A decoupling method for permanent magnet synchronous planar motor

Abstract

The present invention relates to a decoupling method for a permanent magnet synchronous planar motor and provides a method for dynamically compensating a permanent magnet synchronous planar motor using an extended state observer. The method can significantly reduce the coupling degree between six degrees of freedom, thereby reducing the influence of a magnetic levitation motor rotor on position closed-loop control of other degrees of freedom during movement, thereby improving the position loop control performance of the magnetic levitation motor.

Description

Technical Field

[0001] The invention relates to the control of a motor, and in particular to a decoupling method of a permanent magnet synchronous planar motor. Background Art

[0002] Permanent Magnet Synchronous Planar Motor (PMSPM) has good comprehensive performance in terms of structure, control accuracy, loss, etc., so it is widely used in modern precision and ultra-precision manufacturing equipment such as lithography machines. Figure 1 As shown. The support methods used by planar motors are mainly mechanical, air-floating and magnetic levitation. Considering that the next generation of lithography machines will use ultraviolet light with a shorter wavelength as the lithography light source in order to achieve higher accuracy and resolution, the lithography process requires the lithography platform to work in a vacuum environment to avoid air absorbing light energy. Mechanical support requires lubrication, and lubricants can pollute the vacuum environment. Air-floating support is also limited by the constraints of the vacuum environment. Therefore, magnetic levitation planar motors are more in line with the development trend of lithography machines.

[0003] Under the condition of an ideal magnetic levitation planar motor model, the decoupling method using the generalized inverse matrix can solve the coupling problem in the magnetic levitation planar motor control system. However, the actual magnetic levitation planar motor model has modeling errors, and the magnetic levitation planar motor also has permanent magnet size deviation, permanent magnet magnetization deviation and manufacturing error. Usually due to the existence of the above unfavorable factors, the decoupling method using the generalized inverse matrix can transform the magnetic levitation planar motor system from a strong coupling system to a weak coupling system. In order to obtain better motion control performance, the decoupling performance of the weak coupling system should be further optimized.

[0004] For the magnetically suspended permanent magnet synchronous planar motor, once the winding structure, winding arrangement and permanent magnet array structure are determined, the coupling relationship of the system is determined. Based on the electromagnetic model of the planar motor, the control current of the mover at different positions is solved in real time by using mathematical and control theory methods, so that the six-degree-of-freedom motion control of the mover can be achieved.

[0005] The decoupling method of generalized inverse matrix can realize decoupling control of magnetic levitation permanent magnet synchronous planar motor, but its decoupling accuracy depends on the accuracy of electromagnetic model. Since the model error caused by machining error is difficult to reflect in modeling, it is of great significance to dynamically compensate for static decoupling.

[0006] The coefficient matrix of the magnetic levitation permanent magnet synchronous planar motor can be obtained according to the electromagnetic force and torque equations. The electromagnetic decoupling of the permanent magnet synchronous planar motor can be achieved by obtaining the generalized inverse matrix of the coefficient matrix. Usually, there are many ways to decouple the magnetic levitation permanent magnet synchronous planar motor according to the different structures, but the purpose of decoupling is the same, which is to obtain the current that can realize the motion control of the planar motor. The coefficient matrix of the sixteen-phase magnetic levitation planar motor is a 6×16 matrix. The generalized inverse matrix has multiple sets of current solutions. Different solution systems can be selected by adding constraints.

[0007] Ideally, the decoupling method using the generalized inverse matrix can achieve complete decoupling of the system. However, due to factors such as model deviation and motor manufacturing errors, there is still a certain degree of weak coupling between the decoupled subsystems.

[0008] Chinese patent CN201710213921.X discloses a method for measuring the three-degree-of-freedom position of a large-area magnetically levitated planar motor rotor. The measurement system used in this method includes eight Z-direction eddy current sensors, two Y-direction eddy current sensors, an X-direction absolute grating, and a Y-direction absolute grating. It can overcome the interference of the heat dissipation holes on the surface of the magnetic steel on the displacement measurement of the Z-direction eddy current sensor, and realize the accurate measurement of the three degrees of freedom of the planar motor rotor in the stator fixed coordinate system. However, the patent does not make more optimization designs in terms of decoupling.

[0009] Chinese patent CN201811574277.X discloses a coil current switching algorithm based on the magnetic levitation planar motor motion system of a lithography machine, establishes the coupling equation between the six-degree-of-freedom force of the planar motor rotor and the coil current, divides the rotor coil into a switching group and a non-switching group, and then divides the switching group into a sudden switching group and a gradual switching group according to the way the coil leaves the magnetic steel array; the S function is used as the current switching weight function for the sudden switching group, and the cosine function is used as the current switching weight function for the gradual switching group. With the minimum bi-norm of all coil current vectors as the goal, the coupling equation of force and current is solved to obtain the current value of each coil. It can reduce the heating loss of the planar motor coil as much as possible, and at the same time realize the smooth switching of the coil current in the full motion range of the moving coil magnetic levitation planar motor rotor. However, this patent replaces the weight function of the rotor coils in groups, and does not make more optimization designs in terms of decoupling. Summary of the invention

[0010] The purpose of the present invention is to provide a decoupling method for a permanent magnet synchronous planar motor, which solves the problem of optimizing the decoupling performance, reduces the degree of coupling between the six degrees of freedom of the permanent magnet synchronous planar motor, and thereby reduces the influence of the mover on the position closed-loop control of other degrees of freedom during movement, thereby improving the position loop control performance of the permanent magnet synchronous planar motor.

[0011] In order to achieve the above object, the technical solution adopted by the present invention is:

[0012] The present invention provides a decoupling method for a permanent magnet synchronous planar motor, which comprises the following steps:

[0013] S1: Establish the second-order system equation of permanent magnet synchronous planar motor with m-input and m-output;

[0014] S2: Combine and transform the coupling matrix composed of the established model coefficients and the coefficient perturbations caused by the model deviation with the external disturbance and the parts unrelated to the control quantity to obtain the transformed equation;

[0015] S3: Use the extended state observer to treat the unknown external disturbance of the system and the internal disturbance of the model as the total disturbance of the system, observe it as the extended state of the nonlinear uncertain object, establish its mathematical model, combine it with the transformed equation obtained in S2, reasonably select the parameters of its mathematical model, and effectively realize the estimation of the equivalent disturbance;

[0016] S4: Based on the effective estimate of the equivalent disturbance, after nonlinear dynamic compensation of the extended state observer, a new equation is combined, based on which the original system containing unknown uncertainties is regarded as a set of independent single-input and single-output subsystems.

[0017] Preferably, the generalized inverse matrix decoupling is used to transform the strongly coupled system into multiple subsystems with weak coupling. In one of these subsystems, the coupling of other subsystems to the subsystem is regarded as the total disturbance acting on the subsystem, and the extended state observer is used to estimate and compensate.

[0018] For a second-order system with m inputs and m outputs, it can be written as:

[0019]

[0020]

[0021] …… ;

[0022]

[0023] Y 1 =X 1 ,Y 2 =X 2 ,…,Y m =X m ;

[0024] Where Y i 、u i , X i is the output, input, and state variable of the ith subsystem; f iis the external disturbance; g i b is the part that has nothing to do with the control amount; ij , Δb ij The coefficients of the established model and the coefficient perturbations caused by the model deviation respectively;

[0025] Assume that the coupling matrix in the coupled system is reversible and can be written as B = B 0 +ΔB;

[0026]

[0027] Where B0 and ΔB are the static coupling matrix and the parameter perturbation matrix caused by model deviation, respectively;

[0028] definition is the total disturbance of the ith subsystem;

[0029] By definition, the second-order system is written as:

[0030]

[0031] …… ;

[0032]

[0033] Y 1 =X 1 ,Y 2 =X 2 ,…,Y m =X m ;

[0034] Let U=B o u, and u=B 0 -1 U, we get:

[0035]

[0036] …… ;

[0037]

[0038] Y 1 =X 1 ,Y 2 =X 2 ,…,Y m =X m ;

[0039] The mathematical model of the extended state observer is:

[0040] e=Z 1 -Y;

[0041]

[0042]

[0043]

[0044] in,

[0045] When |e|>δ, fal(e,α,δ)=|e| α sign(e), when |e|<δ, fal(e, α, δ) = e / δ 1-α ,

[0046] Where e is the system error, u(t), Y, and b are the control quantity, output, and coefficient of the system respectively; β 1 , β 2 , β 3 are the output error correction gains respectively; α is the nonlinear factor, which is usually 0.5, 0.25 and 0.125; δ is the filtering factor, δ>0; Z 1 , Z 2 , Z 3 are Y tracking signal, Z 1 Differentiated signal, tracking signal of system disturbance.

[0047] Preferably, in the extended state observer mathematical model, Z 3 The observed disturbance is The parameter m in the formula is 6, and the second-order system is written as:

[0048]

[0049]

[0050] …… ;

[0051]

[0052] Y 1 =X 1 ,Y 2 =X 2 ,…,Y m =X m .

[0053] Preferably, an extended state observer is used to estimate the state of the controlled object in real time using the system output, and the unknown external disturbance of the system and the internal disturbance of the model are uniformly regarded as the total disturbance of the system and observed as the extended state of the nonlinear uncertain object to achieve feedback control and disturbance compensation.

[0054] Due to the application of the above technical solution, the present invention has the following advantages compared with the prior art:

[0055] The decoupling method of the permanent magnet synchronous planar motor of the present invention provides a method for dynamically compensating the permanent magnet synchronous planar motor using an extended state observer. The method can significantly reduce the degree of coupling between the six degrees of freedom, thereby reducing the influence of the magnetic levitation motor rotor on the position closed-loop control of other degrees of freedom during movement, thereby improving the position loop control performance of the magnetic levitation motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Hereinafter, some specific embodiments of the present invention will be described in detail in an exemplary and non-limiting manner with reference to the accompanying drawings. In the accompanying drawings:

[0057] Figure 1 It is the structural diagram of permanent magnet synchronous planar motor;

[0058] Figure 2 It is the block diagram of decoupling dynamic compensation of magnetically suspended planar motor. DETAILED DESCRIPTION

[0059] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0060] This example involves an improved method for significantly reducing the degree of coupling between the six degrees of freedom, thereby reducing the influence of the magnetic levitation planar motor rotor on the position closed-loop control of other degrees of freedom during movement, and improving the position loop control performance of the magnetic levitation planar motor.

[0061] 1) Due to the errors in the model, the generalized inverse matrix decoupling is essentially to transform the strongly coupled system into multiple weakly coupled subsystems. In one of these subsystems, the coupling of other subsystems to the subsystem can be regarded as the total disturbance acting on the subsystem, and then the extended state observer is used to estimate and compensate.

[0062] 2) For a second-order system with m inputs and m outputs, it can be written as:

[0063]

[0064]

[0065] …

[0066]

[0067] Y 1 =X 1 ,Y2 =X 2 ,…,Y m =X m

[0068] 3) In the formula, Y i 、u i , X i is the output, input, and state variable of the ith subsystem; f i is the external disturbance; g i b is the part that has nothing to do with the control amount; ij , Δb ij The coefficients of the established model and the coefficient perturbations caused by model deviations respectively.

[0069] 4) Assume that the coupling matrix in the coupled system is reversible and can be written as B = B 0 +ΔB

[0070]

[0071] 6) where B0 and ΔB are the static coupling matrix and the parameter perturbation matrix caused by model deviation, respectively.

[0072] 7) Definition is the total disturbance of the ith subsystem.

[0073] 8) According to the definition of (7), the formula of step (2) can be written as:

[0074]

[0075]

[0076] …

[0077]

[0078] Y 1 =X 1 ,Y 2 =X 2 ,…,Y m =X m

[0079] 9) Let U=B o u, and u=B 0 -1 U, we can get:

[0080]

[0081]

[0082] …

[0083]

[0084] Y 1 =X 1 ,Y 2 =X 2 ,…,Y m =X m

[0085] 10) The function of the extended state observer is to use the system output to estimate the state of the controlled object in real time, and to regard the unknown external disturbance of the system and the internal disturbance of the model as the total disturbance of the system, and observe them as the extended state of the nonlinear uncertain object to realize feedback control and disturbance compensation. Its mathematical model is:

[0086] e=Z 1 -Y

[0087]

[0088]

[0089]

[0090] in,

[0091] When |e|>δ, fal(e,α,δ)=|e| α sign(e), when |e|<δ, fal(e, α, δ) = e / δ 1-α .

[0092] 11) Where e in (10) is the system error, u(t), Y, and b are the control quantity, output, and coefficient of the system respectively; β 1 , β 2 , β 3 are the output error correction gains respectively; α is the nonlinear factor, which is usually 0.5, 0.25 and 0.125; δ is the filtering factor, δ>0; Z 1 , Z 2 , Z 3 are Y tracking signal, Z 1 Differentiated signal, tracking signal of system disturbance.

[0093] 12) For the mathematical model of (10), Z 3 The observed disturbance is As long as the parameters in the formula are properly selected, ESO can better estimate the equivalent disturbance ρi, so formula (9) can be written as:

[0094]

[0095]

[0096] …

[0097]

[0098] Y 1 =X 1 ,Y 2 =X 2 ,…,Y m =X m

[0099] 13) It can be seen from step (12) that after the nonlinear dynamic compensation of ESO, a multi-input, multi-output system with unknown uncertainties can be regarded as a set of independent single-input, single-output subsystems. The dynamic compensation performance of the system depends on the degree of observation of the disturbance by ESO. The parameters in ESO can be adjusted to determine the degree of observation of the system. The degree of accuracy and compensation strength.

[0100] 14) After using ESO for compensation, on the basis of static decoupling, the extended state observer is used to perform dynamic decoupling compensation on the magnetic suspension planar motor system. Since the output of the magnetic suspension planar motor is the displacement and angle in six degrees of freedom, the value of m in step (12) is 6. The block diagram of the decoupling dynamic compensation of the magnetic suspension planar motor system is as follows: Figure 2 As shown. Figure 2 In, x r ~θ zr is the six-degree-of-freedom position input of the magnetic levitation planar motor, x~θ z is the six-degree-of-freedom position output of the magnetic suspension planar motor, f 1 ~f 6 is the external disturbance acting on the six degrees of freedom, x~θ z The axis compensation unit is The internal structure of the compensation unit is the embodiment of the formula in step (9). It can be seen that the given signal is compensated for the disturbance and model deviation through the compensation module, so the system has better decoupling performance.

[0101] There are also applications of extended state observers (or extended state compensators) in servo motors, but the applications of extended state compensators in servo motors and planar motors are different. Extended state compensators are generally used to estimate and compensate for by feedforward items in servo motors. For example, for friction disturbances in precision permanent magnet synchronous servo systems, a friction feedforward compensation method is designed based on the friction model to compensate for the friction disturbances of the system. Alternatively, the extended state observer is introduced into the optoelectronic stable platform servo system to observe the total disturbance of the system, and the observed total disturbance is compensated into the sliding mode controller to better suppress system jitter and improve the system's ability to resist external disturbances, solving the contradiction between the high performance of traditional sliding mode control and system jitter.

[0102] The application of extended state compensator in planar motor is essentially in terms of compensation, which can improve the robustness of the system. The extended state observer can be used to observe the dynamic changes of the macro-dynamic system and compensate for the coupled thrust and other disturbances in the system; the unmodeled dynamic and uncertain external disturbances can be regarded as a comprehensive disturbance term, and the extended state observer can be used to observe and compensate for the comprehensive disturbance term; a rotor position calculation method can be proposed for the nonlinear problem of the drive system under fault mode, and the dynamic performance of the five-phase motor drive system can be improved during operation without position control; the non-parametric uncertainty in the permanent magnet synchronous motor can be divided into two parts: periodic uncertainty and non-periodic uncertainty, and an extended state observer can be designed to estimate the unknown state of the system and compensate for the non-periodic uncertainty, thereby improving the robustness of the system; with Based on the dual closed-loop vector control structure, an extended state observer is added to the control system to track the output signal while compensating for the sum of the internal and external disturbances of the system to enhance the system's anti-disturbance capability; the extended state observer can also be used in the mechanical angular velocity estimation module constructed according to the sliding mode control principle to achieve the estimation of the motor angular velocity, real-time tracking of the speed and load disturbances, and feedback the disturbance to the preceding speed controller for compensation, thereby improving the system control accuracy; for the problem of high-performance control of permanent magnet synchronous motors without position sensors in the full speed range, a hybrid position estimation strategy for load torque compensation can be proposed based on the extended state observer.

[0103] In this example, the use of extended state observer is added on the premise of adopting the generalized inverse matrix decoupling method, which can further improve the decoupling performance of the system and realize the control of six degrees of freedom, three electromagnetic forces and three torques.

[0104] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable people familiar with this technology to understand the contents of the present invention and implement them accordingly. They cannot be used to limit the protection scope of the present invention. Any equivalent changes or modifications made according to the spirit of the present invention should be included in the protection scope of the present invention.

Claims

1. A decoupling method for a permanent magnet synchronous planar motor, It is characterized in that It includes the following steps: S1: Establish the second-order system equation of permanent magnet synchronous planar motor with m-input and m-output; S2: Combine and transform the coupling matrix composed of the established model coefficients and the coefficient perturbations caused by the model deviation with the external disturbance and the parts unrelated to the control quantity to obtain the transformed equation; S3: Use the extended state observer to treat the unknown external disturbance of the system and the internal disturbance of the model as the total disturbance of the system, observe it as the extended state of the nonlinear uncertain object, establish its mathematical model, combine it with the transformed equation obtained in S2, reasonably select the parameters of its mathematical model, and effectively realize the estimation of the equivalent disturbance; S4: Based on the effective estimation of the equivalent disturbance, after the nonlinear dynamic compensation of the extended state observer, a new equation is obtained by combining, based on which the original system containing unknown uncertainties is regarded as a set of independent single-input and single-output subsystems; The generalized inverse matrix decoupling is used to transform the strongly coupled system into multiple subsystems with weak coupling. In one of these subsystems, the coupling of other subsystems to the subsystem is regarded as the total disturbance acting on the subsystem, and the extended state observer is used to estimate and compensate. For a second-order system with m inputs and m outputs, it can be written as: ……； AND 1 = X 1 ,AND 2 = X 2 , …,AND m =X m ; Where Y i 、u i , X i is the output, input, and state variable of the ith subsystem; f i is the external disturbance; g i b is the part that has nothing to do with the control amount; ij , Δb ij The coefficients of the established model and the coefficient perturbations caused by the model deviation respectively; Assume that the coupling matrix in the coupled system is reversible and can be written as B = B 0 +ΔB; Where B 0 , ΔB are the static coupling matrix and the parameter perturbation matrix caused by model deviation respectively; definition is the total disturbance of the ith subsystem; By definition, the second-order system is written as: ……； AND 1 = X 1 ,AND 2 = X 2 , …,AND m =X m ; Let U=B o u, and u=B 0 -1 U, we get: ……； AND 1 = X 1 ,AND 2 = X 2 , …,AND m =X m ; The mathematical model of the extended state observer is: e=Z 1 -Y; in, When |e|>δ, fal(e, α, δ) = |e| α sign(e), when |e|<δ, fal(e, α, δ) = e / δ 1-α , Where e is the system error, u(t), Y, and b are the control quantity, output, and coefficient of the system respectively; β 1 , β 2 , β 3 are the output error correction gains respectively; α is the nonlinear factor, which can be any one of 0.5, 0.25 and 0.125; δ is the filtering factor, δ>0; Z 1 , Z 2 , Z 3 are Y tracking signal, Z 1 Differentiated signal, tracking signal of system disturbance.

2. The decoupling method of the permanent magnet synchronous planar motor according to claim 1, Features: In the mathematical model of the extended state observer, Z 3 The observed disturbance is Z i3 = i , where the parameter m is 6, the second-order system is written as: 1 = ρ 1 +U 1 - 1 ≈ In 1 ; 1 = ρ 1 +U 1 - 2 ≈ In 2 ; … … ； m = ρ m +U m - m ≈ In m ; AND 1 = X 1 ,AND 2 = X 2 , …,AND m =X m 。 3. The decoupling method of the permanent magnet synchronous planar motor according to claim 1, Features: The extended state observer is used to estimate the state of the controlled object in real time using the system output. The unknown external disturbance of the system and the internal disturbance of the model are uniformly regarded as the total disturbance of the system and observed as the extended state of the nonlinear uncertain object to achieve feedback control and disturbance compensation.

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