CN113452295A - Sinusoidal electro-magnetic doubly salient motor speed control method based on sliding mode approach law - Google Patents

Sinusoidal electro-magnetic doubly salient motor speed control method based on sliding mode approach law Download PDF

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CN113452295A
CN113452295A CN202110616095.XA CN202110616095A CN113452295A CN 113452295 A CN113452295 A CN 113452295A CN 202110616095 A CN202110616095 A CN 202110616095A CN 113452295 A CN113452295 A CN 113452295A
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sliding mode
law
approach law
approach
sinusoidal
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CN113452295B (en
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于晓东
周波
熊磊
蒋思远
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Nanjing University of Aeronautics and Astronautics
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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
    • 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
    • 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
    • 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
    • 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
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation

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Abstract

The invention discloses a speed control method of a sinusoidal electro-magnetic excitation doubly-salient motor based on a sliding mode approach law, which relates to the technical field of motors, and the method designs the sliding mode approach law aiming at the sinusoidal electro-magnetic excitation doubly-salient motor, can obtain the approach law parameters in the sliding mode approach law by mediation according to the design requirements of the system response time and the sliding mode buffeting after determining the system response time and the expression of the sliding mode buffeting on the approach law parameters based on the sliding mode approach law, then obtains the sliding mode control law based on the sliding mode approach law according to the sliding mode surface expression, finally obtains the sliding mode control law based on the feedforward disturbance observation by a method of feedforward compensation disturbance estimation, and then controls the sliding mode control law, can better solve the inherent contradiction between the system response time and the sliding mode buffeting existing in the traditional sliding mode approach law, and realizes the quick and no-overshoot response of the motor rotating speed, the sliding mode buffeting is weakened, the robustness to the internal and external disturbance of a system is strong, and the method also has the advantage of simplicity and convenience in parameter debugging.

Description

Sinusoidal electro-magnetic doubly salient motor speed control method based on sliding mode approach law
Technical Field
The invention relates to the technical field of motors, in particular to a sinusoidal electric excitation doubly salient motor speed control method based on a sliding mode approximation rule.
Background
As a novel synchronous motor, the sinusoidal electro-magnetic doubly salient motor has good application prospect in the fields of aerospace, ship propulsion, electric automobiles and the like due to the advantages of simple and reliable structure, flexible control, suitability for high-temperature and high-speed occasions and the like. However, in the context of the above application, the sinusoidal electrically excited doubly salient motor is generally complex and variable, and there are a lot of uncertain disturbances including perturbation of motor parameters, disturbance of external loads, and other disturbances caused by unmodeled dynamics, in which case the speed regulation performance of the sinusoidal electrically excited doubly salient motor will be seriously affected.
At present, a sinusoidal electric excitation doubly salient motor mostly adopts a rotating speed (outer ring) and current (inner ring) doubly closed-loop vector control mode, and a rotating speed outer ring regulator adopts the traditional PI control. However, the conventional PI regulator, as a linear regulator, relies on accurate system model parameters, and it is difficult to obtain high-quality speed regulation performance after suffering from motor parameter variation and external uncertainty. The sliding mode control is simple to realize and has strong robustness on system model parameters and uncertain disturbance, and is widely applied to the field of motor speed regulation. However, the implementation process of sliding mode control includes an approach phase and a sliding mode phase, and the approach phase does not have strong robustness, and only has the characteristic in the sliding mode phase.
At present, there are two main methods for solving the problem that the sliding mode control method does not have strong robustness in the approach stage: integral sliding mode control and sliding mode control by adopting an approach law method. The main idea of integral sliding mode control is that an integral term is introduced into the design of a sliding mode surface, and a reasonable integral initial value is designed, so that a system state variable can be positioned on the sliding mode surface from the beginning, an approach stage is eliminated, and the sliding mode stage is directly entered, but a large overshoot is caused under the accumulation effect of integral. The method adopts an approach law to improve the performance of the sliding mode control in the approach stage, and can improve the robust performance of the approach stage, but the currently common approach law methods (including constant velocity approach law, exponential approach law and power approach law) have a contradiction relationship between response rapidity and sliding mode buffeting size while improving the robust performance of the approach stage. Therefore, the research on the sinusoidal electric excitation doubly-salient motor sliding mode speed control method with the global strong robustness performance and the excellent dynamic and stable performances has important significance.
Disclosure of Invention
The invention provides a sinusoidal electro-magnetic doubly salient motor speed control method based on a sliding mode approach law aiming at the problems and the technical requirements, and the technical scheme of the invention is as follows:
a sinusoidal electro-magnetic doubly salient motor speed control method based on a sliding mode approximation law comprises the following steps:
the approach law of a sliding mode for designing a sinusoidal electro-magnetic doubly salient motor is
Figure BDA0003097593010000021
Wherein
Figure BDA0003097593010000022
k is the first sliding mode gain and k>0, f () is a predetermined function of the sliding mode surface s,
Figure BDA0003097593010000023
is an initial time t0The value of the time slip form surface s; alpha, beta and lambda are approach law parameters, alpha belongs to (0,1), and both beta and lambda are greater than 0;
determining the system response time and an expression of sliding mode buffeting on an approach law parameter based on a sliding mode approach law, and determining to obtain values of alpha, beta and lambda by adjusting the approach law parameter to enable the system response time and the sliding mode buffeting to be respectively smaller than corresponding threshold values;
constructing a sliding mode surface expression taking the given mechanical angular velocity and the actual mechanical angular velocity of the sinusoidal electric excitation doubly-salient motor as state variables based on a motion equation of the sinusoidal electric excitation doubly-salient motor;
and obtaining a sliding mode control law of the q-axis current given value based on the sliding mode approach law according to the sliding mode surface expression, and adjusting the q-axis current given value according to the sliding mode control law to control the speed of the sinusoidal electric excitation doubly salient motor.
The further technical scheme is that the expression of the system response time determined based on the sliding mode approach law and related to the parameters of the approach law is
Figure BDA0003097593010000024
The expression of the sliding mode buffeting on the parameters of the approach law is
Figure BDA0003097593010000025
And T is the sampling period of the digital controller, when the approach law parameter is adjusted, alpha is reduced to reduce the system response time, beta is increased to reduce the sliding mode buffeting, and lambda is reduced to reduce the system response time on the basis of increasing beta.
The further technical scheme is that an expression of system response time and sliding mode buffeting related approach law parameters is determined based on a sliding mode approach law, and the expression comprises the following steps:
defining the moment t when the system state reaches the sliding mode surface s for the first timesAnd at tsValue of the time slip form surface s
Figure BDA0003097593010000026
In time interval [ t ] for sliding mode approximation law0,ts]The inner definite integral yields:
Figure BDA0003097593010000027
when in use
Figure BDA0003097593010000028
While, the slip form surface s is in the time interval [ t0,ts]If the internal constant is greater than 0, the integral result is determined to be
Figure BDA0003097593010000031
When in use
Figure BDA0003097593010000032
While, the slip form surface s is in the time interval [ t0,ts]If the internal constant is less than 0, the integral result is determined to be
Figure BDA0003097593010000033
Will be provided with
Figure BDA0003097593010000034
And
Figure BDA0003097593010000035
the expression of the system response time and the approach law parameter obtained by integrating the definite integral results under two conditions is
Figure BDA0003097593010000036
The further technical scheme is that the adjusting of the approach law parameters comprises the following steps:
determining constraint conditions of the approach law parameters alpha, beta and lambda based on an expression of system response time and the approach law parameters and an expression of sliding mode buffeting
Figure BDA0003097593010000037
Regulating alpha, beta and lambda under the constraint condition.
The further technical scheme is that a predetermined function f () in the sliding mode approach law is a hyperbolic tangent function tanh (), and
Figure BDA0003097593010000038
the further technical scheme is that the motion equation of the sinusoidal electric excitation doubly salient motor is as follows
Figure BDA0003097593010000039
Is the practice of a sinusoidal electrically excited doubly salient machineDerivative of mechanical angular velocity ω, J0Is the motor moment of inertia, P, of the nominal modelrIs the number of poles of the rotor of the motor,
Figure BDA00030975930100000310
mutual inductance of any phase armature winding and excitation winding of a motor of a nominal model, ifIs the motor excitation current iqIs the actual value of the q-axis current, d (t) is the lumped disturbance that varies with time t;
the method further comprises:
establishing an extended state disturbance observer based on a motion equation of a sinusoidal electric excitation doubly-salient motor and obtaining an observer estimation value of lumped disturbance d (t) as a lumped disturbance estimation value
Figure BDA00030975930100000311
Lumped disturbance estimation value through feedforward compensation disturbance estimation method
Figure BDA00030975930100000312
And introducing a sliding mode control law to obtain a sliding mode control law based on disturbance observation, and adjusting the q-axis current given value and controlling the speed of the sinusoidal electric excitation doubly salient motor according to the sliding mode control law based on disturbance observation.
The further technical scheme is that the extended state disturbance observer established based on the motion equation of the sinusoidal electric excitation doubly salient motor is as follows:
Figure BDA0003097593010000041
wherein the content of the first and second substances,
Figure BDA0003097593010000042
an observer estimate representing the actual mechanical angular velocity ω,
Figure BDA0003097593010000043
to represent
Figure BDA0003097593010000044
The derivative of (a) of (b),
Figure BDA0003097593010000045
to represent
Figure BDA0003097593010000046
Derivative of, gamma1And gamma2Is observer gain and satisfies
Figure BDA0003097593010000047
ξ denotes the bandwidth parameter.
The further technical scheme is that the sliding mode surface expression is s ═ x1+cx2Wherein c is a second sliding mode gain and c>0，x1、x2Is a state variable of a sinusoidal electric excitation doubly salient motor and has
Figure BDA0003097593010000048
ω*The mechanical angular speed is given to the sinusoidal electric excitation doubly salient motor; obtained q-axis current given value based on disturbance observation
Figure BDA0003097593010000049
The sliding mode control law is as follows:
Figure BDA00030975930100000410
the further technical scheme is that a sliding mode control law of a q-axis current given value based on a sliding mode approach law is obtained according to a sliding mode surface expression, and the sliding mode control law comprises the following steps:
for the sliding mode surface expression s ═ x1+cx2After derivation, the obtained derivative is compared with a sliding mode approximation law of known approximation law parameters alpha, beta and lambda
Figure BDA00030975930100000411
Solving to obtain a sliding mode control law of the q-axis current given value;
wherein, for the state variable x1、x2The result after derivation is
Figure BDA00030975930100000412
Figure BDA00030975930100000413
Is that
Figure BDA00030975930100000414
The derivative of (a) of (b),
Figure BDA00030975930100000415
for the actual value i of the q-axis currentqThe derivative of (c).
The beneficial technical effects of the invention are as follows:
the application discloses a sinusoidal electro-magnetic doubly salient motor speed control method based on a sliding mode approach law, which can better solve the inherent contradiction between system response time and sliding mode buffeting in the traditional sliding mode approach law, realize the quick and overshoot-free response of the motor speed, weaken the sliding mode buffeting, and have stronger robustness on internal and external disturbances of a system. Moreover, the method provides a system response time expression and a sliding mode buffeting expression, thereby providing a parameter constraint condition of the proposed sliding mode approach law and reducing the parameter debugging difficulty of the regulator.
Furthermore, the method realizes more accurate estimation of the lumped disturbance of the system, and can obtain smaller first sliding mode gain by a feedforward compensation disturbance estimation method on the premise of not sacrificing anti-interference performance so as to achieve the effect of restraining sliding mode buffeting.
Drawings
Fig. 1 is a schematic flow chart of obtaining a sliding mode control law according to an embodiment of the present application.
Fig. 2 is a schematic flow chart of obtaining a sliding mode control law according to another embodiment of the present application.
Fig. 3 is a control schematic diagram of the extended state disturbance observer in the present application.
Fig. 4 is a control schematic diagram of the sliding mode control law in the present application.
Fig. 5 is a control schematic diagram of a sinusoidal electro-magnetic doubly salient machine for speed control based on the method of the present application.
Detailed Description
The following further describes the embodiments of the present invention with reference to the drawings.
The application discloses a sinusoidal electro-magnetic doubly salient motor speed control method based on a sliding mode approach law, which comprises the following steps, please refer to a flow schematic diagram shown in fig. 1:
step 1, designing a sliding mode approach law of a sinusoidal electro-magnetic doubly salient motor as follows:
Figure BDA0003097593010000051
wherein k is the first sliding mode gain and k>And (3) selecting the value of k to ensure the anti-interference performance of the system, then reducing buffeting and overshoot as much as possible on the basis, wherein the larger the value of k is, the larger the buffeting is, and the overshoot is easy to cause, and when the value of k is selected, compromise treatment is carried out according to the anti-interference performance, the slipform buffeting and the overshoot, and specific values of the value of k are not limited by the application.
Figure BDA0003097593010000052
Is an initial time t0The value of the slip form surface s. Alpha, beta and lambda are approximate law parameters, alpha is belonged to (0,1), beta and lambda are both larger than 0, and the approximate law parameters alpha, beta and lambda are unknown parameters in the step.
f () is a predetermined function of the sliding mode surface s, which can be set as sgn () function in a conventional manner. Optionally, in order to further suppress the buffeting problem of the sliding mode system, the predetermined function f () may be further modified from a conventional sgn () function to a hyperbolic tangent function tanh (), and
Figure BDA0003097593010000053
at the moment, slideThe modulo approximation law is written as
Figure BDA0003097593010000054
And 2, determining the system response time and an expression of the sliding mode buffeting relative to an approach law parameter based on a sliding mode approach law, and determining to obtain values of alpha, beta and lambda by adjusting the approach law parameter to enable the system response time and the sliding mode buffeting to be respectively smaller than corresponding threshold values.
(1) The expression of the system response time determined based on the sliding mode approach law and the parameters of the approach law is
Figure BDA0003097593010000061
The determination process is as follows:
assume an initial time of system state t0Then the initial time t0Value of the surface s of the time-slip form
Figure BDA0003097593010000062
Indicates an initial time t0Where the system state is located. Defining the moment t when the system state reaches the sliding mode surface s for the first timesThen time tsValue of the surface s of the time-slip form
Figure BDA0003097593010000063
At a time tsThe system state is at the position and has
Figure BDA0003097593010000064
In time interval [ t ] for sliding mode approximation law0,ts]The inner definite integral yields:
Figure BDA0003097593010000065
due to the initial time t0The location of the system state is uncertain and will therefore exist
Figure BDA0003097593010000066
And
Figure BDA0003097593010000067
two cases are:
when in use
Figure BDA0003097593010000068
While, the slip form surface s is in the time interval [ t0,ts]If the internal constant is greater than 0, the above-mentioned result of constant integration is
Figure BDA0003097593010000069
When in use
Figure BDA00030975930100000610
While, the slip form surface s is in the time interval [ t0,ts]If the internal constant is less than 0, the above-mentioned definite integral result is
Figure BDA00030975930100000611
Will be provided with
Figure BDA00030975930100000612
And
Figure BDA00030975930100000613
the expression of the system response time and the approach law parameter obtained by integrating the definite integral results under two conditions is
Figure BDA00030975930100000614
(2) The expression of the sliding mode buffeting relative to the approach law parameters determined based on the sliding mode approach law is
Figure BDA00030975930100000615
And T in the expression is the sampling period of the digital controller.
When adjusting alpha, beta and lambda, determining the constraint conditions of the approach law parameters alpha, beta and lambda based on the expression of the system response time and the expression of the sliding mode buffeting and the approach law parameters
Figure BDA00030975930100000616
Regulating alpha, beta and lambda under the constraint condition. As can be seen from the above equation, in order to ensure that the response speed is fast enough, i.e. the system response time is small enough, the value of α should be as small as possible. In order to ensure that the buffeting of the sliding mode is as small as possible, the value of beta is large. Because the value of beta is large, the value of lambda is small to ensure small system response time. Therefore, when the approach law parameter is adjusted, alpha is reduced to reduce the system response time, beta is increased to reduce the sliding mode buffeting, lambda is reduced on the basis of increasing beta to reduce the system response time, and values of alpha, beta and lambda are determined and obtained until the threshold value is met. Therefore, the setting of the approach law parameters is well documented, and the debugging difficulty of the parameters of the controller is reduced. Meanwhile, the inherent contradiction between the system response time of the traditional sliding mode approach law and the sliding mode buffeting can be effectively solved according to the approach law parameter design method.
Obtained by transforming constraint conditions of the parameters alpha, beta and lambda of the approach law
Figure BDA0003097593010000071
Order to
Figure BDA0003097593010000072
x>0, then
Figure BDA0003097593010000073
Due to the fact that
Figure BDA0003097593010000074
The function g' (x) is therefore a monotonically decreasing function. And also
Figure BDA0003097593010000075
Therefore, g' (x)>0, so the function g (x) is a monotonically decreasing function.
Figure BDA0003097593010000076
Order to
Figure BDA0003097593010000077
The above formula is rewritten as
Figure BDA0003097593010000078
So g (x)<1，x>0. That is to say
Figure BDA0003097593010000079
λ>0. Namely, it is
Figure BDA00030975930100000710
λ>0. Therefore, it is necessary to
Figure BDA00030975930100000711
So that
Figure BDA00030975930100000712
This is true.
And 3, constructing a sliding mode surface expression taking the given mechanical angular velocity and the actual mechanical angular velocity of the sinusoidal electric excitation doubly-salient motor as state variables based on the motion equation of the sinusoidal electric excitation doubly-salient motor. It should be noted that the steps are not in a specific sequence with steps 1 and 2.
Defining a state variable x of a sinusoidal electro-magnetic doubly salient machine1、x2Is composed of
Figure BDA00030975930100000713
ω*Is the given mechanical angular speed of the sine electric excitation doubly salient motor,
Figure BDA00030975930100000714
is the derivative of the actual mechanical angular velocity omega of the sinusoidal electric excitation doubly salient motor, and the motion equation of the sinusoidal electric excitation doubly salient motor defines
Figure BDA00030975930100000715
The calculation formula of (2). Based on the state variable x1、x2The expression of the constructed sliding mode surface is s ═ x1+cx2C is a second sliding mode gain and c>0。
Sinusoidal electric excitation doubly salient motorThe equation of motion can be expressed as
Figure BDA00030975930100000716
Wherein, J0Is the motor moment of inertia, P, of the nominal modelrIs the number of poles of the rotor of the motor,
Figure BDA00030975930100000717
mutual inductance of any phase armature winding and excitation winding of a motor of a nominal model, ifIs the motor excitation current iqIs the actual value of the q-axis current. d (t) is the lumped disturbance over time t, including the motor parameter perturbation and the load disturbance, expressed as:
Figure BDA00030975930100000718
wherein, Δ J, Δ Lpf、ΔTLRespectively representing the moment of inertia J and the mutual inductance L of excitationpfAnd a load torque TLParameter of (d), epsilonωIs the unmodeled part of the system, | D (t) | is less than or equal to D, and D is a constant.
Then for the state variable x1、x2The result after derivation is
Figure BDA0003097593010000081
Figure BDA0003097593010000082
Is that
Figure BDA0003097593010000083
The derivative of (a) of (b),
Figure BDA0003097593010000084
for the actual value i of the q-axis currentqThe derivative of (c).
And 4, obtaining a sliding mode control law of the q-axis current given value based on the sliding mode approach law according to the sliding mode surface expression, adjusting the q-axis current given value according to the sliding mode control law, and controlling the speed of the sinusoidal electric excitation doubly salient motor. In particular, to sliding mode surface tableX is1+cx2Taking a derivative of x1、x2Substituting the derived result into the sliding mode approximation law with known approximation law parameters alpha, beta and lambda
Figure BDA0003097593010000085
And equality is achieved, so that the sliding mode control law of the given value of the q-axis current can be solved.
If the lumped disturbance is not considered, the obtained q-axis current given value
Figure BDA0003097593010000086
The sliding mode control law is as follows:
Figure BDA0003097593010000087
the q-axis current setpoint may then be followed
Figure BDA0003097593010000088
The sliding mode control law of the method adjusts the given value of the q-axis current.
If the lumped disturbance is considered, in an optional embodiment, the method further includes the following steps, please refer to the flowchart shown in fig. 2:
(1) establishing an extended state disturbance observer based on a motion equation of a sinusoidal electric excitation doubly-salient motor and obtaining an observer estimation value of lumped disturbance d (t) as a lumped disturbance estimation value
Figure BDA0003097593010000089
The extended state disturbance observer obtained by establishing is as follows:
Figure BDA00030975930100000810
wherein the content of the first and second substances,
Figure BDA00030975930100000811
observation representing actual mechanical angular velocity ωThe value of the device is estimated by the device,
Figure BDA00030975930100000812
to represent
Figure BDA00030975930100000813
The derivative of (a) of (b),
Figure BDA00030975930100000814
to represent
Figure BDA00030975930100000815
The derivative of (c). Gamma ray1And gamma2Is observer gain and satisfies
Figure BDA00030975930100000816
Xi represents a bandwidth parameter, and the larger xi is, the faster response speed is, but the more easily large noise is introduced; conversely, the slower the response speed, the less the noise. Therefore, the trade-off between rapidity and noise should be made to select the appropriate ξ. Fig. 3 shows a block diagram of the extended state disturbance observer according to the present application.
(2) Lumped disturbance estimation value through feedforward compensation disturbance estimation method
Figure BDA00030975930100000817
And introducing a sliding mode control law to obtain a sliding mode control law based on disturbance observation, and adjusting the q-axis current given value and controlling the speed of the sinusoidal electric excitation doubly salient motor according to the sliding mode control law based on disturbance observation. In integrating the disturbance estimation value
Figure BDA0003097593010000091
After a sliding mode control law of a q-axis current given value is introduced through a feedforward compensation interference estimation method, the obtained q-axis current given value based on disturbance observation
Figure BDA0003097593010000092
The sliding mode control law is as follows:
Figure BDA0003097593010000093
based on the application, the hyperbolic tangent function tanh () is adopted as the basis of the predetermined function f (), and further, the complete function can be obtained
Figure BDA0003097593010000094
The control block diagram is shown in fig. 4.
The q-axis current setpoint based on the disturbance observation can then be followed
Figure BDA0003097593010000095
The sliding mode control law of the method adjusts the given value of the q-axis current. By the method for estimating the feedforward compensation interference, a smaller first sliding mode gain k can be obtained on the premise of not sacrificing the anti-interference performance, so that the effect of suppressing the sliding mode buffeting is achieved.
Selecting a Lyapunov function and designing a sliding mode approximation law according to the application
Figure BDA0003097593010000096
And constructed s ═ x1+cx2And analyzing the stability of the sliding mode control law obtained by the application by using the sliding mode surface expression. By utilizing the Lyapunov stability theory, a Lyapunov function is taken as
Figure BDA0003097593010000097
Derived to obtain
Figure BDA0003097593010000098
The existence condition and the arrival condition of the sliding mode are met, the sliding mode motion of the system can be guaranteed, and the motor sliding mode approach law control system designed by the application is stable.
To obtain a q-axis current set value based on disturbance observation
Figure BDA0003097593010000099
Taking the sliding mode control law as an example, after the sliding mode control law is obtained, the obtained sliding mode control law based on disturbance observation and d-axis given current are used
Figure BDA00030975930100000910
And the high-performance control operation of the sinusoidal electrically-excited doubly-salient motor system is realized by an inner ring PI regulator in an SVPWM mode. The control block diagram of the sinusoidal electric excitation doubly salient motor sliding-mode control law provided by the invention is shown in fig. 5.
Firstly, detecting a rotor position angle theta of a sinusoidal electro-magnetic doubly salient motor in real time through a position sensor to obtain an actual mechanical angular velocity omega of the motor, and combining the actual mechanical angular velocity omega with a given mechanical angular velocity omega*And then the real-time deviation omega can be obtained*- ω. Then, according to Clake _ Park conversion, sampling I by three-phase currenta、Ib、IcObtaining the actual value i of the d-axis currentdAnd the actual value of q-axis current iq. Then, the designed sliding mode control law is adopted to control a rotating speed ring of the motor system, and a q-axis current given value based on disturbance observation is obtained
Figure BDA0003097593010000101
d-axis given current
Figure BDA0003097593010000102
And d-axis current actual value idQ-axis current setpoint based on disturbance observation
Figure BDA0003097593010000103
And the actual value i of the q-axis currentqAfter difference is made respectively, d-axis voltage u is obtained through respective inner ring PI regulatorsdAnd q-axis voltage uq. Then, to udAnd uqObtaining the voltage u under a two-phase static coordinate system by adopting Inv _ Park transformationαAnd uβ. And finally, obtaining a duty ratio driving signal to drive the voltage source inverter through a Space Vector Pulse Width Modulation (SVPWM) mode, thereby realizing high-performance control on the sinusoidal electric excitation doubly salient motor.
What has been described above is only a preferred embodiment of the present application, and the present invention is not limited to the above embodiment. It is to be understood that other modifications and variations directly derivable or suggested by those skilled in the art without departing from the spirit and concept of the present invention are to be considered as included within the scope of the present invention.

Claims (9)

1. A sinusoidal electric excitation doubly salient motor speed control method based on a sliding mode approximation law is characterized by comprising the following steps:
the approach law of a sliding mode for designing a sinusoidal electro-magnetic doubly salient motor is
Figure FDA0003097592000000011
Wherein
Figure FDA0003097592000000012
k is the first sliding mode gain and k>0, f () is a predetermined function of the sliding mode surface s,
Figure FDA0003097592000000013
is an initial time t0The value of the time slip form surface s; alpha, beta and lambda are approach law parameters, alpha belongs to (0,1), and both beta and lambda are greater than 0;
determining the system response time and an expression of the sliding mode buffeting on an approach law parameter based on the sliding mode approach law, and determining to obtain values of alpha, beta and lambda by adjusting the approach law parameter to enable the system response time and the sliding mode buffeting to be respectively smaller than corresponding threshold values;
constructing a sliding mode surface expression taking the given mechanical angular velocity and the actual mechanical angular velocity of the sinusoidal electric excitation doubly-salient motor as state variables based on the motion equation of the sinusoidal electric excitation doubly-salient motor;
and obtaining a sliding mode control law of the q-axis current given value based on the sliding mode approach law according to the sliding mode surface expression, and adjusting the q-axis current given value according to the sliding mode control law to control the speed of the sinusoidal electrically-excited doubly-salient motor.
2. The method of claim 1,
the expression of the system response time determined based on the sliding mode approach law and the parameters of the approach law is
Figure FDA0003097592000000014
The expression of the sliding mode buffeting on the parameters of the approach law is
Figure FDA0003097592000000015
(T represents the sampling period of the digital controller), when the approach law parameter is adjusted, reducing alpha to reduce the system response time, increasing beta to reduce the sliding mode buffeting, and reducing lambda to reduce the system response time on the basis of increasing beta.
3. The method of claim 2, wherein determining a system response time and an expression for sliding mode buffeting with respect to an approach law parameter based on the sliding mode approach law comprises:
defining the moment t when the system state reaches the sliding mode surface s for the first timesAnd has tsValue of the surface s of the time-slip form
Figure FDA0003097592000000019
For the sliding mode approximation rule in a time interval [ t0,ts]The inner definite integral yields:
Figure FDA0003097592000000016
when in use
Figure FDA0003097592000000018
While, the slip form surface s is in the time interval [ t0,ts]If the internal constant is greater than 0, the integral result is determined to be
Figure FDA0003097592000000017
When in use
Figure FDA0003097592000000021
While, the slip form surface s is in the time interval [ t0,ts]If the internal constant is less than 0, the integral result is determined to be
Figure FDA0003097592000000022
Will be provided with
Figure FDA0003097592000000023
And
Figure FDA0003097592000000024
the expression of the system response time and the approach law parameter obtained by integrating the definite integral results under two conditions is
Figure FDA0003097592000000025
4. The method of claim 2, wherein adjusting the approach law parameters comprises:
determining constraint conditions of the approach law parameters alpha, beta and lambda based on an expression of system response time and the approach law parameters and an expression of sliding mode buffeting
Figure FDA0003097592000000026
Adjusting alpha, beta and lambda under the constraint condition.
5. The method of claim 1,
the predetermined function f () in the sliding mode approach law is a hyperbolic tangent function tanh (), and
Figure FDA0003097592000000027
6. the method according to any one of claims 1 to 5,
the motion equation of the sinusoidal electric excitation doubly salient motor is
Figure FDA0003097592000000028
Figure FDA0003097592000000029
Is the derivative, J, of the actual mechanical angular velocity omega of the sinusoidal electrically excited doubly salient machine0Is the motor moment of inertia, P, of the nominal modelrIs the number of poles of the motor rotor, Lpf0Mutual inductance of any phase armature winding and excitation winding of a motor of a nominal model, ifIs the motor excitation current iqIs the actual value of the q-axis current, d (t) is the lumped disturbance that varies with time t;
the method further comprises:
establishing an extended state disturbance observer based on the motion equation of the sinusoidal electric excitation doubly-salient motor and obtaining an observer estimation value of lumped disturbance d (t) as a lumped disturbance estimation value
Figure FDA00030975920000000210
The lumped disturbance estimation value is estimated through a feedforward compensation disturbance estimation method
Figure FDA00030975920000000211
And introducing the sliding mode control law to obtain a sliding mode control law based on disturbance observation, and adjusting the q-axis current given value according to the sliding mode control law based on disturbance observation to control the speed of the sinusoidal electric excitation doubly salient motor.
7. The method of claim 6, wherein the extended state disturbance observer based on the equations of motion for the sinusoidal electrically excited doubly salient machine is established as:
Figure FDA0003097592000000031
wherein the content of the first and second substances,
Figure FDA0003097592000000032
an observer estimate representing the actual mechanical angular velocity ω,
Figure FDA0003097592000000033
to represent
Figure FDA0003097592000000034
The derivative of (a) of (b),
Figure FDA0003097592000000035
to represent
Figure FDA0003097592000000036
Derivative of, gamma1And gamma2Is observer gain and satisfies
Figure FDA0003097592000000037
ξ denotes the bandwidth parameter.
8. The method of claim 6, wherein the sliding-mode surface expression is s-x1+cx2Wherein c is a second sliding mode gain and c>0，x1、x2Is the state variable of the sinusoidal electric excitation doubly salient motor and has
Figure FDA0003097592000000038
ω*Is the given mechanical angular velocity of the sinusoidal electrically excited doubly salient motor; obtained q-axis current given value based on disturbance observation
Figure FDA0003097592000000039
The sliding mode control law is as follows:
Figure FDA00030975920000000310
9. the method according to claim 8, wherein obtaining a sliding mode control law for a given value of q-axis current based on the sliding mode approach law according to the sliding mode surface expression comprises:
for the sliding mode surface expression s ═ x1+cx2After derivation, the obtained derivative is compared with a sliding mode approximation law of known approximation law parameters alpha, beta and lambda
Figure FDA00030975920000000311
Solving to obtain a sliding mode control law of the q-axis current given value;
wherein, for the state variable x1、x2The result after derivation is
Figure FDA00030975920000000312
Figure FDA00030975920000000313
Is that
Figure FDA00030975920000000314
The derivative of (a) of (b),
Figure FDA00030975920000000315
for the actual value i of the q-axis currentqThe derivative of (c).
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