Magnetic suspension bearing terminal sliding mode control method based on Luenberger observer

Abstract

The invention provides a magnetic suspension bearing terminal sliding mode control method based on a Luenberger observer, and belongs to the technical field of bearing control. According to the method, a mathematical model of an active magnetic suspension bearing control system is established; establishing a state-space equation of the active magnetic suspension bearing control system; a terminal sliding mode surface and a terminal sliding mode control law are constructed and designed; estimating the state of the active magnetic suspension bearing control system by using a Luenberger observer; a gain matrix and a feedback gain matrix of the observer are adjusted to realize state feedback control; stable suspension of the magnetic suspension bearing is realized; according to the magnetic suspension bearing terminal sliding mode control method based on the Luenberger observer, the dynamic response speed and stability of an active magnetic suspension bearing control system can be remarkably improved; the introduction of the terminal sliding mode control ensures that the state of the active magnetic suspension bearing control system can be quickly and accurately converged to an expected value, and the chattering phenomenon in the traditional sliding mode control is reduced.

Description

Technical Field

[0001] The invention relates to the technical field of bearing control, and in particular to a terminal sliding mode control method of a magnetic suspension bearing based on a Romberg observer. Background Art

[0002] Magnetic bearing technology uses electromagnetic force to suspend the rotor in the air to achieve contactless rotation. This technology eliminates friction and wear in traditional mechanical bearings, providing higher speeds, more precise control and lower maintenance requirements. Magnetic bearings are mainly composed of electromagnets, high-precision sensors, controllers and power supplies, which can accurately control the position and attitude of the rotor to ensure its stable operation without any physical contact. This technology is widely used in aerospace, high-speed rotating equipment, precision medical equipment and other fields, and is favored for its ability to provide high efficiency, low energy consumption and long life operation.

[0003] There are lumped uncertainties in the magnetic suspension motor system. The first is the uncertainty of the system parameters, including the parameter perturbations of the current-force coefficient and the displacement-force coefficient due to the errors introduced in the linearization process of the electromagnetic force of the magnetic suspension bearing; the second is the unstructured uncertainty caused by the unmodeled dynamics of the system, such as the temperature drift of the displacement sensor, the influence of the power amplifier circuit itself and the external temperature, as well as hysteresis, magnetic loss, rotor gyroscopic effect, etc. These uncertain factors act together on the active magnetic bearing system, resulting in certain differences between its mathematical model and the actual system.

[0004] In view of the system parameter changes and external disturbances of the active magnetic bearing system, a sliding mode method based on disturbance observer is proposed to achieve disturbance suppression. The state observer can estimate the state of the system based on the input and output information of the system, and these estimated states can replace the real state for state feedback control. In this way, an observer-based state feedback control system is realized. The observer can estimate and compensate for the total disturbance estimate including system parameter changes and external disturbances, thereby maintaining the stability and performance of the system. The terminal sliding mode control of the nonlinear terminal sliding surface provides faster finite time convergence and higher control accuracy. Although the traditional sliding mode control can ensure the robustness of the system, its main disadvantage is the existence of chattering on the sliding surface, and the convergence speed of the system is usually limited. Terminal sliding mode control improves these problems by introducing nonlinear terms, so that the system state can converge to the equilibrium point in a finite time instead of infinitely approaching. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a magnetic bearing terminal sliding mode control method based on a Lumberg observer in view of the deficiencies in the above-mentioned prior art. The Lumberg observer of the method is used to accurately estimate the system state, especially those internal variables that are difficult to measure directly, and the sliding mode control uses these estimates to design a robust control law to ensure that the system performance is insensitive to parameter changes and external disturbances; the Lumberg observer provides real-time feedback on the system state, so that the sliding mode controller can effectively guide the system state to the desired trajectory in the presence of uncertainty and interference; this control strategy shows excellent performance and high robustness in the fields of motor control and aircraft attitude control; by carefully designing the observer and the controller, the system can achieve rapid response and high-precision tracking, while reducing or eliminating the vibration phenomenon, thereby improving the smoothness and reliability of the control.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: a terminal sliding mode control method of a magnetic bearing based on a Romberg observer, comprising the following steps:

[0007] Step 1: The axial motion of the rotor is set to be decoupled from the radial motion, and the rotation of the rotor is controlled by a drive inverter and decoupled from the radial motion; a mathematical model of the active magnetic bearing control system is established based on the control force generated by the magnetic bearing, air friction and the centrifugal force of the rotor;

[0008] The mathematical model of the active magnetic bearing control system is described as follows:

[0009]

[0010] Among them, K z and K i are the displacement force stiffness and current force stiffness of the active magnetic bearing control system, i z is the current flowing through the axial magnetic bearing coil, m is the mass of the rotor, c is the friction constant, f d is the external disturbance force, z is the rotor position, is the rotor speed, is the acceleration of the rotor;

[0011] Step 2: Determine the lumped disturbance of the active magnetic bearing control system and establish the state space equation of the active magnetic bearing control system;

[0012] Through the external disturbance and the parameter changes of the active magnetic bearing control system, the lumped disturbance of the active magnetic bearing control system is obtained, as shown in the following formula:

[0013] d=△K z z+△K i i z +fd

[0014] Where d is the total disturbance of the active magnetic bearing control system, △K z and △K i are the changes of displacement force stiffness and current force stiffness of the active magnetic bearing control system respectively;

[0015] The lumped disturbance of the active magnetic bearing control system is assumed to be bounded and first-order differentiable, and satisfies the inequality: |d|<δ, where δ is a positive constant;

[0016] The state space equation of the active magnetic bearing control system is further established as shown in the following formula:

[0017]

[0018] Among them, A is the active magnetic bearing control system matrix, B is the input matrix, D is the output matrix, and u is the terminal sliding mode control law;

[0019] Assume z1 and z2 are the state variables of the active magnetic bearing control system, z1 = z, u=i z ,get

[0020] Let z = [z1, z2] T , thus we get

[0021]

[0022] Step 3: Construct the terminal sliding mode surface according to the state space equation of the active magnetic bearing control system, use the saturation function to eliminate the chattering phenomenon in the terminal sliding mode control, and use the terminal sliding mode control law to control the difference between the reference set trajectory and the actual position trajectory of the rotor, that is, the tracking error and its first-order derivative converge to zero in a finite time;

[0023] According to the state space equation of the active magnetic bearing control system, the terminal sliding surface at time t is constructed. Where e(t) is the rotor tracking error, and the rotor tracking error is the reference set trajectory z of the rotor. m The difference between (t) and the actual position trajectory z(t), that is, e(t) = z m (t)-z(t), is the first-order derivative of the tracking error e(t), λ is a designed constant, and λ>0, p and q are positive odd numbers, satisfying p>q;

[0024] The saturation function sat(s(t)) is used to eliminate the chattering phenomenon in the terminal sliding mode control, and the terminal sliding mode control law u(t) at time t is obtained as follows:

[0025]

[0026] Among them, the saturation function Symbolic Function A positive constant indicating the saturation level;

[0027] Under the action of the terminal sliding mode control law u(t), the tracking error e(t) will satisfy the finite time Arrival terminal sliding surface When the terminal sliding surface s(t) = 0 is reached, the dynamic characteristics of the active magnetic bearing control system are determined as the first-order derivative of the tracking error Finally in a limited time Converge to the desired equilibrium point or its neighborhood by using terminal sliding mode control, tracking the error e(t) and its first-order derivative will converge to zero in a finite time;

[0028] Step 4: Use the Lumberg observer to estimate the state of the active magnetic bearing control system, determine the characteristic equation required for the feedback gain matrix K to generate, and select the gain matrix L to ensure that the tracking error decays to 0 in time and remains at 0, and is independent of the input terminal sliding mode control law and the initial state of the active magnetic bearing control system; improve the estimation accuracy of the interference by adjusting the parameters of the Lumberg observer, so that the Lumberg observer can still maintain a high estimation accuracy when facing external disturbances, thereby achieving stable suspension of the magnetic bearing;

[0029] The characteristic equation required for generating the feedback gain matrix K is |A-BK|=0;

[0030] The active magnetic bearing control system is represented as a state space model as follows:

[0031]

[0032] Where C is the output matrix, y is the output displacement of the rotor;

[0033] The state equation of the Lumberg observer is:

[0034]

[0035] in, is the estimated state, is the first-order derivative of the estimated state, is the estimated output;

[0036] The gain matrix L is selected so that all eigenvalues ​​of A-LC have negative real parts. The control law for state feedback using the estimated state constructed by the Lumberg observer is: Where v is the control input, K is the feedback gain matrix of the Lumberg observer, the eigenvalues ​​of the matrix A-BK are the poles of the closed-loop system, and the matrix K is selected to configure the poles of the closed-loop system to the desired position;

[0037] The state feedback control based on the Romberg observer is:

[0038]

[0039] Even in the presence of disturbances, the estimation accuracy of the disturbances is improved by adjusting the parameters of the Lumberg observer, so that the Lumberg observer can still maintain a high estimation accuracy when facing external disturbances, thereby achieving stable suspension of the magnetic bearing.

[0040] The beneficial effects of adopting the above technical scheme are: a terminal sliding mode control method for a magnetic bearing based on a Lumberg observer provided by the present invention adopts a terminal sliding mode control method for a magnetic bearing based on a Lumberg observer, which can significantly improve the dynamic response speed and stability of an active magnetic bearing control system; the method accurately estimates the state of the active magnetic bearing control system through a Lumberg observer, and compensates for parameter changes and external disturbances of the active magnetic bearing control system in real time, thereby reducing the influence of uncertainty factors on the active magnetic bearing control system; at the same time, the introduction of terminal sliding mode control ensures that the state of the active magnetic bearing control system can converge to the expected value quickly and accurately, reduces the chattering phenomenon in traditional sliding mode control, optimizes the overall performance, and realizes stable, fast and precise control of the active magnetic bearing control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 A flow chart of a terminal sliding mode control method of a magnetic bearing based on a Romberg observer provided by an embodiment of the present invention;

[0042] Figure 2 A schematic diagram of a mathematical model of an active magnetic bearing control system provided by an embodiment of the present invention;

[0043] Figure 3 A structural diagram of a terminal sliding surface provided by an embodiment of the present invention;

[0044] Figure 4 A schematic diagram of a Lumberg observer estimating an active magnetic bearing control system provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0045] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0046] In this embodiment, a terminal sliding mode control method of a magnetic bearing based on a Lumberg observer is provided. Figure 1 As shown, the following steps are included:

[0047] Step 1: Set the axial motion of the rotor to be decoupled from the radial motion, and the rotation of the rotor is controlled by the drive inverter and decoupled from the radial motion; Based on the control force generated by the magnetic bearing, air friction, and centrifugal force of the rotor, a mathematical model of the active magnetic bearing control system is established, such as Figure 2 As shown;

[0048] In this embodiment, the control force generated by the magnetic bearing, air friction, and centrifugal force of the rotor are taken into consideration to establish the following Figure 2 The mathematical model of the active magnetic bearing control system shown in the figure, the magnetic bearing system is mainly composed of a motor rotor, a magnetic bearing stator coil and a magnetic bearing control system; the control system includes a displacement sensor, a controller, an electromagnet, a thrust plate and a power amplifier; the displacement sensor is responsible for real-time detection of the rotor position signal, and the displacement controller outputs a control signal after performing internal calculations on the displacement controller after making a difference between the ideal position value and the position value detected by the sensor. The control signal is generally a PWM wave signal to control the switch in the power amplifier; the power amplifier controls the coil current i by changing the PWM wave duty cycle. z The size of the rotor upper and lower coil currents are i0+i z and i0-i z The magnetic force difference between the upper and lower parts of the rotor is related to the control current. When the control current i z When the magnetic field changes, the magnetic force difference between the upper and lower parts of the rotor changes, thereby realizing the control of the motor rotor position;

[0049] The mathematical model of the active magnetic bearing control system is described as follows:

[0050]

[0051] Among them, K z and K i are the displacement force stiffness and current force stiffness of the active magnetic bearing control system, i z is the current flowing through the axial magnetic bearing coil, m is the mass of the rotor, c is the friction constant, f d is the external disturbance force, z is the rotor position, is the rotor speed, is the acceleration of the rotor;

[0052] This embodiment takes a single-degree-of-freedom magnetic bearing system as an example, does not consider the coupling between the degrees of freedom, and assumes that the radial degree-of-freedom models are consistent, and adopts a magnetic bearing terminal sliding mode control method based on a Romberg observer to control the magnetic bearing system;

[0053] Step 2: Determine the lumped disturbance of the active magnetic bearing control system and establish the state space equation of the active magnetic bearing control system;

[0054] Through the external disturbance and the parameter changes of the active magnetic bearing control system, the lumped disturbance of the active magnetic bearing control system is obtained, as shown in the following formula:

[0055] d=△K z z+△K i i z +f d

[0056] Where d is the total disturbance of the active magnetic bearing control system, △K z and △K i are the changes of displacement force stiffness and current force stiffness of the active magnetic bearing control system respectively;

[0057] Since the speed, external disturbance and parameter changes of the active magnetic bearing control system are bounded, the lumped disturbance is also bounded. Since the lumped disturbance of the active magnetic bearing control system will not change infinitely fast, the lumped disturbance of the active magnetic bearing control system is set to be bounded and first-order differentiable, and satisfies the inequality: |d|<δ, where δ is a positive constant;

[0058] The state space equation of the active magnetic bearing control system is further established as shown in the following formula:

[0059]

[0060] Among them, A is the active magnetic bearing control system matrix, B is the input matrix, D is the output matrix, and u is the terminal sliding mode control law;

[0061] Assume z1 and z2 are the state variables of the active magnetic bearing control system, z1 = z, u=i z , we can get Let z = [z1, z2] T , thus we get

[0062] In this embodiment, the derivation process of further establishing the state space equation of the active magnetic bearing control system is as follows:

[0063] (1) Known Available Due to the external interference f d and active magnetic bearing control system △K z and △K i The parameter changes, so

[0064] (2) Let d = △K z z+△K i i z +f d ,so

[0065] (3) Let z1 = z, Available

[0066] (4) Order Therefore Also because so

[0067] Step 3: Construct the terminal sliding mode surface according to the state space equation of the active magnetic bearing control system, use the saturation function to eliminate the chattering phenomenon in the terminal sliding mode control, and use the terminal sliding mode control law to control the difference between the reference set trajectory and the actual position trajectory of the rotor, that is, the tracking error and its first-order derivative converge to zero in a finite time;

[0068] According to the state space equation of the active magnetic bearing control system, the terminal sliding surface at time t is constructed. Where e(t) is the rotor tracking error, and the rotor tracking error is the reference set trajectory z of the rotor. m The difference between (t) and the actual position trajectory z(t), that is, e(t) = z m (t)-z(t), is the first-order derivative of the tracking error e(t), λ is a designed constant, and λ>0, p and q are positive odd numbers, satisfying p>q;

[0069] When s(t)≠0, the sufficient condition for the existence of the terminal sliding mode is Where ζ>0 is the control gain;

[0070] The saturation function sat(s(t)) is used to eliminate the chattering phenomenon in the terminal sliding mode control, and the terminal sliding mode control law u(t) at time t is obtained as follows:

[0071]

[0072] Among them, the saturation function Symbolic Function φ is a positive constant, indicating the saturation level. The size of φ affects the degree of jitter. When φ is infinitely small, the saturation function is a sign function. It does not mean that the smaller the jitter, the better. Jitter will affect the control speed and control accuracy. Accuracy and speed are often not achieved at the same time.

[0073] Under the action of the terminal sliding mode control law u(t), the tracking error e(t) will satisfy the finite time Arrival terminal sliding surface When the terminal sliding surface s(t) = 0 is reached, the dynamic characteristics of the active magnetic bearing control system are determined as the first-order derivative of the tracking error Finally in a limited time Converge to the desired equilibrium point or its neighborhood by using terminal sliding mode control, tracking the error e(t) and its first-order derivative will converge to zero in a finite time;

[0074] In this embodiment, when designing the terminal sliding surface, it is necessary to allow the points of the state space equation of the active magnetic bearing control system to reach the terminal sliding surface s=0 in a finite time, and the state space is divided into two parts, s<0 and s>0. The moving points on the switching surface include three situations: a constant point I, a starting point S, and an end point E. For example, Figure 3 As shown, and at point E, when s<0 When s>0

[0075] In this embodiment, in the terminal sliding surface, the constant point I represents the position where the state of the active magnetic bearing control system is stable on the terminal sliding surface, indicating that the performance of the active magnetic bearing control system meets the design requirements and the state will not deviate from the predetermined trajectory. The starting point S is the initial point where the state of the active magnetic bearing control system begins to approach the terminal sliding surface. The goal of the sliding mode control is to guide the state of the active magnetic bearing control system from this point to the terminal sliding surface; the dead point E is the final stable point of the state of the active magnetic bearing control system on the terminal sliding surface. When s<0, the stop point E satisfies the condition at point E. When s>0 At this time, not only does the state of the active magnetic bearing control system remain on the terminal sliding surface, but its speed also drops to zero, indicating that the active magnetic bearing control system has stabilized at or near the desired equilibrium point; these three points together describe the transition process of the system state from the initial state to the final stable state. The design of the sliding mode control needs to ensure that the system can smoothly pass through these points to achieve fast and accurate dynamic response;

[0076] Step 4: Use Figure 4The Lumberg observer shown estimates the state of the active magnetic bearing control system, determines the characteristic equation required for generating the feedback gain matrix K, selects the gain matrix L to ensure that the tracking error e(t) decays to 0 in time and remains 0, and is independent of the input terminal sliding mode control law u and the initial state z(0) of the active magnetic bearing control system; the estimation accuracy of the interference is improved by adjusting the parameters of the Lumberg observer, so that the Lumberg observer can still maintain a high estimation accuracy when facing external disturbances, thereby achieving stable suspension of the magnetic bearing;

[0077] The Lumberg observer uses the real active magnetic bearing control system output to perform error feedback correction to construct a closed-loop observer. The Lumberg observer can estimate the total disturbance including the active magnetic bearing control system parameter changes and external disturbances, thus solving the problem of not being able to obtain a completely accurate model.

[0078] The characteristic equation required for generating the feedback gain matrix K is |A-BK|=0;

[0079] The active magnetic bearing control system is represented as a state space model as follows:

[0080]

[0081] Where C is the output matrix, y is the output displacement of the rotor;

[0082] The state equation of the Lumberg observer is:

[0083]

[0084] in, is the estimated state, is the first-order derivative of the estimated state, is the estimated output;

[0085] The gain matrix L is selected so that all eigenvalues ​​of A-LC have negative real parts. The absolute value of the negative real part will affect the speed of the active magnetic bearing state approximation. The absolute value of the negative real part of the eigenvalue is positively correlated with the speed of the active magnetic bearing state approximation. Therefore, when time t->∞, The Lumberg observer can accurately observe the state of the active magnetic bearing;

[0086] The control law for state feedback using the estimated state constructed by the Lumberg observer is: Where v is the control input, K is the feedback gain matrix of the Lumberg observer, the eigenvalues ​​of the matrix A-BK are the poles of the closed-loop system, and the matrix K is selected to configure the poles of the closed-loop system to the desired position;

[0087] The state feedback control based on the Romberg observer is:

[0088]

[0089] Even in the presence of disturbances, the estimation accuracy of the disturbances is improved by adjusting the parameters of the Lumberg observer, so that the Lumberg observer can still maintain a high estimation accuracy when facing external disturbances, thereby achieving stable suspension of the magnetic bearing.

[0090] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some or all of the technical features therein. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A terminal sliding mode control method for a magnetic bearing based on a Romberg observer, characterized in that: The following steps are involved: Step 1: The axial motion of the rotor is set to be decoupled from the radial motion, and the rotation of the rotor is controlled by a drive inverter and decoupled from the radial motion; a mathematical model of the active magnetic bearing control system is established based on the control force generated by the magnetic bearing, air friction and the centrifugal force of the rotor; Step 2: Determine the lumped disturbance of the active magnetic bearing control system and establish the state space equation of the active magnetic bearing control system; Step 3: Construct the terminal sliding mode surface according to the state space equation of the active magnetic bearing control system, use the saturation function to eliminate the chattering phenomenon in the terminal sliding mode control, and use the terminal sliding mode control law to control the difference between the reference set trajectory and the actual position trajectory of the rotor, that is, the tracking error and its first-order derivative converge to zero in a finite time; Step 4: Use the Lumberg observer to estimate the state of the active magnetic bearing control system, determine the characteristic equation required to generate the feedback gain matrix K, and select the gain matrix L to ensure that the tracking error decays to 0 in time and remains at 0, and is independent of the input terminal sliding mode control law and the initial state of the active magnetic bearing control system; improve the estimation accuracy of the interference by adjusting the parameters of the Lumberg observer, so that the Lumberg observer can still maintain a high estimation accuracy when facing external disturbances, thereby achieving stable suspension of the magnetic bearing.

2. The terminal sliding mode control method of a magnetic bearing based on a Romberg observer according to claim 1 is characterized in that: The specific method of step 2 is: The lumped disturbance of the active magnetic bearing control system is obtained through external disturbance and parameter changes of the active magnetic bearing control system. The lumped disturbance of the active magnetic bearing control system is assumed to be bounded and first-order differentiable, and satisfies the inequality: |d|<δ, where δ is a positive constant; Further establish the state space equation of active magnetic bearing control system; Assume z1 and z2 are the state variables of the active magnetic bearing control system, z1 = z, u=i z ,get Let z = [z1, z2] T , thus we get 3. The terminal sliding mode control method of a magnetic bearing based on a Romberg observer according to claim 2 is characterized in that: The mathematical model of the active magnetic bearing control system is described as follows: Among them, K z and K i are the displacement force stiffness and current force stiffness of the active magnetic bearing control system, i z is the current flowing through the axial magnetic bearing coil, m is the mass of the rotor, c is the friction constant, f d is the external disturbance force, z is the rotor position, is the rotor speed, is the acceleration of the rotor.

4. The terminal sliding mode control method of a magnetic bearing based on a Romberg observer according to claim 3 is characterized in that: The lumped disturbance of the active magnetic bearing control system is shown in the following formula: d=△K z z+△K i i z +f d Where d is the total disturbance of the active magnetic bearing control system, △K z and △K i They are the changes of displacement force stiffness and current force stiffness of the active magnetic bearing control system respectively.

5. The terminal sliding mode control method of a magnetic bearing based on a Romberg observer according to claim 4 is characterized in that: The state space equation of the active magnetic bearing control system is shown in the following formula: Among them, A is the active magnetic bearing control system matrix, B is the input matrix, D is the output matrix, and u is the terminal sliding mode control law.

6. The terminal sliding mode control method of a magnetic bearing based on a Romberg observer according to claim 5 is characterized in that: The specific method of step 3 is: According to the state space equation of the active magnetic bearing control system, the terminal sliding surface at time t is constructed. Where e(t) is the rotor tracking error, and the rotor tracking error is the reference set trajectory z of the rotor. m The difference between (t) and the actual position trajectory z(t), that is, e(t) = z m (t)-z(t), is the first-order derivative of the tracking error e(t), λ is a designed constant, and λ>0, p and q are positive odd numbers, satisfying p>q; The saturation function sat(s(t)) is used to eliminate the chattering phenomenon in the terminal sliding mode control, and the terminal sliding mode control law u(t) at time t is obtained as follows: Among them, the saturation function Symbolic Function φ is a positive constant, indicating the saturation level; Under the action of the terminal sliding mode control law u(t), the tracking error e(t) will satisfy the finite time Arrival terminal sliding surface When the terminal sliding surface s(t) = 0 is reached, the dynamic characteristics of the active magnetic bearing control system are determined as the first-order derivative of the tracking error Finally in a limited time Converge to the desired equilibrium point or its neighborhood by using terminal sliding mode control, tracking the error e(t) and its first-order derivative will converge to zero in a finite time.

7. The terminal sliding mode control method of a magnetic bearing based on a Romberg observer according to claim 6 is characterized in that: The specific method of step 4 is: The gain matrix L is selected so that all eigenvalues ​​of A-LC have negative real parts. The control law for state feedback using the estimated state constructed by the Lumberg observer is: Where v is the control input, K is the feedback gain matrix of the Lumberg observer, the eigenvalues ​​of the matrix A-BK are the poles of the closed-loop system, and the matrix K is selected to configure the poles of the closed-loop system to the desired position; Even in the presence of disturbances, the estimation accuracy of the disturbances is improved by adjusting the parameters of the Lumberg observer, so that the Lumberg observer can still maintain a high estimation accuracy when facing external disturbances, thereby achieving stable suspension of the magnetic bearing.

8. The terminal sliding mode control method of a magnetic bearing based on a Romberg observer according to claim 7 is characterized in that: The characteristic equation required for generating the feedback gain matrix K is |A-BK|=0.

9. The terminal sliding mode control method of a magnetic bearing based on a Romberg observer according to claim 8 is characterized in that: The active magnetic bearing control system is represented as a state space model as follows: Among them, C is the output matrix and y is the output displacement of the rotor.

10. The terminal sliding mode control method of a magnetic bearing based on a Romberg observer according to claim 9, characterized in that: The state equation of the Lumberg observer is: in, is the estimated state, is the first-order derivative of the estimated state, is the estimated output; The state feedback control based on the Romberg observer is:

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