A self-adaptive control method for a high-precision magnetic suspension motion platform with high degrees of freedom

Abstract

This invention discloses an adaptive control method for a high-precision magnetic levitation motion platform with multiple degrees of freedom, belonging to the field of precision electromechanical motion control technology. It addresses the technical problems of existing magnetic levitation motion platforms, including dynamic nonlinearity, mutual interference of magnetic flux among multiple degrees of freedom, inability of traditional fixed-parameter PID controllers to adapt to magnetic saturation and environmental disturbances, low efficiency of manual parameter tuning, and chattering in sliding mode control. This invention first establishes a nonlinear dynamic model of the magnetic levitation platform using the Lagrange energy method, and then uses differential geometric state feedback linearization to transform the nonlinear dynamic system into independent linear subsystems, simplifying the system control logic. A composite control architecture combining an RBF radial basis function neural network and incremental PID is built, utilizing the neural network to dynamically update the three main control parameters of the PID online, while simultaneously adding a motion trajectory feedforward compensation module to offset trajectory errors caused by sensor and power amplifier delays and mover inertia. This invention eliminates the need for manual tuning of control parameters, effectively suppresses platform attitude jitter and operational volatility, achieves a repeatability accuracy of 300nm under axis linkage, and exhibits superior operational stability compared to traditional PID and sliding mode variable structure control. It can replace imported magnetic levitation precision motion platforms and is suitable for micro-nano packaging, optical inspection, and semiconductor wafer processing scenarios.

Description

Technical Field

[0001] This invention relates to the fields of precision motion control and magnetic levitation mechatronics, specifically to an adaptive control method for a high-degree-of-freedom magnetic levitation motion platform. Background Technology

[0002] The magnetic levitation motion platform relies on electromagnetic attraction to achieve contactless levitation and drive of the moving part, completely eliminating friction, wear, and lubrication pollution of mechanical guide rails. It is a core equipment for nanoscale ultra-precision manufacturing and is widely used in fields such as lithography machine workpiece stages, micro-optical device inspection, and MEMS micro-assembly.

[0003] Existing magnetic levitation platform control schemes have significant drawbacks: First, the electromagnetic force and excitation current of magnetic levitation electromagnets are inherently nonlinear, and there is magnetic flux crosstalk between multi-axis electromagnets. Conventional Taylor first-order local linearization can only achieve approximate linearity at the center point of the magnetic gap, and the control accuracy rapidly decreases after deviating from the center point. Second, traditional fixed-parameter PID controllers can only adapt to a single steady-state condition. When faced with time-varying disturbances such as workshop temperature fluctuations, long-term use of electromagnets causing magnetic performance decay, and ground micro-vibrations, engineers need to manually adjust the parameters repeatedly on-site, resulting in long debugging cycles and poor versatility. Third, while sliding mode variable structure control has strong anti-disturbance capabilities, the control quantity has inherent high-frequency chattering, which can excite micro-vibrations of the mover and cannot meet the 300nm-level repeatability positioning accuracy requirements.

[0004] Existing technologies do not combine global state feedback linearization with neural network adaptive parameter tuning, and cannot simultaneously solve the three types of problems: system nonlinearity, time-varying operating conditions, and hardware delay. Therefore, they are difficult to meet the requirements of domestic ultra-precision positioning. Hence, this adaptive control method is proposed. Summary of the Invention

[0005] To address the shortcomings of existing magnetic levitation platforms, such as small nonlinear correction range, reliance on manual adjustment of controller parameters, chattering in sliding mode control, and large hardware timing delay errors, this invention provides an adaptive control method for a high-degree-of-freedom magnetic levitation motion platform. This method achieves full-domain nonlinear linearization, fully automatic adaptive tuning of control parameters, and dynamic compensation for trajectory errors. It stabilizes the platform's repeatability accuracy within 300nm, reduces system operational volatility, and enables the replacement of imported equipment.

[0006] The structure of the magnetic levitation platform adapted to this invention is as follows: the mover is an integrated permanent magnet levitation platform, the stator is distributed with 8 sets of levitation electromagnets and 4 sets of horizontal drive electromagnets, the platform can realize X / Y horizontal translation, Z-axis vertical levitation, pitch around the X-axis, and roll around the Y-axis, with no rotational degree of freedom; the detection end adopts a laser grating sensor with a resolution of 0.1nm, and the main control adopts an XC7K325T FPGA chip to ensure microsecond-level computing speed.

[0007] Nonlinear dynamic modeling with degrees of freedom: Abandoning the commonly used simplified linear modeling approach, this model considers three types of nonlinear disturbances: magnetic gap leakage, core magnetic saturation, and air damping. Time-varying nonlinear dynamic equations are established by calculating the translational and rotational kinetic energy of the mover, the magnetic potential energy of the electromagnet, and the air damping loss in the magnetic gap using Lagrange's formula. The model directly incorporates a temperature coefficient to correct for magnetic gap deformation errors caused by ambient temperature changes, eliminating the need for additional temperature compensation hardware.

[0008] Global State Feedback Precise Linearization: Unlike local Taylor approximation linearization, this method uses differential geometry theory to perform relative order verification on the state equations of the dimensional system. The verification shows that the total relative order of the system equals the dimension of the state variables, satisfying the global linearization condition. By constructing nonlinear state feedback terms to cancel out internal nonlinear terms, the multivariable nonlinear system is transformed into five sets of independent second-order linear systems. Linearization covers the entire working stroke of the platform, eliminating control blind spots.

[0009] The RBF neural network adaptive PID control logic consists of three layers: an inner-layer incremental PID controller responsible for closed-loop error adjustment, which avoids platform jitter caused by sudden changes in control inputs compared to positional PID controllers; an upper three-layer RBF neural network comprising an input layer, a hidden layer, and an output layer; a four-dimensional input vector representing real-time displacement deviation, attitude angle deviation, coil excitation current, and ambient temperature; 12 neurons in the hidden layer extracting nonlinear features; and the output layer directly outputs the three PID parameters. The network uses gradient descent to update weights, avoiding parameter oscillations, with an iteration period of 1ms, meeting the real-time requirements of precision platforms.

[0010] Dual feedforward compensation for timing and inertia: At the hardware level, all sensors and power amplifiers are synchronized through the FPGA global clock, and the timing deviation is controlled within 0.5μs; at the algorithm level, the motioner acceleration signal is collected, the inertial rebound amount during acceleration and deceleration is predicted, and the excitation current is corrected 2.5ms in advance to eliminate overshoot and lag problems during start-stop.

[0011] Excellent nonlinear correction effect: It achieves full-domain linearization across the entire magnetic gap, with a nonlinear error ≤20nm, solving the problem of limited working range of traditional local linearization. Strong adaptability: No manual modification of PID parameters is required throughout the process. It automatically adapts to complex working conditions such as magnetic performance decay, temperature change, and ground micro-vibration, improving on-site commissioning efficiency by more than 90%. Improved control precision and stability: Compared with traditional PID, the dynamic response speed is improved by 32%; compared with sliding mode variable structure control, high-frequency chattering is eliminated; the steady-state fluctuation rate of the table is reduced by 51%; and the repeatability of axis linkage is stabilized at 300nm. High compatibility with domestic production: Pure algorithm optimization does not require modification of the existing magnetic levitation hardware structure, the transformation cost is low, and it can directly replace the imported magnetic levitation motion platform of the same specification. Detailed Implementation

[0012] A magnetic levitation platform with a stroke of 10mm × 10mm and a levitation magnetic gap of 5mm was selected for field testing. The ambient temperature was 22-28℃, and the ground micro-vibration amplitude was ≤50nm. First, the platform structural parameters were entered to complete the dynamic modeling, and the FPGA was used for offline system relative order verification. During online operation, the grating sensor collected platform attitude and displacement data every 0.2ms, which was input into the RBF neural network. The neural network updated a set of PID parameters every 1ms; timing and inertial feedforward compensation were simultaneously enabled. The results of continuous 72-hour operation test showed a platform repeatability accuracy of 287nm, a steady-state fluctuation rate of 0.021%, and no attitude jitter or trajectory drift.

[0013] Comparative Example 1: Traditional fixed-parameter PID, under the same working conditions, the repeatability is 524nm and the fluctuation rate is 0.073%. Manual parameter adjustment is required after temperature change. Comparative Example 2: Sliding mode variable structure control, the repeatability is 351nm, but there is high-frequency jitter, which cannot be used for optical inspection scenarios. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the overall control architecture of the present invention; Figure 2 Here is a block diagram of the internal structure of the RBF neural network-PID; Figure 3 This is a schematic diagram showing the direction of motion of the platform's degrees of freedom; Figure 4 A comparison curve of positioning errors for three control algorithms.

[0015] Figure 1 Labels: 1-FPGA main control unit, 2-grating displacement acquisition module, 3-RBF neural network parameter tuning module, 4-incremental PID control module, 5-feedforward compensation module, 6-electromagnetic drive power amplifier, 7-magnetic levitation moving platform Figure 2 Labels: 21-Input layer, 22-Hidden layer, 23-Output layer, 24-PID parameter output port Figure 3 Labels: 31 - X-axis translation, 32 - Y-axis translation, 33 - Z-axis suspension, 34 - X-axis pitch, 35 - Y-axis roll Figure 4 Labels: 41 - Error curve of the algorithm of this invention, 42 - Error curve of traditional PID, 43 - Error curve of sliding mode variable structure, the horizontal axis is running time, and the vertical axis is positioning error (nm).

Claims

1. An adaptive control method for a high-precision magnetic levitation motion platform with multiple degrees of freedom, characterized in that, This invention relates to a magnetic levitation motion platform with X-axis translation, Y-axis translation, Z-axis suspension, X-axis pitch, and Y-axis roll degrees of freedom. The platform hardware includes an FPGA main control unit, a nano-grating displacement sensor, a multi-channel electromagnetic drive amplifier, and a levitation electromagnet assembly. The control method includes the following steps: S1. Establish a nonlinear dynamic model with degrees of freedom: Based on the second type of Lagrange energy equation, collect the kinetic energy of the mover, electromagnetic potential energy, and magnetic gap damping dissipation energy, and incorporate the electromagnetic saturation, leakage magnetic field, and ambient temperature magnetic gap deformation disturbance parameters to construct a set of input-output nonlinear dynamic equations. S2. Linearization of global state feedback: The relative order of the system is determined for the nonlinear dynamic model obtained in S1, and a nonlinear state feedback compensation function is constructed to map the nonlinear system in the working range of 0-20mm of global magnetic gap into 5 sets of unrelated second-order linear single-input single-output subsystems, thereby eliminating the inherent nonlinear characteristics of the system. S3. Construct an RBF neural network-PID composite controller: Use incremental PID as the bottom closed-loop feedback controller to achieve real-time correction of displacement error; build a three-layer RBF radial basis neural network, take the displacement of the mover, attitude angle, coil current and ambient temperature collected by the grating sensor as the network input, and output the PID proportional coefficient Kp, integral coefficient Ki and derivative coefficient Kd. Iterate and update the network weights every 1ms through gradient descent method to complete the adaptive adjustment of parameters. S4. Trajectory feedforward and timing synchronization compensation: Based on the real-time motion acceleration of the mover, the inertial impact is predicted, and the electromagnetic force compensation command is output in advance to offset the start-stop overshoot; the sampling timing of the sensor and power amplifier is unified through the microsecond-level clock bus inside the FPGA to eliminate the trajectory deviation caused by hardware delay.

2. The adaptive control method for a high-precision magnetic levitation motion platform with multiple degrees of freedom according to claim 1, characterized in that, In S3, the number of hidden layer neurons in the RBF neural network is set to 12, the activation function is Gaussian radial basis function, and the learning rate is set to 0.08 to avoid network iterative divergence. An adaptive control method for a high-precision magnetic levitation motion platform with multiple degrees of freedom according to claim 1, characterized in that, The inertial compensation command advance output time in S4 is fixed at 2.5ms, which is suitable for the motion requirements of the magnetic levitation mover in the full speed range of 0.01-0.5m / s. An adaptive control method for a high-precision magnetic levitation motion platform with multiple degrees of freedom according to claim 1, characterized in that, After S2 linearization, the nonlinear error of the system throughout its entire stroke is controlled within 20nm.

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