A Method for Estimating the Rotor Position and Speed of PMSM Using a Robust Adaptive Observer

Abstract

The invention discloses a method for estimating the rotor position and speed of a PMSM with a strong adaptive observer, which specifically includes the following steps: Step 1, constructing the state equation of the permanent magnet synchronous motor; Step 2, constructing a strong adaptive observer based on the state equation obtained in Step 1 to estimate the extended back electromotive force; Step 3, estimating the rotor position and speed of the permanent magnet synchronous motor through the enhanced phase-locked loop with the estimated extended back electromotive force obtained in Step 2. The invention solves the problems that the existing sliding mode observer has large fluctuations and poor accuracy in estimating the rotor position and speed of the permanent magnet synchronous motor due to the sign function or non-linear function and the low-pass filter.

Description

Technical Field

[0001] The present invention belongs to the technical field of permanent magnet synchronous motor control, and particularly relates to a method for estimating the rotor position and speed of a PMSM with a robust adaptive observer. Background Technique

[0002] Permanent magnet synchronous motors (PMSMs) have many advantages such as small volume, high power density, and wide speed regulation range, and have extensive application value in military, industrial, medical, household appliances and other fields. The control performance of permanent magnet synchronous motors depends severely on the accurate acquisition of rotor position and speed. However, installing mechanical sensors will not only increase the volume and cost of the system, but also reduce the reliability of the system. Therefore, the accurate estimation of the rotor position and speed of a permanent magnet synchronous motor without installing mechanical sensors is crucial.

[0003] Currently, among the methods for estimating the rotor position and speed of permanent magnet synchronous motors, the sliding mode observer controls the system state to tend to the set sliding surface and generates a sliding mode by pre-selecting the sliding surface and the sliding mode control function. It has strong robustness to parameter changes, internal disturbances and external interferences, and thus has been widely studied and applied. However, the sign function or non-linear function in the sliding mode observer will cause chattering phenomena, resulting in large fluctuations and poor accuracy of the estimated rotor position and speed. Moreover, the added low-pass filter will deteriorate the dynamic performance of the system and cause the estimated rotor position to lag behind the actual rotor position. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for estimating the rotor position and speed of a PMSM with a robust adaptive observer, so as to solve the problem that the existing sliding mode observer has large fluctuations and poor accuracy in estimating the rotor position and speed of a permanent magnet synchronous motor due to the sign function or non-linear function and the low-pass filter.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A method for estimating the rotor position and speed of a PMSM with a robust adaptive observer specifically includes the following steps:

[0007] Step 1, construct the state equation of the permanent magnet synchronous motor, and the specific method is as follows:

[0008] The voltage equation of the permanent magnet synchronous motor in the αβ two-phase stationary coordinate system is shown in formula (1):

[0009]

[0010] Among them, u α 、u β are the components of the stator voltage on the α-axis and β-axis respectively, iα , i β are the components of the stator current on the α-axis and β-axis respectively, p is the differential operator, and R s is the stator resistance, and e α = -[(L d - L q )i d ω r + ω r ψ f sinθ r , e β = [(L d - L q )i d ω r + ω r ψ f cosθ r , e α and e β are the components of the extended back electromotive force on the α-axis and β-axis respectively, L d is the d-axis inductance, L q is the q-axis inductance, i d is the component of the stator current on the d-axis, ψ f is the permanent magnet flux linkage, ω r is the actual rotor speed, and θ r is the actual rotor position;

[0011] The differential equation of the stator current is obtained through Equation (1) as shown in Equation (2):

[0012]

[0013] Step 2. Construct a robust adaptive observer to estimate the extended back electromotive force based on the permanent magnet synchronous motor state equation obtained in Step 1. The specific approach is as follows:

[0014] Step 2.1. Construct a robust adaptive observer for the differential equation of the stator current obtained through Equation (2) as shown in Equation (3):

[0015]

[0016] where is the estimated value of i α , is the estimated value of i β , and f a is the adaptive function of the adaptive observer;

[0017] The adaptive functions and in Equation (3) are the estimated extended back electromotive forces on the α-axis and β-axis respectively as shown in Equation (4):

[0018]

[0019] Among them, is the estimated value of the α-axis extended back electromotive force e α ; is the estimated value of the β-axis extended back electromotive force e β ;

[0020] Step 2.2: Design the adaptive function f in the strong adaptive observer in Step 2.1 a ;

[0021] The adaptive function f in the strong adaptive observer a determines the estimation accuracy and dynamic performance of the strong adaptive observer. The adaptive function f a should be adaptively adjusted following the frequency of the extended back electromotive force, and should have a high gain and no phase shift at the frequency of the extended back electromotive force. Design the adaptive function f of the strong adaptive observer a as shown in Equation (5):

[0022]

[0023] where ω α is the center frequency, ω e is the estimated rotational speed, ω α = ω e , the center frequency ω α follows the estimated rotational speed ω e and adaptively changes. s is the complex frequency, μ is an adjustable parameter. The larger μ is, the smaller the amplitude and phase changes near the center frequency, and the stronger the robustness to the center frequency, but the frequency selection performance decreases and the noise suppression ability decreases. When the motor is in dynamic state, μ should be increased to enhance the robustness to the center frequency and improve the stability. When the motor is in steady state, μ should be decreased to enhance the noise suppression ability; λ is the gain coefficient. The larger λ is, the greater the gain at the center frequency and the better the frequency selection characteristics, but too large a gain coefficient λ is likely to cause the system to become unstable; k is an adjustable parameter. The larger the value of k, the faster the dynamic response of the adaptive observer, but too large a k will cause the center frequency of the adaptive function f a to shift, resulting in the estimated rotor position lagging behind the actual rotor position. Therefore, the adjustable parameter k should be adjusted according to the operating state of the motor. When the motor is operating in dynamic state, k should be increased to increase the tracking performance of the adaptive observer. When the motor is operating in steady state, k should be decreased to ensure the accuracy of the center frequency;

[0024] Step 3: Estimate the rotor position and rotational speed of the permanent magnet synchronous motor through an enhanced phase-locked loop using the estimated extended back electromotive force obtained in Step 2. The specific method is as follows:

[0025] The rotor position error signal calculated from the extended back electromotive force estimated by formulas (3) and (4) is shown in formula (8):

[0026]

[0027] where θ e is the estimated rotor position and ε is the rotor position error signal;

[0028] The rotor position error signal ε is adjusted by an enhanced loop filter to obtain the estimated rotational speed as shown in formula (9):

[0029]

[0030] where ω σ = ω * is an adjustable parameter, and ω σ adapts to adjust following the set rotational speed ω * ;

[0031] Integrating the estimated rotational speed ω e gives the estimated rotor position as shown in formula (10):

[0032]

[0033] Furthermore, the adjustment method of the adjustable parameter μ described in step 2.2 is shown in formula (6):

[0034]

[0035] where ω * is the set rotational speed.

[0036] Furthermore, the adjustment method of the adjustable parameter k described in step 2.2 is shown in formula (7):

[0037]

[0038] where ω * is the set rotational speed.

[0039] Furthermore, λ = 70 as described in step 2.2.

[0040] The beneficial effects of the present invention are:

[0041] Compared with the method of estimating the rotor position and speed using a traditional sliding mode observer, the strong adaptive observer adopted in the present invention does not cause chattering phenomena, and a low-pass filter is not required during the process of estimating the rotor position and speed, thus avoiding the problem of the estimated rotor position lagging behind the actual rotor position caused by the low-pass filter. The enhanced phase-locked loop suppresses the rotor position error of the traditional phase-locked loop when the speed ramp is given, and the adjustable parameter ω of the enhanced loop filter in the enhanced phase-locked loop σ follows the set speed ω * and adaptively adjusts, improving the dynamic performance and noise suppression ability of the system. Description of the Drawings

[0042] Figure 1 is the block diagram of the vector control system adopted in the PMSM rotor position and speed estimation method using a strong adaptive observer of the present invention;

[0043] Figure 2 is the block diagram of the strong adaptive observer adopted in the PMSM rotor position and speed estimation method using a strong adaptive observer of the present invention, Figure 2 (a) is the block diagram of the strong adaptive observer for estimating the extended back electromotive force of the α-axis, Figure 2 (b) is the block diagram of the strong adaptive observer for estimating the extended back electromotive force of the β-axis;

[0044] Figure 3 is the block diagram of the enhanced phase-locked loop structure adopted in the PMSM rotor position and speed estimation method using a strong adaptive observer of the present invention. Detailed Embodiment

[0045] The present invention will be described in detail below in conjunction with the drawings and specific embodiments.

[0046] A PMSM rotor position and speed estimation method using a strong adaptive observer, in which the block diagram of the vector control system of the PMSM rotor position and speed estimation method using a strong adaptive observer is as Figure 1 shown.

[0047] A PMSM rotor position and speed estimation method using a strong adaptive observer is specifically implemented according to the following steps:

[0048] Step 1, construct the state equation of the permanent magnet synchronous motor, and the specific method is as follows:

[0049] The voltage equation of the permanent magnet synchronous motor in the αβ two-phase stationary coordinate system is shown in formula (1):

[0050]

[0051] Among them, u α 、u βare the components of the stator voltage on the α-axis and β-axis, respectively, and i α , i β are the components of the stator current on the α-axis and β-axis, respectively, p is the differential operator, and R s is the stator resistance, and e α =-[(L d -L q )i d ω r +ω r ψ f sinθ r , e β =[(L d -L q )i d ω r +ω r ψ f cosθ r , e α and e β are the components of the extended back electromotive force on the α-axis and β-axis, respectively, L d is the d-axis inductance, L q is the q-axis inductance, i d is the component of the stator current on the d-axis, ψ f is the permanent magnet flux linkage, ω r is the actual rotor speed, and θ r is the actual rotor position;

[0052] The differential equation of the stator current is obtained through Equation (1) as shown in Equation (2) below:

[0053]

[0054] Step 2. Construct a strong adaptive observer as shown in Figure 2 to estimate the extended back electromotive force using the state equation obtained in Step 1. The specific method is as follows:

[0055] Step 2.1. Construct a strong adaptive observer for the differential equation of the stator current obtained through Equation (2) as shown in Equation (3):

[0056]

[0057] where is the estimated value of i α , is the estimated value of i β , and f a is the adaptive function of the adaptive observer;

[0058] The adaptive functions and The estimated α-axis extended back electromotive force and β-axis extended back electromotive force are shown in Equation (4) as follows:

[0059]

[0060] Wherein, is the estimated value of the α-axis extended back electromotive force e α , is the estimated value of the β-axis extended back electromotive force e β ;

[0061] Step 2.2: Design the adaptive function f a in the strong adaptive observer in Step 2.1;

[0062] The characteristics of the adaptive function f a in the strong adaptive observer determine the estimation accuracy and dynamic performance of the strong adaptive observer. The adaptive function f a should be adaptively adjusted following the frequency of the extended back electromotive force and should have a high gain and no phase shift at the frequency of the extended back electromotive force. The adaptive function f a of the strong adaptive observer is designed as shown in Equation (5):

[0063]

[0064] Wherein, ω α is the center frequency, ω e is the estimated rotational speed, ω α =ω e . When the motor runs for the first time, the initial value of ω e is given as 0. After that, the center frequency ω α follows the rotational speed ω e estimated in Step 3 and adaptively changes. s is the complex frequency, μ is an adjustable parameter. The larger μ is, the smaller the amplitude and phase changes near the center frequency are, and the stronger the robustness to the center frequency is, but the frequency selection performance decreases and the noise suppression ability decreases. When the motor is in dynamic state, μ should be increased to enhance the robustness to the center frequency and improve the stability. When the motor is in steady state, μ should be decreased to enhance the noise suppression ability; λ is the gain coefficient. The larger λ is, the larger the gain at the center frequency is and the better the frequency selection characteristics are, but too large gain coefficient λ is likely to cause the system to become unstable. Take λ = 70; k is an adjustable parameter. The larger the value of k is, the faster the dynamic response of the adaptive observer is, but too large k will cause the center frequency of the adaptive function f a to shift, resulting in the estimated rotor position lagging behind the actual rotor position. Therefore, the adjustable parameter k should be adjusted according to the operating state of the motor. When the motor is running in dynamic state, k should be increased to increase the tracking performance of the adaptive observer. When the motor is running in steady state, k should be decreased to ensure the accuracy of the center frequency;

[0065] The adjustable parameter μ is adjusted as shown in formula (6):

[0066]

[0067] where ω * is the set speed;

[0068] The adjustable parameter k is adjusted as shown in formula (7):

[0069]

[0070] Step 3: Estimate the rotor position and speed of the permanent magnet synchronous motor through the enhanced phase-locked loop from the estimated extended back electromotive force obtained in Step 2. The specific method is as follows: Figure 3 Estimate the rotor position error signal from the extended back electromotive force estimated by formulas (3) and (4) as shown in formula (8):

[0071] where θ

[0072]

[0073] is the estimated rotor position, and ε is the rotor position error signal; e The rotor position error signal ε is adjusted through an enhanced loop filter to obtain the estimated speed as shown in formula (9):

[0074] where ω

[0075]

[0076] is an adjustable parameter, ω σ = ω * follows the set speed ω σ and is adaptively adjusted; * Integrate the estimated speed ω

[0077] e to obtain the estimated rotor position as shown in formula (10):

[0078]

[0079] The vector control system block diagram adopted by the PMSM rotor position and speed estimation method using a robust adaptive observer is as shown in Figure 1 The system consists of 3 PI regulators to form a double-loop control of the speed loop and the current loop. The output of the speed loop PI regulator is used as the input of the maximum torque per ampere control (MTPA). The current command output by MTPA is used as the input of the current loop PI regulator, and the output of the current regulator controls the power electronic converter.

[0080] ​The stator current \(i\) of the permanent magnet synchronous motor in the three-phase stationary coordinate system is detected by a current Hall sensor a 、\(i\) b 、\(i\) c ; The detected three-phase stator currents \(i\) a 、\(i\) b 、\(i\) c are transformed into the current values \(i\) α 、\(i\) β in the two-phase stationary coordinate system through the abc / αβ transformation; \(i\) α 、\(i\) β are transformed into the current values \(i\) d 、\(i\) q in the two-phase synchronous rotating coordinate system through the αβ / dq transformation; The two-phase voltages \(u\) α 、\(u\) β and the two-phase currents \(i\) α 、\(i\) β in the two-phase stationary coordinate system are used as the inputs of the strong adaptive observer as shown in Figure 2 , and the output of the strong adaptive observer is the estimated extended back electromotive force The estimated extended back electromotive force passes through the enhanced phase-locked loop as shown in Figure 3 to obtain the estimated rotor \(\theta\) e and the rotational speed \(\omega\) e ; The difference is taken between the given rotational speed \(\omega\) * of the speed loop and the rotational speed \(\omega\) e estimated by the phase-locked loop, and after passing through the PI controller of the speed loop, the electromagnetic torque given value is output. Then, the given excitation current and the given torque current are obtained by the maximum torque per ampere (MTPA); The difference is taken between the given excitation current and the feedback current \(i\) d , and after passing through the PI controller of the current loop, the \(d\)-axis voltage is output. The difference is taken between the given excitation current and the feedback current \(i\) q , and after passing through the PI controller of the current loop, the \(q\)-axis voltage is output. After passing through the dq / αβ transformation, the two-phase voltages \(u\) α 、\(u\) β in the two-phase stationary coordinate system are obtained, and then through SVPWM modulation, the three-phase inverter is controlled, and finally the permanent magnet synchronous motor is driven to work.

[0081] Although the specific embodiments of the present invention have been described above, those skilled in the art should understand that this is only an example, and the protection scope of the present invention is defined by the appended claims. Without departing from the principle and essence of the present invention, those skilled in the art can make various changes or modifications to these embodiments, but these changes and modifications all fall within the protection scope of the present invention.

Claims

1. A method for estimating the rotor position and speed of a PMSM using a strong adaptive observer, characterized in that, Specifically, it includes the following steps: Step 1, construct the state equation of the permanent magnet synchronous motor. The specific method is as follows: In the αβ two-phase stationary coordinate system, the voltage equation of the permanent magnet synchronous motor is shown in Formula (1): where u α and u β are the components of the stator voltage on the α-axis and β-axis respectively, i α and i β are the components of the stator current on the α-axis and β-axis respectively, p is the differential operator, R s is the stator resistance, e α =-[(L d -L q )i d ω r +ω r ψ f sinθ r , e β =[(L d -L q )i d ω r +ω r ψ f cosθ r , e α and e β are the components of the extended back electromotive force on the α-axis and β-axis respectively, L d is the d-axis inductance, L q is the q-axis inductance, i d is the component of the stator current on the d-axis, ψ f is the permanent magnet flux linkage, ω r is the actual rotor speed, θ r is the actual rotor position; The differential equation of the stator current is obtained from Formula (1) as shown in Formula (2): Step 2, construct a strong adaptive observer to estimate the extended back electromotive force based on the state equation of the permanent magnet synchronous motor obtained in Step 1. The specific method is as follows: Step 2.1, construct a strong adaptive observer from the differential equation of the stator current obtained from Formula (2) as shown in Formula (3): Among them, is the estimated value of i α , is the estimated value of i β , and f a is the adaptive function of the adaptive observer; Adaptive function in formula (3) and are the estimated α-axis extended back electromotive force and β-axis extended back electromotive force respectively, as shown in formula (4): wherein, is the estimated value of the α-axis extended back electromotive force e α , is the estimated value of the β-axis extended back electromotive force e β ; Step 2.2, design the adaptive function f in the strong adaptive observer in Step 2.1 a ; Adaptive function f in the robust adaptive observer a The characteristics of a determine the estimation accuracy and dynamic performance of the robust adaptive observer. The adaptive function f a should be adaptively adjusted following the frequency of the extended back electromotive force, and should have a high gain and no phase shift at the frequency of the extended back electromotive force. The adaptive function f of the robust adaptive observer is designed as shown in Equation (5): Among them, ω α is the center frequency, ω e is the estimated rotational speed, ω α = ω e , the center frequency ω α follows the estimated rotational speed ω e to adaptively change. s is the complex frequency, μ is an adjustable parameter. The larger μ is, the smaller the amplitude and phase changes near the center frequency, and the stronger the robustness to the center frequency, but the frequency selection performance decreases, and the noise suppression ability decreases. When the motor is in dynamic state, μ should be increased to enhance the robustness to the center frequency and improve stability. When the motor is in steady state, μ should be decreased to enhance the noise suppression ability; λ is the gain coefficient. The larger λ is, the greater the gain at the center frequency, and the better the frequency selection characteristics, but too large a gain coefficient λ is likely to cause the system to become unstable; k is an adjustable parameter. The larger the value of k, the faster the dynamic response of the adaptive observer, but too large a k will cause the center frequency of the adaptive function f a to shift, resulting in the estimated rotor position lagging behind the actual rotor position. Therefore, the adjustable parameter k should be adjusted according to the operating state of the motor. When the motor is operating in dynamic state, k should be increased to improve the tracking performance of the adaptive observer. When the motor is operating in steady state, k should be decreased to ensure the accuracy of the center frequency; Step 3, estimate the rotor position and speed of the permanent magnet synchronous motor by the enhanced phase-locked loop using the estimated extended back electromotive force obtained in Step 2. The specific method is as follows: Calculate the rotor position error signal from the estimated extended back electromotive force estimated by Formulas (3) and (4) as shown in Formula (8): where θ e is the estimated rotor position and ε is the rotor position error signal; The rotor position error signal ε is adjusted by the enhanced loop filter to obtain the estimated speed as shown in Formula (9): Among them, ω σ = ω * is an adjustable parameter, and ω σ adapts to the set rotational speed ω * for adaptive adjustment; For the estimated rotational speed ω e Integrating gives the estimated rotor position as shown in Equation (10):

2. The method for estimating the rotor position and speed of a PMSM using a strong adaptive observer according to claim 1, characterized in that, The adjustment method of the adjustable parameter μ described in Step 2.2 is shown in Formula (6): where ω * is the set rotational speed.

3. The method for estimating the rotor position and speed of a PMSM using a strong adaptive observer according to claim 1, wherein The adjustment method of the adjustable parameter k described in Step 2.2 is shown in Formula (7): where, ω * is the set rotational speed.

4. The method for estimating the rotor position and speed of a PMSM using a strong adaptive observer according to claim 1, wherein In Step 2.2, λ = 70.

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