CN112910327A - Design method of fault-tolerant observer of brushless direct current motor under rotor eccentric fault - Google Patents
Design method of fault-tolerant observer of brushless direct current motor under rotor eccentric fault Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
- H02P6/08—Arrangements for controlling the speed or torque of a single motor
- H02P6/085—Arrangements for controlling the speed or torque of a single motor in a bridge configuration
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M7/00—Conversion of AC power input into DC power output; Conversion of DC power input into AC power output
- H02M7/42—Conversion of DC power input into AC power output without possibility of reversal
- H02M7/44—Conversion of DC power input into AC power output without possibility of reversal by static converters
- H02M7/48—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
- H02M7/53—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
- H02M7/537—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters
- H02M7/5387—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
- H02P23/12—Observer control, e.g. using Luenberger observers or Kalman filters
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- Control Of Motors That Do Not Use Commutators (AREA)
Abstract
The invention discloses a method for designing a fault-tolerant observer of a brushless direct current motor under the condition of rotor eccentric fault, which comprises the following steps: step one, building a brushless direct current motor body module to form a control object; step two, constructing a sliding-mode observer module; step three, induction of inductance identification; and step four, completing the design of the fault-tolerant observer. The invention can accurately and effectively observe the counter electromotive force value of the brushless DC motor no matter under the condition that the brushless DC motor is in a normal state or the rotor is in a static eccentric fault, and has important significance for certain occasions needing safe operation of the brushless DC motor even if the brushless DC motor is in a fault.
Description
Technical Field
The invention relates to the technical field of brushless direct current motor control, in particular to a design method of a fault-tolerant observer of a brushless direct current motor under the condition of rotor eccentricity fault.
Background
Brushless direct current motors (BLDCMs) are widely used in the fields of aerospace, industrial automation manufacturing and the like due to the advantages of fast dynamic response, wide speed regulation range, easy control and the like. In order to reduce the cost and some applications requiring space saving, the related control technology without position sensor becomes a hot point of research. An important point in the sensorless control is how to accurately acquire the back electromotive force of the brushless dc motor. However, when a static eccentric fault of the rotor occurs due to an ellipse of the stator or an assembly error of the rotor, a back electromotive force waveform is distorted and the brushless dc motor is not stably operated. How to accurately acquire counter electromotive force and perform position-sensorless control under a static eccentric fault becomes very important.
In the conventional position-sensorless control, a sliding-mode observer (SMO) is widely applied due to the advantages of good stability, strong robustness to disturbance and the like. However, many domestic and foreign scholars are sliding-mode observers designed under the condition that the BLDCM structure is normal. Even though some researchers propose a sinusoidal current injection method to estimate the counter electromotive force on line, the problems of poor robustness and the like still exist. Therefore, it is desirable to design an observer that can accurately acquire the back emf, has good robustness, and can stably operate under normal or static rotor eccentricity faults.
Disclosure of Invention
The invention aims to solve the problem that a traditional sliding mode observer cannot accurately observe a back electromotive force value of a brushless direct current motor under the static eccentric fault of a rotor, and provides a fault-tolerant observer design method of the brushless direct current motor under the eccentric fault of the rotor, which is good in robustness, high in accuracy and strong in adaptability and is based on the traditional sliding mode observer and Lyapunov (Lyapunov) stability theory.
In order to achieve the above purpose, the invention provides the following technical scheme:
the method for designing the fault-tolerant observer of the brushless direct current motor under the eccentric fault of the rotor is characterized by comprising the following steps of:
step one, building a brushless direct current motor body module to form a control object
(1) Building a direct-current power supply and a three-phase full-bridge control module according to the control characteristics of the brushless direct-current motor;
(2) building a body module according to the physical structure of the brushless direct current motor;
(3) building an electromagnetic torque and motion equation module according to a mathematical model of the brushless direct current motor;
step two, constructing a sliding-mode observer module
Building a sliding mode observer module aiming at the static eccentric fault of the rotor of the brushless direct current motor according to a state equation of the sliding mode observer and a mathematical equation of the brushless direct current motor;
step three, induction inductance identification
Establishing an inductance identification module by utilizing a Lyapunov stability theory and a mathematical model deduced by a sliding-mode observer, and obtaining real-time and accurate inductance parameters according to the self-adaptive identification rate;
step four, completing the design of the fault-tolerant observer
And (4) replacing the inductance parameters in the sliding mode observer in real time by the inductance parameters identified in the third step to form a closed loop whole, so that the back electromotive force value of the brushless direct current motor under the static eccentric fault of the rotor can be accurately observed.
Further, in the first step, the power supply of the brushless dc motor is a dc power supply, and the driving mode of the brushless dc motor is full-bridge driving.
Further, in the first step, the body module includes a three-phase winding stator resistor, a modifiable three-phase winding stator inductor, and a modifiable three-phase winding back-emf.
Further, in the first step, the electromagnetic torque may be expressed as:
in the formula, omega is the mechanical angular speed of the brushless direct current motor;
the equation of motion is:
wherein: t isL-a load torque;
j-rotor moment of inertia;
BV-viscous friction coefficient.
Further, in the second step, an equation of the sliding mode observer module under the static eccentricity fault of the brushless dc motor rotor is as follows:
wherein: k ═ diag (K)1,k2,k3)，H＝diag(h1,h2,h3) K, H is a sliding mode gain matrix;
further, the third step comprises the following specific steps:
according to the Lyapunov stability theory, a non-negative function is established:
wherein: epsilon is the back emf observation error; mu.s1＞0、μ2＞0、μ3＞0；
Deriving the non-negative function:
wherein:
order to
Obtaining the parameter identification rate by sorting
Wherein: mu ═ mu1 μ2 μ3]T
By means of the constraint of the parameter identification rate, the inductance identification parameters are adjusted, and then the inductance parameters of the three groups of stator wires can be accurately identified.
Compared with the prior art, the invention has the advantages that: the invention can accurately and effectively observe the counter electromotive force value of the brushless DC motor no matter under the condition that the brushless DC motor is in a normal state or the rotor is in a static eccentric fault, and has important significance for certain occasions needing safe operation of the brushless DC motor even if the brushless DC motor is in a fault. The invention realizes the accurate observation of the back electromotive force of the brushless direct current motor by a method of combining the sliding-mode observer and the inductance identification, the fault-tolerant observer can ensure that the inductance value of the stator can be identified and the back electromotive force value can be accurately observed within a wider rotating speed and eccentricity range, and meanwhile, the fault-tolerant observer forms a closed loop, thereby greatly improving the robustness and the reliability of the whole system and being suitable for application occasions of various brushless direct current motors.
Drawings
Fig. 1 is a schematic diagram of an equivalent circuit of a brushless dc motor according to the present invention.
Fig. 2 is a schematic diagram comparing a healthy rotor with a static eccentric failed rotor according to the present invention.
Fig. 3 is a block diagram of the overall structure of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further specifically described below by way of embodiments in combination with the accompanying drawings.
The method for designing the fault-tolerant observer of the brushless direct current motor under the condition of the eccentric fault of the rotor comprises the following steps:
the method comprises the following steps: building a brushless DC motor body module to form a control object
As can be seen from fig. 1, the input of the brushless dc motor is divided into two parts, namely, a power supply and a controller. The power supply is a direct current power supply, and proper voltage is selected according to parameters of the brushless direct current motor. The controller part is mainly composed of T1、T2、T3、T4、T5And T6Six power switch devices, wherein the upper bridge arm is T1、T3、T5Three power switch devices, the lower bridge arm is T4、T6、T2And the upper and lower bridge arms of the three power switching devices supply power to the stator winding of the brushless direct current motor in a pairwise conduction mode, and the conduction phases are different by 120 degrees each time. Finally, an annular magnetic field is formed in the motor, so that the permanent magnet rotor rotates by the electromagnetic force. The three-phase back electromotive force of the brushless dc motor also forms a trapezoidal wave waveform having a phase difference of 120 degrees. The voltage equation of the brushless dc motor is:
wherein R is the stator resistance; l isab、Lbc、LcaIs a wire stator inductance; e.g. of the typeab、ebc、ecaIs the winding wire back potential; i.e. iab、ibc、icaA stator line current for the winding; u. ofab、ubc、ucaIs the winding line voltage.
Meanwhile, as can be seen from fig. 1, the brushless dc motor is selected as a star-connected motor, and the three-phase stator windings are connected to a point, which is called a neutral point, and the neutral point is not led out, so that the phase voltage and the phase current are relatively troublesome to obtain. And it can be seen that the direction of the three-phase back electromotive force is opposite to the direction of the current, and the electromagnetic torque of the brushless dc motor is also determined by the back electromotive force and the current. The electromagnetic torque can be expressed as:
where Ω is the mechanical angular velocity of the motor. Including the voltage equation and the torque equation, a complete mathematical model of a point system is formed, and a motor motion equation is introduced:
wherein: t isL-a load torque;
j-rotor moment of inertia;
BV-viscous friction coefficient.
Normally, a brushless direct current motor is built up, but the brushless direct current motor related to the invention is a motor with a static eccentric rotor. The details of the static eccentricity of the rotor can be seen in figure 2. Normally, the rotor axis and the stator axis are located at the same central point. However, the rotor axis under the static eccentric fault is deviated, and the mechanical angle of the rotor is changed accordingly. It can be seen from fig. 2 that the air gap between the stator and the rotor varies due to the deviation of the rotor axis, and the variation is not different, so that the air gap permeance varies correspondingly; the air gap flux density is related to the air gap flux guide, and it can be seen from fig. 2 that the cross-sectional area of each phase of air gap of the three-phase winding is different, and the phase inductance changes and the inductance of each phase changes differently at the moment by combining physical knowledge; meanwhile, the back electromotive force of the brushless direct current motor is changed. In order to simulate the situation, the prepared rotor of the brushless direct current motor needs to be disassembled and assembled again, and the static eccentricity of the rotor of the brushless direct current motor is artificially caused in a manner of adding a gasket, so that the back electromotive force observation can be conveniently expanded. Meanwhile, the line current and the line voltage of the brushless direct current motor when the AB phase, the BC phase and the CA phase are conducted need to be measured in real time and used as the input of the fault-tolerant observer, and the specific implementation method is that the line current and the line voltage are directly led out from the output end of the controller module.
Step two: structure sliding-mode observer module
Before constructing the sliding mode observer module, firstly, the input of the sliding mode observer is determined as the line current and the line voltage of the brushless direct current motor in the step one. The sliding mode observer has the basic principle that the deviation between the observer output and the motor measurable output is utilized to correct the observer estimation value, so that the deviation between the observer state and the motor state gradually approaches 0. The unified equation of the traditional sliding-mode observer is as follows:
a, B and C are respectively system matrix, input matrix and output matrix; g is an observation gain matrix, and the convergence speed and performance of the observer can be improved by selecting a proper gain value; sgn () is a sign function.
For the condition of the static eccentric fault of the rotor of the brushless direct current motor mentioned in the step one, and the analysis conclusion of the step one is that under the condition of the static eccentric fault of the rotor of the brushless direct current motor, the inductance of each phase of the three-phase winding is changed differently, so that when the sliding mode observer is constructed, the internal inductance parameter needs to be changed into three different inductance parameters instead of the condition that the inductance parameters in the traditional sliding mode observer are changed synchronously.
Combining the mathematical model of the brushless direct current motor listed in the step one, a sliding mode observer under the static eccentricity fault of the rotor of the brushless direct current motor can be constructed, and the equation is as follows:
wherein: k ═ diag (K)1,k2,k3)，H＝diag(h1,h2,h3) K, H is a sliding mode gain matrix;
the state equation of the brushless direct current motor is as follows:
in the formula: coefficient matrix
Coefficient matrix
Line current
Counter potential
Subtracting the sliding-mode observer equation from the state equation of the brushless direct current motor to obtain an observation error equation:
and the sliding-mode observer has a specified observation error sliding-mode surface of
Entering sliding mode by sliding mode observerThe condition of the state is sTs' < 0. Then combining with the observation error equation to obtain the sliding mode gain k1The value taking conditions are as follows:
k2and k3Can be according to k1And so on. In actual operation, the observer can be ensured to enter a sliding mode state according to the sliding mode gain. When the observer enters a sliding mode state, according to an equivalent input control theory, a current observation error and a derivative thereof meet the condition that s is equal to s' is equal to 0, the equation is substituted into the first three rows of an observation error equation, and a switching function z in the sliding mode state can be obtained after simplification:
wherein:
and substituting the switching function into the observation error equation for three lines to obtain a counter potential observation error derivative equation epsilon' ═ Hz. And finishing the implementation of the sliding-mode observer part. At this time, the sliding mode observer can observe the back electromotive force of the brushless direct current motor through the line current and the line voltage input in the step one and the inductance parameter set according to the brushless direct current motor parameter through the operation. But the back emf of the machine in the event of a rotor eccentricity fault in which inductance changes are to be observed requires the introduction of inductance identification.
Step three: introducing inductance identification
In order to obtain real-time inductance parameters of the brushless direct current motor under the condition of static eccentric faults of the rotor, the parameters need to be obtained through an inductance identification method. The inductance identification method used by the invention is obtained by utilizing a nonnegative function form of the Lyapunov stability theory, and establishes a nonnegative function:
wherein mu1＞0、μ2＞、0μ3＞；
If V' < 0 can be guaranteed, the equilibrium point ε is 0 and Δ Lab、ΔLbc、ΔLcaIs asymptotically stable. Since the sampling frequency is much higher than the current frequency, the current and inductance are considered constant between samples, so the inductance derivative is considered to be 0. Then, the derivation of the non-negative function is combined with the switching function z in the second step to obtain a derivation equation of the non-negative function as follows:
wherein
To ensure that the derivative equation is less than zero, the following equation needs to be satisfied:
the equation is sorted to obtain the parameter identification rate
Wherein mu is [ mu ]1 μ2 μ3]T. Tong (Chinese character of 'tong')Through the constraint of the parameter identification rate, the inductance identification parameters are adjusted, and then the inductance parameters of the three groups of stator wires can be accurately identified. And combining the sliding mode observer in the second step with the inductance identification in the third step.
Step four: complete the design of fault-tolerant observer
And (4) under the normal condition of the brushless direct current motor, setting the inductance parameter in the sliding mode observer in the step two as the standard parameter of the motor, and observing the back electromotive force. When the static eccentric fault of the rotor occurs in the brushless direct current motor, the three-phase inductance of the motor changes differently, the inductance parameter in the sliding mode observer in the step two is a change value at the moment, so that the inductance parameter which is identified by the inductance identification method in the step three is required to be identified, then the inductance parameter in the sliding mode observer in the step two is updated according to the inductance parameter identified by the step three, a closed loop whole is formed, the back electromotive force accurate observation under the static eccentric fault of the rotor is completed, and the closed loop whole is called as a fault-tolerant observer. The overall structure thereof is shown in fig. 3.
The invention can accurately and effectively observe the counter electromotive force value of the brushless DC motor no matter under the condition that the brushless DC motor is in a normal state or the rotor is in a static eccentric fault, and has important significance for certain occasions needing safe operation of the brushless DC motor even if the brushless DC motor is in a fault. The invention realizes the accurate observation of the back electromotive force of the brushless direct current motor by a method of combining the sliding-mode observer and the inductance identification, the fault-tolerant observer can ensure that the inductance value of the stator can be identified and the back electromotive force value can be accurately observed within a wider rotating speed and eccentricity range, and meanwhile, the fault-tolerant observer forms a closed loop, thereby greatly improving the robustness and the reliability of the whole system and being suitable for application occasions of various brushless direct current motors.
Claims (6)
1. The method for designing the fault-tolerant observer of the brushless direct current motor under the eccentric fault of the rotor is characterized by comprising the following steps of:
step one, building a brushless direct current motor body module to form a control object
(1) Building a direct-current power supply and a three-phase full-bridge control module according to the control characteristics of the brushless direct-current motor;
(2) building a body module according to the physical structure of the brushless direct current motor;
(3) building an electromagnetic torque and motion equation module according to a mathematical model of the brushless direct current motor;
step two, constructing a sliding-mode observer module
Building a sliding mode observer module aiming at the static eccentric fault of the rotor of the brushless direct current motor according to a state equation of the sliding mode observer and a mathematical equation of the brushless direct current motor;
step three, induction inductance identification
Establishing an inductance identification module by utilizing a Lyapunov stability theory and a mathematical model deduced by a sliding-mode observer, and obtaining real-time and accurate inductance parameters according to the self-adaptive identification rate;
step four, completing the design of the fault-tolerant observer
And (4) replacing the inductance parameters in the sliding mode observer in real time by the inductance parameters identified in the third step to form a closed loop whole, so that the back electromotive force value of the brushless direct current motor under the static eccentric fault of the rotor can be accurately observed.
2. The method for designing a fault-tolerant observer of a brushless direct current motor under the eccentric fault of a rotor according to claim 1, wherein in the step one, a power supply of the brushless direct current motor is a direct current power supply, and a driving mode of the brushless direct current motor is full-bridge driving.
3. The method for designing a fault-tolerant observer of a brushless DC motor under eccentric rotor fault according to claim 1, wherein in the first step, the body module comprises three-phase winding stator resistance, modifiable three-phase winding stator inductance and modifiable three-phase winding back electromotive force.
4. The method for designing the fault-tolerant observer of the brushless direct-current motor under the eccentric fault of the rotor according to claim 1, wherein in the step one, the electromagnetic torque can be expressed as:
in the formula, omega is the mechanical angular speed of the brushless direct current motor;
the equation of motion is:
wherein: t isL-a load torque;
j-rotor moment of inertia;
BV-viscous friction coefficient.
5. The method for designing the fault-tolerant observer of the brushless direct current motor under the rotor eccentricity fault according to claim 1, wherein in the second step, an equation of the sliding-mode observer module under the static eccentricity fault of the rotor of the brushless direct current motor is as follows:
wherein: k ═ diag (K)1,k2,k3)，H＝diag(h1,h2,h3) K, H is a sliding mode gain matrix;
6. the method for designing the fault-tolerant observer of the brushless direct current motor under the eccentric fault of the rotor according to claim 1, wherein the specific steps of the third step are as follows:
according to the Lyapunov stability theory, a non-negative function is established:
wherein: epsilon is the back emf observation error; mu.s1＞0、μ2＞0、μ3＞0；
Deriving the non-negative function:
wherein:
order to
Obtaining the parameter identification rate by sorting
Wherein: mu ═ mu1 μ2 μ3]T
By means of the constraint of the parameter identification rate, the inductance identification parameters are adjusted, and then the inductance parameters of the three groups of stator wires can be accurately identified.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115189619A (en) * | 2022-07-27 | 2022-10-14 | 宁波奥克斯电气股份有限公司 | A brushless DC motor and its control method, device and readable storage medium |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101951211A (en) * | 2010-07-23 | 2011-01-19 | 南京航空航天大学 | Brushless direct current motor electromagnetic torque observation method based on self-adapting slipform observer |
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Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101951211A (en) * | 2010-07-23 | 2011-01-19 | 南京航空航天大学 | Brushless direct current motor electromagnetic torque observation method based on self-adapting slipform observer |
Non-Patent Citations (1)
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| 郭鸿浩等: "无刷直流电机转矩观测与电感自适应辨识", 《中国电机工程学报》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115189619A (en) * | 2022-07-27 | 2022-10-14 | 宁波奥克斯电气股份有限公司 | A brushless DC motor and its control method, device and readable storage medium |
| CN115189619B (en) * | 2022-07-27 | 2024-06-04 | 宁波奥克斯电气股份有限公司 | Brushless direct current motor, control method and device thereof and readable storage medium |
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