A Sensorless Control Strategy for Brushless DC Motors

Abstract

The present invention relates to a sensorless control strategy for a brushless DC motor, belonging to the technical field of motor control. First, the state equation is derived with the line current as the state variable, and based on this, the sliding mode observation equation and the sliding mode observation error equation are designed; secondly, a multi-order sliding mode surface and an adaptive reaching law are designed, and combined with the observation error equation, a sliding mode control law is constructed to obtain the initial estimated value of the line back electromotive force, and the Lyapunov function is used to verify the system stability; then, a variable parameter Kalman filter is designed to filter the initial estimated value to obtain the final estimated value of the line back electromotive force; finally, the rotor position detection and the rotational speed calculation are realized according to the final estimated value of the line back electromotive force. The present invention suppresses the chattering problem of the sliding mode control and improves the estimation accuracy of the rotor position and the rotational speed.

Description

Technical Field

[0001] The present invention belongs to the technical field of motor control, and relates to a sensorless control strategy for a brushless DC motor. Background Art

[0002] At present, brushless DC motors are becoming more and more widely used. The integration of the motor body and the controller has an overall large volume, which will limit its application scope. Traditional position sensors have problems of increasing the overall volume of the system and insufficient accuracy in harsh environments. Therefore, the sensorless control technology has become a research hotspot.

[0003] Among the current sensorless technologies for brushless DC motors, the most widely used is the back electromotive force method. It obtains the commutation point by detecting the zero crossing of the motor back electromotive force, specifically including the terminal voltage method, the freewheeling diode method, the third harmonic back electromotive force method, and the line back electromotive force method. Traditional back electromotive force methods all obtain the zero crossing of the back electromotive force by building a hardware circuit, which increases the complexity of the controller. Moreover, after obtaining the zero crossing of the back electromotive force, it is necessary to artificially delay by 30° electrical angle to obtain the commutation point, resulting in a large error.

[0004] Obtaining the motor line back electromotive force through an observer can not only avoid adding a hardware circuit, but also the zero crossing of the line back electromotive force directly corresponds to the commutation point, without the need for artificial delay and with higher accuracy. The observer algorithms mainly include the sliding mode algorithm, the model reference adaptive algorithm, etc. The sliding mode algorithm has the advantages of being insensitive to system parameter changes and having a rapid response, and is widely used in the field of motor back electromotive force detection. However, the chattering problem inherent in the sliding mode control will cause harm to the system, and its observation results contain high-frequency harmonics, which need to be filtered by a low-pass filter. However, the use of the low-pass filter will cause phase delay, resulting in insufficient accuracy of rotor position detection. Summary of the Invention

[0005] Technical Problems to be Solved

[0006] In order to avoid the deficiencies of the prior art, the present invention proposes a sensorless control strategy for a brushless DC motor. Aiming at the chattering problem caused by the sliding mode observer when obtaining the motor line back electromotive force and the problem that the result contains high-frequency harmonics and requires filtering by a low-pass filter, which leads to phase delay, a new sensorless control strategy based on a sliding mode observer and a Kalman filter is proposed. A multi-order adaptive sliding mode observer is designed to obtain the motor line back electromotive force and a variable parameter Kalman filter is used to filter the observation result, effectively suppressing the chattering problem inherent in the sliding mode control, reducing the high-frequency components in the observation result of the sliding mode observer, and improving the estimation accuracy of the rotor position and speed.

[0007] Technical Solution

[0008] A sensorless control strategy for a brushless DC motor, characterized by the following steps:

[0009] Step 1: Derive the motor state equation with line current as the state variable, and design the observation equation and observation error equation of the sliding mode observer;

[0010] Step 2: Design a multi-order sliding mode surface and an adaptive reaching law to form a sliding mode control law; calculate the sliding mode control law to obtain the initial estimate of the line back electromotive force:

[0011]

[0012] where: c1, c2 are greater than 0, s = [s ab s bc T , x represents the observation error of the line current, h1 satisfies v = [v ab v bc T ;

[0013] The is a multi-order sliding mode surface that introduces the first derivative term and integral term of the line current observation error;

[0014] The is an adaptive reaching law that introduces the line current observation error and its first derivative term in the gain term, k1, k2, k3 > 0;

[0015] The is to use a variable slope saturation function simgode(s) instead of the traditional switching function sgn(s) in the adaptive reaching law, a > 0;

[0016] The adaptive reaching law uses a variable slope saturation function simgode(s) instead of the traditional switching function sgn(s), where a > 0;

[0017] Step 3: Filter the initial estimate of the line back electromotive force using a variable parameter Kalman filter to obtain the final estimate of the line back electromotive force

[0018] Step 4: Confirm the rotor position according to the final estimate of the line back electromotive force and control the winding commutation after detecting the zero crossing of the line back electromotive force, and calculate the rotational speed using the interval time between adjacent zero crossings of the line back electromotive force.

[0019] Verify the stability of the sliding mode control law using the Lyapunov function.

[0020] ​​The variable-parameter Kalman filter adopts an improved linear Kalman filter. The specific parameter values of the variance matrix R of the observation noise are determined by the distance from the system state to the sliding mode surface in the sliding mode motion, and are expressed as:

[0021] In the formula, r1, r2 > 0.

[0022] The method for confirming the rotor position based on the estimated final value of the line back electromotive force in step 4 and controlling the winding commutation after detecting the zero crossing of the line back electromotive force is as follows: The zero crossing of the line back electromotive force corresponds one-to-one with the commutation point of the motor. The positive and negative combinations of the three-phase line back electromotive forces divide the 360° electrical angle into 6 sectors, and the conducting phases within each sector remain unchanged. When the zero crossing of any one-phase line back electromotive force is detected, the rotor position is judged according to the positive and negative of the three-phase line back electromotive forces, and the switching devices are controlled to turn on and off according to the commutation logic shown in the following table, where "-1" represents that the line back electromotive force is negative and "1" represents that the line back electromotive force is positive;

[0023]

[0024] The calculation of the motor speed In the formula, n is the speed in r / min; T represents the time between adjacent zero crossings of the line back electromotive force in seconds.

[0025] Beneficial effects

[0026] A sensorless control strategy for a brushless DC motor proposed by the present invention belongs to the technical field of motor control. First, the state equation is derived with the line current as the state variable, and the sliding mode observation equation and the sliding mode observation error equation are designed accordingly. Secondly, a multi-order sliding mode surface and an adaptive reaching law are designed, and the sliding mode control law is constructed in combination with the observation error equation to obtain the initial estimated value of the line back electromotive force, and the Lyapunov function is used to verify the system stability. Then, a variable-parameter Kalman filter is designed to filter the initial estimated value to obtain the final estimated value of the line back electromotive force. Finally, the rotor position detection and speed calculation are realized based on the final estimated value of the line back electromotive force. The present invention suppresses the chattering problem of the sliding mode control and improves the estimation accuracy of the rotor position and speed.

[0027] The present invention designs a multi-order adaptive sliding mode observer to obtain the line back electromotive force of the motor, and designs a variable-parameter Kalman filter to filter out the high-frequency components in the sliding mode observation results to obtain the final observation result of the line back electromotive force, and uses the line back electromotive force information to realize rotor position detection and speed calculation. In the design of the sliding mode observer, the present invention designs a multi-order sliding mode surface and an adaptive reaching law, which can ensure the convergence speed and robustness while suppressing system chattering. Using a variable-parameter Kalman filter to process the sliding mode observation results can reduce the high-frequency components in the sliding mode observation results on the premise of generating a very small phase delay, and can reduce the influence of the process noise of the system and the observation noise of the sliding mode observer on the calculation results, improving the observation accuracy of the line back electromotive force; the specific value of the observation noise variance matrix of the Kalman filter is determined by the distance from the system state to the sliding mode surface during the sliding mode motion, which can better eliminate the influence of the observation noise of the sliding mode observer on the calculation results. The strategy proposed by the present invention can effectively suppress the chattering problem of the sliding mode control, improve the estimation accuracy of the rotor position and speed, and at the same time has strong robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is the double closed-loop control block diagram of the brushless DC motor based on the novel sensorless control strategy.

[0029] Figure 2 is the overall block diagram of the line back electromotive force observation algorithm combining a multi-order adaptive sliding mode observer and a variable-parameter Kalman filter.

[0030] Figure 3 is the waveform relationship diagram of the line back electromotive force and the stator current of the brushless DC motor. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0031] The present invention will be further described in combination with the embodiments and the drawings:

[0032] The present invention combines a sliding mode observer and a Kalman filter to obtain the line back electromotive force, and judges the rotor position and calculates the speed according to the observation result of the line back electromotive force. The overall block diagram when it is applied to the double closed-loop control of the brushless DC motor is as Figure 1 shown.

[0033] As Figure 2 shown, the present invention is carried out according to the following steps:

[0034] Step 1: Construct the motor state equation with the line current as the state variable, and deduce the observation equation and the observation error equation of the sliding mode observer

[0035] The terminal voltage equation of the brushless DC motor in the three-phase stationary coordinate system is:

[0036]

[0037] where, ia 、i b 、i c are the phase currents of the three-phase winding, U a 、U b 、U c are the terminal voltages of the three-phase winding, e a 、e b 、e c are the back electromotive forces of the three phases, u n is the neutral point voltage of the winding, R is the phase resistance, and L is the equivalent phase inductance.

[0038] Subtracting and simplifying the three equalities in the terminal voltage equation pairwise gives the line voltage equation as:

[0039]

[0040] where, i ab 、i bc are the line currents, U ab 、U bc are the line voltages, e ab 、e bc are the line back electromotive forces.

[0041] Deriving the motor state equation with the line current as the state variable according to the line voltage equation, we get:

[0042]

[0043] The line back electromotive force of the motor satisfies e ab +e bc +e ca =0, that is, observing e ab 、e bc allows us to calculate e ca , so the observation equation of the sliding mode observer designed in combination with the motor state equation is:

[0044]

[0045] where, is the observed value of the line current, v ab 、v bc represent the corresponding sliding mode control laws.

[0046] Subtracting the observation equation from the state equation gives the observation error equation of the sliding mode observer as:

[0047]

[0048] where, is the observation error of the line current, and on the sliding mode surface there is Therefore, when the system state point moves to the sliding mode surface, the following can be obtained from the observation error equation

[0049]

[0050] wherein, represents the initial value of the estimated line back electromotive force obtained by the sliding mode observer.

[0051] Step 2: Design a multi-order sliding mode surface and an adaptive reaching law, construct a sliding mode control law to obtain the initial value of the estimated line back electromotive force, and verify its stability using the Lyapunov function

[0052] Take the line current observation error itself, its first derivative term, and the integral term to form a multi-order sliding mode surface:

[0053]

[0054] wherein, c1, c2 > 0, s = [s ab s bc T , The introduction of the first derivative term dx / dt makes the discontinuous control action concentrated on the higher-order differential of the line current observation error, reducing the chattering of the sliding mode motion; the introduction of the integral term ∫xdt can reduce the distance from the initial state of the system to the sliding mode surface and improve the convergence speed.

[0055] The designed adaptive reaching law is:

[0056]

[0057] wherein, k1, k2, k3 > 0; simgode(s) is a variable slope saturation function, where a > 0, this function is continuous and smooth, and the slope near s = 0 is adjusted in real time according to the magnitude of the line current observation error, which can effectively suppress the chattering of the system near the sliding mode surface.

[0058] The reaching law designed by the present invention consists of a variable speed term and an exponential term . When the system is far from the sliding mode surface, the exponential term plays a key role, making the reaching speed adjustable in real time according to the observation error; when the system state approaches the sliding mode surface, the variable speed term plays a key role, and its gain term introduces the absolute value of the error and its derivative, which can limit the reaching speed when the error change rate is too large, reduce chattering, and at the same time, when the system state reaches near the sliding mode surface, its gain term will not be 0, ensuring the robustness of the observer near the sliding mode surface.

[0059] Derive the multi-order sliding mode surface with respect to the left and right to obtain: ​

[0060]

[0061] Combined with the adaptive reaching law, we get:

[0062]

[0063] Integrating both sides of the above equation and considering stability, we get the sliding mode control law:

[0064]

[0065] In the formula, h1 satisfies v=[v ab v bc ] T .

[0066] Next, we use the Lyapunov function to verify its stability and construct the Lyapunov function as follows:

[0067]

[0068] Taking its derivative we get:

[0069]

[0070] because and The form is the same, and only one of them is calculated below:

[0071]

[0072] The same can be proved Established, so there is It holds, so we can see that the system is stable.

[0073] Step 3: Design a variable parameter Kalman filter to filter the estimated initial value to obtain the estimated final value of the line back EMF;

[0074] The estimated initial value of the line back EMF obtained by the sliding mode observer contains high-frequency noise, and the error is larger than the actual value. Therefore, a variable parameter Kalman filter is used to filter the estimated initial value to obtain an estimated final value with a smaller error. When establishing the state equation and observation equation of the system, the actual line back EMF is taken as the state variable, and the estimated initial value of the line back EMF obtained by the sliding mode observer is taken as the observation variable. Because the sampling period is very small, for the convenience of calculation, it is assumed that the motor back EMF does not change within a sampling period, thus obtaining:

[0075]

[0076] In the formula, X(k)=[E ab (k) E bc(k)] T Denote the actual line back electromotive force at the k-th moment; Denote the initial estimated value of the line back electromotive force obtained by the sliding mode observer at the k-th moment; A represents the state transition matrix, H represents the observation matrix, W(k - 1) represents the process noise, and its variance matrix is Q; V(k) represents the observation noise, which measures the error between the calculation result of the sliding mode observer and the actual value, and its variance matrix is R.

[0077] When using the Kalman filter, it is necessary to preset the initial value X(0) of the state variable, the covariance matrix P(0) of the initial value, and the variance matrices Q and R of the noise in advance. In the present invention, X(0) = [a a] T 、 where a, b, and c are all constants greater than 0; and the specific form of the variance matrix R of the observation noise is where r1 > 0, 0 < r2 < 1, and s corresponds to the value of the multi-order sliding mode surface function at the current moment. The observation noise measures the error between the calculation result of the sliding mode observer and the actual value. In the sliding mode motion, the observation noise is different when the distance from the system state point to the sliding mode surface is different. Therefore, setting the specific value of R according to the distance from the system state to the sliding mode surface in the sliding mode motion can achieve a better filtering effect.

[0078] After confirming the above parameters, the calculation can be carried out according to the Kalman filter recurrence algorithm, and a more accurate estimated final value can be obtained from the initial estimated value of the line back electromotive force obtained by the sliding mode observer. Taking the k-th moment as an example to introduce the calculation process of the Kalman filter, the optimal estimated value mentioned below is the estimated final value of the line back electromotive force calculated by the Kalman filter.

[0079] First, calculate the prior estimated value at the k-th moment according to the optimal estimated value calculated at the (k - 1)-th moment and the variance matrix P(k / k - 1) of the prediction error. The specific formulas are:

[0080]

[0081] P(k / k - 1) = A · P(k - 1) · A T +Q

[0082] Then, calculate the Kalman filter gain K according to the following formula k , where R(k) represents the variance matrix of the observation noise obtained from the value of the multi-order sliding mode surface function s at the k-th moment,

[0083] K k = P(k / k - 1)H T (HP(k / k - 1)HT + R(k)) -1

[0084] Then, calculate the error between the observed value Z(k) of the sliding mode observer at the k-th moment and the prior estimate value and correct the prior estimate value with the Kalman filter gain to obtain the optimal estimate value at the k-th moment

[0085]

[0086] Finally, update the optimal estimate variance matrix P(k) at the k-th moment for use in the calculation at the (k + 1)-th moment.

[0087] P(k) = P(k / k - 1) - K k HP(k / k - 1)

[0088] Through the above recurrence formula, the initial value of the back electromotive force of the line with large error and noise obtained by the sliding mode observer can be used to obtain the final estimate value with smaller error According to the relationship of the back electromotive force of the line e ab + e bc + e ca = 0, the

[0089] In summary, by combining the multi-order adaptive sliding mode observer and the variable parameter Kalman filter, the final estimate value of the back electromotive force of the line with accuracy meeting the control requirements is obtained

[0090] Step 4: Confirm the rotor position according to the final estimate value of the back electromotive force of the line to control the winding commutation, and at the same time calculate the rotational speed by using the zero crossing point of the back electromotive force of the line.

[0091] Figure 3 shows the relationship between the back electromotive force of the brushless DC motor and the stator current. It can be seen that the zero crossing point of the back electromotive force of the line corresponds one-to-one with the commutation point of the motor. The positive and negative combinations of the three-phase back electromotive force can divide the 360° electrical angle into 6 sectors and the conducting phase within each sector remains unchanged. After detecting the zero crossing point of any one of the back electromotive forces of the line, the rotor position can be judged according to the positive and negative of the three-phase back electromotive force, and the switching devices can be controlled to turn on and off according to the commutation logic shown in the following table, where "-1" represents that the back electromotive force is negative and "1" represents that the back electromotive force is positive.

[0092]

[0093] The rotational speed of the motor is indispensable information for realizing speed closed-loop control. From Figure 3It can be known that the distance between adjacent line back electromotive force zero-crossing points always corresponds to 60° electrical angle. Therefore, for a motor with p pole pairs, the motor speed can be calculated by the following formula.

[0094] In the formula, n is the speed, with the unit of r / min; T represents the time between adjacent line back electromotive force zero-crossing points, with the unit of seconds.

Claims

1. A sensorless control strategy for a brushless DC motor, characterized in that The steps are as follows: Step 1: Derive the motor state equation with the line current as the state variable, and design the observation equation and observation error equation of the sliding mode observer; Step 2: Design a multi-order sliding mode surface and an adaptive reaching law to form a sliding mode control law; Calculate the sliding mode control law to obtain the initial estimated value of the line back electromotive force: where: c1, c2 are greater than 0, s = [s ab s bc T , x represents the observed error of the line current, h1 satisfies v = [v ab v bc T ;​​ The is a multi-order sliding mode surface that introduces the first derivative term and integral term of the line current observation error; The is an adaptive reaching law that introduces the line current observation error and its first derivative term into the gain term, where k1, k2, k3 > 0; The uses a variable slope saturation function simgode(s) to replace the traditional switching function sgn(s) in the adaptive reaching law, where a > 0; In the above-mentioned adaptive reaching law, a variable-slope saturation function simgode(s) is used to replace the traditional switching function sgn(s). where a > 0; Step 3: Use a variable parameter Kalman filter to filter the initial estimate of the line back electromotive force to obtain the final estimate of the line back electromotive force Step 4: Confirm the rotor position according to the final estimated value of the line back electromotive force, control the winding commutation after detecting the zero crossing of the line back electromotive force, and calculate the rotational speed using the interval time between adjacent zero crossings of the line back electromotive force.

2. The sensorless control strategy for a brushless DC motor according to claim 1, characterized in that: Use the Lyapunov function to verify the stability of the sliding mode control law.

3. The sensorless control strategy for a brushless DC motor according to claim 1, characterized in that: The variable parameter Kalman filter adopts an improved linear Kalman filter, and the specific parameter value of the variance matrix R of the observation noise is determined by the distance from the system state to the sliding mode surface in the sliding mode motion, expressed as: wherein, r1, r2 >

0.

4. The sensorless control strategy for a brushless DC motor according to claim 1, characterized in that: In step 4, confirming the rotor position according to the final estimated value of the line back electromotive force and controlling the winding commutation after detecting the zero crossing of the line back electromotive force is as follows: The zero crossing of the line back electromotive force corresponds one-to-one with the motor commutation point. The positive and negative combinations of the three-phase line back electromotive forces divide the 360° electrical angle into 6 sectors, and the conducting phases within each sector remain unchanged; when detecting the zero crossing of any one of the line back electromotive forces, judge the rotor position according to the positive and negative of the three-phase line back electromotive forces, and control the on and off of the switching devices according to the commutation logic shown in the following table, where "-1" represents that the line back electromotive force is negative and "1" represents that the line back electromotive force is positive; 。 5. The sensorless control strategy for a brushless DC motor according to claim 1, characterized in that: The calculated motor speed In the formula, n is the speed in r / min; T represents the time between adjacent zero-crossing points of the back electromotive force in seconds.

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