A synchronous control method for a double-controlled four-electromagnetic suspension system

Abstract

The application provides a double-controlled four-electromagnetic suspension system synchronous control method, relates to the technical field of microelectronic processing, and is based on fuzzy adaptive sliding mode control and an improved deviation coupling control and specifically comprises the following steps: for a single electromagnetic suspension system, a fuzzy adaptive sliding mode control method is adopted, a controller is designed on the basis of a non-singular fast terminal sliding mode surface, unknown terms in the controller are adaptively estimated by using a fuzzy logic system, and unknown disturbances are online approximated and dynamically compensated; for a four-electromagnetic suspension system, an improved deviation coupling synchronous control structure is adopted, air gaps of the four-electromagnetic suspension system are input into a position compensator of each single system, and the four-electromagnetic suspension system is compensated in terms of synchronization error, so that the synchronization error of the four-electromagnetic suspension systems with coupling relationship is reduced, and the rapidity and robustness of the single electromagnetic suspension system and the coordinated synchronization of the four-electromagnetic suspension system are improved.

Description

Technical Field

[0001] This invention relates to the field of microelectronics fabrication technology, and in particular to a synchronous control method for a dual-control four-electromagnetic levitation system. Background Technology

[0002] Since the advent of the information revolution, high-tech industries centered on integrated circuits have developed rapidly. The demand for semiconductors and other microelectronic products has surged, leading to increasingly stringent requirements for positioning accuracy, movement speed, and processing environment in microelectronics manufacturing. Traditional linear positioning motion platforms utilize guide rail contact mechanical positioning, mostly employing rotary servo motors and ball screw drives. This is a core component in equipment manufacturing and is widely used in CNC machine tools and other fields. However, this structure, with its intermediate links such as couplings, lead screws, and bearings, results in high system inertia and limited dynamic response and frequency. Furthermore, elastic deformation, friction, and backlash in these intermediate links cause lag in the positioning platform, significantly reducing positioning accuracy. As linear motors have matured and replaced traditional drive methods, direct drive eliminates intermediate transmission links, achieving "zero transmission." This method offers advantages such as zero backlash, reduced friction, high precision, and high speed. However, direct linear motor drive still suffers from friction and wear, failing to meet the demands of ultra-precision machining in microelectronics manufacturing. Therefore, air-floating motion platforms combining air suspension technology and linear motors have emerged, achieving frictionless operation, long lifespan, and ultra-high precision. However, air-bearing supports suffer from low stiffness, weak load-bearing capacity, susceptibility to external interference, and difficulty in adapting to vacuum environments, which still limit positioning accuracy. Magnetic levitation technology, with its non-contact, frictionless, high-speed, low-noise, low-pollution, long-life, and high-precision characteristics, has become an important area of ​​scientific research and has already been applied in fields such as magnetic levitation trains and ultra-high-speed bearings. When applied to microelectronic linear machining positioning platforms, magnetic levitation technology can not only meet the requirements of high-speed and high-precision positioning, improving the production efficiency and product quality of linear motion platforms, but also meet the needs of ultra-clean manufacturing environments.

[0003] Because a magnetic levitation platform is an open-loop unstable system, and microelectronics requires extremely high positioning accuracy, reaching the nanometer level, the requirements for the controller are extremely high. The control strategies used by the controller are mainly divided into linear and nonlinear types, including PID control, sliding mode control, fuzzy control, neural networks, and passive control. Among these, sliding mode control is the most mature and has been widely used in various fields. Compared with other control strategies, sliding mode control has a non-fixed controlled object structure, lower modeling accuracy requirements, simpler structure, and faster response speed. However, the switching term in sliding mode control, while improving robustness, can cause system chattering. Moreover, the motion of the sliding mode is asymptotically stable within a finite time, and its convergence speed is determined by the parameters set in the sliding surface, resulting in a relatively fixed convergence speed and poor adaptability. For a differential magnetic levitation platform supported by four electromagnetic levitation systems, the gaps between the systems must be synchronized; otherwise, the stability of the platform's motion will be compromised, severely affecting the machining positioning accuracy. Summary of the Invention

[0004] This invention proposes a dual-control synchronous control method for a four-electromagnetic levitation system, aiming to solve the problems of slow response speed and poor anti-disturbance capability of a single electromagnetic levitation system, as well as insufficient synchronization accuracy when four electromagnetic levitation systems work together.

[0005] This invention provides a synchronous control method for a dual-control four-electromagnetic levitation system, used to control a magnetic levitation machining and positioning platform. This control method is based on fuzzy adaptive sliding mode control and improved deviation coupling control, and specifically includes the following steps:

[0006] Step 1: Establish a mathematical model of the magnetic levitation processing and positioning platform;

[0007] Step 2: Based on the mathematical model, design a non-singular fast terminal sliding mode controller for the single electromagnetic levitation system in the magnetic levitation processing and positioning platform;

[0008] Step 3: Use fuzzy adaptive control to dynamically compensate for unknown disturbances in the non-singular fast terminal sliding mode controller, thus forming a fuzzy adaptive sliding mode controller;

[0009] Step 4: Determine the stability of the fuzzy adaptive sliding mode controller and calculate the adaptive law;

[0010] Step 5: Based on the mathematical model, an improved deviation coupling control structure is designed for the four electromagnetic levitation systems in the magnetic levitation processing and positioning platform. In this structure, the weighted average of the air gap deviations of each electromagnetic levitation system is introduced as steady-state fine-tuning.

[0011] Furthermore, the specific method for establishing the mathematical model of the magnetic levitation processing and positioning platform in step 1 includes:

[0012] Taking the vertically downward direction as the positive direction of the single electromagnetic levitation system, and using a differential connection for the electromagnets of the magnetic levitation platform, the resultant electromagnetic force exerted by the upper and lower electromagnets on the guide rail in the single electromagnetic levitation system is:

[0013]

[0014] in, Vacuum permeability N represents the number of turns in the coil; A represents the cross-sectional area of ​​the iron core, in meters. 2 I0 is the bias current, i is the control current, and the excitation currents of the upper and lower electromagnets are I0+i, respectively. z with I0-i z , The air gap for magnetic levitation at equilibrium is denoted by z, and z is the vertical displacement of the levitation body relative to the equilibrium position.

[0015] Expanding the resultant electromagnetic force at the equilibrium position (i,z) = (0,0) using Taylor series, we get:

[0016]

[0017] in, It is the current force coefficient; Here, i is the displacement force coefficient, and i0 is the current offset introduced by the system to counteract the platform's gravity G.

[0018] The dynamic model of the magnetic levitation platform of this differential four-electromagnetic levitation system is established using the Lagrange method. The Lagrange equations are:

[0019]

[0020] Where T is the total kinetic energy of the system of particles, and qi is the generalized displacement of the system of particles. Let Q be the generalized velocity of the system of particles; if all forces acting on the system of particles are definite, then the generalized force Q is... i This can be expressed in terms of the potential energy of a system of point masses, namely:

[0021]

[0022] Therefore, the Lagrange equation can be written in the following form:

[0023]

[0024] Let L = TV represent the difference between the system's kinetic energy T and potential energy V, where L is called the Lagrange function or kinetic potential; then the Lagrange equation can be expressed in terms of kinetic potential as follows:

[0025]

[0026] in, It is the partial derivative of the Lagrange function L. It is the potential energy gradient term of the i-th generalized force of the system, describing the force tendency of the system in the i-th degree of freedom. It is the i-th generalized momentum of the system, which describes the inertia of the system in the i-th degree of freedom;

[0027] Let α and β be the rotational degrees of freedom of the magnetic levitation platform about the x and y axes, and z be the translational degrees of freedom in the vertical direction. Then z1, z2, z3, and z4 are the translational degrees of freedom of the four levitation electromagnets in the z direction, respectively. Let m be the translational velocity of each of the four levitation electromagnets in the z-direction, and let m be the mass of the magnetic levitation platform.

[0028] The translational kinetic energy is:

[0029]

[0030] The rotational kinetic energy is:

[0031]

[0032] The total kinetic energy of the system is the sum of the two kinetic energies, and the total kinetic energy T of the system is:

[0033]

[0034] Where a and b are the center distances of the levitation electromagnet in the Y-axis and X-axis directions, respectively. and These are the moments of inertia of the suspension platform about the X-axis and Y-axis, respectively.

[0035] Substituting the formula for the total kinetic energy of the system into the Lagrange equation, we obtain the following dynamic model:

[0036]

[0037] Where F1, F2, F3, and F4 are the electromagnetic attraction forces of four differential electromagnets, defined as follows: for The equivalent mass for the corresponding degree of freedom, and the coupling mass are: i1, i2, i3, and i4 are the control currents for the four differential electromagnets. Let Z be the translational acceleration of each of the four levitation electromagnets in the z-direction, then we get

[0038]

[0039] The system dynamics equations can then be simplified to:

[0040]

[0041] in,

[0042]

[0043] in, Here is the displacement matrix. For the current matrix, and These are the current force coefficient and displacement force coefficient of the nth differential electromagnet, respectively. For the quality matrix, Here is the displacement stiffness matrix. Current stiffness matrix.

[0044] Furthermore, the specific method for designing a non-singular fast terminal sliding mode controller for the single electromagnetic levitation system in the magnetic levitation processing and positioning platform based on the mathematical model in step 2 includes:

[0045] Let the reference air gap of the magnetic levitation system be The actual air gap is The air gap error of a single electromagnetic levitation system is defined as: Define the non-singular fast terminal sliding surface as:

[0046]

[0047] in, Let be the independent variable and the first derivative of the independent variable, respectively. The coefficients of the sliding surface k1, k2>0; λ>1; p, q are positive odd numbers and satisfy p>q;

[0048] The expression for the non-singular fast terminal sliding surface with air gap error e as the variable is as follows:

[0049]

[0050] in, , , These are the air gap error, the reference air gap, and the rate of change of the actual air gap, respectively.

[0051] The derivative expression for the sliding surface is:

[0052]

[0053] in, It is the second derivative of the air gap error;

[0054] Equation of state in a magnetic levitation platform Below, the derivative of the sliding surface is:

[0055]

[0056] Non-singular fast terminal sliding mode control typically employs a strategy of equivalent control plus switching control, i.e. The equivalent control law for non-singular fast terminal sliding mode control can be derived from the sliding surface derivative as follows:

[0057]

[0058] The switching control law is usually chosen based on the constant-rate approach law, i.e. Under these conditions, the final non-singular fast terminal sliding mode control law is:

[0059]

[0060] Where η is the switching gain, sgn(s) is the sign function, and D is the disturbance experienced by the system.

[0061] Furthermore, the specific method for constructing the fuzzy adaptive sliding mode controller by dynamically compensating for unknown disturbances in the non-singular fast terminal sliding mode controller using fuzzy adaptive control in step 3 includes:

[0062] by Design a fuzzy system with fuzzy input variables;

[0063] The inference part of the fuzzy controller uses the minimum value fuzzy inference method, and the defuzzification part uses the weighted average method. The output of the fuzzy system is:

[0064]

[0065] in, They are respectively Input the membership functions of variables x1 and x2; These are the fuzzy sets corresponding to x1 and x2, respectively; Let p1 and p2 be the number of fuzzy rules for x1 and x2, respectively, and p1 and p2 be the number of fuzzy sets for x1 and x2, respectively. It serves as the weighting center for the output values ​​of the fuzzy system.

[0066] As a free parameter, a two-dimensional fuzzy vector is introduced. Then, the output of the fuzzy system can be expressed as:

[0067]

[0068] The parameter θ is dynamically adjusted according to the adaptive law, and the optimal parameter is... The derivation formula is as follows:

[0069]

[0070] in, To determine the output of the fuzzy system at the air gap x under unknown parameters θ, In the optimal estimation parameter θ * The output of the lower fuzzy system at air gap x, For parameters A set;

[0071] The fuzzy adaptive sliding mode control law is:

[0072] .

[0073] Furthermore, the specific method for determining the stability of the fuzzy adaptive sliding mode controller and calculating the adaptive law in step 4 includes:

[0074] Define the free parameter error as Minimize the fuzzy estimation error as

[0075] Define Lyapunov functions as follows:

[0076] Then its derivative

[0077] in, It is adaptive gain;

[0078] Substitution We can obtain:

[0079]

[0080] when At that time, the adaptive law is calculated as follows:

[0081]

[0082] At this time According to Lyapunov's stability theorem, the fuzzy adaptive sliding mode control system is asymptotically stable.

[0083] Furthermore, the specific method for designing an improved deviation coupling control structure for the four electromagnetic levitation systems in the magnetic levitation processing and positioning platform based on the mathematical model in step 5, and introducing a weighted average of the air gap deviations of each electromagnetic levitation system as a steady-state fine-tuning method in this structure, includes:

[0084] A position compensator is set for each electromagnetic levitation system in the magnetic levitation processing and positioning platform to generate a synchronous compensation signal;

[0085] By introducing the weighted average of the air gap deviations of each electromagnetic levitation system into the position compensator as a steady-state fine-tuning term, an improved deviation coupling control structure is obtained.

[0086] The weighting coefficients in the weighted average are determined based on the proportion of the absolute value of the air gap deviation of each electromagnetic levitation system to the sum of the absolute values ​​of the air gap deviations of the four electromagnetic levitation systems:

[0087] .

[0088] Compared with the prior art, the present invention has the following advantages:

[0089] 1. For a single electromagnetic levitation system, while maintaining the good characteristics of sliding mode control, such as strong robustness to parameter perturbations and external uncertainties, non-singular fast terminal sliding mode control can improve the dynamic performance of sliding mode, avoid singular phenomena, and achieve fast convergence. Fuzzy adaptive control can dynamically compensate for disturbances, better handle the influence of fuzzy approximation error, ensure convergence in finite time, and improve response speed.

[0090] 2. Since the platform's levitation requires the joint operation of four electromagnetic levitation systems, this invention employs an improved deviation coupling synchronization control method that adds a weighted average value as steady-state fine-tuning to ensure good coordination and synchronization performance of the four electromagnetic levitation systems. This method overcomes the monotonicity of using deviation coupling control alone, and also considers that when the disturbance of a single electromagnetic levitation system is too large, the system with larger fluctuations can be prioritized for response, thereby improving the synchronization adjustment speed and overall synchronization accuracy.

[0091] Based on the implementation methods provided in the above aspects, this application can be further combined to provide more implementation methods. Attached Figure Description

[0092] The above and other objects, features, and advantages of exemplary embodiments of the present invention will become readily apparent upon reading the following detailed description with reference to the accompanying drawings. In the drawings, several embodiments of the invention are illustrated by way of example and not limitation, with the same or corresponding reference numerals denoteing the same or corresponding parts, wherein:

[0093] Figure 1 This is a structural diagram of the differential magnetic levitation platform of the present invention;

[0094] Figure 2 This is a schematic diagram showing the position of the differential electromagnet of the present invention;

[0095] Figure 3 This is a structural diagram of the single electromagnetic levitation system of the differential magnetic levitation platform of the present invention;

[0096] Figure 4A schematic diagram of the deviation coupling control of four electromagnetic levitation systems;

[0097] Figure 5 This is a schematic diagram of the position compensator of the electromagnetic levitation system in the deviation coupling control structure.

[0098] Figure 6 This is a schematic diagram of the position compensator for the electromagnetic levitation system in the improved deviation coupling control structure.

[0099] Figure 7 The overall structure of a DSP-based magnetic levitation platform system for microelectronics fabrication;

[0100] Figure 8 A comparison of air gap curves for non-singular fast terminal sliding mode control, fuzzy sliding mode control, and fuzzy adaptive sliding mode control in a single electromagnetic levitation system without applied disturbance;

[0101] Figure 9 A comparison of air gap curves for non-singular fast terminal sliding mode control, fuzzy sliding mode control, and fuzzy adaptive sliding mode control when a periodic disturbance is applied to a single electromagnetic levitation system;

[0102] Figure 10 shows the air gap curve of the improved deviation coupling control when a periodic disturbance is applied to the four electromagnetic levitation systems.

[0103] In the diagram: 1. Linear motor mover; 2. Linear motor stator; 3. Power amplifier; 4. Suspension electromagnet; 41. First differential suspension electromagnet; 42. Second differential suspension electromagnet; 43. Third differential suspension electromagnet; 44. Fourth differential suspension electromagnet; 5. Guide electromagnet; 51. First pair of differential guide electromagnets; 52. Second pair of differential guide electromagnets; 6. Position sensor; 7. Guide rail; 8. Suspension component; 9. Upper electromagnet; 10. Upper coil; 11. Lower coil; 12. Lower electromagnet. Detailed Implementation

[0104] The exemplary embodiments disclosed in this application will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of this application are shown in the drawings, it should be understood that this application can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of this application and to fully convey the scope of this application to those skilled in the art. Unless otherwise specified, the technical means used in the embodiments are conventional means well known to those skilled in the art.

[0105] The present invention discloses a synchronous control method for a dual-control four-electromagnetic levitation system, the specific steps of which include:

[0106] (1) Establish a mathematical model for the magnetic levitation processing and positioning platform;

[0107] (2) Non-singular fast terminal sliding mode control is adopted for the single electromagnetic levitation system;

[0108] (3) Fuzzy adaptive control is used to dynamically compensate for unknown disturbances encountered in non-singular fast terminal sliding mode control;

[0109] (4) Determine the stability of the fuzzy adaptive sliding mode control and calculate the adaptive law;

[0110] (5) Design the deviation coupling control structure of the four systems, and add the weighted average of the deviation as steady-state fine-tuning to improve the speed and accuracy of synchronization.

[0111] like Figure 1 The differential magnetic levitation platform structure diagram shows that the upper and lower electromagnets constitute the levitation electromagnet 4. The control signal and bias signal of the upper and lower electromagnets are added and subtracted by the same controller and then sent to the power amplifier 3, which in turn sends the signal to the electromagnets. The electromagnetic attraction generated by the upper and lower electromagnets separates the levitation component 8 from the guide rail 7. The position sensor 6 transmits this air gap signal to the controller, thus cyclically keeping the levitation component 8 stably levitated. Under the action of the linear motor mover 1 and the linear motor stator 2, the levitation component 8 moves along the guide rail 7 in the X direction, and the guide electromagnet 5 controls the direction of the levitation component 8 under the same controller.

[0112] like Figure 2 It can be observed that the linear machining positioning platform uses a four-electromagnetic levitation system to jointly control the same platform. The first differential levitation electromagnet 41, the second differential levitation electromagnet 42, the third differential levitation electromagnet 43, and the fourth differential levitation electromagnet 44 are symmetrically distributed at the four corners of the levitation component 8. The first differential guide electromagnet 51 and the second differential guide electromagnet 52 are installed on both sides of the guide rail to achieve a guiding function. To enable the platform to levitate accurately, quickly, and stably, this invention employs fuzzy adaptive sliding mode control for the single electromagnetic levitation system and an improved deviation coupling synchronous control for the four electromagnetic levitation systems.

[0113] The specific steps for designing a fuzzy adaptive sliding mode controller for a single electromagnetic levitation system are as follows:

[0114] Step 1: Construct a mathematical model of the controlled object—the electromagnetic levitation system;

[0115] The structure of the single electromagnetic levitation system of the differential magnetic levitation platform is shown in the attached figure. Figure 3As shown. The upper electromagnet 9, upper coil 10, lower coil 11, and lower electromagnet 12 constitute a differential electromagnet structure. Neglecting the leakage flux of the iron core and the magnetic reluctance between the iron core and the magnetic conductor, it is assumed that the magnetic field in the iron core and air gap is uniformly distributed. Simultaneously, taking the vertically downward direction as the positive direction of the single electromagnetic levitation system, and using a differential connection for the electromagnets of the magnetic levitation platform, the resultant electromagnetic force exerted by the upper and lower electromagnets on the guide rail is:

[0116] (1)

[0117] in, Vacuum permeability N represents the number of turns in the coil; A represents the cross-sectional area of ​​the iron core, in meters. 2 I0 is the bias current, i is the control current, and the excitation currents of the upper and lower electromagnets are I0+i, respectively. z with I0-i z , The air gap for magnetic levitation at equilibrium is denoted by z, and z is the vertical displacement of the levitation body relative to its equilibrium position.

[0118] Considering the nonlinearity of the magnetic levitation system, by performing a Taylor expansion of the resultant electromagnetic force at the equilibrium position (i,z) = (0,0), and omitting second-order and higher-order small quantities, we obtain:

[0119] (2)

[0120] in, This is called the current force coefficient; It is called the displacement force coefficient, and i0 is the current offset introduced by the system to counteract the platform's gravity G.

[0121] As attached Figure 2 As shown, there is coupling between the four vertically levitating electromagnets. To establish the dynamic model of this differential magnetic levitation platform, the Lagrange method is used, and the Lagrange equations are:

[0122] (3)

[0123] In the formula, T is the total kinetic energy of the system of particles, and q i For the generalized displacement of the system of particles, Let Q be the generalized velocity of the system of particles; if all forces acting on the system of particles are definite, then the generalized force Q is... i This can be expressed in terms of the potential energy of a system of point masses, namely:

[0124] (4)

[0125] Therefore, the Lagrange equation can be written in the following form:

[0126] (5)

[0127] Let L = TV represent the difference between the system's kinetic energy T and potential energy V. L is called the Lagrange function or kinetic potential. The Lagrange equation can then be expressed in terms of kinetic potential as follows:

[0128] (6)

[0129] in, It is the partial derivative of the Lagrange function L. It is the potential energy gradient term of the i-th generalized force of the system, describing the force tendency of the system in the i-th degree of freedom. It is the i-th generalized momentum of the system, which describes the inertia of the system in the i-th degree of freedom;

[0130] Let α and β be the rotational degrees of freedom of the magnetic levitation platform about the x and y axes, and z be the translational degrees of freedom in the vertical direction. Then z1, z2, z3, and z4 are the translational degrees of freedom of the four levitation electromagnets in the z direction, respectively. Let m be the translational velocity of each of the four levitation electromagnets in the z-direction, and let m be the mass of the magnetic levitation platform.

[0131] The translational kinetic energy is:

[0132] (7)

[0133] The rotational kinetic energy is:

[0134] (8)

[0135] The total kinetic energy of the system is the sum of the two kinetic energies, and the total kinetic energy T of the system is:

[0136] (9)

[0137] Where a and b are the center distances of the levitation electromagnet in the Y-axis and X-axis directions, respectively. and These are the moments of inertia of the suspension platform about the X-axis and Y-axis, respectively.

[0138] Substituting equation (9) into the Lagrange equation, we obtain the dynamic model as follows:

[0139] (10)

[0140] Where F1, F2, F3, and F4 are the electromagnetic attraction forces of four differential electromagnets, defined as follows: for The equivalent mass for the corresponding degree of freedom, and the coupling mass are: i1, i2, i3, and i4 are the control currents for the four differential electromagnets. Let Z be the translational acceleration of each of the four levitation electromagnets in the z-direction, then we get

[0141] (11)

[0142] The system dynamics equations can then be simplified to:

[0143] (12)

[0144] in,

[0145]

[0146] in, Let be the displacement matrix. For the current matrix, and These are the current force coefficient and displacement force coefficient of the nth differential electromagnet, respectively. For the quality matrix, Here is the displacement stiffness matrix. Current stiffness matrix.

[0147] Step 2: Design of a non-singular fast terminal sliding mode controller;

[0148] Let the reference air gap of the magnetic levitation system be The actual air gap is The air gap error of a single electromagnetic levitation system is defined as: Because magnetic levitation requires high speed, the non-singular fast terminal sliding surface is defined as:

[0149] (13)

[0150] in, Let x be the independent variable and the first derivative of the independent variable of the sliding surface, respectively, and let x be the air gap state variable. The sliding surface coefficients k1 and k2 are greater than 0; λ is greater than 1; p and q are positive odd numbers and satisfy p > q.

[0151] Substituting the air gap error e into equation (13), we can obtain the following expression for the sliding surface:

[0152] (14)

[0153] in, , , These are the rates of change of air gap error, reference air gap, and actual air gap, respectively.

[0154] Based on the dynamic model of the magnetic levitation platform, the state equation of the magnetic levitation platform is obtained as follows:

[0155] (15)

[0156] Non-singular fast terminal sliding mode control typically employs a strategy of equivalent control plus switching control, i.e. Ignoring external interference, when , At that time, the selected sliding surface ensures that e converges to 0. Taking the derivative with respect to the sliding surface:

[0157] (16)

[0158] in, It is the second derivative of the air gap error;

[0159] Substituting the state equation of the magnetic levitation platform into the derivative of the sliding surface, we can obtain the new derivative of the sliding surface:

[0160] (17)

[0161] Furthermore, the equivalent control law for non-singular fast terminal sliding mode control can be obtained:

[0162] (18)

[0163] For the system to move along the sliding mode switching surface, the following conditions must be met. The switching control law is usually chosen based on the constant-rate approach law in the approach law, that is, the switching control law is:

[0164] (19)

[0165] Where η is the switching gain and sgn(s) is the sign function.

[0166] Let D be the disturbance experienced by the system. Then the non-singular fast terminal sliding mode control law is:

[0167] (20)

[0168] Step 3: Design of the fuzzy adaptive compensation controller;

[0169] The fuzzy adaptive compensation controller is designed to approximate and dynamically compensate for unknown disturbances to the system online, thereby improving the response speed and anti-interference capability of a single electromagnetic levitation system.

[0170] In the design of fuzzy logic systems, the selection For fuzzy input variables, a Gaussian membership function is used to design the fuzzification interface. The membership function expression is as follows:

[0171] (twenty one)

[0172] In this fuzzy controller, both input variables and one output variable will be defined with five fuzzy sets: {NB (negative large), NS (negative small), Z (zero), PS (positive small), PB (positive large)}. Based on event experience, the fuzzy rule table for the magnetic levitation linear machining positioning platform is obtained as follows:

[0173]

[0174] The fuzzy inference part of the fuzzy controller design uses the minimum value inference method, and the defuzzification part uses the weighted average method. The output of the fuzzy system is:

[0175] (twenty two)

[0176] in, They are respectively Input the membership functions of variables x1 and x2; These are the fuzzy sets corresponding to x1 and x2, respectively; Let p1 and p2 be the number of fuzzy rules for x1 and x2, respectively, and p1 and p2 be the number of fuzzy sets for x1 and x2, respectively. It serves as the weighting center for the output values ​​of the fuzzy system.

[0177] These are free parameters, introducing a two-dimensional fuzzy vector. Then, the output of the fuzzy system can be expressed as:

[0178] (twenty three)

[0179] The parameter θ is dynamically adjusted according to the adaptive law, and the optimal parameter is... The derivation formula is as follows:

[0180] (twenty four)

[0181] In the formula, To determine the output of the fuzzy system at the air gap x under unknown parameters θ, In the optimal estimation parameter θ * The output of the lower fuzzy system at air gap x, For parameters A set;

[0182] The fuzzy adaptive sliding mode control law is then:

[0183] (25)

[0184] Step 4: Adaptive law calculation and stability assessment;

[0185] In optimal parameters Below, the free parameter error is To minimize the fuzzy estimation error:

[0186] (26)

[0187] Define Lyapunov functions as

[0188] Then its derivative (27)

[0189] in, It is the adaptive gain, which is a positive real number.

[0190] Substitution We can obtain:

[0191] (28)

[0192] when At that time, the adaptive law is calculated as follows:

[0193] ,Right now (29)

[0194] According to Lyapunov's stability theorem, the fuzzy adaptive sliding mode control system is asymptotically stable.

[0195] The above steps outline the design principle and implementation method of a fuzzy adaptive sliding mode controller for a single electromagnetic levitation system. The next step is to design an improved deviation-coupled synchronization controller to reduce the synchronization error of the four electromagnetic levitation systems.

[0196] Design of an improved deviation-coupled synchronization controller:

[0197] Step 1: Design the deviation coupling control and synchronization control structure;

[0198] Combined with appendix Figure 4 The schematic diagram of the deviation coupling control structure illustrates that the position compensator is the core of the deviation coupling control, providing position compensation signals to each individual electromagnetic levitation system. After receiving the position compensation signal, each individual electromagnetic levitation system moves closer to the positions of the other three systems, thereby increasing the synchronization of the four systems. The structure of the position compensator for the first individual electromagnetic levitation system is shown in the attached diagram. Figure 5 As shown, the compensation gain in the position compensator of this invention is the ratio of the absolute value of the air gap deviation of the current single electromagnetic levitation system to the absolute value of the air gap deviation of other single electromagnetic levitation systems:

[0199] (30)

[0200] In the formula, K 12The air gap deviation compensation gain of the first single electromagnetic levitation system relative to the second single electromagnetic levitation system, K 13 The air gap deviation compensation of the first single electromagnetic levitation system is increased compared to the third single electromagnetic levitation system, K 14 The air gap deviation compensation gain of the first single electromagnetic levitation system relative to the fourth single electromagnetic levitation system;

[0201] Practice and theory show that adopting a deviation-coupled control system structure significantly improves the synchronization effect of the four electromagnetic levitation systems. However, if the air gap fluctuation amplitude of any one system is much larger than that of the others, the control structure cannot prioritize responding to the system with larger fluctuations, resulting in lag in the tracking of other systems and slow synchronization adjustment. Furthermore, this control structure only focuses on the positional coupling between the current system and other systems. When a system experiences a steady-state error due to a disturbance, the error will be indirectly transmitted to other systems through compensation signals, leading to a decrease in overall synchronization accuracy.

[0202] Therefore, it is evident that improvements are needed to the deviation coupling control structure.

[0203] Step 2: Design an improved position compensator for deviation coupling control;

[0204] This invention, based on the original position compensator as dynamic control, adds a weighted average of the deviations of four single electromagnetic levitation systems as steady-state fine-tuning, further improving the accuracy and speed of synchronous control. The position compensator for the single electromagnetic levitation system 1 in the improved deviation coupling control is shown in the attached figure. Figure 6 As shown, the weighting coefficient is the proportion of the absolute value of its own systematic deviation to the sum of the absolute values ​​of the four systematic deviations:

[0205] (31)

[0206] In the formula, w1 is the air gap error weighting coefficient of the first single electromagnetic levitation system relative to the reference air gap, w2 is the air gap error weighting coefficient of the second single electromagnetic levitation system relative to the reference air gap, w3 is the air gap error weighting coefficient of the third single electromagnetic levitation system relative to the reference air gap, and w4 is the air gap error weighting coefficient of the fourth single electromagnetic levitation system relative to the reference air gap.

[0207] The system's working process:

[0208] Reference Figure 7This document describes the overall structure and operation of a DSP-based magnetic levitation platform system for microelectronics processing. Upon power-on, the JTAC circuit transmits the desired levitation air gap signal to the DSP processor. The DSP processes the signal and sends it to the peripheral D / A module. The D / A module converts the digital output from the DSP into analog signals for four individual electromagnetic levitation systems. The analog signals are added to the bias current and amplified by a power amplifier to obtain a signal of appropriate magnitude to drive the upper electromagnet of each individual electromagnetic levitation system. The analog signals are subtracted from the bias current and amplified again to obtain a signal of appropriate magnitude to drive the lower electromagnet of each individual electromagnetic levitation system. The upper and lower electromagnets generate appropriate electromagnetic attraction, stabilizing the platform's levitation. The signals used to drive the electromagnets are transmitted to the A / D conversion module via a current feedback module. At this time, the four gratings detect the output air gap signals of the four electromagnetic levitation systems respectively. These four output air gap signals are sent to the DSP controller through the gratings. The improved position compensator of each of the four subsystems of the DSP controller outputs the position compensation signal of the current subsystem according to the air gap signals of the four subsystems. The position compensation signal of the subsystem is subtracted from the output air gap signal to obtain the total control quantity. This control quantity is a digital quantity, which is converted into an analog quantity by the peripheral D / A module and sent to the subsequent circuits of the four levitation subsystems to realize the levitation of the platform. This cycle continues.

[0209] Example

[0210] Basic parameters of the magnetic levitation system: mass of the levitation component m = 3.44 kg, number of turns of the levitation electromagnet winding N = 380, core area of ​​the levitation electromagnet A = 2.1 × 10⁻⁶ -4 m 2 The resistance of the levitation electromagnet winding is R = 9.78. The desired output of the levitation electromagnet is the levitation air gap z. d =1.5×10 -4 m.

[0211] Based on the above basic parameters, the parameters of the non-singular fast terminal sliding mode controller are as follows: according to the existence conditions of the sliding surface and the stability conditions of the control law, a set of relatively suitable parameters for the non-singular fast terminal sliding mode controller is obtained, namely k1=1.8, k2=0.0015, λ=1.6, p=9, q=7, η=5.

[0212] The equivalent control law is:

[0213]

[0214] Switching control law is

[0215] Parameters of the fuzzy adaptive compensator: The universe of discourse of the input variables of the fuzzy logic system, the air gap z and the air gap change rate zc, are both [-2 2], the universe of discourse of the output D is [-2 2], and the adaptive gain in the adaptive law is 10.

[0216] Based on the above parameters, the DSP sends a signal to the electromagnetic levitation system, applying a force of 1.5 × 10⁻⁶ to the platform's levitation system. -4 The step response signal of the suspended air gap of m.

[0217] Experimental results of a single electromagnetic levitation system are as follows Figure 8 , Figure 9 As shown. Figure 8 The figure shows a comparison of air gap curves for non-singular fast terminal sliding mode control, fuzzy sliding mode control, and fuzzy adaptive sliding mode control in a single electromagnetic levitation system without applied disturbance. Experimental results show that fuzzy adaptive sliding mode control has the best system dynamic performance. Non-singular fast terminal sliding mode control reaches the desired air gap in 0.1s, fuzzy sliding mode control in 0.05s, and fuzzy adaptive sliding mode control in 0.03s. The speed of fuzzy adaptive sliding mode control is significantly better than the other two control strategies. Figure 9 The air gap curves of non-singular fast terminal sliding mode control, fuzzy sliding mode control, and fuzzy adaptive sliding mode control are compared after applying a periodic disturbance with an amplitude of 4.730N to a single electromagnetic levitation system. The experimental results show that the fuzzy adaptive sliding mode control has the best anti-interference ability. After the disturbance is added at 0.2s, it reaches stability and has the smallest fluctuation at 0.215s. After the disturbance ends at 0.3s, it returns to the desired air gap at 0.302s.

[0218] Figure 10 shows the synchronization experiment results of the four electromagnetic levitation systems after applying periodic disturbances with amplitudes of 4.816N, 4.730N, 4.644N, and 4.558N, respectively. Figure 10(a) shows the global air gap curve within 1 second under fuzzy adaptive sliding mode control and improved deviation coupling control. The system reaches the desired air gap in 0.063s, showing a fast response speed. After the disturbance is added at 0.2s, the overall fluctuation of the improved deviation coupling control is very small, demonstrating strong anti-interference ability. Figure 10(b) shows the locally magnified air gap curve when the disturbance is added from 0.2s to 0.25s under the improved deviation coupling control. It can be seen that the overall fluctuation under the improved deviation coupling control only reaches 1.506×10. -4 m, which improves the precision of microelectronics processing.

[0219] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A synchronous control method for a dual-control four-electromagnetic levitation system, used to control a magnetic levitation machining and positioning platform, characterized in that, This control method is based on fuzzy adaptive sliding mode control and improved deviation coupling control, and specifically includes the following steps: Step 1: Establish a mathematical model of the magnetic levitation processing and positioning platform; Step 2: Based on the mathematical model, design a non-singular fast terminal sliding mode controller for the single electromagnetic levitation system in the magnetic levitation processing and positioning platform; Step 3: Use fuzzy adaptive control to dynamically compensate for unknown disturbances in the non-singular fast terminal sliding mode controller, thus forming a fuzzy adaptive sliding mode controller; Step 4: Determine the stability of the fuzzy adaptive sliding mode controller and calculate the adaptive law; Step 5: Based on the mathematical model, an improved deviation coupling control structure is designed for the four electromagnetic levitation systems in the magnetic levitation processing and positioning platform. In this structure, the weighted average of the air gap deviations of each electromagnetic levitation system is introduced as steady-state fine-tuning.

2. The synchronous control method for a dual-control four-electromagnetic levitation system according to claim 1, characterized in that, The specific method for establishing the mathematical model of the magnetic levitation processing and positioning platform in step 1 includes: Taking the vertically downward direction as the positive direction of the single electromagnetic levitation system, and using a differential connection for the electromagnets of the magnetic levitation platform, the resultant electromagnetic force exerted by the upper and lower electromagnets on the guide rail in the single electromagnetic levitation system is: in, Vacuum permeability N represents the number of turns in the coil; A represents the cross-sectional area of ​​the iron core, in meters. 2 I0 is the bias current, i is the control current, and the excitation currents of the upper and lower electromagnets are I0+i, respectively. z with I0-i z , The air gap for magnetic levitation at equilibrium is denoted by z, and z is the vertical displacement of the levitation body relative to the equilibrium position. Expanding the resultant electromagnetic force at the equilibrium position (i,z) = (0,0) using Taylor series, we get: in, It is the current force coefficient; Here, i is the displacement force coefficient, and i0 is the current offset introduced by the system to counteract the platform's gravity G. The dynamic model of the magnetic levitation platform of this differential four-electromagnetic levitation system is established using the Lagrange method. The Lagrange equations are: Where T is the total kinetic energy of the system of particles, and qi is the generalized displacement of the system of particles. Let Q be the generalized velocity of the system of particles; if all forces acting on the system of particles are definite, then the generalized force Q is... i This can be expressed in terms of the potential energy of a system of point masses, namely: Therefore, the Lagrange equation can be written in the following form: Let L = TV represent the difference between the system's kinetic energy T and potential energy V, where L is called the Lagrange function or kinetic potential; then the Lagrange equation can be expressed in terms of kinetic potential as follows: in, It is the partial derivative of the Lagrange function L. It is the potential energy gradient term of the i-th generalized force of the system, describing the force tendency of the system in the i-th degree of freedom. It is the i-th generalized momentum of the system, which describes the inertia of the system in the i-th degree of freedom; Let α and β be the rotational degrees of freedom of the magnetic levitation platform about the x and y axes, and z be the translational degrees of freedom in the vertical direction. Then z1, z2, z3, and z4 are the translational degrees of freedom of the four levitation electromagnets in the z direction, respectively. Let m be the translational velocity of each of the four levitation electromagnets in the z-direction, and let m be the mass of the magnetic levitation platform. The translational kinetic energy is: The rotational kinetic energy is: The total kinetic energy of the system is the sum of the two kinetic energies, and the total kinetic energy T of the system is: Where a and b are the center distances of the levitation electromagnet in the Y-axis and X-axis directions, respectively. and These are the moments of inertia of the suspension platform about the X-axis and Y-axis, respectively. Substituting the formula for the total kinetic energy of the system into the Lagrange equation, we obtain the following dynamic model: Where F1, F2, F3, and F4 are the electromagnetic attraction forces of four differential electromagnets, defined as follows: for The equivalent mass for the corresponding degree of freedom, and the coupling mass are: i1, i2, i3, and i4 are the control currents for the four differential electromagnets. Let Z be the translational acceleration of each of the four levitation electromagnets in the z-direction, then we get The system dynamics equations can then be simplified to: in, in, Here is the displacement matrix. For the current matrix, and These are the current force coefficient and displacement force coefficient of the nth differential electromagnet, respectively. For the quality matrix, Here is the displacement stiffness matrix. Current stiffness matrix.

3. The synchronous control method for a dual-control four-electromagnetic levitation system according to claim 1, characterized in that, The specific method for designing a non-singular fast terminal sliding mode controller for the single electromagnetic levitation system in the magnetic levitation processing and positioning platform based on the mathematical model in step 2 includes: Let the reference air gap of the magnetic levitation system be The actual air gap is The air gap error of a single electromagnetic levitation system is defined as: Define the non-singular fast terminal sliding surface as: in, Let be the independent variable and the first derivative of the independent variable, respectively. The coefficients of the sliding surface k1, k2>0; λ>1; p, q are positive odd numbers and satisfy p>q; The expression for the non-singular fast terminal sliding surface with air gap error e as the variable is as follows: in, , , These are the rates of change of air gap error, reference air gap, and actual air gap, respectively. The derivative expression for the sliding surface is: in, It is the second derivative of the air gap error; Equation of state in a magnetic levitation platform Below, the derivative of the sliding surface is: Non-singular fast terminal sliding mode control typically employs a strategy of equivalent control plus switching control, i.e. The equivalent control law for non-singular fast terminal sliding mode control can be derived from the sliding surface derivative as follows: The switching control law is usually chosen based on the constant-rate approach law, i.e. Under these conditions, the final non-singular fast terminal sliding mode control law is: Where η is the switching gain, sgn(s) is the sign function, and D is the disturbance experienced by the system.

4. The synchronous control method for a dual-control four-electromagnetic levitation system according to claim 1, characterized in that, The specific method for constructing a fuzzy adaptive sliding controller by using fuzzy adaptive control to dynamically compensate for unknown disturbances in the non-singular fast terminal sliding mode controller in step 3 includes: by Design a fuzzy system with fuzzy input variables; The inference part of the fuzzy controller uses the minimum value fuzzy inference method, and the defuzzification part uses the weighted average method. The output of the fuzzy system is: in, They are respectively Input the membership functions of variables x1 and x2; These are the fuzzy sets corresponding to x1 and x2, respectively; Let p1 and p2 be the number of fuzzy rules for x1 and x2, respectively, and p1 and p2 be the number of fuzzy sets for x1 and x2, respectively. It serves as the weighting center for the output values ​​of the fuzzy system. As a free parameter, a two-dimensional fuzzy vector is introduced. Then, the output of the fuzzy system can be expressed as: The parameter θ is dynamically adjusted according to the adaptive law, and the optimal parameter is... The derivation formula is as follows: in, To determine the output of the fuzzy system at the air gap x under unknown parameters θ, In the optimal estimation parameter θ * The output of the lower fuzzy system at air gap x, For parameters A set; The fuzzy adaptive sliding mode control law is: 。 5. The synchronous control method for a dual-control four-electromagnetic levitation system according to claim 1, characterized in that, The specific method for determining the stability of the fuzzy adaptive sliding mode controller and calculating the adaptive law in step 4 includes: Define the free parameter error as Minimize the fuzzy estimation error as Define Lyapunov functions as follows: Then its derivative in, It is adaptive gain; Substitution We can obtain: when At that time, the adaptive law is calculated as follows: At this time According to Lyapunov's stability theorem, the fuzzy adaptive sliding mode control system is asymptotically stable.

6. The synchronous control method for a dual-control four-electromagnetic levitation system according to claim 1, characterized in that, Step 5, based on the mathematical model, describes the design of an improved deviation coupling control structure for the four electromagnetic levitation systems in the magnetic levitation processing and positioning platform. The specific method for introducing a weighted average of the air gap deviations of each electromagnetic levitation system as a steady-state fine-tuning feature in this structure includes: A position compensator is set for each electromagnetic levitation system in the magnetic levitation processing and positioning platform to generate a synchronous compensation signal; By introducing the weighted average of the air gap deviations of each electromagnetic levitation system into the position compensator as a steady-state fine-tuning term, an improved deviation coupling control structure is obtained. The weighting coefficients in the weighted average are determined based on the proportion of the absolute value of the air gap deviation of each electromagnetic levitation system to the sum of the absolute values ​​of the air gap deviations of the four electromagnetic levitation systems: 。

Images