Permanent magnet synchronous motor sensorless control method of integral adaptive observer

Abstract

The invention relates to the technical field of motor control, in particular to an integral self-adaptive observer method for permanent magnet synchronous motor sensorless control, which comprises the following steps of: 1, taking a surface-mounted permanent magnet synchronous motor as a research object, selecting a two-phase static coordinate system under a two-phase static coordinate system, the error i between the actual value and the estimated value of the stator current is a state variable; 2, designing a finite time integral sliding mode function s, and enabling the system to converge in finite time; a smooth H (i) function is designed, the function weakens buffeting caused by constant high switching gain, a finite time integral sliding mode function is further provided, a fuzzy rule is designed to adjust back electromotive force feedback gain, the sine degree of back electromotive force is made to be better, the estimation performance of the rotor position and speed is improved, and the method is suitable for large-scale popularization and application. And the accurate observation performance is still kept under the complex working condition.

Description

Technical Field

[0001] The invention relates to the technical field of motor control, and in particular to a sensorless control method for a permanent magnet synchronous motor using an integral adaptive observer. Background Art

[0002] Permanent magnet synchronous motors have the advantages of high power density, wide speed regulation range, and fast dynamic response. They have been widely used in servo drives, electric vehicles and other fields. In order to make the permanent magnet synchronous motor control system have higher performance, it is necessary to obtain accurate motor speed and rotor position information. The traditional method is to install a mechanical position sensor in the system, but the use of mechanical sensors will increase the instability and cost of the system. To solve this problem, scholars have proposed a position sensorless control method.

[0003] At present, position sensorless control methods are mainly divided into two categories: one is based on high-frequency signal injection; the other is based on fundamental wave mathematical model. Among them, high-frequency signal injection method is suitable for the case where the motor runs at zero speed or low speed, and fundamental wave mathematical model method is suitable for the case where the motor runs at medium and high speed. This type of method extracts rotor position and speed information from the back electromotive force. It mainly includes extended Kalman filter algorithm, model reference adaptive control algorithm, sliding mode observer algorithm and intelligent algorithm combined with machine learning or fuzzy rules, etc. Most of these methods have the defects of complex structure, large amount of calculation, high requirements on digital processor performance and poor robustness.

[0004] Compared with other methods, the sliding mode observer method has the advantages of simple algorithm, insensitivity to motor parameter changes, and strong robustness. It can weaken the impact of system parameter changes and disturbances. In the traditional sliding mode observer method, sign function and low-pass filter are used to obtain the back-electromotive force signal. The introduction of low-pass filter will cause phase delay, and the system using sign function will inevitably have the problem of high-frequency jitter. Summary of the invention

[0005] The object of the present invention is to provide a sensorless control method for a permanent magnet synchronous motor using an integral adaptive observer to solve the problems raised in the above background technology.

[0006] The purpose of the present invention can be achieved through the following technical solutions:

[0007] An integral adaptive observer method for position sensorless control of a permanent magnet synchronous motor comprises the following steps:

[0008] Step 1: Take the surface-mounted permanent magnet synchronous motor as the control object, and select the error i between the actual value and the estimated value of the stator current in the two-phase stationary coordinate system as the state variable;

[0009] The stator current state equation can be expressed as:

[0010]

[0011] In the formula, u α 、u β 、i α 、i β 、e α and e β Represent the stator voltage, stator current and back electromotive force on the α-β axis respectively; R is the stator resistance; L s is the stator inductance.

[0012] Among them, the back electromotive force can be expressed as:

[0013]

[0014] In the formula, ω e , f and θ e They represent electrical angular velocity, permanent magnet flux and electrical angle respectively.

[0015] In order to obtain the estimated back EMF, the sliding mode observer is designed as:

[0016]

[0017] In the formula, and represents the estimated value of stator current; and Represents the stator current estimation error; sign() is a discontinuous function - a switching function; g is the sliding mode gain.

[0018] Therefore, the stator current error state equation can be expressed as:

[0019]

[0020] From the stator current error state equation, we know that when the system state variable approaches the sliding surface The back EMF can be expressed as:

[0021]

[0022] Step 2: Design a finite time integral sliding mode function s to make the system converge within a finite time;

[0023] Since the integral has a filtering effect, the chattering can be suppressed. In view of the problem that the traditional integral sliding mode function cannot converge in a finite time, an improved finite integral sliding mode function is designed as follows:

[0024]

[0025] In the formula, λ1, λ2>0; q∈(0,1).

[0026] The mathematical expression of the function H(i) of the system state variable i is:

[0027]

[0028] In the formula, m>0.

[0029] This function has isotropic properties, i.e.

[0030]

[0031] Step 3, design fuzzy rules to adjust the parameters of the back-EMF observer in real time, and construct an integral adaptive observer;

[0032] The integral adaptive sliding mode current observer is designed as:

[0033]

[0034] Rewrite the integral adaptive sliding mode current observer into vector form:

[0035]

[0036] In the formula, u s =[u α ,u β ] T ;v s =[v α , v β ] T ;

[0037] In order to improve the performance of the current observer, the proposed control law v s By the equivalent control law v eq and the switching control law v sw Among them, v s The specific expression is:

[0038] v s =v eq +v sw

[0039]

[0040] v sw =﹣εs-ρH(s)

[0041] Where, ε>0; ρ>0;

[0042] Step 4: Propose a closed-loop phase tracker, use the actual value of the rotor position and the estimated value to phase-lock to obtain the rotor position error compensation, and output the final rotor position after combining it with the basic rotor position.

[0043] The closed-loop speed is the speed after filtering by a low-pass filter, while the unfiltered speed is used in the sliding mode observer. There must be a deviation η between the estimated rotor position and the actual rotor position. error for:

[0044]

[0045] In the formula, represents the unfiltered speed, Indicates the estimated speed.

[0046] In addition, in order to compensate for the rotor position estimation error caused by the low-pass filter and the phase-locked loop, the expression of the error δ is defined as:

[0047]

[0048] δ contains the rotor position error information. By using the closed-loop phase tracking principle of the phase-locked loop and locking the actual position with the estimated position, the error compensation l can be obtained. Its expression is:

[0049]

[0050] In the formula, K p is the proportionality coefficient; T i is the integration time constant.

[0051] Based on the above analysis, the rotor position error compensation can be obtained by the error compensation amount l and the deviation amount η error The rotor position can be finally expressed as:

[0052]

[0053] In the formula, is the rotor position output by the phase-locked loop.

[0054] Beneficial effects of the present invention:

[0055] (1) The present invention designs a smooth H(i) function, which weakens the jitter caused by a constant high switching gain. It further proposes a finite time integral sliding mode function and designs fuzzy rules to adjust the back EMF feedback gain, so that the sinusoidality of the back EMF is better, the estimation performance of the rotor position and speed is improved, and accurate observation performance is still maintained under complex working conditions.

[0056] (2) The present invention proposes a closed-loop phase tracker, which uses the actual value and the estimated value to lock the phase to obtain the error compensation amount. The rotor position error after compensation is small. The proposed method not only improves the estimation performance of the rotor position and speed, but also maintains accurate observation performance under speed change, load addition and reduction and low-speed conditions.

[0057] (3) The experimental results verify the effectiveness of the proposed integral adaptive observer method for position sensorless control of permanent magnet synchronous motors. This control strategy can provide a reference for position sensorless control of permanent magnet synchronous motors. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0059] Figure 1 It is a block diagram of position sensorless control of a permanent magnet synchronous motor provided by an embodiment of the present invention;

[0060] Figure 2 is a flow chart of position sensorless control of a permanent magnet synchronous motor provided by an embodiment of the present invention;

[0061] Figure 3 is a comparison diagram of the effects of the function provided by the embodiment of the present invention and the hyperbolic tangent function;

[0062] Figure 4 is a structural diagram of an integral adaptive observer provided by an embodiment of the present invention;

[0063] Figure 5 The results of the experimental comparison of the estimated rotation speed between the position sensorless control method provided by the embodiment of the present invention and the existing method;

[0064] Figure 6 The figure is a comparison experiment result of the rotation speed error between the position sensorless control method provided by the embodiment of the present invention and the existing method;

[0065] Figure 7 It is a comparison chart of rotor position error experimental results of the position sensorless control method provided by an embodiment of the present invention and the existing method. DETAILED DESCRIPTION

[0066] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0067] In this embodiment, a 400W surface-mounted permanent magnet motor is used as the control object. Based on the speed and current double closed-loop control structure, the rotor position obtained by the present invention is used for vector control. The control block diagram is as follows: Figure 1 As shown, the specific execution flow chart of this embodiment is as follows Figure 2 shown.

[0068] like Figure 1 As shown, the present invention provides an integral adaptive observer method for position sensorless control of a permanent magnet synchronous motor, and the specific implementation steps include:

[0069] Step 1: Real-time rotor position estimation based on integral adaptive observer:

[0070] First, the three-phase stator currents a, b, and c of the permanent magnet synchronous motor are collected. a 、i b and i c The collected three-phase stator current is transformed from the natural coordinate system (ABC) to the two-phase stationary coordinate system (α-β) through Clark coordinate transformation, so as to obtain the stator current i in the two-phase stationary coordinate system α and i β ;

[0071] Clark transformation matrix T 3s / 2r The expression is:

[0072]

[0073] Then, a permanent magnet synchronous motor current model in a two-phase stationary coordinate system (α-β) is established, and an integral sliding mode current observer is constructed according to the permanent magnet synchronous motor current model in a two-phase stationary coordinate system (α-β);

[0074] The current model of the permanent magnet synchronous motor based on the two-phase stationary coordinate system (α-β) is:

[0075]

[0076] In the formula, u α 、u β 、i α 、i β 、e α and e βRepresent the stator voltage, stator current and back electromotive force on the α-β axis respectively; R is the stator resistance; L s is the stator inductance.

[0077] The integral sliding mode current observer based on the two-phase stationary coordinate system (α-β) is:

[0078]

[0079] Rewrite equation (3) into vector form:

[0080]

[0081] In the formula, u s =[u α ,u β ] T ;v s =[v α , v β ] T ; “^” indicates an estimated value.

[0082] Among them, the proposed control law v s By the equivalent control law v eq and the switching control law v sw Among them, v s The specific expression is:

[0083]

[0084] Where, ε>0; ρ>0; “~” indicates the error between the estimated value and the actual value.

[0085] The mathematical expression of the function H(i) of the system state variable i is:

[0086]

[0087] In the formula, m>0.

[0088] Finally, using the stator current i in the two-phase stationary coordinate system α 、i β and stator voltage u α 、u β , which is input into the integral adaptive observer to calculate the equivalent back electromotive force of the α-β axis;

[0089] Subtracting equation (2) from equation (3), the stator current error state equation is:

[0090]

[0091] When the system reaches the sliding mode, we can get:

[0092]

[0093] According to formula (8), the equivalent back electromotive force in formula (7) can be expressed as:

[0094]

[0095] Step 2: Based on the rotor position compensation of the closed-loop phase correction link, the equivalent back EMF output by the back EMF observer is used as the input of the phase-locked loop to extract the rotor position information and compensate for the rotor position error:

[0096] The rotor position error compensation process based on the phase-locked loop is as follows:

[0097] The expression of the phase-locked loop rotor position ΔE is:

[0098]

[0099] In the formula, e s =ω e ψ f ;ω e , f and θ e They represent electrical angular velocity, permanent magnet flux and electrical angle respectively.

[0100] When the rotor position error is small, after normalizing equation (10), the rotor position error is:

[0101]

[0102] The estimated speed can be expressed as:

[0103]

[0104] The closed-loop speed is the speed after filtering by a low-pass filter, while the unfiltered speed is used in the sliding mode observer. There must be a deviation η between the estimated rotor position and the actual rotor position. error for:

[0105]

[0106] In the formula, represents the unfiltered speed, Indicates the estimated speed.

[0107] In addition, in order to compensate for the rotor position estimation error caused by the low-pass filter and the phase-locked loop, the expression of the error δ is defined as:

[0108]

[0109] δ contains the rotor position error information, and the error compensation l can be obtained by using the closed-loop phase tracking principle of the phase-locked loop.

[0110] Based on the above analysis, the rotor position error compensation can be obtained by the error compensation amount l and the deviation amount η error The rotor position can be finally expressed as:

[0111]

[0112] In the formula, is the rotor position output by the phase-locked loop; This is the rotor position finally estimated by the method of the present invention. Based on the position obtained by this method, position sensorless control of the permanent magnet synchronous motor in the medium and high speed range can be realized.

[0113] according to Figure 1 The control block diagram shown in the figure builds a motor drive control system experimental platform. Among them, the PMSM nameplate parameters are: rated power 400W; rated speed 3000r / min; resistance 0.25Ω; inductance 0.5mH; moment of inertia 0.00003kg·m 2 ; Back EMF coefficient 6.8V / m / s; Pole pair 4; Rated voltage 48V; Rated current 12.5A. Load torque is generated by a brushed DC motor. Figure 3 The effect of the function proposed by the present invention is compared with that of the hyperbolic tangent function. Both functions are smooth and continuous, but the function proposed by the present invention is smoother near the zero point, which is beneficial to reducing jitter. Figure 5 and Figure 6 The speed comparison test results are under the conditions of 1000r / min speed and sudden increase or decrease of rated load 1.27N. Figure 5 The experimental results for estimating the rotation speed are compared. The x-axis represents time and the y-axis represents the estimated rotation speed. The upper and lower parts of the figure are the experimental curves of the method of the present invention and the traditional method, respectively. When the load is added or reduced for 10s and 20s, the rotation speed of the method of the present invention changes to -40r / min and +42r / min, and the rotation speed of the traditional method changes to -55r / min and +61r / min. Figure 6 The speed error comparison experimental results are shown in Figure 1. The x-axis represents time, and the y-axis represents the speed error. The upper and lower parts of the figure are the experimental curves of the method of the present invention and the traditional method, respectively. The speed estimation errors of the method of the present invention and the traditional method are ±19r / min and ±37r / min, respectively. Figure 5 and Figure 6 It can be seen that the integral adaptive observer proposed in the present invention has a more stable speed. Figure 7The experimental results of the rotor position error comparison under the condition of a speed of 1000r / min and a sudden increase or decrease in the rated load of 1.27N. The x-axis represents time, and the y-axis represents the rotor position error. The upper and lower parts of the figure are the experimental curves of the method of the present invention and the traditional method, respectively. Figure 7 It can be seen that the rotor position error of the method of the present invention is -2° to 4°, and the rotor position error of the traditional method is -3° to 4°, so the integral adaptive observer proposed in the present invention has a smaller position offset.

[0114] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

Claims

1. An integral adaptive observer method for position sensorless control of a permanent magnet synchronous motor, characterized in that: The following steps are involved: Step (1), taking a surface-mounted permanent magnet synchronous motor as a research object, selecting the error i between the actual value and the estimated value of the stator current in a two-phase stationary coordinate system as a state variable; Step (2), designing a finite time integral sliding mode function s so that the system converges within a finite time; Step (3), designing fuzzy rules to adjust the parameters of the back-EMF observer in real time, and constructing an integral adaptive observer to improve the performance of the back-EMF observation; Step (4), the closed-loop phase tracker uses the actual value of the rotor position and the estimated value to phase-lock to obtain the rotor position error compensation, and outputs the final rotor position after combining it with the basic rotor position.

2. The method of integrating adaptive observer for position sensorless control of a permanent magnet synchronous motor according to claim 1, characterized in that: In step (1), the expression of the state variable i is as follows: In the formula, and represents the stator current estimation error; and i α ,i β Represent the estimated and actual values ​​of the stator current respectively.

3. The method of integrating adaptive observer for position sensorless control of a permanent magnet synchronous motor according to claim 1, characterized in that: In the step (2), the expression of the finite time integral sliding mode function s is as follows: Where λ1,λ2>0;q∈(0,1) The mathematical expression of the function H(i) of the system state variable i is: In the formula, m>0.

4. The method of integrating adaptive observer for position sensorless control of a permanent magnet synchronous motor according to claim 1, characterized in that: In step (3), the expression of the integral adaptive observer is as follows: In the formula, R s , L s Respectively represent the stator resistance and inductance; u α ,u β Represents the stator voltage; v α , v β Represents the control law.

5. The method of integral adaptive observer for position sensorless control of a permanent magnet synchronous motor according to claim 4, characterized in that: Rewrite the expression of the integral adaptive observer into vector form: In the ceremony, u s =[u α , u β ] T ;v s =[v α , v β ] T .

6. The method of integral adaptive observer for position sensorless control of a permanent magnet synchronous motor according to claim 5, characterized in that: In step (3), in order to improve the performance of the current observer, the proposed control law v s By the equivalent control law v eq and the switching control law v sw Composition, where v s The specific expression is: v s =v eq +v sw v sw =-εs—ρH(s) In the formula, ε>0; ρ>0.

7. The method of integral adaptive observer for position sensorless control of a permanent magnet synchronous motor according to claim 1, characterized in that: In step (3), the specific steps of the closed-loop phase tracker are as follows: First, the closed-loop speed is the speed after filtering by a low-pass filter, while the unfiltered speed is used in the sliding mode observer. There must be a deviation η between the estimated rotor position and the actual rotor position. error for: In addition, in order to compensate for the rotor position estimation error caused by the low-pass filter and the phase-locked loop, the expression of the error δ is defined as: δ contains the rotor position error information, and the error compensation l can be obtained by using the closed-loop phase tracking principle of the phase-locked loop.

8. The method of integral adaptive observer for position sensorless control of a permanent magnet synchronous motor according to claim 7, characterized in that: In step (3), the rotor position error compensation is calculated by the error compensation l and the deviation η error The rotor position can be finally expressed as: In the formula, is the rotor position output by the phase-locked loop.

Images