阅读说明：本技术 适用于磁悬浮球形电机的分数阶pid滑模观测器设计方法 (Design method of fractional order PID sliding-mode observer suitable for magnetic suspension spherical motor ) 是由 杨东升 熊浩杰 马占超 肖军 周博文 孙维东 高筱婷 王昕� 于 2019-09-24 设计创作，主要内容包括：本发明提供一种适用于磁悬浮球形电机的分数阶PID滑模观测器设计方法,涉及无位置传感器技术领域。该方法首先采集磁悬浮球形电机三相电流值和三相电压值,进而构建滑模观测器的数学模型；利用构建的滑模观测器数学模型计算磁悬浮球形电机在两相静止坐标系下的反电动势和定子电流估计值；同时以定子电流估计值的误差作为滑模面,构造滑模观测器的切换函数,并采用Prelu函数作为滑模观测器开关函数；然后利用分数阶PID对滑模观测器的切换函数中的滑模增益进行参数调节和整定；并由计算得到的反电动势得到真实转子电角度和电角速度的估计值。本发明方法有效的抑制了磁悬浮球形电机滑模观测器的抖振,能够设计出稳定的滑模观测器。(The invention provides a design method of a fractional order PID sliding mode observer suitable for a magnetic suspension spherical motor, and relates to the technical field of no position sensor. Firstly, acquiring three-phase current values and three-phase voltage values of a magnetic suspension spherical motor, and further constructing a mathematical model of a sliding mode observer; calculating the back electromotive force and the stator current estimated value of the magnetic suspension spherical motor under a two-phase static coordinate system by utilizing the constructed mathematical model of the sliding-mode observer; meanwhile, taking the error of the estimated value of the stator current as a sliding mode surface, constructing a switching function of a sliding mode observer, and taking a Prelu function as a switching function of the sliding mode observer; then, parameter adjustment and setting are carried out on the sliding mode gain in the switching function of the sliding mode observer by utilizing the fractional order PID; and obtaining estimated values of the true rotor electrical angle and the electrical angular velocity from the calculated back electromotive force. The method effectively inhibits buffeting of the sliding mode observer of the magnetic suspension spherical motor, and can design a stable sliding mode observer.)

1. A design method of a fractional order PID sliding-mode observer suitable for a magnetic suspension spherical motor is characterized by comprising the following steps: the method comprises the following steps:

step 1: collecting three-phase current value i of magnetic suspension spherical motor_a、i_b、i_cAnd three-phase voltage value u_a、u_b、u_cClark conversion is carried out on the three-phase voltage value and the current value to obtain the voltage u under the two-phase static coordinate system_α、u_βAnd current i_αAnd i_β(ii) a Constructing a voltage equation under a two-phase static coordinate system, and transforming the voltage equation to obtain a current i_αAnd i_βThereby obtaining a mathematical model of the sliding-mode observer;

step 2: calculating the back electromotive force of the magnetic suspension spherical motor under a two-phase static coordinate system by utilizing the mathematical model of the sliding-mode observer constructed in the step 1

and step 3: constructing a transfer function of a fractional order PID, approximating the fractional order PID controller to a continuous high-order integer order PID controller by utilizing an improved Oustaloup approximation method, then constructing a fractional order differential integral operator model, and carrying out parameter regulation and setting on sliding mode gain in a switching function of a sliding mode observer;

and 4, step 4: back electromotive force calculated from step 2

And 5: by applying a counter electromotive force to the counter electromotive force obtained in step 4

step 6: utilizing the current estimated value of the magnetic suspension spherical motor in the step 2

2. The design method of the fractional order PID sliding-mode observer suitable for the magnetic suspension spherical motor according to claim 1 is characterized in that: the specific method of the step 1 comprises the following steps:

clark conversion is carried out on the three-phase voltage value and the current value of the collected magnetic suspension spherical motor to obtain the voltage u under a two-phase static coordinate system_α、u_βAnd current i_αAnd i_βThe following formula shows:

the voltage equation under the two-phase static coordinate system of the structure is shown as the following formula:

wherein R is_sIs stator resistance, L_sFor stator inductance, p is the differential operator, ω is the electrical angular velocity of the rotor,. psi_fThe magnetic flux linkage is formed by the permanent magnet and the stator, and theta is the rotor electrical angle;

the voltage equation is deformed to obtain the current i under a two-phase coordinate system_αAnd i_βThe equation of equilibrium of (a) is shown as follows:

the equilibrium equation is simplified to:

pi_s＝A·i_s+B·v_s+ψ_f·v_i

wherein i_sIs composed of

further simplifying to obtain a mathematical model of the sliding-mode observer, wherein the following formula is shown:

wherein the content of the first and second substances,

3. The design method of the fractional order PID sliding-mode observer suitable for the magnetic suspension spherical motor according to claim 2 is characterized in that: the specific method of the step 2 comprises the following steps:

using current i in a two-phase coordinate system_αAnd i_βThe balance equation of (2) obtains the back electromotive force under a two-phase static coordinate system

wherein t is time;

the switching function of the sliding mode observer is constructed by utilizing the mathematical model of the sliding mode observer, and the following formula is shown:

wherein the content of the first and second substances,

Wherein, a_iIs a fixed parameter of (1, + ∞).

4. The design method of the fractional order PID sliding-mode observer suitable for the magnetic suspension spherical motor according to claim 3 is characterized in that: the specific method of the step 3 comprises the following steps:

step 3.1: constructing a transfer function of the fractional order PID controller, wherein the transfer function is shown as the following formula:

wherein G is₁(s) is the transfer function of the fractional order PID controller, k_p、k_i、k_dThe controller is a proportional, integral and differential link of a fractional order PID controller, lambda and mu are integral order and differential order, and s is a frequency domain variable;

step 3.2: constructing a differential equation of the fractional order PID controller, wherein the equation is as follows:

u(t)＝k_p·e(t)+k_i·D^-λ·e(t)+k_d·D^μ·e(t)

wherein u (t) is the output of the fractional order PID controller, e (t) is the error input of the fractional order PID controller, and D is the calculus operator;

step 3.3: an improved Oustaloup approximation method is used as a filter, and the fractional order PID controller is approximated to a continuous high-order integer order PID controller;

the transfer function for constructing the improved Oustaloup approximation is shown as follows:

wherein, alpha, d and b are constants, omega_b、ω_hThe upper limit cut-off frequency and the lower limit cut-off frequency of the filter are respectively;

and (3) expanding k(s) Taylor, eliminating higher-order terms, and simplifying the transfer function of the constructed improved Oustaloup approximation continuous filter, wherein the transfer function is shown as the following formula:

wherein G is₂(s) to improve the transfer function of the Oustaloup approximation continuous filter,

step 3.4: fitting the transfer function to a new low-pass filter by using the improved Oustaloup approximation

step 3.5: a fractional order differential integral operator model in the step 3.4 is built in numerical simulation software Matlab/simulink, and a sliding mode gain k in a switching function of a sliding mode observer is used_swAnd the fractional order differential integral operator model is used as an input of the fractional order differential integral operator model, and parameter setting is carried out on the fractional order differential integral operator model.

5. The design method of the fractional order PID sliding-mode observer suitable for the magnetic suspension spherical motor according to claim 4 is characterized in that: the specific method of the step 4 comprises the following steps:

step 4.1: back electromotive force calculated from step 2Constructing a counter electromotive force model, wherein the following formula is shown:

estimated value of rotor electrical angle calculated by back electromotive force modelAs shown in the following equation:

step 4.2: and (3) compensating and deforming the rotor electrical angle obtained in the step (4.1) to obtain a real rotor electrical angle, wherein the formula is as follows:

wherein, theta_efThe method comprises the steps of collecting phase delay errors generated when three-phase current and voltage of a magnetic suspension spherical motor pass through a low-pass filter;

step 4.3: obtaining rotor flux linkage from back electromotive force model

6. the design method of the fractional order PID sliding-mode observer suitable for the magnetic suspension spherical motor according to claim 5 is characterized in that: the specific method of the step 6 comprises the following steps:

constructing a Lyapunov function, wherein the formula is as follows:

wherein the content of the first and second substances,

according to the Lyapunov theorem of stability when

Technical Field

The invention relates to the technical field of position-free sensors, in particular to a design method of a fractional order PID sliding mode observer suitable for a magnetic suspension spherical motor.

Background

In recent years, with the development of science and technology, the degree of social industrialization is higher and higher, and the motor is subjected to stricter requirements as a supporting type machine for mutual conversion between mechanical energy and electric energy. The traditional mechanical bearing motor is not suitable for occasions with high rotating speed, high precision and low loss requirements. When a traditional motor runs at a high speed, the friction between a mechanical bearing and a shaft of the traditional motor has large resistance, and the friction causes vibration, abrasion and noise, so that the motor is hot, the service life is greatly reduced, and the maintenance cost is increased.

The magnetic suspension bearing technology supports the rotor of the motor to suspend by generating suspension magnetic force, so that the motor is separated from the bearing. The magnetic bearing has the advantages of no need of lubrication, no friction, long service life and the like, and is applied to the fields of aerospace, robots, machining and the like. It has certain advantages over conventional mechanical bearings, but also has some problems. The use of magnetic bearings for suspension in the motor requires three bearings, two radial bearings and one axial bearing, which limits the space usage of the motor and affects the critical rotational speed of the motor. In order to solve the problem, a torque winding of the motor is added with a winding of a radial bearing, so that the function of the motor for rotating and suspending simultaneously is realized, and the motor can be called as a bearingless motor.

For a long time, people have conducted extensive research on single-degree-of-freedom motors, and along with the development of multi-degree-of-freedom complex motion precision devices such as mechanical arms, multi-degree-of-freedom motor systems are more and more emphasized by people. The magnetic suspension spherical motor is based on a magnetic suspension technology and a motor technology, generates a suspension magnetic force to support a motor rotor to suspend, and generates a magnetic torque to directly drive the rotor to rotate. Since the rotor is spherical, a magnetically levitated spherical motor combines a torque winding and a levitation winding, also known as a bearingless motor.

In order to perform high-precision control on the magnetic suspension spherical motor, a position sensor is usually used for detecting the position of a rotor, so that the volume of a system and the rotational inertia of the rotor are increased, the cost of the system is increased, and the reliability of the system is reduced. Therefore, there is a need to develop a position sensorless technique.

At present, two methods for estimating the position and the speed of a rotor applied to a motor are available, one is to estimate the position of the rotor by using back electromotive force or flux linkage, and the common methods are a Longeberg observer, a sliding mode observer and an extended Kalman filter observer. And the other is a high-frequency signal injection method utilizing the salient pole effect of the motor. The Sliding Mode Observer (SMO) method is favored for its strong robustness, simple computation, and convenience for engineering application and digital implementation, but has the problem of low-speed buffeting.

Disclosure of Invention

The invention aims to solve the technical problem of the prior art, and provides a design method of a fractional order PID sliding mode observer suitable for a magnetic suspension spherical motor, which eliminates low-speed buffeting of a magnetic suspension spherical motor system, enhances the robustness of the system, and improves the anti-interference capability and the dynamic performance of a traditional control system.

In order to solve the technical problems, the technical scheme adopted by the invention is as follows: the design method of the fractional order PID sliding mode observer suitable for the magnetic suspension spherical motor comprises the following steps:

step 1: collecting three-phase current value i of magnetic suspension spherical motor_α、i_b、i_cAnd three-phase voltage value u_α、u_b、u_cClark conversion is carried out on the three-phase voltage value and the current value to obtain the voltage u under the two-phase static coordinate system_α、u_βAnd current i_αAnd i_β(ii) a Constructing a voltage equation under a two-phase static coordinate system, and transforming the voltage equation to obtain a current i_αAnd i_βThereby obtaining a mathematical model of the sliding-mode observer;

performing Clark conversion on the three-phase voltage value and the current value to obtain a voltage u under a two-phase static coordinate system_α、u_βAnd current i_αAnd i_βThe following formula shows:

the voltage equation under the two-phase static coordinate system of the structure is shown as the following formula:

wherein R is_sIs stator resistance, L_sFor stator inductance, p is the differential operator, ω is the electrical angular velocity of the rotor,. psi_fThe magnetic flux linkage is formed by the permanent magnet and the stator, and theta is the rotor electrical angle;

the voltage equation is deformed to obtain the current i under a two-phase coordinate system_αAnd i_βThe equation of equilibrium of (a) is shown as follows:

the equilibrium equation is simplified to:

pi_s＝A·i_s+B·v_s+ψ_f·v_i

wherein i_sIs composed of

a is

B is

v_sIs composed of

v_iIs composed of

E is a 2 x 2 identity matrix;

further simplifying to obtain a mathematical model of the sliding-mode observer, wherein the following formula is shown:

wherein the content of the first and second substances,

in order to differentiate the stator current estimate,

as stator current estimate, k_swIn order to obtain the gain of the sliding mode,

is a switching function;

step 2: calculating the back electromotive force of the magnetic suspension spherical motor under a two-phase static coordinate system by utilizing the mathematical model of the sliding-mode observer constructed in the step 1And stator current estimate

Error of stator current estimated valueConstructing a switching function of the sliding mode observer as a sliding mode surface, and adopting a Prelu function as a switching function of the sliding mode observer;

using current i in a two-phase coordinate system_αAnd i_βThe balance equation of (2) obtains the back electromotive force under a two-phase static coordinate systemAs shown in the following equation:

wherein t is time;

the switching function of the sliding mode observer is constructed by utilizing the mathematical model of the sliding mode observer, and the following formula is shown:

wherein the content of the first and second substances,

for rotor electrical angle estimation, Prelu is a parametrically modified linear unit of formula

Wherein, a_iIs a fixed parameter of (1, + ∞);

and step 3: constructing a transfer function of the fractional order PID, approximating the fractional order PID controller to a continuous high-order integer order PID controller by utilizing an improved Oustaloup approximation method, then constructing a fractional order differential integral operator model, and performing sliding mode gain k in the switching function of the sliding mode observer obtained in the step 2_swAdjusting and setting parameters;

step 3.1: constructing a transfer function of the fractional order PID controller, wherein the transfer function is shown as the following formula:

wherein G is₁(s) is the transfer function of the fractional order PID controller, k_p、k_i、k_dThe controller is a proportional, integral and differential link of a fractional order PID controller, lambda and mu are integral order and differential order, and s is a frequency domain variable;

step 3.2: constructing a differential equation of the fractional order PID controller, wherein the equation is as follows:

u(t)＝k_p·e(t)+k_i·D^-λ·e(t)+k_d·D^μ·e(t)

wherein u (t) is the output of the fractional order PID controller, e (t) is the error input of the fractional order PID controller, and D is the calculus operator;

step 3.3: an improved Oustaloup approximation method is used as a filter, and the fractional order PID controller is approximated to a continuous high-order integer order PID controller;

the transfer function for constructing the improved Oustaloup approximation is shown as follows:

wherein, alpha, d and b are constants, omega_b、ω_hThe upper limit cut-off frequency and the lower limit cut-off frequency of the filter are respectively;

and (3) expanding k(s) Taylor, eliminating higher-order terms, and simplifying the transfer function of the constructed improved Oustaloup approximation continuous filter, wherein the transfer function is shown as the following formula:

wherein G is₂(s) to improve the transfer function of the Oustaloup approximation continuous filter,

n is the filter order;

step 3.4: fitting the transfer function to a new low-pass filter by using the improved Oustaloup approximation

Packaging the obtained product into a fractional order differential integral operator model;

step 3.5: a fractional order differential integral operator model in the step 3.4 is built in numerical simulation software Matlab/simulink, and a sliding mode gain k in a switching function of a sliding mode observer is used_swThe fractional order differential integral operator model is used as input of the fractional order differential integral operator model, and parameter setting is carried out on the fractional order differential integral operator model;

and 4, step 4: back electromotive force calculated from step 2

Constructing a back electromotive force model, and calculating to obtain an estimated value of the rotor electrical angle by the back electromotive force model

Compensating the electrical angle of the rotor to obtain a real rotor electrical angle theta; and obtaining rotor flux linkage from the back electromotive force model

Step 4.1: back electromotive force calculated from step 2

Constructing a counter electromotive force model, wherein the following formula is shown:

estimated value of rotor electrical angle calculated by back electromotive force modelAs shown in the following equation:

step 4.2: and (3) compensating and deforming the rotor electrical angle obtained in the step (4.1) to obtain a real rotor electrical angle, wherein the formula is as follows:

wherein, theta_efThe method comprises the steps of collecting phase delay errors generated when three-phase current and voltage of a magnetic suspension spherical motor pass through a low-pass filter;

step 4.3: obtaining rotor flux linkage from back electromotive force model

As shown in the following equation:

and 5: by applying a counter electromotive force to the counter electromotive force obtained in step 4

And rotor flux linkage

Calculating to obtain an estimated value of the electrical angular velocity of the rotor

As shown in the following equation:

step 6: utilizing the current estimated value of the magnetic suspension spherical motor in the step 2

Constructing a Lyapunov function with the current actual value, and performing stability analysis on the designed sliding mode observer;

constructing a Lyapunov function, wherein the formula is as follows:

wherein the content of the first and second substances,

omega is an estimated value and an actual value of the rotor electrical angular velocity respectively;

according to the Lyapunov theorem of stability when

And (4) judging that the sliding mode observer is stable.

Adopt the produced beneficial effect of above-mentioned technical scheme to lie in: the invention provides a design method of a fractional order PID sliding-mode observer suitable for a magnetic suspension spherical motor, which comprises the following steps:

(1) the sign function is replaced by the parameterized modified linear unit Prelu, the buffeting phenomenon is weakened, the calculation speed and the convergence speed of the parameterized modified linear unit Prelu are higher than those of a common sigmod function and a common tanh function, and the parameterized modified linear unit Prelu has stronger robustness.

(2) An improved Oustaloup approximation method is adopted to approximate the fractional order controller into a continuous high-order integer order system, and the defect that the boundary fitting effect of the Oustaloup approximation method at a frequency band endpoint is not ideal is overcome. The sliding mode gain in the switching function of the sliding mode observer is set by utilizing the fractional order PID, and the buffeting of the sliding mode observer of the magnetic suspension spherical motor is effectively inhibited.

(3) And the feedforward control is utilized to perform phase compensation on the rotor electrical angle, so that the influence of system errors on the observation result is reduced.

Drawings

FIG. 1 is a schematic diagram of a magnetic levitation spherical motor suitable for use in accordance with an embodiment of the present invention;

fig. 2 is a flowchart of a design method of a fractional order PID sliding-mode observer suitable for a magnetic levitation spherical motor according to an embodiment of the present invention;

FIG. 3 is a system diagram for designing a sliding-mode observer according to an embodiment of the present invention;

FIG. 4 is a functional block diagram of a fractional order PID controller provided by an embodiment of the invention;

FIG. 5 is a diagram illustrating a fractional order differential-integral operator model provided by an embodiment of the present invention;

FIG. 6 is a diagram of an implementation of a fractional order PID controller provided by an embodiment of the invention;

fig. 7 is a system diagram for integrally controlling a magnetic levitation spherical motor by using the sliding mode observer designed by the method of the present invention according to the embodiment of the present invention.

In the figure: 1. a rotor shaft; 2. a permanent magnet; 3. a spherical rotor; 4. a stator; 5. a torque winding; 6. a radial winding; 7. a support sheet; 8. an axial winding; 9. a base.

Detailed Description

The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.

The magnetic suspension spherical motor is shown in figure 1, wherein 1 is a rotor rotating shaft and is driven by a spherical rotor 3, a radial winding 6 and a torque winding 5 are jointly embedded on a stator and provide torque and radial suspension force simultaneously, and a supporting sheet 7 of a protection device is additionally arranged at the bottom of the stator and has the function of buffering the falling of the rotor when the motor stops rotating. The axial windings 8 provide an axial suspension force, so that there is no contact and no friction between the rotor and the stator 4.

In the embodiment, a three-phase current and voltage of the magnetic levitation spherical motor are collected to construct a sliding mode observer mathematical model, current deviation is used as a sliding mode surface to construct a switching function, fractional PID is used for setting sliding mode gain of the sliding mode observer, the position of a rotor is compensated to obtain an electrical angle and an electrical angular velocity of the rotor, and design of the fractional PID sliding mode observer suitable for the magnetic levitation spherical motor is achieved. The design method of the fractional order PID sliding-mode observer suitable for the magnetic suspension spherical motor comprises the following steps as shown in FIGS. 2 and 3:

step 1: collecting three-phase current value i of magnetic suspension spherical motor_α、i_b、i_cAnd three-phase voltage value u_α、u_b、u_cClark conversion is carried out on the three-phase voltage value and the current value to obtain the voltage u under the two-phase static coordinate system_α、u_βAnd current i_αAnd i_β(ii) a Constructing a voltage equation under a two-phase static coordinate system, and transforming the voltage equation to obtain a current i_αAnd i_βThereby obtaining a mathematical model of the sliding-mode observer;

performing Clark conversion on the three-phase voltage value and the current value to obtain a voltage u under a two-phase static coordinate system_α、u_βAnd current i_αAnd i_βThe following formula shows:

the voltage equation under the two-phase static coordinate system of the structure is shown as the following formula:

wherein R is_sIs stator resistance, L_sFor stator inductance, p is the differential operator, ω is the electrical angular velocity of the rotor,. psi_fThe magnetic flux linkage is formed by the permanent magnet and the stator, and theta is the rotor electrical angle;

the voltage equation is deformed to obtain the current i under a two-phase coordinate system_αAnd i_βThe equation of equilibrium of (a) is shown as follows:

the equilibrium equation is simplified to:

pi_s＝A·i_s+B·v_s+ψ_f·v_i

wherein i_sIs composed of

A is

B is

v_sIs composed of

v_iIs composed ofE is a 2 x 2 identity matrix;

further simplifying to obtain a mathematical model of the sliding-mode observer, wherein the following formula is shown:

wherein the content of the first and second substances,in order to differentiate the stator current estimate,

as stator current estimate, k_swIn order to obtain the gain of the sliding mode,

is a switching function;

step 2: calculating the back electromotive force of the magnetic suspension spherical motor under a two-phase static coordinate system by utilizing the mathematical model of the sliding-mode observer constructed in the step 1

And stator current estimate

Meanwhile, taking the error of the estimated value of the stator current as a sliding mode surface, constructing a switching function of a sliding mode observer, and taking a Prelu function as a switching function of the sliding mode observer;

using current i in a two-phase coordinate system_αAnd i_βThe balance equation of (2) obtains the back electromotive force under a two-phase static coordinate system

As shown in the following equation:

wherein t is time;

the switching function of the sliding mode observer is constructed by utilizing the mathematical model of the sliding mode observer, and the following formula is shown:

wherein the content of the first and second substances,

for rotor electrical angle estimation, Prelu is a parametrically modified linear unit of formula

Wherein, a_iIs a fixed parameter of (1, + ∞);

and step 3: constructing a transfer function of the fractional order PID, and approximating the fractional order PID controller by using an improved Oustaloup approximation method as shown in FIG. 4A continuous high-order integer order PID controller is formed, a fractional order differential integral operator model is constructed, and the sliding mode gain k in the switching function of the sliding mode observer obtained in the step 2 is subjected to_swAdjusting and setting parameters;

step 3.1: constructing a transfer function of the fractional order PID controller, wherein the transfer function is shown as the following formula:

wherein G is₁(s) is the transfer function of the fractional order PID controller, k_p、k_i、k_dThe controller is a proportional, integral and differential link of a fractional order PID controller, lambda and mu are integral order and differential order, and s is a frequency domain variable;

step 3.2: constructing a differential equation of the fractional order PID controller, wherein the equation is as follows:

u(t)＝k_p·e(t)+k_i·D^-λ·e(t)+k_d·D^μ·e(t)

wherein u (t) is the output of the fractional order PID controller, e (t) is the error input of the fractional order PID controller, and D is the calculus operator;

step 3.3: an improved Oustaloup approximation method is used as a filter, and the fractional order PID controller is approximated to a continuous high-order integer order PID controller;

the transfer function for constructing the improved Oustaloup approximation is shown as follows:

wherein, alpha, d and b are constants, omega_b、ω_hThe upper limit cut-off frequency and the lower limit cut-off frequency of the filter are respectively;

and (3) expanding k(s) Taylor, eliminating higher-order terms, and simplifying the transfer function of the constructed improved Oustaloup approximation continuous filter, wherein the transfer function is shown as the following formula:

wherein G is₂(s) to improve the transfer function of the Oustaloup approximation continuous filter,

n is the filter order;

step 3.4: fitting the transfer function to a new low-pass filter by using the improved Oustaloup approximation

Packaging into a fractional order differential integral operator model as shown in FIG. 5;

step 3.5: building the fractional order differential integral operator model in the step 3.4 in the numerical simulation software Matlab/simulink, and as shown in fig. 6, obtaining a sliding mode gain k in the switching function of the sliding mode observer_swThe fractional order differential integral operator model is used as input of the fractional order differential integral operator model, and parameter setting is carried out on the fractional order differential integral operator model;

and 4, step 4: back electromotive force calculated from step 2

Constructing a back electromotive force model, and calculating to obtain an estimated value of the rotor electrical angle by the back electromotive force model

Compensating the electrical angle of the rotor to obtain a real rotor electrical angle theta; and obtaining rotor flux linkage from the back electromotive force model

Step 4.1: back electromotive force calculated from step 2

Constructing a counter electromotive force model, wherein the following formula is shown:

estimated value of rotor electrical angle calculated by back electromotive force model

As shown in the following equation:

step 4.2: and (3) compensating and deforming the rotor electrical angle obtained in the step (4.1) to obtain a real rotor electrical angle, wherein the formula is as follows:

wherein, theta_efThe method comprises the steps of collecting phase delay errors generated when three-phase current and voltage of a magnetic suspension spherical motor pass through a low-pass filter;

step 4.3: obtaining rotor flux linkage from back electromotive force model

As shown in the following equation:

and 5: by applying a counter electromotive force to the counter electromotive force obtained in step 4

And rotor flux linkage

Calculating to obtain an estimated value of the electrical angular velocity of the rotor

As shown in the following equation:

step 6: utilizing the current estimated value of the magnetic suspension spherical motor in the step 2

Constructing a Lyapunov function with the current actual value, and performing stability analysis on the designed sliding mode observer;

constructing a Lyapunov function, wherein the formula is as follows:

wherein the content of the first and second substances,

omega is an estimated value and an actual value of the rotor electrical angular velocity respectively;

according to the Lyapunov theorem of stability when

And (4) judging that the sliding mode observer is stable.

In this embodiment, a constructed stable sliding-mode observer is added to a magnetic suspension spherical motor control system, and as shown in fig. 7, a current i in a two-phase stationary coordinate system is added_α、i_βAnd voltage u_α、u_βAs input and output position angle of sliding mode observerTo Park converters, speed of rotation

The output after PI control is sent to an SVPWM controller, and pulse waves are output to a three-phase inverter, so that the magnetic suspension spherical control is controlledAn electric motor.

Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.