CN112152528B - Permanent magnet synchronous motor speed regulation control method based on self-adaptive terminal sliding mode - Google Patents
Permanent magnet synchronous motor speed regulation control method based on self-adaptive terminal sliding mode 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
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
- H02P21/0007—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using sliding mode control
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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
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
- H02P21/0017—Model reference adaptation, e.g. MRAS or MRAC, useful for control or parameter estimation
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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
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/05—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation specially adapted for damping motor oscillations, e.g. for reducing hunting
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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
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
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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
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
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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
- H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
- H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
- H02P25/022—Synchronous motors
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Abstract
The invention discloses a permanent magnet synchronous motor speed regulation control method based on a self-adaptive terminal sliding mode, which comprises the steps of firstly establishing a dynamic equation describing the relation between the q-axis current and the speed output omega of a stator of a permanent magnet synchronous motor; then designing a speed loop controller of the permanent magnet synchronous motor by using a terminal sliding mode control algorithm; then, according to a sliding mode control theory, establishing a relation between system disturbance and control gain, and estimating an average value of the high-frequency switching signal by using a differential observer; finally, an adaptive law is designed to optimize the switching gain. The invention has the advantages that: the designed sliding mode surface effectively avoids the singularity phenomenon of the system at a balance point, and the convergence performance of the system is improved by introducing a nonlinear term; the average value of the high-frequency switching signal is estimated by utilizing a differential observer, so that the problem that the high-frequency switching signal is difficult to measure in the actual working condition is solved; the designed self-adaptive law enables the terminal sliding mode controller to select proper switch gain according to the disturbance magnitude, the buffeting of the system is obviously weakened, and the anti-disturbance performance of the system is enhanced.
Description
Technical Field
The invention relates to the technical field of speed regulation control of permanent magnet synchronous motors, in particular to a permanent magnet synchronous motor speed regulation control method based on a self-adaptive terminal sliding mode.
Background
The permanent magnet synchronous motor has the advantages of small volume, simple structure, small rotational inertia, high efficiency and the like, and is widely applied to the fields of robots, aerospace, industrial automation and the like. In recent years, due to the rapid development of power electronic technology, microelectronic technology and rare earth permanent magnet materials, permanent magnet synchronous motors are widely applied in practical engineering. However, the permanent magnet synchronous motor is a time-varying and complex nonlinear system, and the traditional linear PI control is difficult to meet the control requirements in practical application.
In order to improve the control performance of the permanent magnet synchronous motor, researchers begin to research a nonlinear control scheme suitable for a speed regulating system of the permanent magnet synchronous motor, wherein the sliding mode variable structure control is widely concerned due to the advantages of insensitivity to parameter perturbation of a controlled object, strong anti-interference capability, high response speed, easiness in implementation and the like.
In sliding mode control, when the system state track tends to a balance point, the system can not strictly move on the sliding mode surface but shuttle on two sides of the sliding mode surface, so that the system can generate buffeting. At present, the problem of buffeting is an important problem which is urgently needed to be solved in the application of sliding mode control to a permanent magnet synchronous motor. In order to weaken the buffeting phenomenon of sliding mode control, students combine a sliding mode control method with other excellent algorithms to improve the control precision of the permanent magnet synchronous motor.
Disclosure of Invention
The invention provides a permanent magnet synchronous motor speed regulation control method based on a self-adaptive terminal sliding mode, which not only improves the control precision of the permanent magnet synchronous motor, but also weakens the buffeting of a system to a great extent and improves the anti-interference performance. The technical scheme adopted by the invention is as follows:
a permanent magnet synchronous motor speed regulation control method based on a self-adaptive terminal sliding mode specifically comprises the following steps:
step 1: according to a mathematical model of the permanent magnet synchronous motor, a kinetic equation describing the relation between the q-axis current of the stator and the output rotating speed omega is constructed;
step 2: designing a speed loop controller of the permanent magnet synchronous motor based on a terminal sliding mode control theory;
and 3, step 3: according to a sliding mode control theory, establishing a relation between disturbance and control gain, and estimating an average value of a high-frequency switching signal by using a differential observer;
and 4, step 4: and (3) designing an adaptive law based on the relation between the disturbance and the control gain in the step (3).
Further, in step 1, the kinetic equation between the stator q-axis current and the output rotation speed ω is:
wherein, the first and the second end of the pipe are connected with each other,
omega is the mechanical angular velocity of the motor, i q Is the motor stator q-axis current, B is the friction coefficient, T L As the load torque, n p The number of the pole pairs of the motor is,
is the flux linkage, and J is the moment of inertia.
Considering the uncertainty of the system, the above equation is rewritten as:
where Δ a, Δ b, Δ c are uncertainty terms, g (T) = T L -Ji q Δa+JωΔb+JΔc。
Further, in the step 2, a sliding mode variable x is defined 1 ＝ω r -ω，
It is possible to obtain:
in the formula, ω r In order to achieve the desired speed of rotation,
is a lumped perturbation of the system.
The terminal sliding mode is designed as follows:
wherein beta is more than 0, p and q are positive odd numbers, and p/q is more than 1 and less than 2.
Further, according to the sliding mode control theory, the speed loop controller is designed as follows:
wherein k (t) is control gain, u is output of the controller, i.e. reference current of q axis
Further, in step 3, based on the controller in step 2, the relationship between the control gain and the disturbance may be obtained as follows:
k(t)·[sign(s) av ]＝d(t)
therein, [ sign(s)] aν D (t) is the lumped disturbance of the system, which is the average value of the high frequency switching signal.
Further, sign(s) in step 3] aν Measured by the following differential observer:
in the formula
λ 0 ,λ 1 ,λ 2 Is a normal number, L is a normal number, the output z of the observer 0 Is [ sign(s)] aν Estimate of z -1 Is an auxiliary variable, z 1 Is composed of
An estimate of (d).
Further, in the step 4, according to the relationship between the control gain and the disturbance, the state variable σ is defined as
σ＝|z 0 |-h
In the formula, h is a constant between (0, 1) and tends to be 1. The object is that when the high frequency switching signal approaches 1, the gain k (t) approaches d (t). Based on this, the adaptive law is designed to:
where xi is the adaptive coefficient, M is the normal number, k - ,k + Are all normal numbers, and have k (t) e [ k ∈ [) - ,k + ]In the expression [ x] + Symbol is marked as
Furthermore, as can be seen from the adaptive law, as the disturbance changes, k (t) will find the minimum value meeting the condition, so as to achieve the purpose of weakening the system buffeting.
The invention has the following beneficial effects:
1) Compared with the traditional sliding mode control algorithm, the terminal sliding mode control method improves the convergence performance of the system by introducing the nonlinear term when designing the sliding mode surface, and the steady-state tracking precision is higher.
2) In the design of the controller, the sliding mode surface is selected, so that the singularity phenomenon of the system at a balance point can be effectively avoided, and the robustness in the actual motor speed regulation control is strong.
3) The average value of the high-frequency switching signal is estimated by using the differential observer, the method is simple, rapid convergence can be realized, and the problem that the high-frequency signal is difficult to measure in actual working conditions is solved.
4) The design of the self-adaptive law enables the control gain to be changed constantly according to the size of the disturbance on the motor, so that k (t) is always slightly larger than the upper limit of the disturbance, and the buffeting of the system is obviously weakened while the convergence of the system is ensured.
Drawings
Fig. 1 is a vector control block diagram of a permanent magnet synchronous motor.
Fig. 2 is a rotation speed waveform diagram of the permanent magnet synchronous motor.
Fig. 3 is a waveform diagram of buffeting at the rotational speed of the permanent magnet synchronous motor.
Fig. 4 is a waveform diagram of q-axis current.
Fig. 5 is a waveform diagram of the load torque under the control of the adaptive terminal sliding mode.
Detailed Description
The invention will be further explained with reference to the drawings.
The invention discloses a self-adaptive terminal sliding mode control method, which is used for speed regulation control of a permanent magnet synchronous motor. In order to make the object, technical scheme and beneficial effect of the present invention clearer and clearer, the present invention will be further explained by the accompanying drawings and research examples.
Fig. 1 is a vector control block diagram of a permanent magnet synchronous motor of the present invention, which includes: (1) a permanent magnet synchronous motor module; (2) a speed loop module; (3) two current loop modules; (4) a coordinate transformation module; (5) an SVPWM module; and (6) an inverter module.
Based on the control system, the speed regulation control method of the permanent magnet synchronous motor of the invention is explained by the following specific examples:
TABLE 1 PERMANENT-MAGNET SYNCHRONOUS MOTOR PARAMETER TABLE
Step one, constructing a kinetic equation describing the relation between the q-axis current and the output rotating speed omega of the stator of the permanent magnet synchronous motor:
in the formula (I), the compound is shown in the specification,
omega is the mechanical angular velocity of the motor, i q Is the motor stator q-axis current, B is the friction coefficient, T L For load torque, n p The number of the pole pairs of the motor is,
is the flux linkage, and J is the moment of inertia.
Considering the uncertainty of the system, the formula (1) is rewritten as:
where Δ a, Δ b, Δ c are uncertainty terms, g (T) = T L -Ji q Δa+JωΔb+JΔc。
Step two, taking omega r To the desired speed, the system is brought to the desired speed ω r And the difference is obtained with the actual rotating speed omega fed back by the motor:
the following is derived from equation (3):
in the formula (I), the compound is shown in the specification,
is a lumped perturbation of the system.
Taking a terminal sliding mode surface as follows:
wherein beta is more than 0, p and q are positive odd numbers, and p/q is more than 1 and less than 2.
Combining formulas (4) and (5), the speed loop controller is designed as follows:
wherein u is the output of the controller, namely the given value of the stator q-axis current
k (t) is the high frequency switching gain, the value of which is related to the system buffetingIs in direct proportion.
Step three, ordering according to the sliding mode control theory
Obtain the equivalent control u eq Comprises the following steps:
from equation (7), the disturbance d (t) in the equivalent control is unknown.
Therefore, based on the controller (6), an average control u is obtained av Comprises the following steps:
from the sliding mode control theory, the controller (8) converges to the controller (7), and thus:
k(t)·[sign(s)] aν ＝d(t) (9)
therein, [ sign(s)] aν The average value of the high-frequency switching signal can be obtained by the following differential observer:
in the formula
λ 0 ,λ 1 ,λ 2 Is a normal number, L is a normal number, the output z of the observer 0 Is [ sign(s)] aν Estimate of z -1 Is an auxiliary variable, z 1 Is composed of
An estimate of (d).
Step 4, defining a state variable sigma as
σ＝|z 0 |-h (11)
Where h is a constant between (0, 1) tending to 1. The purpose is that when the high frequency switching signal approaches 1, the gain k (t) approaches d (t). Based on this, the adaptive law is designed to:
where xi is the adaptive coefficient, M is the normal number, k - ,k + Are all normal numbers, and there is k (t) epsilon [ k [ ] - ,k + ]In the expression [ x] + Symbol is marked as
It can be observed from the adaptation law (12) that when the control gain k (t) e [ k ] - ,k + ]When, the M term is 0.
Step five, in order to more clearly illustrate the control effect of the invention, a simulation model is built in simulink:
in the example, the expected rotation speed of the motor is set to be 1000r/min, and the motor parameters are shown in the table 1. To test the noise immunity of the system, a load of 2N · m was applied to the motor at t =0.1s and removed at t =0.2 s.
Fig. 2 is a rotating speed waveform diagram of a permanent magnet synchronous motor, and it can be observed that the system has better tracking performance and interference rejection capability under the control of a self-adaptive terminal sliding mode. Fig. 3 is a waveform diagram of buffeting at the rotating speed of the permanent magnet synchronous motor, fig. 4 is a waveform diagram of q-axis current, and it can be seen through comparison of two control strategies that buffeting of the system is obviously reduced after a self-adaptive algorithm is added. Fig. 5 is a waveform diagram of the load torque under the control of the adaptive terminal sliding mode, and it can be seen that the overshoot of the torque is small, and the good stability of the system is shown.
The above-listed series of detailed descriptions are merely specific illustrations of possible embodiments of the present invention, and they are not intended to limit the scope of the present invention, and all equivalent means or modifications that do not depart from the technical spirit of the present invention are intended to be included within the scope of the present invention.
Claims (1)
1. A permanent magnet synchronous motor speed regulation control method based on a self-adaptive terminal sliding mode is characterized by comprising the following steps:
step 1: establishing a kinetic equation of the relation between the stator q-axis current and the output rotating speed omega;
and 2, step: designing a speed loop controller of the permanent magnet synchronous motor;
the specific implementation of the step 2 comprises the following steps:
defining a sliding-mode variable x 1 ＝ω r -ω，
It is possible to obtain:
in the formula, ω r In order to be able to set the desired rotational speed,
is a lumped perturbation of the system;
designing a terminal sliding mode surface:
wherein beta is more than 0, p and q are positive odd numbers, and p/q is more than 1 and less than 2;
the speed loop controller is designed as follows:
wherein k (t) is control gain, u is output of the controller, i.e. reference current of q axis
And step 3: establishing a relation between disturbance and control gain, and estimating an average value of the high-frequency switching signal by using a differential observer;
the method for controlling the gain and the disturbance is established as follows:
making the speed loop control
Obtain the equivalent control u eq Comprises the following steps:
as shown in equation (7), the disturbance d (t) in the equivalent control is unknown;
therefore, based on the controller (6), an average control u is obtained av Comprises the following steps:
and the controller (8) converges on the controller (7), thus obtaining:
k(t)·[sign(s)] av ＝d(t) (9)
therein, [ sign(s)] av D (t) is the lumped disturbance of the system, which is the average value of the high frequency switching signal;
and 4, step 4: designing a self-adaptive law based on the relation between the disturbance and the control gain in the step 3;
in the step 1, a kinetic equation between the stator q-axis current and the output rotating speed ω is as follows:
wherein the content of the first and second substances,
omega is the mechanical angular velocity of the motor, i q Is the motor stator q-axis current, B is the friction coefficient, T L For load torque, n p The number of the pole pairs of the motor is,
is a magnetic linkage, and J is rotational inertia;
when considering the uncertainty of the system, the above equation is rewritten as:
where Δ a, Δ b, Δ c are uncertainty terms, g (T) = T L -Ji q Δa+JωΔb+JΔc；
Average value [ sign(s) of the high-frequency switching signal] aν Measured by the following differential observer:
in the formula
λ 0 ,λ 1 ,λ 2 Is a normal number, L is a normal number, the output z of the observer 0 Is [ sign(s)] aν Is estimated value of z -1 Is an auxiliary variable, z 1 Is composed of
An estimated value of (d);
the step 4 is realized by the following steps: defining a state variable σ as
σ＝|z 0 |-h
In the formula, h is a constant between (0, 1) and tends to 1, and when the high frequency switching signal tends to 1, the gain k (t) tends to d (t), z 0 Is the output of the observer;
the adaptive law is designed as:
where xi is adaptive coefficient, M is normal number, k - ,k + Are all normal numbers, and there is k (t) epsilon [ k [ ] - ,k + ]In the expression [ x] + Symbol is marked as
Observed by the adaptation law (12) when the control gain k (t) is e [ k ] - ,k + ]When M can be 0, buffeting is significantly attenuated.
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| CN103412484A (en) * | 2013-07-18 | 2013-11-27 | 北京控制工程研究所 | Moment control gyro frame disturbance moment restraining method |
| CN105591524A (en) * | 2016-02-24 | 2016-05-18 | 江苏大学 | Permanent magnet rotating speed difference clutch and self-adaption nonsingular terminal slip form rotating speed control method thereof |
| CN106788044A (en) * | 2017-02-16 | 2017-05-31 | 江苏大学 | A kind of permagnetic synchronous motor self adaptation non-singular terminal sliding-mode control based on interference observer |
| CN109850015A (en) * | 2019-02-21 | 2019-06-07 | 江苏大学 | A kind of self-adjustable electric vehicle active front wheel steering control method of control parameter |
| CN110262255A (en) * | 2019-07-16 | 2019-09-20 | 东南大学 | A kind of mechanical arm Trajectory Tracking Control method based on adaptive terminal sliding mode controller |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103412484A (en) * | 2013-07-18 | 2013-11-27 | 北京控制工程研究所 | Moment control gyro frame disturbance moment restraining method |
| CN105591524A (en) * | 2016-02-24 | 2016-05-18 | 江苏大学 | Permanent magnet rotating speed difference clutch and self-adaption nonsingular terminal slip form rotating speed control method thereof |
| CN106788044A (en) * | 2017-02-16 | 2017-05-31 | 江苏大学 | A kind of permagnetic synchronous motor self adaptation non-singular terminal sliding-mode control based on interference observer |
| CN109850015A (en) * | 2019-02-21 | 2019-06-07 | 江苏大学 | A kind of self-adjustable electric vehicle active front wheel steering control method of control parameter |
| CN110262255A (en) * | 2019-07-16 | 2019-09-20 | 东南大学 | A kind of mechanical arm Trajectory Tracking Control method based on adaptive terminal sliding mode controller |
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