CN104977901B - Triaxial movement platform modified cross-coupling control device and method - Google Patents

Abstract

An improved cross-coupling control device and method for a three-axis motion platform, characterized in that: the device includes three parts: a main circuit, a control circuit and a control object; the main circuit includes an AC voltage regulating module, a rectifying and filtering module, and an IPM inverter module; The invention adopts a contour error estimation method in three-axis coordinated control, establishes a three-axis contour error model, improves the structure of cross-coupling control, and designs a three-dimensional space contour error controller.

Description

Improved cross-coupling control device and method for three-axis motion platform

Technical field: The present invention provides an improved cross-coupling control device and method for a three-axis motion platform, which belongs to the technical field of numerical control.

Background technology: In the modern CNC machining system, the contour control of the two-axis XY platform can no longer meet people's processing requirements for complex components. Therefore, the contour control technology of the three-axis motion platform is introduced to realize the precise machining of the contour of the three-dimensional parts in space. The three-axis motion platform is directly driven by the permanent magnet synchronous linear motor, which avoids the intermediate transmission link of "ball + screw", and improves the processing efficiency of the system.

Invention content:

Purpose of the invention: The present invention provides an improved cross-coupling control device and method for a three-axis motion platform, and its purpose is to solve the existing problems of the previous methods.

Technical solution: the present invention is achieved through the following technical solutions:

An improved cross-coupling control device for a three-axis motion platform, characterized in that: the device includes three parts: a main circuit, a control circuit, and a control object; the main circuit includes an AC voltage regulation module, a rectification and filtering module, and an IPM inverter module; the control circuit Including DSP processor, current sampling circuit, mover position sampling circuit, voltage adjustment circuit, IPM isolation drive circuit and IPM protection circuit; the control object is a three-phase permanent magnet linear synchronous motor, and the body is equipped with a grating ruler; current sampling circuit, The mover position sampling circuit, voltage adjustment circuit, IPM isolation drive circuit and IPM protection circuit are all connected to the DSP processor, the IPM isolation drive circuit and IPM protection circuit are connected to the IPM inverter module, and the current sampling circuit is connected to the three The phase permanent magnet linear synchronous motor, the voltage adjustment circuit is connected to the AC voltage regulation module, the AC voltage regulation module is connected to the rectification filter module, the rectification filter module is connected to the IPM inverter module, the IPM inverter module is connected to the three-phase permanent magnet linear synchronous motor, and the three-phase permanent magnet linear synchronous motor is connected to the three-phase permanent magnet linear synchronous motor. The grating ruler on the magnetic linear synchronous motor is connected with the mover position sampling circuit.

The improved cross-coupling control method of the three-axis motion platform implemented by the above-mentioned improved cross-coupling control device of the three-axis motion platform is characterized in that: the method adopts a contour error estimation method to establish a contour error model of the three-axis motion platform , and combined single-axis tracking control with three-axis cross-coupling control, the previous cross-coupling control structure was improved, thus ensuring that the single-axis tracking accuracy and contour accuracy of the system approached zero.

Single-axis tracking control, single-axis tracking control adopts position-speed loop double closed-loop control mode, single-axis tracking control system design.

The speed loop uses a pseudo-differential feedback controller with feedforward, that is, the PDFF controller, and its control algorithm is expressed as:

Among them, k _f is the feed-forward compensation gain, _ki is the integral gain, and k _p is the proportional gain; the relationship between the speed loop control input v _d (s) and the actual output speed function v _a (s) is:

The relationship between the disturbance input ξ(s) and the actual output velocity function v _a (s) is:

The controlled object adopts permanent magnet synchronous linear motor, and its transfer function is

Among them, G ₀ (s)=1/(Ms+B) is the actual controlled object, and K _f is the electromagnetic thrust coefficient.

The position loop adopts a proportional controller, and the coefficient is k _x , so the transfer function of the whole single-axis tracking control system can be expressed as:

By setting a fixed disturbance ξ, it can be verified that the system has strong anti-interference ability and fast response ability.

The steps of this method are as follows:

The present invention comprises the following concrete steps:

Step 1: Establish the contour error model of the three-axis motion platform:

The three-axis motion platform is made of two vertical permanent magnet synchronous linear motors (PMLSM). The permanent magnet linear synchronous electromechanical equation is:

In the formula, F _e : electromagnetic thrust; M: the total mass of the mover and the load carried by the mover of the permanent magnet linear motor; i _q is the q-axis current of the mover; K _f : electromagnetic thrust coefficient; B: viscous friction coefficient ; F: The total disturbance force on the system. v is the velocity of the mover; is the mover acceleration;

Select x(t) and v(t) as system state variables, that is, the state equation of PMLSM can be rewritten as

Among them, v(t) is the motor mover speed; u=i _q represents the control input of the motor; x(t) is the position output of the linear motor.

Therefore, a direct-drive three-axis motion platform can be composed of three second-order differential equations:

That is, the form of the state space is:

where z ₁ (t)=[x ₁ (t) x ₂ (t) x ₃ (t)] ^T , u=[u ₁ u ₂ u ₃ ] ^T , ρ=[F ₁ F ₂ F ₃ ] ^T , A ₁₁ =0, A ₁₂ =I, A ₂₁ =0, A ₂₂ =diag(-B _i /M _i ), i=x, y, z, are 3 * 3 matrix;

Step 2: The contour error model of the three-axis motion platform is established:

In a three-axis motion platform, the accuracy of contour error model estimation directly affects the contour control performance. Assuming a three-axis motion platform is the command position, P is the actual position, and the position error vector is The contour error vector is R ₀ and R ₁ are two points on the command position, which are recorded as R ₀ (x ₀ , y ₀ , z ₀ ) and R ₁ (x ₁ , y ₁ , z ₁ ); Q point is the command position vector At a point on , the coordinates are labeled Q(x,y,z). The distance from point P to point R ₁ is the position error vector Expressed in a mathematical relational form:

vector for

The linear equation of the command position derived from the three points of R ₀ , R ₁ and Q is:

Assume actual position P to command position The shortest distance for the vector Therefore the vector for

vector with vector are perpendicular to each other, and the inner product is zero; After finding the parameter t and substituting it into the equation (12), the coordinate Q can be obtained. After the coordinate Q is calculated, the contour error value can be further obtained, and finally the contour error can be deduced for

From formula (14), it can be known that the contour error Components on the x-axis, y-axis and z-axis;

Step 3: Compensator Design for Contour Errors

In order to reduce the contour error, it is hoped that the actual position P can move toward the command position vector corrections, except for corrections to the position error vector In addition to the axis components E _x , E _y , E _z , additional contour error vectors need to be compensated Therefore, choose the vector As contour error between actual position and command position The amount of compensation depends on the size of λ. Therefore, put As the compensation amount of the whole system, the compensation relationship from the actual position to the expected position is:

Through formula ( ₁₅ ), it can not only compensate the tracking error from the actual position point P to the expected position point R1, but also compensate the contour error between the two points, making it close to the command position. And then get the whole compensation amount Components on each axis:

Formula (16) can make the composite vector Approaching to the command position path, where λ is the cross-coupling gain value, which affects the correction speed of the contour error. by synthetic vector The geometric relationship shows that the larger the value of λ, The more it deviates from the command path, the corrected contour error vector the amount will be large;

Step 4: Single-Axis Tracking Controller Design

In order to ensure the contour accuracy of the three axes, single-axis tracking control is also essential. In the present invention, the single-axis tracking control adopts the control mode combining the speed loop controller and the position loop controller, and the speed loop controller adopts the PDFF control scheme. The position loop controller k _x adopts proportional control mode;

Step 5: Contour Controller Design

From the aforementioned contour error estimation method, it can be known that the contour error only with the command position It is related to the actual position P and belongs to the geometric relationship of the position. Therefore, the designed cross-coupling controller is located in the position loop part of the control system, which improves the previous cross-coupling control structure.

The input of the cross-coupling controller is the given position R _x , R _y and R _z of the three-axis motion platform and the tracking error E _x , E _y and E _z of each axis. ex, _ey , and _ez are the profile error components for each axis output _by the cross-coupled controller.

The inventive method is finally realized by the control program embedded in the DSP processor, and its control process is carried out in the following steps:

Step 1 System initialization;

Step 2 Allow TN1 and TN2 interrupts;

Step 3 Start T1 underflow interrupt;

Step 4 program data initialization;

Step 5 Turn on the general interrupt;

Step 6 interrupt waiting;

Step 7 TN1 interrupt processing sub-control program;

Step 8 ends.

Wherein in the step 7, the T1 interrupt processing sub-control program follows the steps below:

Step 1: T1 interrupts the sub-control program;

Step 2 protect the site;

Step 3 Determine whether the initial positioning has been performed; if yes, go to step 4, otherwise go to step 10;

Step 4 Current sampling, CLARK transformation, PARK transformation;

Step 5 Determine whether position adjustment is required; otherwise, go to step 7;

Step 6 Position adjustment interrupt processing sub-control program;

Step 7 d q-axis current regulation;

Step 8 PARK inverse transformation;

Step 9 Calculate CMPPx and PWM output;

Step 10 position sampling;

Step 11 Initial positioning procedure;

Step 12 restore the scene;

Step 13 Return from interrupt.

Wherein in the step 6, the position adjustment interrupt processing sub-control program follows the steps below:

Step 1 Position adjustment interrupt sub-control program;

Step 2 Read the encoder value;

Step 3 judge the angle;

Step 4 Calculate the distance traveled;

Step 5 Execute the position controller;

Step 6 Calculate the current command and output it;

Step 7 interrupt return.

Advantages and effects: The present invention provides an improved cross-coupling control device and method for a three-axis motion platform. With the increase of people's requirements for complex components, the precise contour control of the multi-axis motion platform is compared with the previous representative two-axis XY In terms of platform contour control, the research on precision contour motion control of multi-axis motion platform high-performance contour machining has important practical significance and broad application prospects. And the multi-axis motion platform adopts the direct drive mode of multiple permanent magnet synchronous linear motors, which avoids the intermediate transmission link of "ball + screw", so that the load is only directly thrust by the linear motors, eliminating the problems caused by the traditional transmission mechanism. The zero-gap transmission from the linear motor to the controlled object is realized, making the linear motor the main driving mode of high-speed and high-precision servo control system.

Aiming at the problem of the contour control accuracy of complex components in the existing control technology, the present invention adopts a contour error estimation method in the three-axis coordinated control, establishes a three-axis contour error model, improves the structure of the cross-coupling control, and designs A three-dimensional space contour error controller is developed.

The controller designed by the present invention is applied to a two-by-two vertical numerical control platform of X-Y-Z axes driven by a linear motor. The experimental system is shown in Figure 2. The position of the stage is connected to a linear encoder for each drive axis with a sensor resolution of 0.1 micron. The speed of each drive shaft is calculated from the reverse difference of the position measurement, and the sampling period is 2 ms.

The invention includes the establishment of a contour error model of a three-axis motion platform, so that the system can complete the spatial contour trajectory tracking task; the design of a single-axis tracking controller ensures that the tracking error of each axis is within a small range; the design of the contour controller reduces The contour error of the system; the geometric relationship of the contour error model, as shown in Figure 3; the geometric relationship of the contour error compensation, as shown in Figure 4; the design of the single-axis tracking controller, as shown in Figure 1; the design of the three-axis contour controller, As shown in Figure 5.

The invention mainly takes the three-axis motion platform as the research object, and ensures the machining accuracy of the parts by controlling the overall contour error of the three axes. In order to improve the precision of contour machining, many scholars are committed to researching various feedforward and feedback control strategies to improve the single-axis tracking precision, thereby indirectly improving the precision of contour motion control. Such as feed-forward controller, zero-phase error tracking controller, PID control, adaptive control, robust control and other methods can reduce single-axis tracking error. However, the reduction of single-axis tracking error cannot guarantee the overall contour accuracy. Therefore, single-axis tracking control and inter-axis coordinated control are two important factors that affect the contour accuracy of the three-axis motion platform system. The single-axis tracking control adopts the control method combining the position loop and the speed loop. The position loop is proportional control, and the speed loop is PDFF control, which can ensure a faster response speed and tracking accuracy of the single axis. In order to improve the coordination between the axes, the cross-coupling controller (CCC) is generally used in the contour control of the axes to coordinate the difference in dynamic performance caused by the mismatch of parameters and reduce the contour error of the system. To solve this problem, the present invention adopts a contour error estimation method to establish a contour error model between three axes. On this basis, the traditional cross-coupling control structure is improved, and a three-axis cross-coupling controller is designed. Through verification, this method can effectively improve the contour accuracy between the three axes.

Description of drawings:

Figure 1 Block diagram of single-axis tracking control system

Fig. 2 is the experimental system designed by the present invention

Figure 3 is a geometric relationship diagram of the linear contour error vector

Figure 4 is a geometric relationship diagram of contour error compensation

Figure 5 Block diagram of cross-coupling control of three-axis motion platform

Fig. 6 realizes the designed permanent magnet linear synchronous motor vector control system hardware structure hardware block diagram of the present invention

Fig. 7 is the flow chart of vector control system program in the method of the present invention

Fig. 8 is a flow chart of the position adjustment interrupt processing sub-control program of the method of the present invention

Fig. 9 is the schematic diagram of the control system realizing the present invention

(a) Schematic diagram of the main circuit of the motor control system

(b) Schematic diagram of A and B phase current sampling circuits

(c) Schematic diagram of grating ruler signal sampling circuit

(d) Schematic diagram of the IPM hardware drive circuit.

The specific embodiment: the present invention will be further described below in conjunction with accompanying drawing:

As shown in Figure 1, the present invention provides an improved cross-coupling control device and method for a three-axis motion platform, (1) system hardware structure

The main circuit of the control system for realizing the present invention is shown in Fig. 9(a). The voltage regulation circuit adopts the reverse voltage regulation module EUV-25A-II, which can realize 0-220V isolation voltage regulation. The rectification filter unit adopts bridge type uncontrollable rectification, large capacitor filter, and appropriate resistance-capacity absorption circuit, which can obtain the constant DC voltage required for IPM work. The IPM uses Fuji 6MBP50RA060 intelligent power module, with a withstand voltage of 600V, a maximum current of 50A, and a maximum operating frequency of 20kHz. The IPM is powered by four independent 15V drive power supplies. The main power input terminals (P, N), output terminals (U, V, W), and the main terminals are fixed with their own screws, which can realize current transmission. P and N are the input terminals of the main power supply after rectification, transformation and smoothing of the inverter. P is the positive terminal and N is the negative terminal. The three-phase alternating current output by the inverter is connected to the motor through the output terminals U, V, and W.

The core of the control circuit of the present invention is the TMS320F2812 processor, and its supporting development board includes target read-only memory, analog interface, eCAN interface, serial boot ROM, user indicator light, reset circuit, and can be configured as RS232/RS422/RS485 Asynchronous serial port, SPI synchronous serial port and off-chip 256K*16-bit RAM.

The current sampling in the actual control system adopts the Hall current sensor LT58-S7 of LEM Company. The A and B phase currents are detected by two Hall current sensors to obtain current signals, which are converted into 0-3.3V voltage signals through the current sampling circuit, and finally converted into binary numbers with 12-bit precision by the A/D conversion module of TMS320LF2812 , and stored in the value register. A, B-phase current sampling circuit shown in Figure 9 (b). The adjustable resistor VR2 adjusts the signal amplitude, and the adjustable resistor VR1 adjusts the signal offset. By adjusting these two resistors, the signal can be adjusted to 0~3.3V, and then sent to the AD0 and AD1 pins of the DSP. . The regulator tube in the figure is to prevent the signal sent to the DSP from exceeding 3.3V, causing the DSP to be damaged by high voltage. The operational amplifier adopts OP27, the power supply is connected to positive and negative 15V voltage, and the decoupling capacitor is indirect between the voltage and the ground. The input terminal of the circuit is connected with a capacitor filter to remove high-frequency signal interference and improve sampling accuracy.

The A-phase and B-phase pulse signals output by the grating ruler should be isolated by a fast optocoupler 6N137, and then the signal level will be converted from 5V to 3.3V through a voltage divider circuit, and finally connected to the two-way orthogonal encoding pulse interface of DSP QEP1 and QEP2. The circuit principle is shown in Fig. 9(c). Figure 9(d) shows the schematic diagram of the six-way isolated drive circuit. It should be pointed out that the IPM fault protection signal is aimed at non-repetitive transient faults, which are realized in this system through the following measures: the fault output signal of IPM is connected to the DSP through optical coupling pins, to ensure that the DSP puts all event manager output pins in a high-impedance state in time when the IPM fails.

(2) System software implementation

The program flowchart of the vector control system in the method of the present invention is shown in FIG. 7 . Fig. 8 is a flow chart of the position adjustment interrupt processing sub-control program of the method of the present invention. The main program of the software includes system initialization; opening INT1, INT2 interrupt; allowing timer interrupt; timer interrupt processing subroutine. The initialization procedure includes closing all interrupts, DSP system initialization, variable initialization, event manager initialization, AD initialization and quadrature encoding pulse QEP initialization. The interrupt service subroutine includes the protection interrupt subroutine and the T1 underflow interrupt service subroutine. Other parts such as mover initial positioning, PID adjustment, vector conversion, etc. are all executed in the timer TI underflow interrupt processing subroutine.

The protection interrupt response generated by the IPM protection signal is an external interrupt, and the INT1 interrupt priority is higher than that of the timer T1. IPM will automatically send a protection signal in abnormal conditions such as overcurrent and overvoltage, and this signal is converted and connected to the power drive protection pin of DSP Once an abnormal situation occurs, the DSP will enter the protection interrupt subroutine, first prohibit all interrupts, and then block the PWM output to stop the motor immediately, protecting the motor and IPM.

To start the vector control system smoothly, it is necessary to know the initial position of the mover. Using the software, a DC current with a constant amplitude can be passed through the mover of the motor to make the stator generate a constant magnetic field. This magnetic field interacts with the constant magnetic field of the rotor. The motor mover moves to the position where the two flux linkages coincide. The initial positioning of the mover, the reading of AD sampling values, the calculation of the position of the motor mover, coordinate transformation, PID adjustment, and the generation of SVPWM waveform comparison values are all completed in the T1 underflow interrupt service subroutine.

The details are as follows:

As shown in Figure 6, the device includes three parts: main circuit, control circuit and control object; the main circuit includes AC voltage regulation module, rectification and filtering module and IPM inverter module; the control circuit includes DSP processor, current sampling circuit, mover Position sampling circuit, voltage adjustment circuit, IPM isolation drive circuit and IPM protection circuit; the control object is a three-phase permanent magnet linear synchronous motor, and the body is equipped with a grating scale; current sampling circuit, mover position sampling circuit, voltage adjustment circuit, IPM Both the isolated drive circuit and the IPM protection circuit are connected to the DSP processor, the IPM isolation drive circuit and the IPM protection circuit are connected to the IPM inverter module, the current sampling circuit is connected to the three-phase permanent magnet linear synchronous motor through the Hall sensor, and the voltage adjustment circuit is connected to AC voltage regulation module, the AC voltage regulation module is connected to the rectification and filtering module, the rectification and filtering module is connected to the IPM inverter module, the IPM inverter module is connected to the three-phase permanent magnet linear synchronous motor, the grating scale and the mover on the three-phase permanent magnet linear synchronous motor position sampling circuit connection.

The improved cross-coupling control method of the three-axis motion platform adopts a contour error estimation method to establish the contour error model of the three-axis motion platform, and combines the single-axis tracking control with the three-axis cross-coupling control, which improves the previous The cross-coupling control structure ensures that the single-axis tracking accuracy and contour accuracy of the system are close to zero.

The single-axis tracking control adopts the control mode combining the position loop and the speed loop. The design of the single-axis tracking control system is shown in Figure 1. 1/(Ms+B) is the actual controlled object, K _f is the electromagnetic thrust coefficient, and x _r is The input reference instruction, x _p is the actual output position. The single-axis tracking control adopts the position-speed loop combined control method, the position loop adopts proportional control, the speed loop adopts PDFF controller, k _x is the proportional gain of the position loop; k _f in the speed loop is the feed-forward compensation gain, and _ki is Integral gain, k _p is the proportional gain; ξ is the external disturbance, by setting a fixed disturbance, it can be verified that the system has strong anti-interference ability and fast response ability.

In the traditional contour machining, the contour accuracy control is generally only aimed at the XY plane, and it is difficult to extend to the three-dimensional space, which has great limitations for the actual NC machining. Therefore, a contour error estimation method is used to establish a three-axis motion platform space contour error model. And according to the claims, the improved cross-coupling control method is used to improve the contour tracking performance and the contour accuracy.

The steps of this method are as follows:

The present invention comprises the following concrete steps:

Step 1: Establish the contour error model of the three-axis motion platform:

The three-axis motion platform is made of two vertical permanent magnet synchronous linear motors (PMLSM). The permanent magnet linear synchronous electromechanical equation is:

In the formula, F _e : electromagnetic thrust; M: the total mass of the mover and the load carried by the mover of the permanent magnet linear motor; i _q is the q-axis current of the mover; K _f : electromagnetic thrust coefficient; B: viscous friction coefficient ; F: The total disturbance force on the system. v is the velocity of the mover; is the mover acceleration;

Select x(t) and v(t) as system state variables, that is, the state equation of PMLSM can be rewritten as

Among them, v(t) is the motor mover speed; u=i _q represents the control input of the motor; x(t) is the position output of the linear motor.

Therefore, a direct-drive three-axis motion platform can be composed of three second-order differential equations:

That is, the form of the state space is:

where z ₁ (t)=[x ₁ (t) x ₂ (t) x ₃ (t)] ^T , u=[u ₁ u ₂ u ₃ ] ^T , ρ=[F ₁ F ₂ F ₃ ] ^T , A ₁₁ =0, A ₁₂ =I, A ₂₁ =0, A ₂₂ =diag(-B _i /M _i ), i=x, y, z, are 3 * 3 matrix;

Step 2: The contour error model of the three-axis motion platform is established:

In a three-axis motion platform, the accuracy of contour error model estimation directly affects the contour control performance. Fig. 3 is a graph of the geometric relation of the linear contour error vector. in, is the command position, P is the actual position, and the position error vector is The contour error vector is R ₀ and R ₁ are two points on the command position, respectively recorded as R ₀ (x ₀ ,y ₀ ,z ₀ ), R ₁ (x ₁ ,y ₁ ,z ₁ ); shortest distance as vector That is, the contour error vector from the actual position to the reference position The coordinates of the point Q are labeled Q(x,y,z). The distance from point P to point R ₁ is the position error vector

The linear equation of the command position derived from the three points of R ₀ , R ₁ and Q is:

It can be seen from Figure 4 that the vector with vector are perpendicular to each other, and the inner product is zero; After finding the parameter t and substituting it into the equation (6), the coordinate Q can be obtained. After the coordinate Q is calculated, the contour error value can be further obtained, and finally the contour error can be deduced for

From formula (6), it can be known that the contour error Components on the x-axis, y-axis and z-axis;

Step 3: Compensator Design for Contour Errors

According to Figure 4, in order to reduce the contour error, it is hoped that the actual position P can be directed to the command position vector corrections, except for corrections to the position error vector In addition to the axis components E _x , E _y , E _z , additional contour error vectors need to be compensated It can be seen from vector geometric addition and subtraction that the selected vector As a compensation between the actual position and the command position, it is close to the command position. total compensation The components on each axis can be expressed as:

Formula (7) can make the composite vector Approaching to the command position path, where λ is the cross-coupling gain value, which affects the correction speed of the contour error. by synthetic vector The geometric relationship shows that the larger the value of λ, The more it deviates from the command path, the corrected contour error vector the amount will be large;

Step 4: Single-Axis Tracking Controller Design

In order to ensure the contour accuracy of the three axes, single-axis tracking control is also essential. In the present invention, the single-axis tracking control adopts the control mode combining the speed loop controller and the position loop controller, and the speed loop controller adopts the PDFF control scheme. The position loop controller k _x adopts proportional control mode;

Step 5: Contour Controller Design

From the contour error estimation method mentioned above, it can be known that the contour error e is only related to the command position R and the actual position P, which belongs to the geometric relationship of the position. Therefore, the designed cross-coupling controller is located in the position loop part of the control system, which improves the The structure block diagram of the previous cross-coupling control structure is shown in Figure 5.

The input of the cross-coupling controller is the given position R _x , R _y and R _z of the three-axis motion platform and the tracking error E _x , E _y and E _z of each axis. ex, _ey , and _ez are the profile error components for each axis output _by the cross-coupled controller. And comparing the structural block diagram of the three-axis cross-coupling controller designed in the present invention with the structural block diagram used in the past, the contour error compensation of the present invention has been completed before the position loop controller. From the geometric relationship of contour error compensation, it can be seen that when the gain value K _p in the position loop controller is adjusted, the contour error compensation will be affected at the same time Its effect is equivalent to adjusting the The magnitude of , rather than the direction, but the direction at this time is determined by the magnitude of the cross-coupling gain value λ. Therefore, the adjustments of K _p and λ are independent of each other, which are magnitude and direction respectively. However, in the previous cross-coupled controller structure, the compensation amount is placed after the controller. When adjusting K _p , its effect is equivalent to only adjusting the size of. Therefore, the method proposed in the present invention takes the contour error compensation amount The direction and magnitude of are changed at the same time, which increases the matching problem of the most appropriate adjustment between the position loop gain K _p and the cross-coupling gain λ in the structure diagram.

The input of the cross-coupling controller is the given position R _x , R _y and R _z of the three-axis motion platform and the tracking error E _x , E _y and E _z of each axis. ex, _ey , and _ez are the profile error components for each axis output _by the cross-coupled controller.

The inventive method is finally realized by the control program embedded in the DSP processor, and its control process is carried out in the following steps:

Step 1 System initialization;

Step 2 Allow TN1 and TN2 interrupts;

Step 3 Start T1 underflow interrupt;

Step 4 program data initialization;

Step 5 Turn on the general interrupt;

Step 6 interrupt waiting;

Step 7 TN1 interrupt processing sub-control program;

Step 8 ends.

Wherein in the step 7, the T1 interrupt processing sub-control program follows the steps below:

Step 1: T1 interrupts the sub-control program;

Step 2 protect the site;

Step 3 Determine whether the initial positioning has been performed; if yes, go to step 4, otherwise go to step 10;

Step 4 Current sampling, CLARK transformation, PARK transformation;

Step 5 Determine whether position adjustment is required; otherwise, go to step 7;

Step 6 Position adjustment interrupt processing sub-control program;

Step 7 d q-axis current regulation;

Step 8 PARK inverse transformation;

Step 9 Calculate CMPPx and PWM output;

Step 10 position sampling;

Step 11 Initial positioning procedure;

Step 12 restore the scene;

Step 13 Return from interrupt.

Wherein in the step 6, the position adjustment interrupt processing sub-control program follows the steps below:

Step 1 Position adjustment interrupt sub-control program;

Step 2 Read the encoder value;

Step 3 judge the angle;

Step 4 Calculate the distance traveled;

Step 5 Execute the position controller;

Step 6 Calculate the current command and output it;

Step 7 interrupt return.

The invention is aimed at directly driving a three-axis motion platform, and the advantages of the invention mainly lie in establishing a three-dimensional space contour error model and a method for controlling the space contour error. It solves the problem that in the modern processing system, people's demand for complex components is increasing, but the processing accuracy of complex components cannot be met. The present invention is mainly aimed at reducing single-axis tracking errors and contour errors. The single-axis tracking error uses the control method combining the position loop controller and the speed loop controller to ensure that the single-axis tracking error is within a good accuracy range. Control of contour error between three axes This invention mainly proposes a new contour error estimation model to estimate the contour error, and applies it to the three-axis cross-coupling contour controller, improving the control structure of the three-axis cross-coupling controller . Through the combination of the above two parts, the contour error of the three-axis motion platform system is finally approaching zero.

Claims (6)

1. An improved cross coupling control method of a three-axis motion platform is characterized in that: the method is implemented by adopting the following devices: the device comprises a main circuit, a control circuit and a control object; the main circuit comprises an alternating current voltage regulating module, a rectifying and filtering module and an IPM inversion module; the control circuit comprises a DSP processor, a current sampling circuit, a rotor position sampling circuit, a voltage adjusting circuit, an IPM isolation drive circuit and an IPM protection circuit; the control object is a three-phase permanent magnet linear synchronous motor, and a grating ruler is arranged on the machine body; the intelligent power supply comprises a current sampling circuit, a rotor position sampling circuit, a voltage adjusting circuit, an IPM isolation driving circuit and an IPM protection circuit, wherein the current sampling circuit, the rotor position sampling circuit, the voltage adjusting circuit, the IPM isolation driving circuit and the IPM protection circuit are all connected with a DSP (digital signal processor), the IPM isolation driving circuit and the IPM protection circuit are connected with an IPM (intelligent power management) inversion module, the current sampling circuit is connected to a three-phase permanent magnet linear synchronous motor through a Hall sensor, the voltage adjusting circuit is connected with an alternating current voltage adjusting module, the alternating current voltage adjusting module is connected with a rectification filter module, the rectification filter module is connected with the IPM inversion module, the IPM;

the method adopts a contour error estimation algorithm to establish a contour error model of the three-axis motion platform, combines single-axis tracking control with three-axis cross coupling control, and improves the prior cross coupling control structure, thereby ensuring that the single-axis tracking precision and the contour precision of the system approach to zero;

single-axis tracking control, wherein the single-axis tracking control adopts a position-speed loop double closed loop control mode and a single-axis tracking control system is designed;

the speed loop employs a pseudo-differential feedback controller with feedforward, i.e., a PDFF controller, whose control algorithm is expressed as:

<mrow> <mi>u</mi> <mo>=</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>t</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>v</mi> <mi>d</mi> </msub> <mo>-</mo> <msub> <mi>v</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>+</mo> <msub> <mi>k</mi> <mi>f</mi> </msub> <msub> <mi>v</mi> <mi>d</mi> </msub> <mo>-</mo> <msub> <mi>k</mi> <mi>p</mi> </msub> <msub> <mi>v</mi> <mi>a</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>

wherein k is_fFor feed-forward compensation of gain, k_iTo integrate the gain, k_pIs a proportional gain; speed loop control input v_d(s) function of actual output velocity v_aThe relationship between(s) is:

<mrow> <mfrac> <mrow> <msub> <mi>v</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>v</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msub> <mi>G</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mi>f</mi> </msub> <mo>+</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <mo>/</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>G</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mi>p</mi> </msub> <mo>+</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <mo>/</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>

disturbance input ξ(s) and actual output velocity function v_aThe relationship between(s) is:

<mrow> <mfrac> <mrow> <msub> <mi>v</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>&amp;xi;</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msub> <mi>G</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>G</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mi>p</mi> </msub> <mo>+</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <mo>/</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>

the controlled object adopts a permanent magnet synchronous linear motor with a transfer function of

<mrow> <msub> <mi>G</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>K</mi> <mi>f</mi> </msub> <msub> <mi>G</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mi>s</mi> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>

Wherein G is₀(s) < 1/(Ms + B) is the actual controlled object, K_fIs the electromagnetic thrust coefficient;

the position ring adopts a proportional controller with the coefficient of k_xTherefore, the transfer function of the entire single-axis tracking control system can be expressed as:

<mrow> <mfrac> <mrow> <msub> <mi>x</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>x</mi> <mi>r</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msub> <mi>k</mi> <mi>x</mi> </msub> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <msub> <mi>v</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>v</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mn>1</mn> <mi>s</mi> </mfrac> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>k</mi> <mi>x</mi> </msub> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <msub> <mi>v</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>v</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mn>1</mn> <mi>s</mi> </mfrac> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msub> <mi>k</mi> <mi>x</mi> </msub> <msub> <mi>v</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>v</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mi>s</mi> <mo>+</mo> <msub> <mi>k</mi> <mi>x</mi> </msub> <msub> <mi>v</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>

by setting the fixed disturbance xi, the system can be verified to have stronger anti-interference capability and quicker response capability.

2. The improved cross-coupling control method for the three-axis motion platform according to claim 1, wherein: the method comprises the following steps:

the invention comprises the following specific steps:

step 1: establishing a three-axis motion platform contour error model:

the three-axis motion platform adopts a PMLSM (permanent magnet synchronous linear motor) with two vertical permanent magnet synchronous motors, and the permanent magnet linear synchronous electromechanical equation is as follows:

<mrow> <msub> <mi>F</mi> <mi>e</mi> </msub> <mo>=</mo> <msub> <mi>K</mi> <mi>f</mi> </msub> <msub> <mi>i</mi> <mi>q</mi> </msub> <mo>=</mo> <mi>M</mi> <mover> <mi>v</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <mi>B</mi> <mi>v</mi> <mo>+</mo> <mi>F</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>

in the formula, F_e: electromagnetic thrust; m: the rotor of the permanent magnet linear motor and the total mass of loads carried by the rotor; i.e. i_qIs the q-axis current of the rotor; k_f: an electromagnetic thrust coefficient; b: a coefficient of viscous friction; f: the total disturbance force applied to the system; v is the mover speed;the rotor acceleration is obtained;

choosing x (t) and v (t) as system state variables, i.e. the state equation of PMLSM can be rewritten as:

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>v</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <mi>v</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <mfrac> <mi>B</mi> <mi>M</mi> </mfrac> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <msub> <mi>K</mi> <mi>f</mi> </msub> <mi>M</mi> </mfrac> <mi>u</mi> <mo>+</mo> <mfrac> <mi>F</mi> <mi>M</mi> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>

wherein v (t) is motor mover speed; u-i_qRepresenting a control input quantity of the motor; x (t) is the position output of the linear motor;

therefore, the direct drive three-axis motion platform can be composed of three 2 nd order differential equations:

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <mfrac> <mi>B</mi> <mi>M</mi> </mfrac> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <msub> <mi>K</mi> <mrow> <mi>f</mi> <mn>1</mn> </mrow> </msub> <mi>M</mi> </mfrac> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>F</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <mfrac> <mi>B</mi> <mi>M</mi> </mfrac> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <msub> <mi>K</mi> <mrow> <mi>f</mi> <mn>2</mn> </mrow> </msub> <mi>M</mi> </mfrac> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>F</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <mfrac> <mi>B</mi> <mi>M</mi> </mfrac> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <msub> <mi>K</mi> <mrow> <mi>f</mi> <mn>3</mn> </mrow> </msub> <mi>M</mi> </mfrac> <msub> <mi>u</mi> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>F</mi> <mn>3</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>

i.e. expressed as a state space, of the form:

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>z</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>A</mi> <mn>11</mn> </msub> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>A</mi> <mn>12</mn> </msub> <msub> <mi>z</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>z</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>A</mi> <mn>21</mn> </msub> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>A</mi> <mn>22</mn> </msub> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>+</mo> <mi>C</mi> <mi>u</mi> <mo>+</mo> <mi>&amp;rho;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>

wherein z is₁(t)＝[x₁(t) x₂(t) x₃(t)]^T，u＝[u₁u₂u₃]^T，ρ＝[F₁F₂F₃]^T，A₁₁＝0，A₁₂＝I，A₂₁＝0，A₂₂＝diag(-B_i/M_i) X, y, z, which are 3 × 3 matrixes;

step 2: establishing a three-axis motion platform contour error model:

in a three-axis motion platform, the accuracy of contour error model estimation directly affects contour control performance; in a hypothetical three-axis motion platformFor commanded position, P is actual position, and position error vector isThe profile error vector isR₀、R₁Are two points in the command position, respectively denoted as R₀(x₀,y₀,z₀)，R₁(x₁,y₁,z₁) (ii) a Point Q is the command position vectorCoordinate Q (x, y, z); point P to point R₁Is a position error vectorExpressed in mathematical relation:

<mrow> <mover> <mi>E</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>=</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>-</mo> <mi>P</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>-</mo> <mi>a</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>-</mo> <mi>b</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>-</mo> <mi>c</mi> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>

vector quantityIs composed of

<mrow> <mover> <mi>R</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>=</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>

From R₀、R₁And Q, deriving a linear equation for the command position as:

<mrow> <mi>L</mi> <mo>:</mo> <mfrac> <mrow> <mi>x</mi> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> </mrow> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mi>y</mi> <mo>-</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> </mrow> <mrow> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mi>z</mi> <mo>-</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> </mrow> <mrow> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> </mrow> </mfrac> <mo>=</mo> <mi>t</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>

assuming an actual position P to a commanded positionIs a vectorThus vectorIs composed of

<mrow> <mover> <mrow> <mi>P</mi> <mi>Q</mi> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mi>t</mi> <mo>-</mo> <mi>a</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mi>t</mi> <mo>-</mo> <mi>b</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mi>t</mi> <mo>-</mo> <mi>c</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;R</mi> <mi>x</mi> </msub> <mi>t</mi> <mo>-</mo> <mi>a</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;R</mi> <mi>y</mi> </msub> <mi>t</mi> <mo>-</mo> <mi>b</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;R</mi> <mi>z</mi> </msub> <mi>t</mi> <mo>-</mo> <mi>c</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>E</mi> <mi>x</mi> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;R</mi> <mi>x</mi> </msub> <mi>t</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>E</mi> <mi>y</mi> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;R</mi> <mi>y</mi> </msub> <mi>t</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>E</mi> <mi>z</mi> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;R</mi> <mi>z</mi> </msub> <mi>t</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>

Vector quantityAnd vectorMutually vertical, the inner product is zero; namely, it isThe obtained parameter t is substituted into equation (12) to obtain coordinate Q, the obtained coordinate Q can be used for further obtaining contour error value, and finally the contour error is deducedIs composed of

From equation (14), the profile error is knownComponents in the x-axis, y-axis, and z-axis;

step three: compensator design for contour error

To reduce profile errors, it is desirable that the actual position P be vectorized to the commanded positionCorrection, other than correcting position error vectorIn each axial component E_x，E_y，E_zIn addition, the contour error vector needs to be compensatedThus, a vector is selectedAs profile error from actual position to commanded positionDepending on the size of λ; thus, the handleAs the compensation amount of the whole system, the compensation relation between the actual position and the expected position is as follows:

<mrow> <mover> <mi>C</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>=</mo> <mover> <mi>E</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>+</mo> <mi>&amp;lambda;</mi> <mover> <mi>e</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>

by the equation (15), it is possible to compensate the actual position point P to the desired position point R₁Can also be usedCompensating the contour error between the two points to make the contour error approach to the command position; thereby obtaining the whole compensationComponent at each axis:

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>C</mi> <mi>x</mi> </msub> <mo>=</mo> <msub> <mi>E</mi> <mi>x</mi> </msub> <mo>+</mo> <msub> <mi>&amp;lambda;e</mi> <mi>x</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>C</mi> <mi>y</mi> </msub> <mo>=</mo> <msub> <mi>E</mi> <mi>y</mi> </msub> <mo>+</mo> <msub> <mi>&amp;lambda;e</mi> <mi>y</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>C</mi> <mi>z</mi> </msub> <mo>=</mo> <msub> <mi>E</mi> <mi>z</mi> </msub> <mo>+</mo> <msub> <mi>&amp;lambda;e</mi> <mi>z</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow>

the resultant vector can be obtained by the equation (16)Approaching to the command position path, wherein lambda is the cross coupling gain value and influences the correction speed of the profile error; from a composite vectorThe larger the lambda value is, the larger the geometrical relationship of (a),correcting the profile error vector for more biased command pathsThe amount of the catalyst is large;

and 4, step 4: single axis tracking controller design

In order to ensure the profile accuracy of three axes, single-axis tracking control is also necessary, the single-axis tracking control adopts a control mode of combining a speed loop controller and a position loop controller, the speed loop controller adopts a PDFF control scheme, and the position loop controller k adopts a PDFF control scheme_xA proportional control mode is adopted;

and 5: contour controller design

From the contour error estimation method mentioned above, the contour error can be knownOnly with the command positionThe cross coupling controller is designed to be positioned in a position loop part of a control system because of the geometrical relation of the position relative to the actual position P, and the prior cross coupling control structure is improved.

3. The improved cross-coupling control method for the three-axis motion platform according to claim 2, wherein: the input of the cross-coupling controller is the input of a three-axis motion platformSet position R_x、R_yAnd R_zAnd tracking error per axis E_x、E_yAnd E_z；e_x、e_yAnd e_zIs the profile error component for each axis of the cross-coupled controller output.

4. The improved cross-coupling control method for the three-axis motion platform according to claim 2, wherein: the method is finally realized by a control program embedded in a DSP processor, and the control process is executed according to the following steps:

step 1, initializing a system;

step 2, allowing TN1 and TN2 to be interrupted;

step 3 starts a T1 underflow interrupt;

step 4, initializing program data;

5, opening total interruption;

step 6, interrupt waiting;

step 7, TN1 interrupts the process of the sub-control program;

and 8, finishing the step.

5. The improved cross-coupling control method for the three-axis motion platform of claim 4, wherein: wherein the T1 interrupt processing sub-control program in step 7 comprises the following steps:

step 1T 1 interrupts the sub-control program;

step 2, protecting the site;

step 3, judging whether the initial positioning is carried out or not; if yes, entering step 4, otherwise entering step 10;

step 4, current sampling, CLARK conversion and PARK conversion;

step 5, judging whether position adjustment is needed; otherwise, entering step 7;

step 6, the position is adjusted to interrupt the sub-control program;

step 7 d q axis current adjustment;

step 8, inverse PARK transformation;

step 9, calculating CMPPx and PWM output;

step 10, sampling the position;

step 11, an initial positioning program;

step 12, restoring the site;

step 13 interrupts the return.

6. The improved cross-coupling control method for the three-axis motion platform of claim 5, wherein: wherein, the position adjusting interrupt processing sub-control program in the step 6 comprises the following steps:

step 1, position adjustment interruption sub-control program;

step 2, reading an encoder value;

step 3, judging an angle;

step 4, calculating the distance traveled;

step 5, executing the position controller;

step 6, calculating and outputting a current command;

step 7 interrupts the return.