Method for controlling horizontal movement of magnetic suspension ruler

Abstract

The invention belongs to the technical field of magnetic levitation rulers, and relates to a magnetic levitation ruler horizontal motion control method, which comprises the following steps: establishing a mathematical model of a horizontal system; according to the constructed mathematical model, estimating the position of the rotor iron core through induced electromotive force derivation to obtain the horizontal position and the deflection angle value of the rotor iron core; rotor iron core horizontal motion control based on SYSTD is carried out; and setting the parameters of the horizontal control system of the magnetic suspension ruler system. A mathematical model is established based on a magnetic circuit and a dynamics principle, the problems of nonlinearity and strong coupling of a magnetic levitation ruler horizontal displacement system are solved by applying an improved active-disturbance-rejection control algorithm, and a system structure is simplified by utilizing a position-sensorless control technology. According to the method, unknown dynamic and external disturbance is taken as total disturbance, and real-time estimation and compensation are carried out through an extended state observer; the ADRC not only can adjust errors, but also can actively process uncertain factors of the system and improve the control efficiency, does not depend on an accurate mathematical model, and is high in adaptability and robustness in a complex system.

Description

Technical Field

[0001] The present invention belongs to the technical field of magnetic levitation rulers, and in particular relates to a method for controlling the horizontal motion of a magnetic levitation ruler. Background Art

[0002] The linear measurement system of a coordinate measuring machine (CMM) consists of a grating scale, a servo motor, and a linear motion mechanism, enabling the measurement of free-form surface components. The magnetic scale's core actuator has autonomous displacement and displacement measurement capabilities, simplifying this measurement system. However, during measurement, the core actuator employs fixed-step linear motion, with a microcontroller counting the steps to determine displacement. This directly impacts the scale's measurement accuracy, as the core's horizontal positioning accuracy directly impacts the scale's measurement accuracy.

[0003] Research has found that combining ADRC with an explicit complementary filter (ADRC-ECF) can address the problem of yaw angle interference suppression in maglev trains. Regarding ECF noise filtering, research has shown that ADRC has stronger interference rejection than PID and more accurate fixed-angle steering. Researchers designed a dual-time-scale ADRC for a specific system to achieve performance recovery, and their effectiveness was verified through experiments with a magnetic levitation ball. The rotor of a maglev turbine is subject to various disturbances, and traditional PID control has limitations. The linear active disturbance rejection controller (LADRC) improves on the shortcomings of PID, but it also suffers from issues such as overshoot. The improved LADRC suppresses uncertainty through a special design, facilitating engineering applications. The tracking differentiator (TD) of ADRC is essential in control systems. Real-world signals contain noise, and traditional differential calculations amplify this noise. TD can suppress this noise, smooth the input signal, and facilitate smooth system transitions. However, TD can experience response lag when processing rapidly changing signals, and the computational complexity of nonlinear TD limits its application in resource-constrained systems. DTOC-TD based on the FHAN algorithm is commonly used in motor control, but traditional FHAN algorithms struggle to balance tracking and filtering capabilities. In the electric vehicle sector, researchers have proposed using the MTD-DADRC controller to address speed regulation issues in permanent magnet synchronous motors. This controller, used for speed loop control, improves system stability and noise immunity, enhances motor speed tracking performance, and, compared to traditional PI controllers, shortens shift speed regulation time and reduces shift shock. Other researchers have proposed using the Active Disturbance Rejection Fractional-Order Controller (ADRFOC) for time-delay systems, enabling independent control of servo and regulation. This controller, composed of Field-Order Operation (FOC) and Medium-Order Operation (MESO), has been validated through mathematical derivation. Experiments on an air-floating motion platform have demonstrated superior performance to typical time-delay ADRC and SIMC-PID controllers.

[0004] However, when using a magnetic levitation scale system for measurement, the mover core uses a fixed-step motion method, resulting in high-frequency fluctuations in its position feedback signal. Classic TD and MTD methods struggle to meet the required response speed when processing such rapidly changing signals, resulting in tracking delay. This impacts the real-time tracking accuracy of the mover core position, further reducing the positioning accuracy of the magnetic levitation scale's horizontal control system, making it impossible to quickly and accurately obtain the mover core's position information. Therefore, a novel magnetic levitation scale horizontal motion control method is urgently needed to effectively address this issue. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for controlling the horizontal motion of a magnetic levitation ruler, establish a mathematical model based on the magnetic circuit and dynamic principles, and use an improved anti-disturbance control algorithm to solve the problems of nonlinearity and strong coupling of the horizontal displacement system of the magnetic levitation ruler.

[0006] The purpose of the present invention is achieved through the following technical solutions:

[0007] A method for controlling the horizontal motion of a magnetic levitation ruler comprises the following steps:

[0008] Step 1: Establish a mathematical model of the horizontal system:

[0009] The permanent magnet of the magnetic levitation scale system is set as the front side of the magnetic levitation scale system, and the suspension control coil is set as the rear side of the magnetic levitation scale system. When energized, coil Co1 generates a forward propulsion force, driving one end of the mover core forward. Coil Co3 drives the other end of the mover core forward. Coils Co2 and Co4 generate a backward propulsion force, driving the mover core backward. There is no wire in the air gap magnetic field in the middle of the mover core, so no reverse interference force can be obtained. The right-side thrust and the left-side thrust of the mover core are calculated based on the Ampere force calculation formula. Newton's second law of motion is used to derive the rigid body dynamics equation of the horizontal system of the mover core. The horizontal displacement coordinate system is converted into the center of mass coordinate system to obtain the horizontal system analysis model of the magnetic levitation scale system.

[0010] Step 2: Based on the mathematical model of step 1, the position of the mover core is estimated by deriving the induced electromotive force to obtain the horizontal position y of the mover core. b , and then the deflection angle ψ is obtained by the gyroscope z The value of

[0011] Step 3: The horizontal position y obtained in step 2 b and deflection angle ψ z , construct the differential tracker SYSTD and perform horizontal motion control of the mover core based on SYSTD;

[0012] Step 4: Parameter adjustment of the horizontal control system of the magnetic levitation scale system is performed, including parameter adjustment of SYSTD, ESO and NLSEF.

[0013] Furthermore, in step 1, the right thrust of the mover core is:

[0014] F rt =F t1 -F t2 (1)

[0015] Where, F t1 is the Ampere force generated by the current flowing through coil Co1, F t2 It is the Ampere force generated by the coil Co2 being energized;

[0016] According to the Ampere force calculation formula, the right thrust F can be obtained rt The calculation formula is:

[0017] F rt =nB r Li cr (2)

[0018] Where n is the sum of the number of turns of the right forward horizontal control coil and the number of turns of the right backward horizontal control coil, B r is the sum of the air gap magnetic field on the right, L is the length of the single-turn horizontal control coil in the air gap magnetic field, i cr is the current of the horizontal control coil on the right side of the mover core; i cr The current i of the right forward horizontal control coil Co1 c1 and the current i of the right rear horizontal control coil Co2 c2 Composition, i c1 and i c2 There are two currents with opposite directions. Looking from the front of the magnetic levitation scale system to the two horizontal control coils Co1 and Co2 on the right, let the current on Co1 coil i c1 When the flow is counterclockwise, its value is positive, which can ensure that the horizontal control coil Co1 generates a forward thrust F t1 ; Assume that the current i on the Co2 coil c2 When the flow is clockwise, its value is negative, which can ensure that the horizontal control coil Co2 produces a backward thrust, then:

[0019]

[0020] When the mover core accelerates forward, i c2 is zero, then, let i cr =i c1 , when the rotor core accelerates backward, i c1 is zero, then, let i cr =i c2 .

[0021] Furthermore, in step 1, the left side thrust of the mover core is:

[0022] F lt =F t3 -F t4 (4)

[0023] Where, F t3 is the Ampere force generated by the current flowing through the coil Co3, F t4 It is the Ampere force generated by the current flowing through the coil Co4;

[0024] According to the Ampere force calculation formula, the left thrust F can be obtained lt The calculation formula is:

[0025] F lt =nB l Li cl (5)

[0026] Where n is the sum of the number of turns of the left forward horizontal control coil and the number of turns of the left backward horizontal control coil, B l is the sum of the air gap magnetic fields on the left, L is the length of the single-turn horizontal control coil in the air gap magnetic field, i cl is the current of the horizontal control coil on the left side of the mover core; i cl The current i of the left forward horizontal control coil Co3 c3 and the current i of the right rear horizontal control coil Co4 c4 Composition. c3 and i c4 There are two currents with opposite directions. Looking from the front of the magnetic levitation scale system to the two horizontal control coils Co3 and Co4 on the left, let the current on the Co3 coil i c3 When it flows counterclockwise, its value is positive, which can ensure that the horizontal control coil Co3 produces a forward thrust; suppose the current i on the Co4 coil is c4 When the flow is clockwise, its value is negative, which can ensure that the horizontal control coil Co4 produces a backward thrust, then:

[0027]

[0028] When the mover core accelerates forward, i c4 is zero, then, let i cl =i c3 , when the rotor core accelerates backward, i c3 is zero, then, let i cl =i c4 .

[0029] Furthermore, in step 1, Newton's second law of motion is used to derive the rigid body dynamics equation of the horizontal system of the mover core, specifically:

[0030]

[0031] The mover core is only subjected to horizontal thrust in the horizontal direction. According to Newton's second law, F lt and F rt Horizontal displacement y on the left side of the mover core bl and the horizontal displacement y on the right side of the mover core br Related, in the horizontal displacement as the research point [y bl ,y br ] coordinate system, according to formula (8), it is located at [y b ,ψ z ] coordinate system, the horizontal displacement coordinate system is converted into the center of mass coordinate system by the following formula;

[0032]

[0033] After sorting out, the horizontal system analysis model of the magnetic levitation scale system is obtained:

[0034]

[0035] The horizontal system of the magnetic levitation scale system is the mathematical model of the magnetic levitation scale system. Its input i cl and i cr , determines the horizontal position y of the mover core b and deflection angle ψ z value.

[0036] Furthermore, in step 2, the horizontal position y of the rotor core b The estimation steps are as follows:

[0037] Connect the two sets of measuring coils on the left in series to obtain the induced electromotive force e on the left l The two sets of measuring coils on the right are connected in series to obtain the induced electromotive force e on the right. r , the calculation formula of the induced electromotive force when the left measuring coil cuts the magnetic lines of force is:

[0038]

[0039] Where B u is the magnetic field strength of the air gap on the upper left side of the rotor core, B d is the air gap magnetic field strength on the lower left side of the mover core, L is the length of the measuring coil in the air gap magnetic field, and S is the displacement of the mover core;

[0040] The mutual inductance M is estimated according to the mutual inductance calculation formula:

[0041]

[0042] Where, Lc is the inductance of the measuring coil; L k is the inductance of the horizontal control coil. L can be calculated c ≈12272μH, L k ≈122μH, M≈1.2×10 -3 H, measuring the induced electromotive force e generated by mutual inductance in the coil c The calculation steps are as follows:

[0043]

[0044] Where i c Is the current of the horizontal control coil. The mover core adopts a fixed-step stepping motion mode, so the current of the horizontal control coil is a square wave signal, which will only cause e on the rising and falling edges. c There is a large fluctuation, and the fluctuation time is affected by the time constant τ of the horizontal control coil k Impact:

[0045]

[0046] Where R is the equivalent resistance of the horizontal control coil, which is 1.4Ω. k It is about 8.7μs, and the rising and falling edges of the horizontal control coil current are 6 times τ k , i.e. 52.2μs;

[0047] SYSTD was used to observe B u 、B d and e l These three signals are low-pass filtered to reduce noise, and the air gap magnetic field intensity and induced electromotive force values ​​are obtained. Substituting them into formula (10), the estimated position value y of the left end of the rotor core is obtained. bl , the estimated value y of the right end position of the rotor core br The same method can be used to obtain y bl 、y br and ψ z Substitute them into formula (8) to estimate y b .

[0048] Furthermore, in step 3, the specific steps of constructing the differential tracker SYSTD are as follows:

[0049] Use the following elementary functions:

[0050]

[0051] Among them, a4>0, a5>0, a4∈R, a5∈R, it can be deduced that:

[0052]

[0053] Construct the second-order system S0:

[0054]

[0055] Design SYSTD time-invariant system S:

[0056]

[0057] Determine whether the zero solution of the system is globally asymptotically stable;

[0058] When the parameter a 41 , a 51 , a 42 , a 52 When both are greater than zero, the system S0 satisfies the Lyapunov global asymptotic stability condition, namely:

[0059]

[0060] Design SYSTD based on the function sys() and construct system S2 as follows:

[0061]

[0062] If a 41 、a 51 、a 42 、a 52 are all positive, and the input signal r(t)(t∈[0,+∞]) Bounded, for any finite time T>0, the solution of system S2 satisfies:

[0063]

[0064] x1(t) converges to r(t), and x2(t) converges to the generalized differential of r(t);

[0065] System S2 is the perturbation form of system S1, and system S2 (19) is SYSTD.

[0066] Furthermore, if in the real domain R 2 There exists an infinitely increasing positive or negative definite function V(x), and in the full phase space, the total derivative of V(x) along the solution of the system S with respect to time t is always negative or always positive, satisfying If the set of points contains only the origin, then the zero solution of the system is globally asymptotically stable.

[0067] Furthermore, according to the active disturbance rejection control law, formula (9) is changed to:

[0068]

[0069] Where w y (t) and w z1 (t) is the equivalent disturbance of the system, which includes coupling and disturbance, ic l and i cr is the control quantity, b y and b z They are the control variables i cl and i cr Control parameters of

[0070] The change of the current of the four horizontal control coils is obtained; the active disturbance rejection controller can w y (t) and w z1 (t) is considered as a comprehensive disturbance of the system, which can be observed and compensated through its ESO; if the control quantity is selected:

[0071]

[0072] After compensation, formula (15) can be rewritten as:

[0073]

[0074] After compensation, y b and ψ z Achieve decoupling and controllability;

[0075] The ESO of the magnetic levitation scale system level control system is as follows:

[0076]

[0077] Where:

[0078]

[0079] Where z1(k), z2(k), and z3(k) are the state variables of the ESO. z1(k) and z2(k) are used to track the state variables of the system, and z3(k) is used to track the state variables of the total disturbance. e1 , β e2 , β e3 is the gain of ESO;

[0080] a1 and δ are unknown parameters. If a1 is less than 1, the function has nonlinear characteristics such as large error and small gain or small error and large gain. δ represents the linear range.

[0081] Furthermore, the following NLSEF is used for the horizontal control system of the magnetic levitation scale system:

[0082]

[0083] Where e1(k) and e2(k) are the deviation and differential between the expected transition process and the estimated value of the system output, a2, a3, δ f1 is the relevant parameter of fal, u0 is the output of NLSEF; b0 is the compensation coefficient;

[0084] ESO is used to track the representative disturbance state variable z3(k) extended from the original system. The control quantity is used to compensate for the disturbance and converted into the control quantity of the integral series. The control quantity is:

[0085]

[0086] From formula (26), we can see that u y＝ u y0- z y3 / b y0 ;u p＝ u p0- z p3 / b p0 ,u y and the horizontal control coil current i cl Proportional to u p and the horizontal control coil current i cr Directly proportional.

[0087] Furthermore, step 4, parameter setting of SYSTD, includes the following steps;

[0088] Assume that the system input signal is Asin(ωt) and define M(A) to describe the nonlinear function f(t) = sys(t):

[0089]

[0090] Among them, e1 and f1 are the first-order Fourier coefficients, that is:

[0091]

[0092] Since f(t) is an odd function, e1=0, let x1(t)-r(t)=Asin(ωt), combined with formula (27), the function sys(x1(t)-r(t),a 41 ,a 51 ) can be transformed into:

[0093]

[0094] The function sys(x2(t) / R,a4,a5) can also be transformed into:

[0095]

[0096] The linearized form of the nonlinear system S2 can be expressed as:

[0097]

[0098] It can be deduced that:

[0099]

[0100] Among them, M1>0, M2>0;

[0101] First, select an appropriate R value so that the bandwidth of SYSTD can cover the spectrum of the measured signal; then, select appropriate M1 and M2 to satisfy formula (32); then adjust M1 and M2 to further balance the contradiction between SYSTD filtering capability and response speed; adjust parameter a 51 and a 52 , adjust the SYSTD amplitude; then adjust the parameter a 41 and a 42 , adjust SYSTD fast tracking capability;

[0102] To adjust the parameters of ESO, first adjust β e3 , and then adjust β from small to large e1 and β e2 ,Before adjusting these three parameters, it is necessary to determine the δ value, δ = h;

[0103] NLSEF parameter tuning, including β f1 , β f2 and adjustment of b0.

[0104] Compared with the prior art, the present invention has the following beneficial effects:

[0105] The present invention establishes a mathematical model based on magnetic circuit and dynamic principles, employs an improved active disturbance rejection control (ADRC) algorithm to address the nonlinear and strong coupling issues of the magnetic levitation scale horizontal displacement system, and simplifies the system structure using position sensorless control technology. Active disturbance rejection control (ADRC) is an advanced control strategy. It treats unknown dynamics and external disturbances as total disturbances, estimating and compensating them in real time through an extended state observer (ESO). ADRC not only regulates errors but also proactively addresses system uncertainties, improving control efficiency. It does not rely on precise mathematical models and exhibits strong adaptability and robustness in complex systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0106] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0107] Figure 1 is a schematic diagram of the horizontal driving force;

[0108] Figure 2 This is a schematic diagram of the measurement coil winding on the left front side of the mover core;

[0109] Figure 3 It is the structural diagram of the horizontal control system;

[0110] Figure 4 The tracking results of SYSTD under different R values;

[0111] Figure 5 shows the effect of sys() parameters on SYSTD tracking results;

[0112] Figure 6 Comparison of tracking characteristics of three TDs;

[0113] Figure 7 The comparison chart of filtering characteristics of three types of TD;

[0114] Figure 8 This is the simulation diagram of the horizontal control system;

[0115] Figure 9 for Figure 8 A partial enlarged view of

[0116] Figure 10 This is the simulation diagram of the horizontal rotation angle of the mover core;

[0117] Figure 11 is the response curve of displacement at starting;

[0118] Figure 12 This is an enlarged view of the overshoot portion of the displacement response curve at startup;

[0119] Figure 13 This is the response curve of the angle at startup. DETAILED DESCRIPTION

[0120] The present invention will be further described below in conjunction with embodiment:

[0121] The present invention will be further described in detail below with reference to the accompanying drawings and examples. It will be understood that the specific embodiments described herein are intended only to illustrate the present invention and are not intended to limit the present invention. It should also be noted that, for ease of description, the accompanying drawings only illustrate portions relevant to the present invention, not all structures.

[0122] It should be noted that similar reference numerals and letters represent similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings. At the same time, in the description of the present invention, the terms "first", "second", etc. are used only to distinguish the description and should not be understood as indicating or implying relative importance.

[0123] At present, when the magnetic levitation scale system is measuring, the mover core adopts a fixed-step stepping motion mode, which has the problem of tracking delay and cannot quickly and accurately obtain the position information of the mover core. In the magnetic levitation scale system, it is very important to obtain accurate position and speed information. In the field of motor control, in the study of permanent magnet linear synchronous motor (PMLSM), the method of combining ADRC speed controller and AFO position estimator can improve the position estimation accuracy, which can be used in the magnetic levitation scale system to improve the position estimation accuracy of the mover core. The ADRC enhanced speed sensorless vector control method of the permanent magnet synchronous motor (PMSM) has strong anti-interference ability and helps to improve the anti-interference ability of the magnetic levitation scale system. The new hybrid algorithm of the switched reluctance motor (SRM) can accurately estimate the motor state and is applied to the magnetic levitation scale system to improve its measurement accuracy. To this end, the present invention proposes a horizontal motion control method of the magnetic levitation scale, which effectively solves the problem of tracking the position feedback signal of the mover core.

[0124] The method for controlling the horizontal motion of a magnetic levitation ruler of the present invention comprises the following steps:

[0125] Step 1: Establish a mathematical model of the horizontal system.

[0126] The permanent magnet of the magnetic levitation scale system serves as the front side of the system, while the suspension control coil serves as the rear side. When energized, coil Co1 generates a forward thrust, driving one end of the mover core forward. Similarly, coil Co3 drives the other end of the mover core forward. Coils Co2 and Co4 generate a backward thrust, driving the mover core backward. There are no conductors in the air gap magnetic field between the mover cores, so no reverse interference force can be generated.

[0127] The schematic diagram of horizontal driving force is as follows Figure 1 As shown in the figure, F t1 is the Ampere force generated by the current flowing through coil Co1, F t2 is the Ampere force generated by the current flowing through the coil Co2, F t3 is the Ampere force generated by the current flowing through the coil Co3, F t4 It is the Ampere force generated by the coil Co4 being energized.

[0128] Therefore, the right thrust of the mover core is:

[0129] F rt =F t1 -F t2 (1)

[0130] According to the Ampere force calculation formula, the right thrust F can be obtained rt The calculation formula is:

[0131] F rt=nB r Li cr (2)

[0132] Where n is the sum of the number of turns of the right forward horizontal control coil and the number of turns of the right backward horizontal control coil. The number of turns of the two sets of coils is 15 each, for a total of 30 turns. r is the sum of the air gap magnetic fields on the right, and L is the length of the single-turn horizontal control coil in the air gap magnetic field.

[0133] i cr is the current of the horizontal control coil on the right side of the mover core, and the current i of the right forward horizontal control coil Co1 c1 and the current i of the right rear horizontal control coil Co2 c2 Composition. c1 and i c2 These are two currents with opposite directions. Looking from the front of the magnetic levitation scale system to the two horizontal control coils Co1 and Co2 on the right, let the current on Co1 coil i c1 When the flow is counterclockwise, its value is positive, which ensures that the horizontal control coil Co1 generates a forward thrust F t1 ; Assume that the current i on the Co2 coil c2 When the flow is clockwise, its value is negative, which can ensure that the horizontal control coil Co2 produces a backward thrust. Then:

[0134]

[0135] When the mover core accelerates forward, i c2 is zero, then let i cr =i c1 When the mover core accelerates backward, i c1 is zero, then let i cr =i c2 .

[0136] Similarly, the thrust on the left side of the mover core is:

[0137] F lt =F t3 -F t4 (4)

[0138] According to the Ampere force calculation formula, the left thrust F can be obtained lt The calculation formula is:

[0139] F lt =nB l Li cl (5)

[0140] Where n is the sum of the number of turns of the left forward horizontal control coil and the number of turns of the left rearward horizontal control coil. The number of turns of each set of coils is 15, for a total of 30 turns. lis the sum of the air gap magnetic fields on the left. L is the length of the single-turn horizontal control coil in the air gap magnetic field.

[0141] i cl is the current of the horizontal control coil on the left side of the mover core, and the current i of the left forward horizontal control coil Co3 c3 and the current i of the right rear horizontal control coil Co4 c4 Composition. c3 and i c4 These are two currents with opposite directions. Looking from the front of the magnetic levitation scale system to the two horizontal control coils Co3 and Co4 on the left, let the current on the Co3 coil i c3 When it flows counterclockwise, its value is positive, which can ensure that the horizontal control coil Co3 produces a forward thrust; suppose the current i on the Co4 coil is c4 When the flow is clockwise, its value is negative, which can ensure that the horizontal control coil Co4 produces a backward thrust. Then:

[0142]

[0143] When the mover core accelerates forward, i c4 is zero, then let i cl =i c3 When the mover core accelerates backward, i c3 is zero, then, let i cl =i c4 .

[0144] The horizontal control coil on the left is far away from the horizontal control coil on the right. The magnetic field interference between them is negligible. Therefore, there is no coupling between the thrust forces at both ends of the mover core.

[0145] The mover core has two degrees of freedom in the horizontal system: (1) vertical motion in the Y direction; (2) rotation angle ψ around the Z axis with the center of mass of the mover core as the center of the circle z .

[0146] The present invention uses Newton's second law of motion to derive the rigid body dynamics equation of the horizontal system of the mover core:

[0147]

[0148] The mover core is only subjected to horizontal thrust in the horizontal direction. According to Newton's second law, F lt and F rt Horizontal displacement y on the left side of the mover core bl and the horizontal displacement y on the right side of the mover core br Related, in the horizontal displacement as the research point [y bl ,y br] coordinate system. However, formula (7) is in the [y b ,ψ z ] coordinate system, the horizontal displacement coordinate system needs to be converted into the center of mass coordinate system through coordinate transformation.

[0149]

[0150] The above formula can be used to convert the horizontal displacement coordinate system into the center of mass coordinate system. After sorting, the horizontal system analysis model of the magnetic levitation scale system is obtained:

[0151]

[0152] It can be seen from formula (9) that the horizontal system of the magnetic levitation scale system is a nonlinear system with dual input and dual output, that is, the mathematical model of the magnetic levitation scale horizontal system. Its input i cl and i cr , determines the horizontal position y of the mover core b and deflection angle ψ z The value of is large, and the system is strongly coupled. Conventional linear control methods cannot effectively control the system. The active disturbance rejection control (ADRC) method is more suitable for the horizontal system of the magnetic levitation scale system.

[0153] Step 2: Based on the mathematical model of step 1, the position of the mover core is estimated by the induced electromotive force derivation method to obtain the horizontal position y of the mover core. b . Declination angle ψ z The value of can be obtained through the nine-axis gyroscope available on the market.

[0154] Horizontal position y of the mover core b The specific estimation method is as follows: the measuring coils on the left rear side, right front side, and right rear side of the rotor core are installed in the same way. Among them, port AB is used to measure the induced electromotive force.

[0155] Connecting the two sets of measuring coils in series on the left side can obtain the induced electromotive force e on the left side l The two sets of measuring coils on the right are connected in series to obtain the induced electromotive force e on the right. r The calculation formula for the induced electromotive force when the left measuring coil cuts the magnetic lines of force is:

[0156]

[0157] Where B u is the magnetic field strength of the air gap on the upper left side of the rotor core, B d is the magnetic field strength in the air gap on the lower left side of the mover core, L is the length of the measuring coil in the air gap magnetic field. S is the displacement of the mover core. The induced electromotive force e r The calculation method of e lThe calculation method is the same as that of , and will not be repeated here.

[0158] In addition, since the measuring coil is wound along the horizontal control coil, the mutual inductance system k between the measuring coil and the horizontal control coil is infinitely close to 1. Therefore, there is mutual inductance between the measuring coil and the horizontal control coil. The mutual inductance M can be estimated according to the mutual inductance calculation formula:

[0159]

[0160] Where, L c is the inductance of the measuring coil; L k is the inductance of the horizontal control coil. L can be calculated c ≈12272μH, L k ≈122μH. Therefore, M≈1.2×10 -3 H. Measure the induced electromotive force e generated by mutual inductance in the coil c The calculation method is as follows:

[0161]

[0162] Where i c Is the current of the horizontal control coil. The mover core adopts a fixed-step stepping motion mode, so the current of the horizontal control coil is a square wave signal, which will only cause e on the rising and falling edges. c There is a large fluctuation. The fluctuation time is affected by the time constant τ of the horizontal control coil. k Impact:

[0163]

[0164] Where R is the equivalent resistance of the horizontal control coil, which is 1.4Ω. k To ensure the accuracy of the calculation, the rising and falling edges of the horizontal control coil current are taken as 6 times of τ. k , i.e. 52.2μs. According to the above method, e c The frequency of the waveform during this period is much higher than the induced electromotive force e l and e r , the amplitude is also large, which can be solved by low-pass filtering noise reduction.

[0165] The present invention utilizes the following SYSTD to observe B u 、B d and e l After completing low-pass filtering and noise reduction on these three signals, we can obtain more accurate values ​​of the air gap magnetic field intensity and induced electromotive force. After substituting them into formula (10), we can calculate a more accurate estimate of the left end position of the mover core y bl The estimated value y of the right end position of the mover corebr The same method can be used to obtain y bl 、y br and ψ z Substituting them into formula (8) respectively can estimate yb.

[0166] Step 3: The horizontal position y obtained in step 2 b and deflection angle ψ z , perform horizontal motion control of the mover core based on SYSTD.

[0167] For the coupled system of magnetic levitation scale system and horizontal system, the present invention solves the decoupling problem in the magnetic levitation scale system and horizontal system by using the characteristics of the automatic disturbance rejection controller, such as low requirement for modeling accuracy and ability to effectively compensate for comprehensive disturbances. b and ψ z ) are regarded as disturbances, which are observed together through the extended state observer and their sum effect (i.e. the total disturbance of the system) is compensated, thereby realizing decoupling control. The essence of this compensation effect is an anti-disturbance effect. This control method has low requirements on the model and is easy to implement. It can solve the decoupling and disturbance suppression problems in horizontal control.

[0168] The ADRC controller for a horizontal control system (LCS) primarily consists of a tracking differentiator (TD), an extended state observer (ESO), and a nonlinear state error feedback control law (NLSEF). However, the differential tracker (TD) in conventional ADRC is not suitable for the stepping motion of the mover core. Therefore, it is necessary to improve the traditional TD and construct a new differential tracker (SYSTD).

[0169] The present invention adopts elementary functions, which are defined as follows:

[0170]

[0171] Among them, a4>0, a5>0, a4∈R, a5∈R. It can be deduced that:

[0172]

[0173] Therefore, the following second-order system S0 can be constructed:

[0174]

[0175] Design SYSTD time-invariant system S:

[0176]

[0177] If in the real domain R 2 Inside:

[0178] (1) There exists an infinitely increasing positive definite function (or negative definite function) V(x);

[0179] (2) There exists in the full phase space that the total derivative of V(x) along the solution of the system S with respect to time t is always negative (or always positive);

[0180] (3) Satisfaction The point set of contains only the origin.

[0181] Then the zero solution of the system is globally asymptotically stable.

[0182] When the parameter a 41 , a 51 , a 42 , a 52 When both are greater than zero, the system S0 satisfies the Lyapunov global asymptotic stability condition, namely:

[0183]

[0184] Next, the present invention designs SYSTD based on the function sys(). The system S2 is constructed as follows:

[0185]

[0186] If a 41 、a 51 、a 42 、a 52 are all positive, and the input signal r(t)(t∈[0,+∞]) is bounded, so for any finite time T>0, the system S2 satisfies:

[0187] (1) The solution of system S2 satisfies:

[0188]

[0189] Furthermore, x1(t) converges to r(t), and x2(t) converges to the generalized differential of r(t).

[0190] (2) System S2 is the perturbation form of system S1.

[0191] System S2 (19) is SYSTD. Obviously, the dynamic performance of SYSTD is affected by the parameter a. 41 、a 51 、a 42 、a 52 , R. Therefore, it is necessary to adjust the parameters of SYSTD to ensure that it is suitable for the horizontal system of the magnetic levitation ruler and complete the improvement of ADRC. Figure 3 In the example above, two SYSTDs are used instead. Figure 3 According to formula (19), Figure 3 v in y0 and v p0 are the input signals r(t) of the two SYSTDs respectively. y1 、v y2 and v p1 、v p2 They are x1(t) and x2(t) of the two SYSTDs respectively.

[0192] Extended State Observer (ESO):

[0193] According to the active disturbance rejection control law, formula (9) is changed to:

[0194]

[0195] Where w y (t) and w z1 (t) is the equivalent disturbance of the system, which includes coupling and disturbance, ic l and i cr is the control quantity, b y and b z They are the control variables i cl and i cr control parameters.

[0196] Thus, the change of the current of the four horizontal control coils is obtained. y (t) and w z1 (t) is considered as a comprehensive disturbance of the system, which can be observed and compensated through its ESO.

[0197]

[0198] After compensation, formula (15) can be rewritten as:

[0199]

[0200] After compensation, y b and ψ z Achieve decoupling and controllability. d For example, it can be seen from formula (23) that the system passes i cl To control y d In formula (23), i cl After parameter adjustment, it becomes w z1 (t) A portion of the equivalent perturbation is then observed and compensated by ESO.

[0201] Similarly, control another degree of freedom ψ z i cr , which will also cause dIn formula (23), i cr After parameter adjustment, it becomes w y (t) is a part of the equivalent disturbance, which is then observed and compensated by the ESO. The ESO of the level control system of the magnetic levitation scale system is as follows:

[0202]

[0203] Where:

[0204]

[0205] Where z1(k), z2(k), and z3(k) are the state variables of the ESO. z1(k) and z2(k) are used to track the state variables of the system, and z3(k) is used to track the state variables of the total disturbance. e1 , β e2 , β e3 is the gain of ESO.

[0206] a1 and δ are parameters to be determined. If a1 is less than 1, the function exhibits nonlinear characteristics, such as large errors with small gains and small errors with large gains. δ represents the linear range, intended to avoid oscillations caused by very small errors with large gains.

[0207] Figure 3 b in y0 and b p0 They are b0 and u of two ESOs respectively. y and u p are u(k) of two ESOs, b0 and u(k) are the inputs of ESO b0u(k). y and u p It is also the input of LCS. y1 、z y2 、z y3 and z p1 、z p2 、z p3 They are z1, z2 and z3 of the two ESOs respectively.

[0208] Nonlinear state error feedback control law (NLSEF):

[0209] The following NLSEF is used for the horizontal control system of the magnetic levitation scale system:

[0210]

[0211] Where e1(k) and e2(k) are the deviation and differential between the expected transition process and the estimated value of the system output, a2, a3, δ f1 is the relevant parameter of fal, u0 is the output of NLSEF; b0 is the compensation coefficient.

[0212] Figure 3 Zhonge y1 、e y2 and e p1 、e p2 They are e1(k) and e2(k) of two NLSEFs respectively. y1 =v y1 -z y1 ;e y2 =v y2 -z y2 ;e p1 =v p1 -z p1 ;e p2 =v p2 -z p2 .u y0 and u p0 is the output of NLSEF.

[0213] Interference compensation:

[0214] In reality, when the rotor core is displaced horizontally, it may encounter sudden changes in load, interference of a certain frequency, and external force impact. Noise signals may also penetrate into the displacement signal, affecting the control.

[0215] ESO is used to track the representative disturbance state variable z3(k) extended from the original system. The control quantity is used to compensate for the disturbance and converted into the control quantity of the integral series. The control quantity is:

[0216]

[0217] From formula (26), we can see that u y＝ u y0- z y3 / b y0 ;u p＝ u p0- z p3 / b p0 .u y and the horizontal control coil current i cl Proportional to u p and the horizontal control coil current i cr Finally, the parameters of the horizontal control system are adjusted to ensure the best system performance.

[0218] Step 4: Adjust the parameters of the horizontal control system of the magnetic levitation scale system.

[0219] The specific setting method is as follows:

[0220] SYSTD parameter adjustment.

[0221] Assume that the system input signal is Asin(ωt) and define M(A) to describe the nonlinear function f(t) = sys(t):

[0222]

[0223] Among them, e1 and f1 are the first-order Fourier coefficients, that is:

[0224]

[0225] Since f(t) is an odd function, e1=0, let x1(t)-r(t)=Asin(ωt), combined with formula (27), the function sys(x1(t)-r(t),a 41 ,a 51 ) can be transformed into:

[0226]

[0227] Similarly, the function sys(x2(t) / R,a4,a5) can also be transformed into:

[0228]

[0229] Therefore, the linearized form of the nonlinear system S2 can be expressed as:

[0230]

[0231] From this, we can deduce that:

[0232]

[0233] Among them, M1>0, M2>0. This can ensure the stability of the system.

[0234] In order to effectively extract the measurement signal, the appropriate R value is selected to make the bandwidth of SYSTD sufficient to cover the spectrum of the measurement signal; then, appropriate M1 and M2 are selected to satisfy formula (32) to ensure the stability of the system; and the contradiction between the filtering ability and the response speed of SYSTD is further balanced by adjusting M1 and M2; and the appropriate a is selected. 41 、a 51 、a 42 、a 52 Meet the requirements of M1 and M2. Generally, adjust parameter a first 51 and a 52 , adjust the SYSTD amplitude; then adjust the parameter a 41 and a 42 , adjust SYSTD fast tracking capability.

[0235] ESO parameter tuning. There are three parameters in ESO that need to be tuned, namely βe1 , β e2 and β e3 β e3 It is the most important of the three parameters.

[0236] When adjusting the parameters, first select the parameter β e3 β e3 If it is too small, the observation accuracy of z3(k) will be insufficient, and z1(k) and z2(k) will lag behind x1(k) and x2(k). e3 If it is too large, it will increase the system fluctuation and even cause the system to oscillate. So adjust β first. e3 to ensure the accuracy of ESO.

[0237] Then, adjust β from small to large e1 and β e2 , to reduce the oscillation of the ESO output. Due to the coupling between the horizontal system of the magnetic suspension scale system, the values ​​of these two parameters should be as small as possible while ensuring the stability of the ESO output.

[0238] In addition, δ to β e1 , β e2 and β e3 Before adjusting these three parameters, it is necessary to determine the value of δ. In the present invention, δ = h.

[0239] NLSEF parameter tuning. There are three parameters in NLSEF that need to be tuned, namely β f1 , β f2 and b0. b0 is the coefficient of the control quantity u. β f1 , β f2 The adjustment method of is similar to the parameter adjustment method of PD.

[0240] The parameters of the mover core of the magnetic suspension scale system are: J α =1.49×10 -2 kg·m 2 , lever arm r = 0.1275m, mass m = 1.83kg. Other main parameters of the ADRC are shown in Table 1.

[0241] Table 1 Other main parameters of the active disturbance rejection controller

[0242]

[0243] Simulation analysis of the feasibility of the horizontal control system of the magnetic levitation scale system.

[0244] The discrete equation of system S2 is:

[0245]

[0246] Where h is the integration step size.

[0247] Next, we will simulate. 41 、a 51 、a 42 、a 52 The influence of different setting values ​​on SYSTD. Since the horizontal movement of the mover core is a step-by-step motion with a set step size of 1mm, the measured signal is close to a sinusoidal signal. Therefore, in the simulation experiment, the given signal uses white noise and a sinusoidal signal, and its equation is:

[0248] r(t)=sin(t)+γn(t) (34)

[0249] Simulation 1: The impact of time scale R on SYSTD tracking characteristics. Let a 41 =144,a 51 =16,a 42 =3,a 52 = 1. Take R = 100, 200, 300, 500 respectively to simulate SYSTD tracking given signal. The results are as follows Figure 4 As shown in the figure, R clearly determines the speed of SYSTD tracking. The smaller R, the slower the tracking speed. However, when R > 300, the tracking speed does not increase significantly, while the oscillation amplitude increases. Therefore, the parameter R has a significant impact on SYSTD tracking accuracy, and the balance between SYSTD dynamic response and noise reduction capability must be considered when selecting its value.

[0250] Simulation 2: The impact of sys() parameters on SYSTD tracking characteristics. When a4 is constant, parameter a5 directly determines the change in sys()'s amplitude; when a5 is constant, parameter a4 directly determines the change in sys()'s tracking rate. Figure 5 shows the SYSTD parameter settings and the tracking results for a given signal containing random noise.

[0251] Obviously, increasing a 41 、a 42 Parameters can effectively improve signal tracking speed, but will lose tracking accuracy, such as Figure 5a and Figure 5c In addition, appropriately increase a 51 、a 52 It can improve the denoising ability of SYSTD, but it will lose the tracking speed, such as Figure 5b and Figure 5d In addition, when the parameters do not meet the constraints required by formula (35) and formula (32), it will cause a large overshoot and seriously reduce the tracking accuracy.

[0252]

[0253] To obtain appropriate SYSTD parameters, considering the impact of linear components on SYSTD tracking and filtering performance, we first roughly select the four parameters of sys() while ensuring system stability, and then adjust R to approach the required tracking speed and accuracy. Furthermore, based on the phenomena in Simulation 2, we adjust a4 and a5 to change the amplitude and rate of change of sys(), thereby adjusting the tracking and filtering performance of SYSTD.

[0254] Simulation 3: Performance comparison simulation of TD, MTD and SYSTD. The parameters of the tracking differentiator are selected for comparison as follows: (1) TD; (2) MTD.

[0255] The formula for TD is:

[0256]

[0257] Where:

[0258]

[0259] (a)a 41 Change, a 51 、a 42 、a 52 unchanged (b)a 42 Change, a 41 、a 51 、a 52 unchanged (c)a 51 Change, a 41 、a 42 、a 52 unchanged (d)a 52 Change, a 41 、a 42 、a 51 constant;

[0260] The performance of differential trackers is primarily determined by their tracking speed and numerical filtering. Given similar filtering performance, the parameters of three TDs are set as shown in Table 2 to compare their tracking characteristics for harmonic signals.

[0261] Table 2 Simulation parameters of three differential trackers: TD, MTD and SYSTD

[0262]

[0263] The results are as follows Figure 6 and Figure 7 shown.

[0264] In order to clearly see the comparison results of the tracking characteristics of the three TDs, a signal composed of a square wave signal with a period of 0.2 seconds and a white noise signal is introduced into the simulation. The equation is:

[0265] r(t)=sgn(sin(t))+γn(t) (38)

[0266] Depend on Figure 6 and Figure 7 It can be seen that SYSTD has the fastest tracking speed and the best filtering effect.

[0267] In order to facilitate the simulation analysis of the feasibility of the horizontal control system of the magnetic levitation scale system, the present invention built a simulation model of the horizontal control system through Simulink, such as Figure 8 shown.

[0268] The parameters of the mover core of the magnetic suspension scale system are: J α =1.49×10 -2 kg·m 2 , lever arm r = 0.1275m, mass m = 1.83kg. Other main parameters of the ADRC are shown in Table 3.

[0269] Table 3 Other main parameters of the active disturbance rejection controller

[0270]

[0271] Assume that t=0s, when the coordinate value of the moving core in the y direction is 0, a given value y is suddenly added. * d =1mm,ψ * z =0rad / s, used to detect the response characteristics of the mover core within one step when the magnetic levitation scale system is performing displacement detection.

[0272] In addition, at t = 0.5s, a y b =0.005mm position disturbance. At t=0.8s, white noise interference is added to simulate external interference. The simulation results are as follows Figure 9 shown.

[0273] Will Figure 9 It is divided into four areas, and the local enlarged pictures of each area are as follows Figure 9 As shown. From area 1, it can be seen that the mover core can reach the given displacement value of 1mm, that is, one step, in about 0.03s after starting. In one step, the mover core first accelerates from a stationary state, moves 0.5mm, and then decelerates to a stationary state. And the displacement curve is relatively smooth within a step, which is conducive to improving the accuracy of the magnetic levitation scale system after subdivision. From area 2, it can be seen that the mover core will overshoot at the end of each step. The overshoot does not exceed 6μm, and the correction is completed within 0.2s. In area 3, the interference can be quickly eliminated. In area 4, the white noise has little effect on the horizontal control system. From Figure 9It can be seen that the horizontal control system of the magnetic levitation scale system is highly robust and the positioning accuracy can reach ±5μm.

[0274] In addition, take the integral of 0-t on both ends of formula (39). Ignoring the constant term, we can get the following formula:

[0275]

[0276] Where n represents the number of turns, B represents the magnetic induction intensity between the air gaps, and I L represents the current of the horizontal control coil, L is the length of the horizontal control coil in the air gap magnetic field, and m is the mass of the mover core. Assuming these quantities are constants, the relationship between the displacement S of the mover core and time t is a quadratic function. This is consistent with Figure 9 The simulation results are consistent with .

[0277] Figure 10 The following are simulations of the horizontal rotation angle of the mover core. As can be seen from the two figures above, the mover core exhibits a slight angular offset on the Z axis during startup. This offset is corrected within approximately 0.2 seconds. The movement distances at both ends are essentially the same, demonstrating that the horizontal control system achieves decoupling control.

[0278] In order to verify the control effect of the horizontal control system, the present invention conducted a mover core horizontal positioning experiment on a magnetic levitation scale system test platform.

[0279] Figure 11 The measured starting response curve of the mover core is given. It can be seen from the curve that the mover core exhibits good response speed and stability during the starting process. In a very short time, the mover core can quickly reach the preset horizontal position and ensure accurate positioning throughout the process. Figure 11 As shown in the figure, at t = 0.5s, the horizontal position of the mover core was adjusted to a set value of 1mm, or one step. The horizontal position of the mover core reached the set value within t = 0.58s, with no significant overshoot. After t = 0.75s, the suspended position of the mover core stabilized at the set value, with an error within ±2μm. The adjustment speed was slightly slower than the simulation indicated.

[0280] from Figure 12 It can be seen that the overshoot of the horizontal control system in actual operation is more than double that in the simulation. The mover core does not reach stability until around t = 0.72s, 0.02s longer than in the simulation. Errors still exist after this point, but are less than ±2μm.

[0281] like Figure 13As shown in the figure, at t = 0.5s, the deflection angle of the mover core changes. At this point, the setpoint for the mover core's horizontal position also undergoes a sudden change, and the horizontal control system begins adjusting the mover core's horizontal position. At t = 0.6s, the deflection angle reaches its maximum value. Before t = 0.8s, the deflection angle returns to zero, completing the transition to the suspended position and stabilizing the mover core at its new horizontal position.

[0282] Clearly, strong coupling also exists when controlling the horizontal position of the left and right ends of the mover core. The horizontal position transition process can interfere with the deflection angle of the mover core. However, the horizontal control system is able to eliminate this interference and complete a step in approximately 0.22 seconds, with a control accuracy of ±2μm. Therefore, the horizontal control system effectively achieves decoupled control and exhibits excellent robustness.

[0283] This invention focuses on the autonomous displacement of a magnetic levitation scale system and achieves innovative results in system control algorithms and structural optimization. The proposed novel differential tracker, SYSTD, effectively solves the problem of tracking the position feedback signal of the mover core. SYSTD is constructed based on specific elementary functions, and its stability is theoretically verified. Phase plane analysis provides a theoretical basis for parameter selection, and a detailed parameter tuning method enhances its operability in practical applications. Simulation results show that SYSTD strikes a good balance between tracking speed and stability, offering faster tracking speed and better filtering performance than traditional TD and MTD. This not only improves the tracking accuracy of the magnetic levitation scale system for the position feedback signal of the mover core but also provides new insights for the design of control algorithms for other similar systems. Regarding system structural optimization, a method of estimating the position of the mover core by wrapping a measuring coil around the horizontal control coil enables sensorless control. This innovation simplifies the system architecture, reduces costs, and improves system reliability. Combined with SYSTD's precise observation of relevant signals, the accuracy of position estimation is further improved, providing a more advantageous solution for the practical application of magnetic levitation scale systems.

[0284] Note that the above are only preferred embodiments of the present invention and the technical principles employed. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and that various obvious changes, readjustments, and substitutions can be made by those skilled in the art without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments and may include many other equivalent embodiments without departing from the concept of the present invention. The scope of the present invention is determined by the scope of the appended claims.

Claims

1. A method for controlling the horizontal motion of a magnetic levitation ruler, characterized in that: The following steps are involved: Step 1: Establish a mathematical model of the horizontal system: The permanent magnet of the magnetic levitation scale system is set as the front side of the magnetic levitation scale system, and the suspension control coil is set as the rear side of the magnetic levitation scale system. When energized, coil Co1 generates a forward propulsion force, driving one end of the mover core forward. Coil Co3 drives the other end of the mover core forward. Coils Co2 and Co4 generate a backward propulsion force, driving the mover core backward. There is no wire in the air gap magnetic field in the middle of the mover core, so no reverse interference force can be obtained. The right-side thrust and the left-side thrust of the mover core are calculated based on the Ampere force calculation formula. Newton's second law of motion is used to derive the rigid body dynamics equation of the horizontal system of the mover core. The horizontal displacement coordinate system is converted into the center of mass coordinate system to obtain the horizontal system analysis model of the magnetic levitation scale system. Step 2: Based on the mathematical model of step 1, the position of the mover core is estimated by deriving the induced electromotive force to obtain the horizontal position y of the mover core. b , and then the deflection angle ψ is obtained by the gyroscope z The value of Step 3: The horizontal position y obtained in step 2 b and deflection angle ψ z , construct the differential tracker SYSTD and perform horizontal motion control of the mover core based on SYSTD; Step 4: Parameter adjustment of the horizontal control system of the magnetic levitation scale system is performed, including parameter adjustment of SYSTD, ESO and NLSEF.

2. A method for controlling horizontal motion of a magnetic levitation ruler according to claim 1, characterized in that: Step 1, the right thrust of the mover core is: F rt =F t1 -F t2 (1) Where, F t1 is the Ampere force generated by the current flowing through coil Co1, F t2 It is the Ampere force generated by the coil Co2 being energized; According to the Ampere force calculation formula, the right thrust F can be obtained rt The calculation formula is: F rt =nB r Yes cr (2) Where n is the sum of the number of turns of the right forward horizontal control coil and the number of turns of the right backward horizontal control coil, B r is the sum of the air gap magnetic field on the right, L is the length of the single-turn horizontal control coil in the air gap magnetic field, i cr is the current of the horizontal control coil on the right side of the mover core; i cr The current i of the right forward horizontal control coil Co1 c1 and the current i of the right rear horizontal control coil Co2 c2 Composition, i c1 and i c2 There are two currents with opposite directions. Looking from the front of the magnetic levitation scale system to the two horizontal control coils Co1 and Co2 on the right, let the current on Co1 coil i c1 When the flow is counterclockwise, its value is positive, which can ensure that the horizontal control coil Co1 generates a forward thrust F t1 ; Assume that the current i on the Co2 coil c2 When the flow is clockwise, its value is negative, which can ensure that the horizontal control coil Co2 produces a backward thrust, then: When the mover core accelerates forward, i c2 is zero, then, let i cr =i c1 , when the rotor core accelerates backward, i c1 is zero, then, let i cr =i c2 .

3. The method for controlling horizontal motion of a magnetic levitation ruler according to claim 1, characterized in that: Step 1, the left side thrust of the mover core is: F lt =F t3 -F t4 (4) Where, F t3 is the Ampere force generated by the current flowing through the coil Co3, F t4 It is the Ampere force generated by the current flowing through the coil Co4; According to the Ampere force calculation formula, the left thrust F can be obtained lt The calculation formula is: F lt =nB l Yes cl (5) Where n is the sum of the number of turns of the left forward horizontal control coil and the number of turns of the left backward horizontal control coil, B l is the sum of the air gap magnetic fields on the left, L is the length of the single-turn horizontal control coil in the air gap magnetic field, i cl is the current of the horizontal control coil on the left side of the mover core; i cl The current i of the left forward horizontal control coil Co3 c3 and the current i of the right rear horizontal control coil Co4 c4 Composition. c3 and i c4 There are two currents with opposite directions. Looking from the front of the magnetic levitation scale system to the two horizontal control coils Co3 and Co4 on the left, let the current on the Co3 coil i c3 When it flows counterclockwise, its value is positive, which can ensure that the horizontal control coil Co3 produces a forward thrust; suppose the current i on the Co4 coil is c4 When the flow is clockwise, its value is negative, which can ensure that the horizontal control coil Co4 produces a backward thrust, then: When the mover core accelerates forward, i c4 is zero, then, let i cl =i c3 , when the rotor core accelerates backward, i c3 is zero, then, let i cl =i c4 .

4. The method for controlling horizontal motion of a magnetic levitation ruler according to claim 1, wherein: Step 1: Use Newton's second law of motion to derive the rigid body dynamics equation of the horizontal system of the mover core, specifically: The mover core is only subjected to horizontal thrust in the horizontal direction. According to Newton's second law, F lt and F rt Horizontal displacement y on the left side of the mover core bl and the horizontal displacement y on the right side of the mover core br Related, in the horizontal displacement as the research point [y bl ,y br ] coordinate system, according to formula (8), it is located at [y b ,ψ z ] coordinate system, the horizontal displacement coordinate system is converted into the center of mass coordinate system by the following formula; After sorting out, the horizontal system analysis model of the magnetic levitation scale system is obtained: The horizontal system of the magnetic levitation scale system is the mathematical model of the magnetic levitation scale system. Its input i cl and i cr , determines the horizontal position y of the mover core b and deflection angle ψ z The value of .

5. The method for controlling horizontal motion of a magnetic levitation ruler according to claim 1, characterized in that: Step 2: The horizontal position y of the rotor core b The estimation steps are as follows: Connect the two sets of measuring coils on the left in series to obtain the induced electromotive force e on the left l The two sets of measuring coils on the right are connected in series to obtain the induced electromotive force e on the right. r , the calculation formula of the induced electromotive force when the left measuring coil cuts the magnetic lines of force is: Where B u is the magnetic field strength of the air gap on the upper left side of the rotor core, B d is the air gap magnetic field strength on the lower left side of the mover core, L is the length of the measuring coil in the air gap magnetic field, and S is the displacement of the mover core; The mutual inductance M is estimated according to the mutual inductance calculation formula: Where, L c is the inductance of the measuring coil; L k is the inductance of the horizontal control coil. L can be calculated c ≈12272μH, L k ≈122μH, M≈1.2×10 -3 H, measuring the induced electromotive force e generated by mutual inductance in the coil c The calculation steps are as follows: Where i c Is the current of the horizontal control coil. The mover core adopts a fixed-step stepping motion mode, so the current of the horizontal control coil is a square wave signal, which will only cause e on the rising and falling edges. c There is a large fluctuation, and the fluctuation time is affected by the time constant τ of the horizontal control coil k Impact: Where R is the equivalent resistance of the horizontal control coil, which is 1.4Ω. k It is about 8.7μs, and the rising and falling edges of the horizontal control coil current are 6 times τ k , i.e. 52.2μs; SYSTD was used to observe B u 、B d and e l These three signals are low-pass filtered to reduce noise, and the air gap magnetic field intensity and induced electromotive force values ​​are obtained. Substituting them into formula (10), the estimated position value y of the left end of the rotor core is obtained. bl , the estimated value y of the right end position of the rotor core br The same method can be used to obtain y bl 、y br and ψ z Substitute them into formula (8) to estimate y b .

6. The method for controlling horizontal motion of a magnetic levitation ruler according to claim 1, characterized in that: Step 3: The specific steps to build the differential tracker SYSTD are as follows: Use the following elementary functions: Among them, a4>0, a5>0, a4∈R, a5∈R, it can be deduced that: Construct the second-order system S0: Design SYSTD time-invariant system S: Determine whether the zero solution of the system is globally asymptotically stable; When the parameter a 41 , a 51 , a 42 , a 52 When both are greater than zero, the system S0 satisfies the Lyapunov global asymptotic stability condition, namely: Design SYSTD based on the function sys() and construct system S2 as follows: If a 41 、a 51 、a 42 、a 52 are all positive, and the input signal r(t)(t∈[0,+∞]) Bounded, for any finite time T>0, the solution of system S2 satisfies: x1(t) converges to r(t), and x2(t) converges to the generalized differential of r(t); System S2 is the perturbation form of system S1, and system S2 (19) is SYSTD.

7. A method for controlling horizontal motion of a magnetic levitation ruler according to claim 6, characterized in that: If in the real domain R 2 There exists an infinitely increasing positive or negative definite function V(x), and in the full phase space, the total derivative of V(x) along the solution of the system S with respect to time t is always negative or always positive, satisfying If the set of points contains only the origin, then the zero solution of the system is globally asymptotically stable.

8. The method for controlling horizontal motion of a magnetic levitation ruler according to claim 6, characterized in that: According to the active disturbance rejection control law, formula (9) is changed to: Where w y (t) and w z1 (t) is the equivalent disturbance of the system, which includes coupling and disturbance, ic l and i cr is the control quantity, b y and b z They are the control variables i cl and i cr Control parameters of The change of the current of the four horizontal control coils is obtained; the active disturbance rejection controller can w y (t) and w z1 (t) is considered as a comprehensive disturbance of the system, which can be observed and compensated through its ESO; if the control quantity is selected: After compensation, formula (15) can be rewritten as: After compensation, y b and ψ z Achieve decoupling and controllability; The ESO of the magnetic levitation scale system level control system is as follows: Where: Where z1(k), z2(k), and z3(k) are the state variables of the ESO. z1(k) and z2(k) are used to track the state variables of the system, and z3(k) is used to track the state variables of the total disturbance. e1 , β e2 , β e3 is the gain of ESO; a1 and δ are unknown parameters. If a1 is less than 1, the function has nonlinear characteristics such as large error and small gain or small error and large gain. δ represents the linear range.

9. The method for controlling horizontal motion of a magnetic levitation ruler according to claim 6, characterized in that: The following NLSEF is used for the horizontal control system of the magnetic levitation scale system: Where e1(k) and e2(k) are the deviation and differential between the expected transition process and the estimated value of the system output, a2, a3, δ f1 is the relevant parameter of fal, u0 is the output of NLSEF; b0 is the compensation coefficient; ESO is used to track the representative disturbance state variable z3(k) extended from the original system. The control quantity is used to compensate for the disturbance and converted into the control quantity of the integral series. The control quantity is: From formula (26), we can see that u y＝ u y0- z y3 / b y0 ;u p＝ u p0- z p3 / b p0 ,u y and the horizontal control coil current i cl Proportional to u p and the horizontal control coil current i cr Directly proportional.

10. The method for controlling horizontal motion of a magnetic levitation ruler according to claim 1, characterized in that: Step 4, SYSTD parameter setting, includes the following steps: Assume that the system input signal is Asin(ωt) and define M(A) to describe the nonlinear function f(t) = sys(t): Among them, e1 and f1 are the first-order Fourier coefficients, that is: Since f(t) is an odd function, e1=0, let x1(t)-r(t)=Asin(ωt), combined with formula (27), the function sys(x1(t)-r(t),a 41 ,a 51 ) can be transformed into: The function sys(x2(t) / R,a4,a5) can also be transformed into: The linearized form of the nonlinear system S2 can be expressed as: It can be deduced that: Among them, M1>0, M2>0; First, select an appropriate R value so that the bandwidth of SYSTD can cover the spectrum of the measured signal; then, select appropriate M1 and M2 to satisfy formula (32); then adjust M1 and M2 to further balance the contradiction between SYSTD filtering capability and response speed; adjust parameter a 51 and a 52 , adjust the SYSTD amplitude; then adjust the parameter a 41 and a 42 , adjust SYSTD fast tracking capability; To adjust the parameters of ESO, first adjust β e3 , and then adjust β from small to large e1 and β e2 ,Before adjusting these three parameters, it is necessary to determine the δ value, δ = h; NLSEF parameter tuning, including β f1 , β f2 and adjustment of b0.

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