CN114123893B - A vehicle dual-winding steering motor current balancing control method and system - Google Patents

Abstract

The invention discloses a current balance control method and a current balance control system for a duplex winding steering motor for a vehicle, wherein the current balance control method comprises the following steps: establishing a double-winding motor current imbalance mathematical model based on double d-q coordinate change; according to the current imbalance mathematical model, the uncertainty of inductance and resistance parameters is considered, and a current imbalance mathematical model with uncertainty parameters is established; designing an RBF neural network to approximate an uncertainty parameter term of the current imbalance mathematical model with uncertainty parameters; and designing a sliding mode controller based on the RBF neural network, and superposing the output of the sliding mode controller and the output of the PI current controller to jointly act on the double-winding motor to realize current balance between two sets of windings of the double-winding steering motor. The method can balance the currents of the two sets of windings on the basis of considering the influence of the uncertainty of the motor parameters, and improves the robustness of the steer-by-wire system.

Description

A vehicle dual-winding steering motor current balancing control method and system

Technical field

The invention belongs to the technical field of automobile steering systems, and specifically relates to a vehicle dual-winding steering motor current balancing control method and system.

Background technique

Existing steer-by-wire systems generally use a single-winding three-phase permanent magnet synchronous motor as the execution motor. When the winding fails, the entire steering motor will fail, seriously reducing the reliability of the steer-by-wire system. The double-winding motor is composed of two sets of three-phase windings. The two sets of windings are electrically independent. The failure of one winding will not affect the normal operation of the other winding. It has good fault tolerance and reliability.

However, the current imbalance caused by the difference in resistance and inductance values between the two sets of windings of a double-winding motor or the imbalance of the power supply voltage caused by the difference between the two sets of inverters will often cause an imbalance in the current between the two sets of windings. phenomenon, which will lead to uneven heating of the double-winding motor, which may damage the insulation structure of the windings, and the winding with the larger current may be overloaded and burned out. Chinese invention patent application number 201711054340.2 announced a multi-phase motor current balance control method based on generalized symmetric component theory. The multi-phase motor is disassembled into n symmetric m-phase systems, and a PI control algorithm is used for current balance control. However, it has not Consider the influence of double-winding motor parameter uncertainty and external disturbance on current balance control.

Contents of the invention

In view of the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a vehicle dual-winding steering motor current balancing control method and system to solve the dual-winding motor current balancing that does not consider the influence of parameter uncertainty in the prior art. Regarding the control problem, the method of the present invention can balance the currents of the two sets of windings on the basis of considering the influence of the uncertainty of the motor parameters, thereby improving the robustness of the steer-by-wire system.

In order to achieve the above objects, the technical solutions adopted by the present invention are as follows:

A vehicle dual-winding steering motor current balancing control method of the present invention, the steps are as follows:

1) Establish a mathematical model of double-winding motor current imbalance based on changes in double d-q coordinates;

2) Based on the current imbalance mathematical model, consider the uncertainty of its inductance and resistance parameters, and establish a current imbalance mathematical model with uncertainty parameters;

3) Design the RBF neural network to approximate the uncertainty parameter terms of the current imbalance mathematical model with uncertainty parameters;

4) Design a sliding mode controller based on the RBF neural network, and superimpose the output of the sliding mode controller with the output of the PI current controller to act on the double winding motor to realize the steering between the two sets of windings of the double winding motor. current balance.

Further, the step 1) specifically includes:

11) Perform d-q coordinate transformation on the three-phase current of the first winding of the double-winding motor to obtain the current components of the three-phase current in the d1-q1 synchronous rotation coordinate system;

12) Perform d-q coordinate transformation on the three-phase current of the second winding of the double-winding motor to obtain the current components of the three-phase current in the d2-q2 synchronous rotation coordinate system;

13) The difference between the q1-axis current component in the d1-q1 synchronous rotating coordinate system and the q2-axis current component in the d2-q2 synchronous rotating coordinate system is used to obtain a current imbalance mathematical model.

Further, the step 1) specifically includes:

Perform d-q transformation on the three-phase current in the natural coordinate system. The d-q coordinate transformation includes Clark and Park coordinate transformation matrices to obtain the model of the transformed double-winding motor in the double d-q coordinate system:

Among them, ω _e is the electrical angular velocity of the motor, u _d1 , u _q1 , u _d2 , u _q2 are the dq-axis stator voltage, i _d1 , i _q1 , i _d2 , i _q2 are the stator currents, is the motor flux linkage, R ₁ and R ₂ are the stator resistance, L _d1 and L _d2 are the stator self-inductance, L _dd and L _qq are the stator mutual inductance of the d-axis and q-axis respectively;/> is the flux linkage amplitude generated by the permanent magnet in each phase winding.

Further, the step 1) specifically includes:

Assume that L _q1 =L _q2 =L _q , R ₁ =R ₂ =R, and the selected state quantity is the q1 axis current in the d1-q1 synchronous rotation coordinate system and the q2 axis in the d2-q2 synchronous rotation coordinate system. The difference of current and its first derivative, that is, x ₁ =i _q1 -i _q2 , Order/> Then the state space equation of the double-winding motor current imbalance mathematical model is expressed as:

Further, the step 2) specifically includes:

Considering the uncertainty parameters and external disturbances, that is, R ₁ , R ₂ , L _q1 , L _q2 , L _qq and L _dd are uncertain, and L _q1 ≠L _q2 , R ₁ ≠R ₂ , let R ₂ =a ·R ₁ ,L _q2 =b·L _q1 , then the state space equation of the double-winding motor current imbalance mathematical model can be rewritten as:

make Then the above formula can be simplified to:

Among them, f and g are unknown nonlinear functions, d(t) is the external disturbance term, and d(t) is bounded, |d(t)|≤D, and D is a positive real number.

Further, the step 3) specifically includes:

The design is based on the RBF neural network to approximate the uncertainty parameters in the current imbalance mathematical model with uncertainty parameters. The input to the RBF neural network is the difference between the q1-axis and q2-axis currents in step 1) and its first-order differential. , the output is the estimated value of the uncertainty parameter item.

Further, step 3) specifically includes: using RBF neural network to approximate the unknown nonlinear functions f and g. The RBF neural network is expressed as:

f(x)＝W ^*T h _f (x)+ε _f

g(x)＝V ^*T h _g (x)+ε _g

Among them, x is the network input, c and b are the parameters of the Gaussian basis function, j is the j-th node of the hidden layer of the network, h _f (x) = [h _j ] ^T , h _g (x) = [h _j ] ^T is the network Gaussian function output, W ^* and V ^* are the ideal weights of the network, ε _f and ε _g are the network approximation errors, ε ≤ ε _N and ε _N are the upper bounds of the network approximation error;

Taking the network input as x=[x ₁ x ₂ ] ^T , the network output (ie, the estimated value of the uncertainty parameter term) is:

Define estimation error for:

in

Further, the step 4) specifically includes:

41) According to the current imbalance mathematical model with uncertainty parameters described in step 3), design the sliding mode including the difference between the q1-axis and q2-axis currents and its first-order differential;

42) Select the exponential reaching law as the reaching law of the sliding mode controller to reduce the chattering phenomenon of the output of the sliding mode controller;

43) Derive the expression of the sliding mode control law according to steps 41) and 42), and use the output of the RBF neural network in step 3) to replace the uncertainty parameter term in the expression of the sliding mode control law, and obtain based on Sliding mode control law of RBF neural network;

44) The output of the sliding mode controller and the output of the PI current controller are superimposed and act together on the double-winding motor. The two sets of windings of the double-winding motor are controlled by independent PI current controllers to track a given current. instruction.

Further, the step 4) specifically includes:

The sliding mode is designed as:

s＝cx ₁ +x ₂

In the formula, c is the sliding mode coefficient;

The exponential approaching law is designed as:

In the formula, k is the gain coefficient of the exponential term, and eta is the gain coefficient of the switching term;

By substituting the sliding mode and the current imbalance mathematical model with uncertainty parameters into the exponential approaching law, we can get:

Therefore, by substituting the RBF neural network output in step 3) into the above equation, the expression of the sliding mode control law based on RBF neural network can be obtained as:

Further, the step 4) also includes:

The output of the sliding mode controller is subtracted from the output of the PI current controller of the first winding and added to the output of the PI current controller of the second winding.

The invention also provides a vehicle dual-winding steering motor current balancing control system, which includes:

The first model building module is used to establish a mathematical model of double-winding motor current imbalance based on changes in double d-q coordinates;

The second model building module establishes a current imbalance mathematical model with uncertainty parameters based on the current imbalance mathematical model and considering the uncertainty of its inductance and resistance parameters;

The uncertainty parameter approximation module is used to design the RBF neural network to approximate the uncertainty parameter terms of the current imbalance mathematical model with uncertainty parameters;

The current control module is used to design a sliding mode controller based on the RBF neural network, and superimpose the output of the sliding mode controller with the output of the PI current controller to work together on the double winding motor to realize the dual winding steering motor. Current balance between sets of windings.

Beneficial effects of the present invention:

The invention can effectively eliminate the current imbalance between the two sets of windings of the double-winding motor, make the currents of the two sets of windings equal, reduce the current imbalance of the double-winding motor, improve the overall performance of the motor, and extend the service life of the motor.

The RBF neural network of the present invention can approximate parameters with any uncertainty, so the current balance control method of the present invention has strong robustness to parameter uncertainty.

Description of the drawings

Figure 1 is a flow chart of the method of the present invention.

Figure 2 is a structural diagram of the relationship between the sliding mode controller and the PI controller based on the RBF neural network of the present invention.

Figure 3 is a structural principle diagram of the sliding mode controller based on RBF neural network of the present invention.

Detailed ways

In order to facilitate the understanding of those skilled in the art, the present invention will be further described below in conjunction with the embodiments and drawings. The contents mentioned in the embodiments do not limit the present invention.

Referring to Figure 1, a vehicle dual-winding steering motor current balancing control method of the present invention has the following steps:

1) Establish a mathematical model of double-winding motor current imbalance based on changes in double d-q coordinates; specifically including:

11) Perform d-q coordinate transformation on the three-phase current of the first winding of the double-winding motor to obtain the current components of the three-phase current in the d1-q1 synchronous rotation coordinate system;

12) Perform d-q coordinate transformation on the three-phase current of the second winding of the double-winding motor to obtain the current components of the three-phase current in the d2-q2 synchronous rotation coordinate system;

13) The difference between the q1-axis current component in the d1-q1 synchronous rotating coordinate system and the q2-axis current component in the d2-q2 synchronous rotating coordinate system is used to obtain a current imbalance mathematical model.

In addition, the step 1) specifically includes:

Perform d-q transformation on the three-phase current in the natural coordinate system. The d-q coordinate transformation includes Clark and Park coordinate transformation matrices to obtain the model of the transformed double-winding motor in the double d-q coordinate system:

Among them, ω _e is the electrical angular velocity of the motor, u _d1 , u _q1 , u _d2 , u _q2 are the dq-axis stator voltage, i _d1 , i _q1 , i _d2 , i _q2 are the stator currents, is the motor flux linkage, R ₁ and R ₂ are the stator resistance, L _d1 and L _d2 are the stator self-inductance, L _dd and L _qq are the stator mutual inductance of the d-axis and q-axis respectively;/> is the flux linkage amplitude generated by the permanent magnet in each phase winding.

And, the step 1) specifically includes:

Assume that L _q1 =L _q2 =L _q , R ₁ =R ₂ =R, and the selected state quantity is the q1 axis current in the d1-q1 synchronous rotation coordinate system and the q2 axis in the d2-q2 synchronous rotation coordinate system. The difference of current and its first derivative, that is, x ₁ =i _q1 -i _q2 , Order/> Then the state space equation of the double-winding motor current imbalance mathematical model is expressed as:

2) Based on the current imbalance mathematical model and considering the uncertainty of its inductance and resistance parameters, establish a current imbalance mathematical model with uncertainty parameters; specifically including:

Considering the uncertainty parameters and external disturbances, that is, R ₁ , R ₂ , L _q1 , L _q2 , L _qq and L _dd are uncertain, and L _q1 ≠L _q2 , R ₁ ≠R ₂ , let R ₂ =a ·R ₁ ,L _q2 =b·L _q1 , then the state space equation of the double-winding motor current imbalance mathematical model can be rewritten as:

make Then the above formula can be simplified to:

Among them, f and g are unknown nonlinear functions, d(t) is the external disturbance term, and d(t) is bounded, |d(t)|≤D, and D is a positive real number.

3) Design the RBF neural network to approximate the uncertainty parameter terms of the current imbalance mathematical model with uncertainty parameters; specifically include:

The design is based on the RBF neural network to approximate the uncertainty parameters in the current imbalance mathematical model with uncertainty parameters. The input to the RBF neural network is the difference between the q1-axis and q2-axis currents in step 1) and its first-order differential. , the output is the estimated value of the uncertainty parameter item.

In addition, the step 3) specifically includes: using RBF neural network to approximate the unknown nonlinear functions f and g. The RBF neural network is expressed as:

f(x)＝W ^*T h _f (x)+ε _f

g(x)＝V ^*T h _g (x)+ε _g

Among them, x is the network input, c and b are the parameters of the Gaussian basis function, j is the j-th node of the hidden layer of the network, h _f (x) = [h _j ] ^T , h _g (x) = [h _j ] ^T is the network Gaussian function output, W ^* and V ^* are the ideal weights of the network, ε _f and ε _g are the network approximation errors, ε ≤ ε _N and ε _N are the upper bounds of the network approximation error;

Taking the network input as x=[x ₁ x ₂ ] ^T , the network output (ie, the estimated value of the uncertainty parameter term) is:

Define estimation error for:

in

4) Design a sliding mode controller based on the RBF neural network, and superimpose the output of the sliding mode controller with the output of the PI current controller to act on the double winding motor to realize the steering between the two sets of windings of the double winding motor. current balance;

Wherein, said step 4) specifically includes:

41) According to the current imbalance mathematical model with uncertainty parameters described in step 3), design the sliding mode including the difference between the q1-axis and q2-axis currents and its first-order differential;

42) Select the exponential reaching law as the reaching law of the sliding mode controller to reduce the chattering phenomenon of the output of the sliding mode controller;

43) Derive the expression of the sliding mode control law according to steps 41) and 42), and use the output of the RBF neural network in step 3) to replace the uncertainty parameter term in the expression of the sliding mode control law, and obtain based on Sliding mode control law of RBF neural network;

44) The output of the sliding mode controller and the output of the PI current controller are superimposed and act together on the double-winding motor. The two sets of windings of the double-winding motor are controlled by independent PI current controllers to track a given current. instruction.

And, said step 4) specifically includes:

The sliding mode is designed as:

s＝cx ₁ +x ₂

In the formula, c is the sliding mode coefficient;

The exponential approaching law is designed as:

In the formula, k is the gain coefficient of the exponential term, and eta is the gain coefficient of the switching term;

By substituting the sliding mode and the current imbalance mathematical model with uncertainty parameters into the exponential approaching law, we can get:

Therefore, by substituting the RBF neural network output in step 3) into the above equation, the expression of the sliding mode control law based on RBF neural network can be obtained as:

The output of the sliding mode controller is subtracted from the output of the PI current controller of the first winding and added to the output of the PI current controller of the second winding.

Referring to Figure 2, the input of the sliding mode controller based on the RBF neural network of the present invention is the difference between the q1 axis current and the q2 axis current of the double winding motor; the output of the sliding mode controller based on the RBF neural network of the present invention and the third The PI controller output of the first winding is subtracted and added to the PI controller output of the second winding, acting on the two sets of windings respectively. The PI controller inputs the deviation between the command current and the actual current, outputs a control voltage and acts on a single winding.

Referring to Figure 3, the sliding mode controller based on the RBF neural network of the present invention includes an uncertain current balance mathematical model, an RBF neural network and a sliding mode control law. The RBF neural network inputs the output of the uncertain current balance mathematical model and its first-order differential, and outputs the estimated value of the uncertainty parameter. The sliding mode control law compares the output of the uncertain current balance mathematical model with the ideal value (that is, the difference between the q1-axis current and the q2-axis current is 0) as the input of the sliding mode control law. The output is subtracted from the PI controller output of the first winding and added to the PI controller output of the second winding, acting on the two sets of windings respectively.

The invention also provides a vehicle dual-winding steering motor current balancing control system, which includes:

The first model building module is used to establish a mathematical model of double-winding motor current imbalance based on changes in double d-q coordinates;

The second model building module establishes a current imbalance mathematical model with uncertainty parameters based on the current imbalance mathematical model and considering the uncertainty of its inductance and resistance parameters;

The uncertainty parameter approximation module is used to design the RBF neural network to approximate the uncertainty parameter terms of the current imbalance mathematical model with uncertainty parameters;

The current control module is used to design a sliding mode controller based on the RBF neural network, and superimpose the output of the sliding mode controller with the output of the PI current controller to work together on the double winding motor to realize the dual winding steering motor. Current balance between sets of windings.

There are many specific ways of application of the present invention. The above are only the preferred embodiments of the present invention. It should be pointed out that for those of ordinary skill in this technical field, several improvements can be made without departing from the principles of the present invention. These improvements Improvements should also be considered as the protection scope of the present invention.

Claims (6)

1. The current balance control method for the vehicular double-winding steering motor is characterized by comprising the following steps of:

1) Establishing a double-winding motor current imbalance mathematical model based on double d-q coordinate change;

2) According to the current imbalance mathematical model, the uncertainty of inductance and resistance parameters is considered, and a current imbalance mathematical model with uncertainty parameters is established;

3) Designing an RBF neural network to approximate an uncertainty parameter term of the current imbalance mathematical model with uncertainty parameters;

4) Designing a sliding mode controller based on an RBF neural network, and superposing the output of the sliding mode controller and the output of a PI current controller to jointly act on the double-winding motor to realize current balance between two sets of windings of the double-winding steering motor;

the step 1) specifically comprises the following steps:

11 D-q coordinate transformation is carried out on the three-phase current of the first winding of the double-winding motor, so that current components of the three-phase current under a d1-q1 synchronous rotation coordinate system are obtained;

12 D-q coordinate transformation is carried out on the three-phase current of the second winding of the double-winding motor, so that current components of the three-phase current under a d2-q2 synchronous rotation coordinate system are obtained;

13 The q1 axis current component under the d1-q1 synchronous rotation coordinate system is differenced with the q2 axis current component under the d2-q2 synchronous rotation coordinate system, and a current imbalance mathematical model is obtained;

the step 1) specifically comprises the following steps:

d-q coordinate transformation is carried out on three-phase current under a natural coordinate system, the d-q coordinate transformation comprises Clark and Park coordinate transformation matrixes, and a model of the transformed double-winding motor under a double d-q coordinate system is obtained:

wherein omega _e U is the electrical angular velocity of the motor _d1 ,u _q1 ,u _d2 ,u _q2 For d-q axis stator voltage, i _d1 ,i _q1 ,i _d2 ,i _q2 For the stator current to be present,r is the flux linkage of the motor ₁ And R is ₂ Is stator resistance L _d1 ，L _d2 For stator self-inductance, L _dd And L _qq The stators respectively have d axis and q axis mutual inductance; />The magnitude of flux linkage generated in each phase winding for the permanent magnet;

the step 1) specifically further includes:

let L be _q1 ＝L _q2 ＝L _q ,R ₁ ＝R ₂ =r, the state quantity is selected as the difference between the q 1-axis current in the d1-q1 synchronous rotation coordinate system and the q 2-axis current in the d2-q2 synchronous rotation coordinate system, i.e.Order theThe state space equation for the double-winding motor current imbalance mathematical model is expressed as:

the step 2) specifically comprises the following steps:

taking into account uncertainty parameters and external disturbances, i.e. R ₁ 、R ₂ 、L _q1 、L _q2 、L _qq And L _dd Is indeterminate, and L _q1 ≠L _q2 ,R ₁ ≠R ₂ Let R ₂ ＝a·R ₁ ,L _q2 ＝b·L _q1 The state space equation of the double-winding motor current imbalance mathematical model is rewritten as:

order theThe above simplification is:

wherein f and g are unknown nonlinear functions, D (t) is an external disturbance term, D (t) is bounded, D (t) is less than or equal to D, and D is a positive real number.

2. The method for controlling current balance of a vehicular dual-winding steering motor according to claim 1, wherein the step 3) specifically comprises:

and (3) designing an RBF neural network based on the uncertainty parameters in the current imbalance mathematical model with the uncertainty parameters, wherein the RBF neural network is input into the difference between the q1 axis and the q2 axis in the step (1) and the first-order differentiation thereof, and the output is the estimated value of the uncertainty parameter item.

3. The method for controlling current balance of a vehicular dual-winding steering motor according to claim 2, wherein the step 3) specifically further comprises: the unknown nonlinear functions f and g are approximated by using an RBF neural network expressed as:

f(x)＝W ^*T h _f (x)+ε _f

g(x)＝V ^*T h _g (x)+ε _g

wherein x is the network input, c, b is the parameter of the Gaussian basis function, j is the j node of the hidden layer of the network, h _f (x)＝[h _j ] ^T ，h _g (x)＝[h _j ] ^T For output of Gaussian basis function of network, W ^* ，V ^* Epsilon as ideal weight of network _f ，ε _g For network approximation error, epsilon is less than or equal to epsilon _N ，ε _N The upper bound of the network approximation error;

taking the network input as x= [ x ] ₁ x ₂ ] ^T The network output is:

defining an estimation errorThe method comprises the following steps:

wherein the method comprises the steps of

4. The method for controlling current balance of a vehicular dual-winding steering motor according to claim 3, wherein the step 4) specifically comprises:

41 Designing a sliding mode comprising the difference between the q1 axis and the q2 axis currents and the first derivative thereof according to the current imbalance mathematical model with uncertainty parameters described in step 3);

42 Selecting an index approach law as an approach law of the sliding mode controller, and reducing a buffeting phenomenon output by the sliding mode controller;

43 Deducing an expression of the sliding mode control law according to the step 41) and the step 42), and using the output of the RBF neural network in the step 3) to replace an uncertainty parameter item in the expression of the sliding mode control law so as to obtain the sliding mode control law based on the RBF neural network;

44 The output of the sliding mode controller and the output of the PI current controller are overlapped and then jointly act on the double-winding motor, and two sets of windings of the double-winding motor are respectively controlled by the independent PI current controllers and are used for tracking given current instructions.

5. The method for controlling current balance of a vehicular dual-winding steering motor according to claim 4, wherein the step 4) specifically comprises:

the sliding mode is designed as follows:

s＝cx ₁ +x ₂

wherein c is a sliding mode coefficient;

the exponential approach law is designed as follows:

wherein k is an exponential gain coefficient, and eta is a switching gain coefficient;

substituting the sliding mode and the current imbalance mathematical model with uncertainty parameters into an exponential approach law to obtain:

therefore, substituting the RBF neural network output in step 3) into the above formula can obtain the expression of the sliding mode control law based on the RBF neural network as follows:

6. the utility model provides a duplex winding turns to motor current balance control system for vehicle which characterized in that includes:

the first model building module is used for building a double-winding motor current imbalance mathematical model based on double d-q coordinate change;

the second model building module is used for building the current unbalance mathematical model with uncertainty parameters by considering the uncertainty of the inductance and resistance parameters according to the current unbalance mathematical model;

the uncertainty parameter approximation module is used for designing an RBF neural network to approximate an uncertainty parameter item of the current imbalance mathematical model with the uncertainty parameter;

the current control module is used for designing a sliding mode controller based on an RBF neural network, and superposing the output of the sliding mode controller and the output of the PI current controller to jointly act on the double-winding motor so as to realize current balance between two sets of windings of the double-winding steering motor;

the first model building module specifically comprises:

d-q coordinate transformation is carried out on three-phase current under a natural coordinate system, the d-q coordinate transformation comprises Clark and Park coordinate transformation matrixes, and a model of the transformed double-winding motor under a double d-q coordinate system is obtained:

wherein omega _e U is the electrical angular velocity of the motor _d1 ,u _q1 ,u _d2 ,u _q2 For d-q axis stator voltage, i _d1 ,i _q1 ,i _d2 ,i _q2 For the stator current to be present,r is the flux linkage of the motor ₁ And R is ₂ Is stator resistance L _d1 ，L _d2 For stator self-inductance, L _dd And L _qq The stators respectively have d axis and q axis mutual inductance; />The magnitude of flux linkage generated in each phase winding for the permanent magnet;

let L be _q1 ＝L _q2 ＝L _q ,R ₁ ＝R ₂ R, the state quantity is selected to be the difference between the q1 axis current in the d1-q1 synchronous rotation coordinate system and the q2 axis current in the d2-q2 synchronous rotation coordinate system and the first order differential thereof, namelyLet->The state space equation for the double-winding motor current imbalance mathematical model is expressed as:

the second model building module specifically comprises:

taking into account uncertainty parameters and external disturbances, i.e. R ₁ 、R ₂ 、L _q1 、L _q2 、L _qq And L _dd Is indeterminate, and L _q1 ≠L _q2 ,R ₁ ≠R ₂ Let R ₂ ＝a·R ₁ ,L _q2 ＝b·L _q1 The state space equation of the double-winding motor current imbalance mathematical model is rewritten as:

order theThe above simplification is:

wherein f and g are unknown nonlinear functions, D (t) is an external disturbance term, D (t) is bounded, D (t) is less than or equal to D, and D is a positive real number.