CN108258949A - A kind of rotor-position adaptive estimation method of noninductive permanent magnet synchronous motor - Google Patents

Abstract

The invention relates to a rotor position self-adaptive estimation method of a non-inductive permanent magnet synchronous motor, comprising the following steps: 1) designing a continuous self-adaptive sliding mode observer for observing the back electromotive force of the motor, and selecting the self-adaptive sliding mode observer 2) The observation value of the continuous adaptive sliding mode observer is used as the flux-like signal that contains the rotor position and velocity direction; 3) The phase-locked loop of the speed information is designed based on the tangent function, and the flux-like signal is obtained from the The rotor position information is obtained from the model signal. Compared with the prior art, the present invention has the advantages of clear structure, simple parameter selection, and the ability to maintain the accuracy of position information estimation under both positive and negative rotation conditions of the motor.

Description

A self-adaptive estimation method for rotor position of non-inductive permanent magnet synchronous motor

technical field

The invention relates to the technical field of motor control, in particular to a rotor position self-adaptive estimation method of a non-inductive permanent magnet synchronous motor.

Background technique

At present, permanent magnet synchronous motors are widely used as high-precision servo motors in many industrial production and precision manufacturing fields. To achieve precise control of the permanent magnet synchronous motor, it is necessary to obtain the position and speed information of the motor rotor; such information is usually obtained by the rotor position sensor installed at the tail of the motor. Installing such sensors will increase the overall size of the motor, increase the purchase cost of the motor, and increase the probability of mechanical failure. These problems limit the use and promotion of permanent magnet synchronous motors to a certain extent. One of the ways to solve this problem is to develop a sensorless observation method for designing the rotor position.

Since the back electromotive force of the permanent magnet synchronous motor contains rotor position and speed information, the estimation method based on the back electromotive force is an idea to realize the non-inductive control of the motor. At present, the discontinuous sliding mode observer is often used in engineering to obtain the rotor back EMF information, and then the sinusoidal phase-locked loop is used to extract the rotor position. There are two problems with this method. First of all, the required gain of the discontinuous sliding mode observer is mainly adjusted through experience during the design process, and the observer needs to be used with a low-pass filter, which will cause a phase delay in the system. Secondly, when the motor speed direction is reversed, the deviation between the estimated result of the sinusoidal phase-locked loop and the real position signal will theoretically reach 180°. Therefore, it is necessary to redesign the parameter values of the PID controller in the phase-locked loop. Use Inconvenient; in addition, the phase-locked loop needs to perform a normalization operation during use, which requires a large amount of calculation.

Contents of the invention

The object of the present invention is to provide a rotor position self-adaptive estimation method of a non-inductive permanent magnet synchronous motor in order to overcome the above-mentioned defects in the prior art.

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

A rotor position self-adaptive estimation method of a non-inductive permanent magnet synchronous motor, comprising the following steps:

1) Design a continuous adaptive sliding mode observer for observing the back electromotive force of the motor, and select the gain of the adaptive sliding mode observer;

2) The observation value of the continuous adaptive sliding mode observer is used as a flux-like signal to extract the rotor position and velocity direction;

3) Design the phase-locked loop of the speed information based on the tangent function, and obtain the rotor position information from the flux-like model signal.

The observation calculation formula of the continuous adaptive sliding mode observer is:

l＝|ω _r |+ξ

Among them, v _α , i _α and v _β , i _β are the voltage and current on the α-axis and β-axis respectively, R _s is the stator resistance, L _s is the stator inductance, ω _r is the rotor electric speed, and the symbol ^ represents the estimated value, k is a normal parameter, the product of k and l is the observer gain, ξ is a constant value with a small value, F(·) is a sigmoid function, and a is an adjustable positive constant parameter.

The selection of parameters k and a in the continuous adaptive sliding mode observer satisfies:

S≤δ

a≤5/δ

_k≥λaf

in, is the current estimation error on the α-axis and β-axis, λ _af is the flux linkage produced by the permanent magnet, s _α and s _β are the corresponding The two sliding mode operators of , S is the vector composed of s _α and s _β two sliding mode operators, δ is the upper bound of the observation error of the sliding mode observer, and e _αβ is the back electromotive force on the α axis and β axis.

The expression of the class flux linkage signal F _eq in the described step 2) is:

Among them, θ _r is the electrical position of the rotor.

When the value of ξ is small enough and the motor rotor speed is in the positive direction, then:

When the rotor speed is reversed, then:

Described step 3) in, the transfer function G _PLL of phase-locked loop is:

Among them, K _P and K _I are parameters of PI controller, and m is a positive integer constant.

Compared with the prior art, the present invention has the following advantages:

The present invention has designed a sliding mode observer and a phase-locked loop structure based on tangent function design, at first, the gain of the sliding mode observer designed for observing the rotor back EMF has included the speed estimation feedback information of the motor rotor, thus from the observer Extract the flux-like model signal including rotor position and speed direction, and then adopt a phase-locked loop structure based on tangent function design to obtain the rotor position in the flux-like model signal. The rotor position estimation method proposed by the present invention has a clear structure , the parameter selection is simple, and it can maintain the accuracy of position information estimation under the two cases of motor forward and reverse.

Description of drawings

Fig. 1 is the structure of the continuous adaptive sliding mode observer designed by the present invention.

Fig. 2 is a schematic structural diagram of a tangent phase-locked loop designed in the present invention.

Fig. 3 is a schematic diagram of the control system of the non-inductive permanent magnet synchronous motor.

Detailed ways

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

Example

The rotor position self-adaptive estimation method of the non-inductive permanent magnet synchronous motor proposed by the invention mainly consists of two parts. The first part is a continuous adaptive sliding mode observer for observing the back EMF of the motor, and the second part is a phase-locked loop for extracting the rotor position and speed information from the observed back EMF.

The dynamic equation of the surface-mounted permanent magnet synchronous motor in the d-q rotating coordinate system can be expressed as:

in, is the derivative operator; u _d , id , L _d and u _q , i _q , _{L q are} the stator voltage, current, and inductance on the d-axis and q-axis respectively. For a non-convex permanent magnet synchronous motor, L _d = L _q = L _s ; R _s is the stator resistance; ω _r is the electric speed of the rotor; λ _af is the flux linkage produced by the permanent magnet.

Formula (1) can obtain the dynamic equation of the motor in the α-β coordinate system through the Park transformation:

Where v _α , i _α and v _β , i _β are the voltage and current on the α-axis and β-axis respectively; θ _r is the electrical position of the rotor, e _α and e _β are the counter electromotive force on the α-axis and β-axis respectively, Satisfy e _α =-ω _r λ _af sin θ _r and e _β =-ω _r λ _af cos θ _r .

1. Design of continuous adaptive sliding mode observer

Based on the system model (2), the structural diagram of the continuous sliding mode observer designed by the present invention is shown in Figure 1. The sliding mode observation calculation formula shown in the schematic diagram is as follows:

Among them, the symbol "^" represents the estimated value, k is a normal number, and the value multiplied by k and l constitutes the observer gain, and the calculation formula of l is as follows:

l＝|ω _r |+ξ (4)

ξ is a constant value with a very small value, its function is to prevent the value of l from becoming 0 when the estimated speed of the motor is 0; ω _r uses the rotor speed estimated by the phase-locked loop in the operation replace. The F(·) function in (3) is a sigmoid function, and its expression is:

In the formula, a is an adjustable positive constant.

The selection rules of parameters k and a in the design of sliding mode adaptive observer are given below.

Subtract (2) from (3) to get:

in, is the current estimation error. According to the principle of sliding mode design, the sliding mode surface is selected for system (6):

In order to ensure the stability of the designed observer, the Lyapunov function is established as follows:

Derivation of the above formula:

According to the Lyapunov stability theorem, when The observer is stable, so kl·F(s)>e is required. Since F(s)∈(0,1), max(|e _α |,|e _β |)=|ω _r |λ _af , combined with formula (4) The value of , can be obtained. To make the observer (3) stable, it is only necessary to make k≥λ _af when designing the gain.

2. Assuming the system is stable, there are From this it is deduced that:

According to the expression of the function F(S), it can be seen that with the increase of the absolute value of S, the value of F(S) is infinitely close to -1 or +1, assuming that between this, S∈(0,δ]. The value is directly related to the size of δ. For the exponential e ^-aS , when the value of a·S increases from 0 to 5, the value of e ^-aS decreases from 1 to below 0.01; in engineering applications, we can think that e ^-aS weakens to 0. When the system is close to the sliding surface and switches back and forth in the stable interval of the surface, there is

S≤δ (12)

a≤5/δ (13)

Combining formulas (11)(12)(13) and specific motor parameter values, the appropriate value range of parameter a can be obtained.

When the observer is stabilized, the estimated value of the back EMF of the motor can be expressed by the following formula:

The present invention does not directly use the estimated counter electromotive force to obtain the motor rotor position and speed, but uses F _eq in the accompanying drawing 1 of the instruction manual. From (14), it can be seen that the observed value is:

When the value of ξ is small enough and the motor rotor speed is in the positive direction

When the rotor speed is reversed

As a flux-like signal, the observed value F _eq contains rotor position information, which can be used to extract rotor position and speed.

2. Phase-locked loop design based on tangent function

In order to extract the rotor position and speed information in F _eq , the phase-locked loop structure designed by the present invention is shown in Figure 2. In this figure, is the integral operator in the frequency domain; K _P and K _I are the gain of the proportional link and the integral link of a PI controller respectively; m is a positive integer constant; the expression of ε can be obtained through calculation as follows:

By adjusting the parameters of the PI controller, the value of ε can converge to 0, and at this time, the estimated value of the rotor electrical angle output by the phase-locked loop is the actual position of the current rotor To get the true position of the rotor, just calculate That's it.

The characteristics of the phase-locked loop are given below.

The error between the rotor position and speed estimated by the phase-locked loop and the real value can be expressed as:

From this, the dynamic characteristics of the phase-locked loop system designed based on the tangent function can be obtained as follows:

It should be noted that this dynamic characteristic gets rid of the shortcomings of the traditional phase-locked loop: the dynamic expression of the system will not change when the motor is rotating forward or reverse. The Jacobian matrix of system (20) is:

The stable point of (20) is (e _θ ,e _ω )=(0,0),(e _θ ,e _ω )=(±π,0), and the value of (21) at the stable point of the system is:

Since the parameters K _P and _KI of the PI controller are both greater than 0, the real parts of the eigenvalues of the matrix in (22) are both less than 0, that is, the PLL system is stable.

The transfer function of the tangent phase-locked loop designed by the present invention is:

Since the system gets rid of the influence of the rotor speed direction, the amplitude-frequency characteristics of the transfer function will not change with the change of the rotor speed, so no normalization operation is needed in the calculation process. Compared with the traditional phase-locked loop designed based on sine function, the amount of calculation is reduced.

Claims (6)

1. A rotor position self-adaptive estimation method of a non-inductive permanent magnet synchronous motor is characterized by comprising the following steps:

1) designing a continuous self-adaptive sliding mode observer for observing the back electromotive force of the motor, and selecting the gain of the self-adaptive sliding mode observer;

2) taking an observed value of a continuous adaptive sliding mode observer as a flux linkage signal containing a rotor position and a speed direction;

3) and designing a phase-locked loop of the speed information based on the tangent function, and acquiring rotor position information from the flux linkage-like model signal.

2. The method according to claim 1, wherein the observation calculation formula of the continuous adaptive sliding mode observer is as follows:

l＝|ω_r|+ξ

wherein v is_α、i_αAnd v_β、i_βThe voltage and current on the α and β axes, respectively, are R_sIs stator resistance, L_sIs stator inductance, ω_rFor the rotor electrical speed, the symbol ^ represents an estimated value, k is a positive constant parameter, the product of multiplying k and l is the observer gain, ξ is a constant with a small value, F (-) is a sigmoid function, and a is an adjustable positive constant parameter.

3. The method for adaptively estimating the rotor position of the non-inductive permanent magnet synchronous motor according to claim 2, wherein parameters k and a in the continuous adaptive sliding mode observer are selected to satisfy the following conditions:

S≤δ

a≤5/δ

k≥λ_af

wherein,for current estimation errors on the α and β axes, λ_afMagnetic flux linkage, s, generated for permanent magnets_α、s_βTo correspond toS is S_α、s_βA vector formed by two sliding mode operators, delta is an upper bound of an observation error of the sliding mode observer, e_αβThe back emf on the α and β axes.

4. The adaptive estimation method for the rotor position of the non-inductive PMSM according to claim 2, wherein the flux linkage-like signal F in step 2)_eqThe expression of (a) is:

wherein, theta_rThe electrical position of the rotor.

5. The method according to claim 4, wherein when the value of ξ is small enough and the speed of the motor rotor is positive, the following steps are performed:

when the rotor speed is reversed, then:

6. the adaptive estimation method for rotor position of non-inductive PMSM according to claim 4, characterized in that in step 3), the phase-locked loopTransfer function G_PLLComprises the following steps:

wherein, K_PAnd K_IM is a positive integer constant, which is a parameter of the PI controller.