can be obtained:

[0027]

[0028] In the formula: To estimate the rotational speed; For function switching signals; i q n represents the stator current component along the quadrature axis. p λ is the number of pole pairs of the motor; mpm B is the flux linkage of the permanent magnet; J is the friction viscosity coefficient; J is the moment of inertia.

[0029] Define the sliding surface as

[0030] In summary, the estimated torque can be obtained. The expression is;

[0031]

[0032] Where T dist To address the noise caused by discontinuous operations of the sign function, a low-pass filter can be introduced to obtain:

[0033]

[0034] Where ω c The cutoff frequency of the low-pass filter:

[0035] Because the discontinuous operation of the sign function used in traditional sliding mode load torque detection introduces high-frequency noise, leading to system chattering, even the introduction of a low-pass filter inevitably introduces system errors and delays during load torque transients. Therefore, this invention designs a sliding mode load torque observer based on an improved sliding mode load torque identification algorithm. It replaces the sliding mode switching signal with a saturation function and improves the identification algorithm by introducing an additional component to represent the average estimated load, which is then incorporated into the speed observer. The new saturation function Z... s1 The expression is:

[0036]

[0037] In the formula: k is the observer gain factor;

[0038] From the above equation, we can obtain a further new equation of motion:

[0039]

[0040] Where: Z es is the large signal of Z s1 ; l is the feedback gain of Z es ;

[0041] Z es can be obtained through a low-pass filter, then the expression of Z es is:

[0042] Z es = Z s1 × ω c / (s + ω c )

[0043] Combined with the sliding mode surface function defined above, the estimated torque has the following expression:

[0044]

[0045] Since the output of the saturation function is limited to k, the value of k should satisfy k ≥ n p T L / (J + Jl):

[0046] In step 3, analyze the improved sliding mode load torque observer, specifically including: when the sliding mode surface S ≥ Δ, combined with the previous formula, Z s1 = Z es = k; when the sliding mode surface S < -Δ, Z s1 = Z es = -k; when -Δ < S < Δ, Z s1 = Z es = S·k / Δ, and this formula can be rewritten as:

[0047]

[0048] Define the sliding mode surface S as the speed error According to the Routh-Hurwitz stability criterion, when S ≥ Δ or S < -Δ, if B / J > 0, the system is always stable; when -Δ < S < Δ, if B / J + k(1 + l) / Δ > 0, the system is also stable. Further, the larger the coefficient of B / J + k(1 + l) / Δ, the larger the damping factor of the system and the shorter the transient time of the system.

[0049] If considering the influence of the low-pass filter, when in the frequency domain system equation, the speed error changes around the sliding surface, that is, -Δ < S < Δ, the equation can be expressed as:

[0050]

[0051] Where s is a complex variable of the Laplace transform, the equation is rewritten as follows to avoid confusion:

[0052]

[0053] in: It is T L The time derivative, according to the Routh-Hurwitz stability criterion:

[0054] When (ω c +B / J+k / Δ)>0 and ω c When (B / J+k / Δ(1+l))>0, the system is stable. From the above analysis, it can be concluded that the designed sliding mode load torque observer system is stable.

[0055] Compared with the prior art, the above-described technical solutions conceived in this invention can achieve the following beneficial effects:

[0056] This invention combines a sliding mode dq observer with an improved sliding mode load torque observer to achieve real-time tracking of the rotor of a surface-mounted permanent magnet synchronous motor. This effectively identifies the load torque, reduces interference from sudden load torque changes in the control system, improves the dynamic response of the system, and weakens the system chattering caused by traditional sliding mode observers. Attached Figure Description

[0057] Figure 1 This is a block diagram of a sensorless control method based on a surface-mounted permanent magnet synchronous motor;

[0058] Figure 2 For the control method flowchart; Detailed Implementation

[0059] This invention provides a control method that combines a sliding mode dq observer based on a synchronous rotating coordinate reference system and a sliding mode torque observer based on an improved load torque identification algorithm. This method improves the dynamic response of the system and reduces the impact of load abrupt disturbances on the control system. The method specifically includes the following steps:

[0060] Step 1: Establish a mathematical model of the permanent magnet synchronous motor and a sliding mode dq observer based on a synchronous rotating coordinate system;

[0061] Step 2: Design an improved sliding mode load torque observer;

[0062] Step 3: Analyze the improved sliding mode load torque observer to achieve accurate identification of the load torque, thereby realizing precise control of the permanent magnet synchronous motor.

[0063] The mathematical model of the permanent magnet synchronous motor established in step 1 ignores iron loss, eddy current loss and saturation effect.

[0064]

[0065] In the formula: U d For direct-axis voltage; U q For quadrature axis voltage; i d i represents the stator current component along the direct axis; q L represents the stator current component along the quadrature axis. d The direct-axis component of inductance; L q n is the component of inductance along the quadrature axis; p λ is the number of pole pairs of the motor; mpm For permanent magnet flux linkage; ω e ω is the electric angular velocity of the motor rotor. r T is the rotor's mechanical angular velocity; L T represents the load torque. e For electromagnetic torque; R s B is the stator resistance; B is the friction viscosity coefficient; J is the moment of inertia; where the direct-axis and quadrature-axis inductances of the surface-mounted permanent magnet synchronous motor are equal, i.e., L d =L q Define the transformation matrix. The expression is:

[0066]

[0067] The voltage and current along the dq axis can then be expressed as:

[0068]

[0069] in: d respectively * q * Voltage components in a coordinate system;

[0070]

[0071] in: d respectively * q * Current components in the coordinate system;

[0072] The expression for the magnetic flux linkage is:

[0073]

[0074] in: d respectively * q * Magnetic flux components in the coordinate system;

[0075] The current equation in the dq coordinate system is further transformed into d * q * Current equations in coordinate system:

[0076]

[0077] The expression for the sliding surface S is defined as follows:

[0078]

[0079] In the formula: This is an estimated value for the direct-axis current; This is an estimated value for the direct-axis current; substituting it into the current equation yields:

[0080]

[0081] Where: f = R s / L d g = 1 / L d , and is the sliding variable of the observer, and k is the sliding mode gain coefficient.

[0082] In step 2, based on the mathematical model of the permanent magnet synchronous motor, the motion state equation of the traditional sliding mode observer can be obtained:

[0083]

[0084] In the formula: To estimate the rotational speed; For function switching signals; i q n represents the stator current component along the quadrature axis. p λ is the number of pole pairs of the motor; mpm B is the flux linkage of the permanent magnet; J is the friction viscosity coefficient; J is the moment of inertia.

[0085] Define the sliding surface as

[0086] In summary, the estimated torque can be obtained. The expression is;

[0087]

[0088] Where T dist To address the noise caused by discontinuous operations of the sign function, a low-pass filter can be introduced to obtain:

[0089]

[0090] Where ω c The cutoff frequency of the low-pass filter:

[0091] Since the discontinuous operation of the sign function used in the traditional sliding mode load torque can cause high-frequency noise, resulting in system chattering, even if a low-pass filter is introduced, system errors and delays will inevitably be introduced during the load torque transient process. Therefore, in this invention, a sliding mode load torque observer based on an improved sliding mode load torque identification algorithm is designed. The saturation function is used to replace the sliding mode switching signal, and the identification algorithm is improved by introducing an additional component to represent the average estimated load and introducing it into the speed observer. Then the new saturation function Z s1 has the following expression:

[0092]

[0093] where: k is the observer gain factor;

[0094] From the above formula, the further new motion state equation can be obtained as:

[0095]

[0096] where: Z es is the large signal of Z s1 ; l is the feedback gain of Z es ;

[0097] Z es can be obtained through a low-pass filter, then the expression of Z es is:

[0098] Z es =Z s1 ×ω c / (s + ω c )

[0099] Combined with the sliding mode surface function defined above, the estimated torque has the following expression:

[0100]

[0101] Since the output of the saturation function is limited to k, the value of k should satisfy k ≥ n p T L / (J + Jl):

[0102] In step 3, the improved sliding mode load torque observer is analyzed, specifically including: when the sliding mode surface S ≥ Δ, combined with the previous formula, Z s1 =Z es =k; when the sliding mode surface S < -Δ, Z s1 =Z es =-k; when -Δ < S < Δ, Z s1 =Z es =S·k / Δ. Thus, the saturation function expression can be rewritten as:

[0103]

[0104] Define the sliding mode surface S as the speed error According to the Routh-Hurwitz stability criterion, when S≥Δ or S<-Δ, if B / J>0, the system is always stable. When -Δ<S<Δ, if B / J + k(1 + l) / Δ>0, the system is also stable. Further, the larger the coefficient of B / J + k(1 + l) / Δ>0, the larger the damping factor of the system and the shorter the transient time of the system.

[0105] If considering the influence of the low-pass filter, when in the frequency-domain system equation, the speed error varies around the sliding surface, that is, -Δ<S<Δ, the equation can be expressed as:

[0106]

[0107] where s is the complex variable of the Laplace transform. To avoid confusion, rewrite the equation as:

[0108]

[0109] where: is the time derivative of T L According to the Routh-Hurwitz stability criterion:

[0110] When (ω c + B / J + k / Δ)>0 and ω c (B / J + k / Δ(1 + l))>0, the system is stable. From the above analysis, it can be concluded that the designed sliding mode load torque observer system is stable.

[0111] The above technical solution conceived by the present invention, compared with the prior art, can achieve the following beneficial effects:

[0112] By combining the sliding mode dq observer and the improved sliding mode load torque observer, the present invention can effectively identify the load torque for the real-time tracking of the surface-mounted permanent magnet synchronous motor rotor, reduce the interference of the load torque mutation control system, improve the dynamic response of the system, and weaken the system chattering caused by the traditional sliding mode observer.

Claims

1. A sensorless control method for surface-mounted permanent magnet synchronous motor, characterized by, Specifically comprising: Step 1, design an improved sliding mode load torque observer, replace the sliding mode switching signal with a saturation function, and improve the identification algorithm, introduce an additional component to estimate the average load, and introduce it into the speed observer; Step 2, rewrite the saturation function expression, use Routh-Hurwitz stability criterion to analyze the stability of the improved sliding mode load torque observer, so as to realize the accurate control of the permanent magnet synchronous motor; The step 1 includes: designing an improved sliding mode load torque observer; According to the mathematical model of the permanent magnet synchronous motor, the motion state equation of the traditional sliding mode load torque observer can be obtained: wherein: is the estimated rotational speed; is the function switching signal; i q is the stator current in the quadrature axis; n p is the number of motor pole pairs; λ mpm is the permanent magnet flux linkage; B is the frictional viscous coefficient; J is the moment of inertia; The sliding surface is defined as The sliding surface is defined as s1 The expression of the new saturation function Z In the formula, k is the gain factor of the observer; From the above formula, a further new motion state equation is obtained: In the formula: Z es For Z s1 Large signal; l is Z es Feedback gain; Z es may be obtained by a low-pass filter, then Z es is expressed as: Z es = Z s1 x ω c / (s + ω c ) where: ω c is the cut-off frequency of the low-pass filter; Combining the previously defined sliding surface function gives the estimated torque The expression for the estimated torque is Since the output of the saturation function is limited to k, the value of k should satisfy k ≥ n p T L (J + Jl): The step 2 includes: rewriting the saturation function expression: When the sliding surface S≥Δ, combining the previous formula, we can get Z s1 = Z es = k, when the sliding surface S<-Δ, we can get Z s1 = Z es = -k, when -Δ<S<Δ, we can get Z s1 = Z es = S·k / Δ, thus the formula is rewritten as: The sliding surface S is defined as the velocity error According to Routh-Hurwitz stability criterion, when S≥Δ or S<-Δ, if B / J>0, the system is always stable, when -Δ<S<Δ, if B / J+k(l+l) / Δ>0, the system is also stable, further, the greater the coefficient of B / J+k(l+l) / Δ, the greater the damping factor of the system, the shorter the transient time of the system, if the influence of the low-pass filter is considered, when the velocity error changes around the sliding surface in the frequency domain system equation, i.e. -Δ<S<Δ, the equation can be expressed as: Where s is the complex variable of Laplace transform, in order to avoid confusion, rewrite the equation as: wherein: is T L is the time derivative of T according to the Routh-Hurwitz stability criterion: when (ω c + B / J + k / Δ) > 0 and ω c The system is stable when (B / J + k / Δ(1 + l)) > 0. From the above analysis, it can be concluded that the designed sliding mode load torque observer system is stable.

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