阅读说明：本技术 基于新型扩张状态观测器的磁悬浮系统自抗扰控制方法 (Magnetic suspension system active disturbance rejection control method based on novel extended state observer ) 是由 陈强 李�杰 王连春 余佩倡 周丹峰 杨清 高明 于 2020-12-30 设计创作，主要内容包括：本发明公开了一种基于新型扩张状态观测器的磁悬浮系统自抗扰控制方法,首先,选定以EMS磁悬浮系统作为控制对象；接着,设计新型扩张状态观测器；然后,基于该新型扩张状态观测器设计自抗扰控制器；最后,选择合适的新型扩张状态观测器和自抗扰控制器参数保证EMS磁悬浮系统的收敛性和稳定性,达到期望的控制性能,实现自抗扰控制。(The invention discloses a magnetic suspension system active disturbance rejection control method based on a novel extended state observer, which comprises the following steps of firstly, selecting an EMS magnetic suspension system as a control object; then, designing a novel extended state observer; then, designing an active disturbance rejection controller based on the novel extended state observer; and finally, selecting proper parameters of the novel extended state observer and the active disturbance rejection controller to ensure the convergence and stability of the EMS magnetic suspension system, achieving the expected control performance and realizing the active disturbance rejection control.)

1. The magnetic suspension system active disturbance rejection control method based on the novel extended state observer is characterized by comprising the following steps of:

s100, selecting an EMS magnetic suspension system as a control object;

s200, designing a novel extended state observer;

s300, designing an active disturbance rejection controller based on the novel extended state observer;

s400, selecting appropriate parameters of the novel extended state observer and the active disturbance rejection controller to ensure the convergence and stability of the EMS magnetic suspension system, achieving the expected control performance and realizing the active disturbance rejection control.

2. The method for controlling active disturbance rejection of a magnetic levitation system based on a novel extended state observer according to claim 1, wherein the step S100 is embodied as: the EMS magnetic suspension system adopts magnetic flux density as a system state, and adopts a cascade control structure to divide the EMS magnetic suspension system into an outer clearance loop sigma_δSum flux density inner loop Σ_BTwo subsystems, sigma_δSum-sigma_BThe expression of (a) is:

in the formula, system stateRespectively, the levitation gap delta and the gap differentialAnd magnetic flux density B, T represents matrix transposition, system input u is electromagnet input voltage, T represents time, f represents₁(t,x₁,x₂,z₁,w₁,u)、f₂(t,x₁,x₂,z₁,w₁U) respectively represent the outer loop of the gap Σ_δSum flux density inner loop Σ_BAn unknown nonlinear continuous system function comprising system structure, time-varying, state, input, perturbation, coupling information, wherein w ═ w₁ w₂]^TRepresenting unknown perturbations, y ═ y₁ y₂]^TRespectively representing the outer ring of the gap ∑_δOutput gap delta and flux density inner loop Σ_BThe output magnetic flux density B.

3. The novel magnetic suspension system active disturbance rejection control method based on the extended state observer is characterized in that a clearance outer ring sigma is combined with total disturbance of the EMS magnetic suspension system_δSum flux density inner loop Σ_BThe expressions for the two subsystems are adjusted by the following process:

1) the gap is externally looped_δSum flux density inner loop Σ_BThe two subsystems are rewritten in the following form:

in the formula, b₁Is a gap outer loop sigma_δCoefficient of nominal value of magnetic flux density B, takenS is the area of the electromagnet pole, m_sTo load mass, u₀Is a vacuum magnetic conductivity; b₂Is magnetic flux density inner loop ∑_BThe nominal value coefficient of the input voltage u of the electromagnet is obtainedN is the number of turns of the electromagnet coil;

2) and transforming equations (3) and (4) into:

f_o,1(t,x₁,x₂,z₁,w₁,u)＝f₁(t,x₁,x₂,z₁,w₁,u)-b₁z₁ (5)

f_o,2(t,x₁,x₂,z₁,w₂,u)＝f₂(t,x₁,x₂,z₁,w₂,u)-b₂u (6)

in the formula (f)_o,1(t,x₁,x₂,z₁,w₁U) is a gap outer loop Σ_δThe part except the nominal input after being written into the form of formula (5) contains unknown nonlinear continuous system function of system structure, time variation, state, input, disturbance and coupling information, f_o,2(t,x₁,x₂,z₁,w₁U) inner loop of magnetic flux density ∑_BAfter the formula (6) is written, the part except the nominal input comprises unknown nonlinear continuous system functions of system structure, time variation, state, input, disturbance and coupling information;

3) defining a gap outer loop ∑_δSum flux density inner loop Σ_BThe overall perturbation, including time-varying, coupled, uncertain and complex perturbations, has an expansion state x₃And z₂：

In the formula (f)_c,1(t,x₁,x₂,z₁,w₁U) is in the expanded state x₃Derivative of f_c,2(t,x₁,x₂,z₁,w₁U) is in the expanded state z₂A derivative of (a);

4) according to the formulas (3) - (8), the gap is subjected to outer loop sigma_δSum flux density inner loop Σ_BThe two subsystems are rewritten in the following form:

4. the magnetic levitation system active disturbance rejection control method based on the novel extended state observer as claimed in claim 3, wherein the gap outer loop Σ_δIs controlled by designing appropriate control inputsSo that the output y₁Can stably track the desired gap delta^*While the other two states x₂And x₃Can be uniformly asymptotically stabilized at the corresponding equilibrium point.

5. The magnetic levitation system active disturbance rejection control method based on the novel extended state observer as claimed in claim 4, wherein the gap outer loop Σ_δIs a second-order system, designs a third-order extended state observer and definesAndare each x₁、x₂And x₃Observation value of, observation error of Andthen the clearance outer loop Σ_δThe corresponding third order extended state observer is designed as follows:

wherein H₁、H₂、H₃And H₄For positive design parameters, sign functions

The observation errors obtained from (9) and (11) are:

then the high order observation error is iteratively calculated:

6. the magnetic levitation system active disturbance rejection control method based on the novel extended state observer as claimed in claim 5, wherein the magnetic flux density is within a loop Σ_BIs controlled by designing the appropriate control input u such that the output y₂Can stabilize and track clearance outer loop sigma fast_δDesired magnetic flux density requiredWhile other states z₂Can be uniformly asymptotically stabilized at the corresponding equilibrium point.

7. The magnetic levitation system active disturbance rejection control method based on the novel extended state observer as claimed in claim 6, wherein the magnetic flux density is within a loop Σ_BIs a first-order system, designs a second-order extended state observer, and defines z₁、z₂Is observed inAndthe observation error isAndmagnetic flux density inner loop Σ_BThe corresponding second order extended state observer is designed as:

wherein H₅、H₆And H₇Is a positive design parameter.

8. The magnetic levitation system active disturbance rejection control method based on the novel extended state observer as claimed in claim 7, wherein the control method is based on a gap outer loop Σ_δCorresponding third-order extended state observer and magnetic flux density inner loop sigma_BCorresponding second-order extended state observer to obtain system state x ═ x₁ x₂ x₃]^TAnd an expanded state x representing the total perturbation₃And z₂Through state feedback, an active disturbance rejection controller is designed, total disturbance is eliminated, system stability is realized, and the expected gap delta is stably tracked^*。

9. The method for controlling the active disturbance rejection of a magnetic levitation system based on a novel extended state observer as claimed in claim 8, wherein the active disturbance rejection controller is designed to be embodied as a set gap outer loop Σ_δADRC of the active disturbance rejection controller_δAnd magnetic flux density inner loop ∑_BADRC of the active disturbance rejection controller_B：

Wherein k is₁、k₂、k₃Is a positive feedback control parameter.

10. The method for controlling active disturbance rejection of a magnetic levitation system based on a novel extended state observer as claimed in claim 9, wherein said step S400 is embodied by selecting a suitable gap outer loop based Σ_δCorresponding third order extended state observer parameter H₁、H₂、H₃、H₄And ADRC_δParameter k₁、k₂By selecting an appropriate flux density based inner loop Σ_BCorresponding second order extended state observer parameters H₅、H₆、H₇And ADRC_BParameter k₃ADRC based on third-order extended state observer_δADRC (active disturbance rejection controller) acting with second-order extended state observer_BThe EMS magnetic suspension system can be converged and stabilized.

Technical Field

The invention belongs to the technical field of magnetic suspension control, and particularly relates to a magnetic suspension system active disturbance rejection control method based on a novel extended state observer.

Background

The electromagnetic-attraction (EMS for short) Magnetic Suspension system realizes non-contact support, is widely applied to systems such as a Magnetic Suspension train, a Magnetic Suspension bearing and the like, can effectively avoid mechanical contact friction, reduces system loss, reduces vibration and noise, reduces maintenance cost and prolongs service life. The basic principle of the electromagnetic attraction type magnetic suspension system is that current is introduced into an electromagnet coil to generate a magnetic field, corresponding electromagnetic attraction is generated at the same time, gravity and various disturbances are overcome, the electromagnetic attraction type magnetic suspension system is suspended in an expected gap, the electromagnetic attraction type magnetic suspension system is an open-loop unstable system essentially, and active control needs to be applied to realize stable suspension. The electromagnetic suspension system is a complex nonlinear, time-varying, coupled, uncertain and disturbed complex system, is difficult to establish an accurate system model, and puts high requirements on the design of a control method.

An Active Disturbance Rejection Controller (ADRC) based on an Extended State Observer (ESO for short) does not need a system model, the whole system including unknown Disturbance and uncertain parts can be taken as a black box, the Extended State Observer can observe the system State and unknown total Disturbance (including dynamic uncertainty, coupling, time-varying and other complex disturbances which are not modeled by the system) according to system input and output information, and then the observed total Disturbance is eliminated by using the ADRC to realize system stable control. However, theoretical research on the extended state observer and active disturbance rejection control is relatively few, and especially, in the condition of ensuring convergence and stability, engineering application generally has complex assumed conditions, convergence conditions and stability conditions, and an actual system is difficult to verify, so that parameter selection lacks theoretical guidance, and is complex to debug and difficult to implement.

Disclosure of Invention

In view of the defects of the active disturbance rejection control based on the extended state observer in theoretical research and engineering application, the invention designs a novel extended state observer by taking an EMS magnetic suspension system as a control object, designs an active disturbance rejection controller based on the extended state observer, ensures the convergence and stability of the magnetic suspension system by selecting proper observer and active disturbance rejection controller parameters, achieves expected control performance and realizes the active disturbance rejection control.

The purpose of the invention is realized by the following technical scheme: the magnetic suspension system active disturbance rejection control method based on the novel extended state observer is provided, and comprises the following steps:

s100, selecting an EMS magnetic suspension system as a control object;

s200, designing a novel extended state observer;

s300, designing an active disturbance rejection controller based on the novel extended state observer;

s400, selecting appropriate parameters of the novel extended state observer and the active disturbance rejection controller to ensure the convergence and stability of the EMS magnetic suspension system, achieving the expected control performance and realizing the active disturbance rejection control.

As a further improvement, the step S100 is embodied as: the EMS magnetic suspension system adopts magnetic flux density as a system state, and adopts a cascade control structure to divide the EMS magnetic suspension system into an outer clearance loop sigma_δSum flux density inner loop Σ_BTwo subsystems, sigma_δSum-sigma_BThe expression of (a) is:

in the formula, system stateRespectively, the levitation gap delta and the gap differentialAnd magnetic flux density B, T represents matrix transposition, system input u is electromagnet input voltage, T represents time, f represents₁(t,x₁,x₂,z₁,w₁,u)、f₂(t,x₁,x₂,z₁,w₁U) respectively represent the outer loop of the gap Σ_δSum flux density inner loop Σ_BAn unknown nonlinear continuous system function comprising system structure, time-varying, state, input, perturbation, coupling information, wherein w ═ w₁ w₂]^TRepresenting unknown perturbations, y ═ y₁ y₂]^TRespectively representing the outer ring of the gap ∑_δOutput gap delta and flux density inner loop Σ_BThe output magnetic flux density B.

As a further improvement, the total disturbance of the EMS magnetic suspension system is combined, and the clearance outer ring sigma is formed_δSum flux density inner loop Σ_BThe expressions for the two subsystems are adjusted by the following process:

1) the gap is externally looped_δSum flux density inner loop Σ_BThe two subsystems are rewritten in the following form:

in the formula, b₁Is a gap outer loop sigma_δCoefficient of nominal value of magnetic flux density B, takenS is the area of the electromagnet pole, m_sTo load mass, u₀Is a vacuum magnetic conductivity; b₂Is magnetic flux density inner loop ∑_BThe nominal value coefficient of the input voltage u of the electromagnet is obtainedN is an electromagnet coilThe number of turns;

2) and transforming equations (3) and (4) into:

f_o,1(t,x₁,x₂,z₁,w₁,u)＝f₁(t,x₁,x₂,z₁,w₁,u)-b₁z₁ (5)

f_o,2(t,x₁,x₂,z₁,w₂,u)＝f₂(t,x₁,x₂,z₁,w₂,u)-b₂u (6)

in the formula (f)_o,1(t,x₁,x₂,z₁,w₁U) is a gap outer loop Σ_δThe part except the nominal input after being written into the form of formula (5) contains unknown nonlinear continuous system function of system structure, time variation, state, input, disturbance and coupling information, f_o,2(t,x₁,x₂,z₁,w₁U) inner loop of magnetic flux density ∑_BAfter the formula (6) is written, the part except the nominal input comprises unknown nonlinear continuous system functions of system structure, time variation, state, input, disturbance and coupling information;

3) defining a gap outer loop ∑_δSum flux density inner loop Σ_BThe overall perturbation, including time-varying, coupled, uncertain and complex perturbations, has an expansion state x₃And z₂：

In the formula (f)_c,1(t,x₁,x₂,z₁,w₁U) is in the expanded state x₃Derivative of f_c,2(t,x₁,x₂,z₁,w₁U) is in the expanded state z₂A derivative of (a);

4) according to formulas (3) to (8),outer loop sigma of gap_δSum flux density inner loop Σ_BThe two subsystems are rewritten in the following form:

as a further improvement, a gap outer loop Σ_δIs controlled by designing appropriate control inputsSo that the output y₁Can stably track the desired gap delta^*While the other two states x₂And x₃Can be uniformly asymptotically stabilized at the corresponding equilibrium point.

As a further improvement, a gap outer loop Σ_δIs a second-order system, designs a third-order extended state observer and definesAndare each x₁、x₂And x₃Observation value of, observation error of Andthen the clearance outer loop Σ_δThe corresponding third order extended state observer is designed as follows:

wherein H₁、H₂、H₃And H₄For positive design parameters, sign functions

The observation errors obtained from (9) and (11) are:

then the high order observation error is iteratively calculated:

as a further improvement, the magnetic flux density is in a loop Σ_BIs controlled by designing the appropriate control input u such that the output y₂Can stabilize and track clearance outer loop sigma fast_δDesired magnetic flux density requiredWhile other states z₂Can be uniformly asymptotically stabilized at the corresponding equilibrium point.

As a further improvement, the magnetic flux density is in a loop Σ_BIs a first-order system, designs a second-order extended state observer, and defines z₁、z₂Is observed inAndthe observation error isAndmagnetic flux density inner loop Σ_BThe corresponding second order extended state observer is designed as:

wherein H₅、H₆And H₇Is a positive design parameter.

As a further improvement, based on the gap outer loop Σ_δCorresponding third-order extended state observer and magnetic flux density inner loop sigma_BCorresponding second-order extended state observer to obtain system state x ═ x₁ x₂ x₃]^TAnd an expanded state x representing the total perturbation₃And z₂Through state feedback, an active disturbance rejection controller is designed, total disturbance is eliminated, system stability is realized, and the expected gap delta is stably tracked^*。

As a further improvement, the design of the active disturbance rejection controller is embodied in that the gap outer loop Σ is set_δADRC of the active disturbance rejection controller_δAnd magnetic flux density inner loop ∑_BADRC of the active disturbance rejection controller_B：

Wherein k is₁、k₂、k₃Is a positive feedback control parameter.

As a further improvement, said step S400 is embodied by selecting a suitable gap-based outer loop Σ_δCorresponding third order extended state observer parameter H₁、H₂、H₃、H₄And ADRC_δParameter k₁、k₂By selecting a suitable flux density based inner ringΣ_BCorresponding second order extended state observer parameters H₅、H₆、H₇And ADRC_BParameter k₃ADRC based on third-order extended state observer_δADRC (active disturbance rejection controller) acting with second-order extended state observer_BThe EMS magnetic suspension system can be converged and stabilized.

The invention provides a magnetic suspension system active disturbance rejection control method based on a novel extended state observer, which comprises the steps of firstly, selecting an EMS magnetic suspension system as a control object; then, designing a novel extended state observer; then, designing an active disturbance rejection controller based on the novel extended state observer; and finally, selecting proper parameters of the novel extended state observer and the active disturbance rejection controller to ensure the convergence and stability of the EMS magnetic suspension system, achieving the expected control performance and realizing the active disturbance rejection control.

Drawings

The invention is further illustrated by means of the attached drawings, but the embodiments in the drawings do not constitute any limitation to the invention, and for a person skilled in the art, other drawings can be obtained on the basis of the following drawings without inventive effort.

FIG. 1 is a flow chart of a magnetic levitation system active disturbance rejection control method based on a novel extended state observer.

FIG. 2 is a gap outer loop sigma based on observation error feedback_δAnd the structural block diagram of the corresponding third-order extended state observer.

Fig. 3 is a structural block diagram of an active disturbance rejection controller based on a novel extended state observer.

Detailed Description

In order to make those skilled in the art better understand the technical solution of the present invention, the following detailed description of the present invention is provided with reference to the accompanying drawings and specific embodiments, and it is to be noted that the embodiments and features of the embodiments of the present application can be combined with each other without conflict.

Referring to fig. 1, the invention provides a magnetic levitation system active disturbance rejection control method based on a novel extended state observer, which comprises the following steps:

s100, selecting an EMS magnetic suspension system as a control object;

considering that a magnetic flux density state feedback structure is simpler and has more advantages in the aspects of system dynamic performance and stability compared with the traditional current state feedback, the EMS magnetic suspension system adopts the magnetic flux density as the system state, and adopts a cascade control structure to divide the EMS magnetic suspension system into an outer gap ring sigma_δSum flux density inner loop Σ_BTwo subsystems, sigma, taking into account system time-variation, coupling, uncertainty and complex disturbances_δSum-sigma_BThe expression of (a) is:

in the formula, system stateRespectively, the levitation gap delta and the gap differentialAnd magnetic flux density B, T represents matrix transposition, system input u is electromagnet input voltage, T represents time, f represents₁(t,x₁,x₂,z₁,w₁,u)、f₂(t,x₁,x₂,z₁,w₁U) respectively represent the outer loop of the gap Σ_δSum flux density inner loop Σ_BAn unknown nonlinear continuous system function comprising system structure, time-varying, state, input, perturbation, coupling information, wherein w ═ w₁ w₂]^TRepresenting unknown perturbations, y ═ y₁ y₂]^TRespectively representing the outer ring of the gap ∑_δOutput gap delta and flux density inner loop Σ_BThe output magnetic flux density B.

S200, designing a novel extended state observer;

first, the gap is circled by sigma_δSum flux density inner loop Σ_BThe two subsystems are rewritten in the following form:

in the formula, b₁Is a gap outer loop sigma_δCoefficient of nominal value of magnetic flux density B, takenS is the area of the electromagnet pole, m_sTo load mass, u₀Is a vacuum magnetic conductivity; b₂Is magnetic flux density inner loop ∑_BThe nominal value coefficient of the input voltage u of the electromagnet is obtainedN is the number of turns of the electromagnet coil;

next, equations (3) and (4) are respectively modified as:

f_o,1(t,x₁,x₂,z₁,w₁,u)＝f₁(t,x₁,x₂,z₁,w₁,u)-b₁z₁ (5)

f_o,2(t,x₁,x₂,z₁,w₂,u)＝f₂(t,x₁,x₂,z₁,w₂,u)-b₂u (6)

in the formula (f)_o,1(t,x₁,x₂,z₁,w₁U) is a gap outer loop Σ_δThe part except the nominal input after being written into the form of formula (5) contains unknown nonlinear continuous system function of system structure, time variation, state, input, disturbance and coupling information, f_o,2(t,x₁,x₂,z₁,w₁U) inner loop of magnetic flux density ∑_BAfter the formula (6) is written, the part except the nominal input comprises unknown nonlinear continuous system functions of system structure, time variation, state, input, disturbance and coupling information;

thirdly, defining a gap outer loop Σ_δSum flux density inner loop Σ_BThe overall perturbation, including time-varying, coupled, uncertain and complex perturbations, has an expansion state x₃And z₂：

In the formula (f)_c,1(t,x₁,x₂,z₁,w₁U) is in the expanded state x₃Derivative of f_c,2(t,x₁,x₂,z₁,w₁U) is in the expanded state z₂A derivative of (a); (ii) a

Finally, the gaps are outer-looped Σ in accordance with equations (3) - (8)_δSum flux density inner loop Σ_BThe two subsystems are rewritten in the following form:

gap outer loop sigma_δIs controlled by designing appropriate control inputsSo that the output y₁Can stably track the desired gap delta^*While the other two states x₂And x₃Can be uniformly asymptotically stabilized at the corresponding equilibrium point. Magnetic flux density inner loop Σ_BIs controlled by designing the appropriate control input u such that the output y₂Can stabilize and track clearance outer loop sigma fast_δDesired magnetic flux density requiredWhile other states z₂Can be uniformly asymptotically stabilized at the corresponding equilibrium point. In practical EMS magnetic levitation systems, reasonable control method design can be combined due to the objective existence of mechanical constraint and electrical constraint, so that the system control input and the derivative thereof are bounded, the system state is bounded under the bounded input, and the system disturbance and the derivative thereof are bounded.

Gap outer loop sigma_δIs a second-order system, designs a third-order extended state observer and definesAndare each x₁、x₂And x₃Observation value of, observation error ofAndthen the clearance outer loop Σ_δThe corresponding third order extended state observer is designed as follows:

wherein H₁、H₂、H₃And H₄For positive design parameters, sign functions

The observation errors obtained from (9) and (11) are:

then the high order observation error is iteratively calculated:

it can be seen that, unlike the conventional extended state observer which only uses measurable output states to design the observer, the observer provided by the invention iteratively calculates the observation errors of each state by using the extended state observer form, and feeds back the observation errors to design the observer. For the measurement noise of the system output and the noise existing in the system state, because the integral action in the observer structure can be effectively eliminated, a good observation signal with low noise and no phase loss can be obtained, including a differential signal which is difficult to obtain through measurement in an actual system. Gap outer loop sigma_δThe structure block diagram of the corresponding three-order expansion state observer is shown in fig. 2 below.

Similarly, the magnetic flux density loop Σ can be designed_BExtended state observer of (1), magnetic flux density inner loop ∑_BIs a first-order system, designs a second-order extended state observer, and defines z₁、z₂Is observed inAndthe observation error isAndmagnetic flux density inner loop Σ_BThe corresponding second order extended state observer is designed as:

wherein H₅、H₆And H₇Is a positive design parameter.

Selecting proper parameters of the second-order extended state observer can ensure the observer to be converged, so that the observed state is ensuredCan quickly and accurately converge to the system state z ═ z₁ z₂]^TI.e. observation errorConverging to 0.

It is worth noting that the invention takes a very general nonlinear time-varying first-order system and second-order system as an example, and carries out the design of the extended state observer, which can represent a large class of systems and can be extended to n-order, and can be applied to a large number of actual systems.

S300, designing an active disturbance rejection controller based on the novel extended state observer;

the invention is based on the above-mentioned gap outer loop sigma_δCorresponding third-order extended state observer and magnetic flux density inner loop sigma_BCorresponding second-order extended state observer can obtain the system state x ═ x₁ x₂ x₃]^TAnd an expanded state x representing the total perturbation₃And z₂Through state feedback, an active disturbance rejection controller is designed, total disturbance is eliminated, system stability is realized, and the expected gap delta is stably tracked^*. Fig. 3 is a structural block diagram of an active disturbance rejection controller based on a novel extended state observer.

Outer loop sigma for setting gap_δADRC of the active disturbance rejection controller_δAnd magnetic flux density inner loop ∑_BADRC of the active disturbance rejection controller_B：

Wherein k is₁、k₂、k₃Is a positive feedback control parameter.

In addition, the parameter k₁、k₂Formed matrixIs a Hurwitz matrix (Helverz matrix) with k₁、k₂、k₃It is also necessary to determine the optimum parameters through debugging.

S400, selecting appropriate parameters of the novel extended state observer and the active disturbance rejection controller to ensure the convergence and stability of the EMS magnetic suspension system, achieving the expected control performance and realizing the active disturbance rejection control. The steps are embodied as follows: by selecting the appropriate gap-based outer loop Σ_δCorresponding third order extended state observer parameter H₁、H₂、H₃、H₄And ADRC_δParameter k₁、k₂By selecting an appropriate flux density based inner loop Σ_BCorresponding second order extended state observer parameters H₅、H₆、H₇And ADRC_BParameter k₃ADRC based on third-order extended state observer_δADRC (active disturbance rejection controller) acting with second-order extended state observer_BThe EMS magnetic suspension system can be converged and stabilized.

It is to be noted that, as long as the parameter H₁＞1、H₂＞1、H₃> 1 and H₄Sufficiently large, i.e. selecting appropriate parameters ensures a gap outer loop Σ_δThe corresponding third-order extended state observer converges to make the clearance outer loop sigma_δObservation stateCan quickly and accurately converge to a clearance outer ring sigma_δState and its expanded state x ═ x₁ x₂ x₃]^TI.e. observation errorConvergence to 0, parameter debugging is simpler, and engineering application is easy to realize; at the same time, H₅、H₆And H₇Provided that the parameter H₅＞1、H₆> 1 and H₇Sufficiently large, i.e. selecting appropriate parameters ensures an inner loop sigma of flux density_BThe corresponding second order extended state observer converges such that the magnetic flux density is within the inner loop ∑_BObservation stateCan quickly and accurately converge to the magnetic flux density inner loop sigma_BState and its expanded state z ═ z₁ z₂]^TI.e. observation errorConverging to 0.

In a word, the invention takes an EMS magnetic suspension system as a control object, designs a novel extended state observer, designs an active disturbance rejection controller based on the extended state observer, ensures the convergence and stability of the magnetic suspension system by selecting proper observer and active disturbance rejection controller parameters, achieves the expected control performance and realizes the active disturbance rejection control.

In the description above, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described herein, and therefore should not be construed as limiting the scope of the present invention.

In conclusion, although the present invention has been described with reference to the preferred embodiments, it should be noted that, although various changes and modifications may be made by those skilled in the art, they should be included in the scope of the present invention unless they depart from the scope of the present invention.