A control system and method for active electromagnetic bearing

Abstract

The present invention discloses a control system and method for an active electromagnetic bearing, wherein a displacement reference value, a rotor displacement, and a displacement error are input into a superhelical sliding mode controller to calculate a control quantity; the final control quantity is input into an AMBs magnetic suspension system to obtain an electromagnetic force; the electromagnetic force is subtracted from the disturbance force to obtain the resultant force on the rotor, the resultant force on the rotor is divided by the rotor mass, and the result is integrated twice continuously to obtain the rotor displacement. The improved superhelical convergence law of the present invention utilizes integral terms and power terms to make the system state smooth near the sliding mode surface, thereby reducing system jitter. The system input quantity in the present invention is much smaller than the system input quantity in other control methods, which means that the energy consumption of the system and the heating of the system will also be reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of active magnetic bearings, and in particular relates to a control system and method for an active electromagnetic bearing. Background Art

[0002] As active magnetic bearing (AMB) technology becomes increasingly mature, AMB has been widely used in high-speed rotating machinery such as compressors, flywheel energy storage and molecular pumps. How to control the magnetic suspension rotor to stably suspend at the desired position has always been an important issue. The traditional engineering method generally adopts PID control, but the AMB system is often subject to some disturbances during operation, and the real system cannot be accurately modeled, and the key parameters of the system are often difficult to obtain. In the magnetic suspension motor control system, factors such as sensor jump, magnetic field fluctuation of active magnetic suspension bearing, and change of rotor imbalance often cause the accuracy of AMBs rotor position control to be affected by unknown disturbances. In addition, the AMBs system linearizes the system during the modeling process, which also leads to the incomplete modeling of the AMBs system and contains unmodeled parts.

[0003] The patent publication number is CN110985541A, and the name is a patent application for a controller for controlling an active magnetic bearing system and a control method thereof. The displacement sensor is used to obtain the rotor displacement signal measurement value x s ; Input it into the phase-locked loop to calculate the rotor displacement signal calculation value and the rotor speed signal calculation value, and feed it back to the sliding mode controller, and adjust the rotor position controller to obtain the required electromagnetic force F smc At the same time, the calculated value of the rotor displacement signal, the calculated value of the speed signal and the sliding mode variable s are input into the single-layer neural network regulator to calculate the compensation force F Δ ; F smc and F Δ The sum is the total electromagnetic force F required to control the rotor to the equilibrium position. ref , and then calculate the reference current; control the magnetic bearing coil current through the current regulator, thereby controlling the rotor to the equilibrium position. When the lumped disturbance exists, in order to stabilize the system, the patent application uses a larger gain value of the sign(s) function in the super-helical sliding mode control, but at this time, the super-helical sliding mode control has a contradiction between suppressing chattering and disturbance. Summary of the invention

[0004] In order to overcome the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a control system and method for an active electromagnetic bearing, which regards the unmodeled part and the unknown disturbance as a lumped disturbance, uses the improved INESO to observe the lumped disturbance, and then compensates it to the system, which can effectively solve the contradiction between super-helical sliding mode control in suppressing vibration and disturbance.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] A control system for an active electromagnetic bearing, comprising:

[0007] The super-helical sliding mode controller is used to calculate the displacement reference value x r , rotor displacement x1, displacement error e1, calculate the control quantity u;

[0008] The first subtractor is used to convert the sliding mode controller output control quantity u and the observer observation value z3 through m / k i After gaining, make a difference to get the final control value u ed ;

[0009] Active electromagnetic bearing system, used to input the final control quantity u ed , we get the electromagnetic force f x ;

[0010] The second subtractor is used to input the electromagnetic force f x and the disturbance force F d Make a difference and get the resultant force on the rotor;

[0011] The product-integral controller is used to input the rotor force and compare it with 1 / ms 2 Multiply and integrate twice to obtain the rotor displacement x1;

[0012] Nonlinear extended state observer for input k i u ed / m and the rotor displacement x1, calculate z3, where k i is the current stiffness coefficient, z3 is the observed value of the expanded state x3, x3 is the lumped disturbance, and x2 is the differential of x1.

[0013] Optionally, the reaching law of the super-helical sliding mode controller is:

[0014]

[0015] Among them, γ>1, 0<λ, η>0, γ, λ and η are all constants; k1 and k2 are both constants greater than 0; s is the sliding surface, which is also the system state.

[0016] Optionally, the control variable u of the super-helical sliding mode controller is calculated as follows:

[0017]

[0018] where |f d | <M,f d is the lumped disturbance, u is the control variable of the super-helical sliding mode controller, ks is the displacement stiffness coefficient, k i is the current stiffness coefficient, k1>0, k2>0, s is the sliding mode surface, m is the rotor mass, x1 is the rotor displacement value, x2 is the differential of x1, x r is the displacement reference value, e1 is the deviation between the displacement reference value and the rotor displacement value; a>0, 1<b<2; M is the upper limit of the disturbance, that is, the maximum value of the disturbance.

[0019] Optionally, the final control quantity u ed The calculation formula is:

[0020]

[0021] Optionally, the expansion state equation of the non-linear extended state observer is:

[0022]

[0023] where x2 is the differential of x1, x3 is the lumped disturbance; z1, z2, z3 are the observed values of the system states x1, x2, x3 respectively; θ1, θ2 and θ3 are all observation errors, θ1 = z1 - x1, θ2 = z2 - x2, θ3 = z3 - x3; β1, β2, β3 are the observer gains.

[0024] Optionally, the non-linear extended state observer includes:

[0025] The first adder, used to input k i u / m, k s / m and z3, and calculate the sum of the three items;

[0026] The first integrator, used to integrate the sum of k i u / m, k s / m and z3 to obtain z2;

[0027] The second integrator, used to integrate z2 to obtain z1;

[0028] The first subtractor, used to subtract the input x1 from z1 to obtain the observation error θ1;

[0029] The second adder, used to calculate the negative sum of the integral of β3u3(θ1), the proportion of β2u2(θ1), and the differential of β1u1(θ1) to obtain z3.

[0030] Optionally, the super-twisting sliding mode controller includes:

[0031] The sign function device, used to calculate the positive and negative of the sliding mode surface s;

[0032] The integrator, used to integrate sign(s);

[0033] A first gainer is used to multiply the integral of sign(s) by k3 to obtain k3∫sign(s)dt;

[0034] The power sign function is used to calculate the power and sign of the input sliding surface s to obtain |s| c sign(s);

[0035] The second amplifier is used to adjust |s| c Multiply sign(s) by k4, and we get k4|s| c sign(s);

[0036] Subtractor, used to k4|s| c Taking the difference between sign(s) and k3∫sign(s)dt, we can obtain the super-helical sliding mode reaching law -k3∫sign(s)dt-k4|s| c sign(s).

[0037] A method for using a control system of an active electromagnetic bearing comprises the following steps:

[0038] Set the displacement reference value x r , rotor displacement x1, displacement error e1, input super-helical sliding mode controller to calculate the control quantity u;

[0039] K i u ed / m and rotor displacement x1 are input into the nonlinear extended state observer to obtain mz3 / k i ;

[0040] The control quantity u and mz3 / k i Make the difference and get the final control amount u ed ;

[0041] The final control quantity u ed Input to the AMBs magnetic levitation system to obtain the electromagnetic force f x ;

[0042] The electromagnetic force f x and the disturbance force F d By making a difference, we can get the resultant force on the rotor, divide the resultant force on the rotor by the rotor mass m, and integrate the result twice in a row to get the rotor displacement x1.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] The present invention improves the superhelical convergence law. The traditional convergence law usually causes system chattering. The improved superhelical convergence law in the present invention uses integral terms and power terms to make the system state smooth near the sliding surface, thereby reducing system chattering. It can accelerate the system state to reach the sliding surface and greatly weaken the chattering, the biggest disadvantage of sliding mode control.

[0045] The present invention improves the structure of the nonlinear extended state observer, making it more accurate in observing the disturbances inside and outside the system. The system input in the present invention is much smaller than the system input in other control methods, which means that the energy consumption and heating of the system will also be reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The drawings described herein are for illustration purposes only and are not intended to limit the scope of the present disclosure in any way.

[0047] In the attached picture:

[0048] Figure 1 It is the structure diagram of superhelix approach law;

[0049] Figure 2 is the waveform of function g;

[0050] Figure 3 is the phase trajectory of the AMB system;

[0051] Figure 4 It is the Bode plot under different bandwidths;

[0052] Figure 5 It is the NESO structure diagram;

[0053] Figure 6 It is the INESO structure diagram;

[0054] Figure 7 It is the overall control structure diagram of the AMB system;

[0055] Figure 8 These are the displacement waveforms of the two controllers without considering lumped disturbances;

[0056] Fig. 9 These are the current waveforms of the two controllers without considering the lumped disturbance;

[0057] Fig.10 It is the displacement waveform of two controllers under lumped disturbance;

[0058] Fig.11 It is the current waveform of two controllers under lumped disturbance;

[0059] Fig.12 It is an analytical comparison diagram of the two observers;

[0060] Fig.13 These are the displacement waveforms of the two controllers after compensation;

[0061] Fig.14 Figure 2 shows the current waveforms of the two controllers after compensation. DETAILED DESCRIPTION

[0062] In order to enable those skilled in the art to better understand the technical solutions in the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0063] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those generally understood by those skilled in the art of the present invention. The terms used herein in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The term "and / or" used herein includes any and all combinations of one or more related listed items.

[0064] It should be noted that in the claims, any reference signs placed between brackets shall not be construed as limiting the claims. The word "comprising" does not exclude the presence of components or steps not listed in the claims. The word "a" or "an" preceding a component does not exclude the presence of a plurality of such components. The present application may be implemented by means of hardware comprising several different components and by means of a suitably programmed computer. In a unit claim enumerating several means, several of these means may be embodied by the same item of hardware. The use of the words first, second, and third etc. does not indicate any order. These words may be interpreted as names.

[0065] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of this application, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0066] The present invention is described in detail below with reference to the accompanying drawings.

[0067] like Figure 7 As shown, a control system of an active electromagnetic bearing of the present invention comprises:

[0068] The super-helical sliding mode controller is used to calculate the displacement reference value x r , rotor displacement x1, displacement error e1, calculate the control quantity u. Among them, the displacement error e1 is the displacement reference value x r Optionally, the input end of the super-helical sliding mode controller is connected to a displacement subtractor, which is used to calculate the displacement reference value x r The difference with the rotor displacement x1.

[0069] The first subtractor is used to convert the sliding mode controller output control quantity u and the observer observation value z3 through m / k i After gaining, make a difference to get the final control value u ed The output end of the super spiral sliding mode controller is connected to the input end of the first subtractor. The input end of the first subtractor is connected to the output end of the super spiral sliding mode controller.

[0070] Active electromagnetic bearing system, used to input the final control quantity u ed , we get the electromagnetic force f x ; The input end of the active electromagnetic bearing system is connected to the output end of the first subtractor.

[0071] The second subtractor is used to input the electromagnetic force f x and the disturbance force F d The resultant force on the rotor is obtained by making a difference; the input end of the second subtractor is connected to the output end of the active electromagnetic bearing system.

[0072] The product-integral controller is used to input the rotor force and compare it with 1 / ms 2 The rotor displacement x1 is obtained by multiplying and integrating twice; the input end of the product-integral controller is connected to the output end of the second subtractor. The input end of the displacement subtractor is connected to the output end of the product-integral controller. The input end of the super-helical sliding mode controller is connected to the output end of the product-integral controller.

[0073] Nonlinear extended state observer for input k i u ed / m and the rotor displacement x1, calculate z3, where k i is the current stiffness coefficient, z3 is the observed value of the extended state x3, x3 is the lumped disturbance, and x2 is the differential of x1. The input end of the nonlinear extended state observer is connected to the output end of the product-integral controller. The output end of the nonlinear extended state observer is connected to an amplifier, which is used to convert z3 and m / k i The output end of the gain device is connected to the first subtractor.

[0074] The nonlinear extended state observer comprises: a first adder for inputting k i u / m、k s / m and z3, calculate the sum of the three terms; the first integrator is used to calculate k i u / m、k s The sum of / m and z3 is integrated to obtain z2. The output end of the first adder is connected to the input end of the first integrator.

[0075] The second integrator is used to integrate z2 to obtain z1; the first subtractor is used to make a difference between z1 and the input x1 to obtain the observation error θ1; the second adder is used to calculate the sum of the negative values ​​of the integral of β3u3(θ1), the proportion of β2u2(θ1), and the differential of β1u1(θ1) to obtain z3. The output end of the first integrator is connected to the input end of the second integrator. The output end of the second integrator is connected to the input end of the second adder.

[0076] The super-helical sliding mode controller comprises: a sign function device for calculating the positive and negative of the input sliding mode surface s; an integrator for integrating sign(s); a first gain device for multiplying the integral of sign(s) by k3 to obtain k3∫sign(s)dt; a power sign function device for calculating the power and positive and negative of the input sliding mode surface s to obtain |s| c sign(s); the second amplifier is used to adjust |s| c Multiply sign(s) by k4, and we get k4|s| c sign(s); subtractor for k4|s| c Taking the difference between sign(s) and k3∫sign(s)dt, we can obtain the super-helical sliding mode reaching law -k3∫sign(s)dt-k4|s| c The output end of the sign function device is connected to the input end of the first gain device. The output end of the power sign function device is connected to the input end of the second gain device. The output end of the first gain device and the output end of the second gain device are both connected to the input end of the subtractor.

[0077] A method for using a control system of an active electromagnetic bearing of the present invention comprises the following steps:

[0078] Set the displacement reference value x r , rotor displacement x1, displacement error e1, input super-helical sliding mode controller to calculate the control quantity u;

[0079] K i *u ed / m and rotor displacement x1 are input into the nonlinear extended state observer to obtain mz3 / k i ;

[0080] The control quantity u and mz3 / k i Make the difference and get the final control amount u ed ;

[0081] The final control quantity u ed Input to the AMBs magnetic levitation system to obtain the electromagnetic force f x ;

[0082] The electromagnetic force f x and the disturbance force F d By making a difference, we can get the resultant force on the rotor, divide the resultant force on the rotor by the rotor mass m, and integrate the result twice in a row to get the rotor displacement x1.

[0083] The control system and method of an active electromagnetic bearing of the present invention has the following specific design process:

[0084] For example, in order to speed up the approach speed and reduce the chattering during the control process, the traditional superhelical approach law has the following structure: Figure 1 shown.

[0085] The specific expression is:

[0086]

[0087] Where k1 and k2 are both positive values, 0 <c<1。

[0088] When the system state is far away from the sliding surface, the switching gain of sign is large, and the system state approaches the sliding surface at a large speed. When the system state is close to the sliding surface, the switching gain of sign is small, and the system state approaches the sliding surface at a small speed. The switching gain of the switching function sign near the sliding surface determines whether the chattering is severe, so the chattering is weakened.

[0089] In order to further speed up the convergence of the system state and weaken the chattering, the following convergence law is now adopted:

[0090]

[0091] Where γ>1, 0<λ, η>0, γ, λ and η are all constants; k1 and k2 are current stiffness coefficients;

[0092] s is the system status.

[0093] The power term is no longer a constant c but a function g, which changes with the system error.

[0094] Figure 2It is the waveform of the function g changing with the error e1. When the error e1 is large at the initial moment, the value of g is large at this time, and the system state approaches the sliding surface at a relatively fast speed. When the error e1 approaches 0, the system state approaches the sliding surface at the speed of the traditional super-twisting reaching law.

[0095] The mathematical model of the single-degree-of-freedom active magnetic bearing is:

[0096]

[0097] Among them, k s and k i are the displacement and current stiffness coefficients respectively, m is the mass of the rotor, and f d is the lumped disturbance.

[0098] Now define the sliding surface as:

[0099]

[0100] where a > 0, 1 < b < 2, e1 = x1 - x r , x r is the displacement reference value, that is, the target position.

[0101] Design the controller as:

[0102]

[0103] where M satisfies |f d | < M.

[0104] Construct the Lyapunov function as:

[0105]

[0106] V(s) is obviously positive definite, and its derivative is:

[0107]

[0108] When e2 ≠ 0, according to the known conditions, both k1 and k2 are positive values, 0 < a, 1 < b < 2, and |f d | < M, then at this time there is:

[0109]

[0110] At this time, the system state s will converge to 0 in a finite time.

[0111] When e2 = 0, now substitute Equation (5) into Equation (3), there is:

[0112]

[0113] According to formula (9), when the system state s>0, When the system state s<0, Figure 3 is the system phase trajectory under this controller. Taking system state s2 as an example, e2=0, , e2 will inevitably decrease in a certain neighborhood (0, +δ), and the system state s2 will inevitably move downward. When the system state s2 reaches the neighborhood (0, +δ), e2≠0, and the system state s2 will reach the sliding surface as concluded by equation (8). The same is true for the system state s2.

[0114] Aggregate interference f d is unknown, and now ESO will observe it and then compensate for it.

[0115] For the second-order AMB rotor system, the lumped disturbance f d Expanding to a new state variable x3, equation (3) can be rewritten as:

[0116]

[0117] Where h is the aggregate interference f d The rate of change.

[0118] According to formula (10), the observed value of the system state variable under LESO can be written as:

[0119]

[0120] Where: L1, L2, L3 are the gains of LESO; z1, z2, z3 are the observed values ​​of system states x1, x2, x3 respectively; θ1=z1-x1, θ2=z2-x2, θ3=z3-x3 are all observation errors.

[0121] Now subtract equation (10) from equation (11) to obtain the error state equation:

[0122]

[0123] The Laplace transform of formula (12) yields:

[0124]

[0125] After rearranging equation (13), the transfer function between the error θ3 and the aggregate interference -x3 is obtained as follows:

[0126]

[0127] In order to make the system stable, assume that equation (14) has three poles all located in the left half plane, s1, s2, s3 are -ω0, ω0 is the bandwidth and is greater than 0, then:

[0128]

[0129] It can be solved as:

[0130]

[0131] Substitute equation (16) into equation (14):

[0132]

[0133] Figure 4 Bode plots at different bandwidths.

[0134] exist Figure 4 Middle: When the x3 frequency is low, z3 tracks x3 better; as the x3 frequency increases, z3's tracking performance of x3 gradually deteriorates. As the bandwidth increases, z3's tracking performance of x3 gradually improves, but too large a bandwidth can easily make it sensitive to other noises in the system.

[0135] Since the LESO has limited observation accuracy for the aggregate disturbance and AMBs is a typical nonlinear system, NESO is used to observe the aggregate disturbance in the AMB system, and equation (12) is rewritten as:

[0136]

[0137] Among them, β1, β2, β3 are the observer gains to be designed, all of which are positive values, and u1(θ1), u2(θ1), and u3(θ1) are the nonlinear functions about θ1 to be designed. u1(θ1), u2(θ1), and u3(θ1) are respectively:

[0138]

[0139] In situations where high precision is required, traditional NESO cannot meet the requirements, so the present invention improves NESO in structure. Figure 5 This is the traditional NESO structure diagram. Figure 6 This is the structural block diagram of the improved INESO.

[0140] Figure 5 The input is k i The observation error θ1 is obtained by subtracting m / u from x1, x1 and its observed value z1.

[0141] The difference between z1 and the nonlinear function β1u1(θ1) can get the differential value of z1, and then the integration of the differential value of z1 can get z1.

[0142] Then k i u / m、k s Linear addition and subtraction of z1 / m, z3 and nonlinear function β2u2(θ1) can yield z2.

[0143] Then, by integrating the nonlinear function -β3u3(θ1), we can get z3, which is the observed value of the disturbance, and then output it to the controller. Figure 6 The z3 in the equation is the sum of the integral of -β3u3(θ1), the proportional of -β2u2(θ1), and the differential of -β1u1(θ1). The differential of z2 is k i u / m、k s The sum of z1 / m and z3 is integrated to get z2, and then integrated again to get z1. z1 is further subtracted from the input x1 to get the error θ1. Nonlinear operations are then performed on the error θ1 to get -β3u3(θ1), -β2u2(θ1), -β1u1(θ1), and then the iteration is continued to get z3, z2, z1, and finally z3 after iterative convergence is output.

[0144] according to Figure 6 The new expanded state equation can be obtained:

[0145]

[0146] NESO parameters are difficult to adjust theoretically, and are usually designed based on experience. Designing appropriate β1, β2, and β3 can make the observation errors θ1, θ2, and θ3 converge to 0 within a finite time.

[0147] The switching gain of the switching function sign in the controller in equation (5) is -(k2|s| g +M), where -k2|s| g The generated chattering is very small, but -M is a constant value. When the system state reaches the sliding surface, it will inevitably cause the system to have chattering, so now modify the controller to:

[0148]

[0149] The derivative of V(s) now becomes:

[0150]

[0151] According to the previously designed INESO, θ3 will converge to 0, and we have:

[0152]

[0153] The system state s can converge in a finite time.

[0154] According to the designed composite controller, the overall control structure of the AMBs system is as follows: Figure 7 shown.

[0155] Figure 7 In the figure, the displacement reference value x r The error e1 is obtained by subtracting the rotor displacement x1. The error e1 and the displacement reference value x r , the rotor displacement x1 is input into the controller, and the super-helical sliding mode controller designed according to formula (5) can obtain the control quantity u, which is equal to the mz3 / k fed back by the observer. i The final control quantity u can be obtained by making a difference ed ,mz3 / k i It is through k i u ed / m and the rotor displacement x1 are input into the observer. The control quantity u ed Input into the AMBs magnetic levitation system to generate the corresponding electromagnetic force f x , and then with the disturbance force F d The resultant force on the rotor can be obtained by making a difference. The resultant force passes through (1 / ms 2 ), that is, the resultant force divided by its mass m and integrated twice to obtain the rotor displacement x1.

[0156] In order to compare the superior performance of SSMC, traditional SMC is added in the verification part. Without considering the lumped disturbance in the AMBs system, SSMC and SMC are:

[0157]

[0158] In formula (24), c>0.

[0159] Figure 8 , Fig. 9 They are the displacement and current waveforms of the two controllers under the fluctuation test. Figure 8 It can be seen that the SSMC reaches the target position faster than the SMC, and the maximum value of the SSMC control current is significantly smaller than the maximum value of the SMC control current. In addition, the SSMC control current waveform is smooth and has no jitter, while the SMC control current has large jitter, which will cause great damage to the actuator and affect the life of the actuator.

[0160] Now consider the disturbance of the AMBs system and assume that f d =sin(20πt)-10. In order to stabilize the system, a controller that takes lumped disturbance into consideration is used, and its expression is:

[0161]

[0162] Fig.10 , Fig.11 The displacement and current waveforms of the two controllers are tested considering the fluctuations under lumped disturbances. Fig.10 In the figure, SSMC reaches the target position faster than SMC, and the maximum value of SSMC control current is smaller than that of SMC control current. However, due to the existence of lumped disturbance, SSMC control current also has certain jitter, and the jitter of SMC control current becomes larger.

[0163] In order to suppress the lumped disturbance from causing the controller to vibrate, an observer is now used to observe and compensate the lumped disturbance. Prior to this, a simulation analysis of NESO and improved INESO is first performed. Fig.12 Denote the two observers for the lumped disturbance f d =sin(2πft), where the frequency f increases from 0 to 300. Fig.11 It can be seen that the observation accuracy of the two observers becomes weaker as the frequency f increases, but it is obvious that the observation accuracy of the designed INESO is far superior to that of the traditional NESO.

[0164] Through the analysis and verification of the observer, the INESO designed by the present invention is now used to observe the lumped disturbance and compensate the observed value. Fig.13 , Fig.14 They are the displacement waveform and control current waveform after compensation, respectively. The SSMC still reaches the target position faster than the SMC, and the control current jitter of the SSMC is greatly weakened. The jitter of the SMC caused by the lumped disturbance is also weakened.

[0165] Those skilled in the art should understand that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can take the form of a complete hardware embodiment, an embodiment combining software and hardware aspects.

[0166] Unless otherwise specified, the working modes or control modes involved in the above embodiments are all conventional working modes or control modes in the art.

[0167] Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0168] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Other modifications or equivalent substitutions made to the technical solution of the present invention by ordinary technicians in the field should be included in the scope of the claims of the present invention as long as they do not depart from the spirit and scope of the technical solution of the present invention.

Claims

1. A control system for an active electromagnetic bearing, characterized in that: include: Super-helical sliding mode controller is used to input displacement reference value x r , rotor displacement x 1. Displacement error e 1. Calculate the control quantity u ; The first subtractor is used to output the control quantity of the super-helical sliding mode controller u and the observer observation z 3 Pass m / k i After gain, make a difference to get the final control amount u ed ; Active electromagnetic bearing system for inputting the final control quantity u ed , and we get the electromagnetic force f x ; The second subtractor is used to input the electromagnetic force f x and disturbance force F d Make a difference and get the resultant force on the rotor; The product-integral controller is used to input the rotor force and combine it with 1 / m Multiply and integrate twice to get the rotor displacement x 1; Nonlinear extended state observer for input k i u ed / m With rotor displacement x 1. Calculate z 3, among which k i is the current stiffness coefficient, z 3 is the expansion state x The observed value of 3, x 3 is the lumped disturbance, x 2 for x Differential of 1; The reaching law of the super-helical sliding mode controller is: in, γ >1,0< , >0, γ、 and are all constants; k 1 and k 2 are all constants greater than 0; s is the sliding surface and also the system state; The control quantity of the super helical sliding mode controller u The calculation formula is: in , f d is the aggregate interference, u is the control variable of the super-helical sliding mode controller, k s is the displacement stiffness coefficient, k i is the current stiffness coefficient, k 1>0、 k 2>0, s is the sliding surface, m is the rotor mass, x 1 is the rotor displacement value, x 2 for x The differential of 1, x r is the displacement reference value, e 1 is the deviation between the displacement reference value and the rotor displacement value; a >0, 1< b <2; M is the upper limit of the disturbance, that is, the maximum value of the disturbance.

2. The control system of an active electromagnetic bearing according to claim 1, characterized in that: The final control amount u ed The calculation formula is: 。 3. The control system of an active electromagnetic bearing according to claim 1, characterized in that: The extended state equation of the nonlinear extended state observer is: in, x 2 for x The differential of 1, x 3 is the lumped disturbance; z 1. z 2. z 3 are system status x 1. x 2. x 3; θ1, θ2 and θ3 are all observation errors, θ1= z 1- x 1. θ2 = z 2- x 2. θ3 = z 3- x 3; β 1. β 2. β 3 is the observer gain; u1, u2, and u3 are the nonlinear functions about θ1 to be designed.

4. The control system of an active electromagnetic bearing according to claim 3, characterized in that: The nonlinear extended state observer comprises: The first adder is used to input k i u / m , k s / m and z 3. Calculate the sum of the three items; The first integrator is used to k i u / m , k s / m and z Integrate the sum of 3 to get z 2; The second integrator is used to z 2Integrate to get z1; The first subtractor of the observer is used to z 1 and the input x 1 is subtracted to obtain the observation error θ1; The second adder is used to calculate β 3 u 3(θ1) integral, β 2 u 2(θ1) ratio, β 1 u The sum of the negative values ​​of the derivatives of 1(θ1) gives z 3.

5. The control system of an active electromagnetic bearing according to claim 1, characterized in that: The super spiral sliding mode controller comprises: Symbolic function for inputting sliding surface s Positive and negative calculations; Integrator, used to integrate sign( s ) points; The first amplifier is used to adjust the sign( s ) multiplied by the integral k 3. Get ; Power sign function, used to apply power to the input sliding surface s Calculate the power and positive and negative, and get ; The second amplifier is used to Multiply k 4. Get ; Subtractor, used for and Taking the difference, we get the super-helical sliding mode reaching law , where k3 is the integral gain coefficient and k4 is the exponential gain coefficient.

6. A method for using a control system of an active electromagnetic bearing according to any one of claims 1 to 5, characterized in that: The following steps are involved: Set the displacement reference value x r , rotor displacement x 1. Displacement error e 1. Input the super-helical sliding mode controller to calculate the control quantity u ; Will k i* u ed / m With rotor displacement x 1-input nonlinear extended state observer obtains mz 3 / k i ; The amount of control u and mz 3 / k i Make a difference and get the final control amount u ed ; The final control volume u ed Input to the AMBs magnetic levitation system to obtain electromagnetic force f x ; The electromagnetic force f x and disturbance force F d Difference, get the resultant force on the rotor, divide the resultant force on the rotor by the rotor mass m , and integrate the result twice to obtain the rotor displacement x 1.

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