CN101114166A

CN101114166A - Contour outline control method for complicated track

Info

Publication number: CN101114166A
Application number: CNA2007100302285A
Authority: CN
Inventors: 柳宁; 王高; 吴国杰; 王思化
Original assignee: Jinan University
Current assignee: Jinan University
Priority date: 2007-09-13
Filing date: 2007-09-13
Publication date: 2008-01-30
Anticipated expiration: 2027-09-13
Also published as: CN100562823C

Abstract

The invention discloses a contour control method of a complex track. The invention is combined with a cross-coupling control framework with contour error pre-compensation function, establishes adaptive data models for the axles participating in the servo movement, determines the identification parameters of the controlled servo objects according to the current target position points and a plurality of historical position point values, and real-timely sets the control parameters with a pole placement algorithm. The method which adjusts the controlled output on the basis of a historical control output and a future control output effectively curbs bounded process interference and improves the accuracy of the contour control and the stability of the process.

Description

Contour control method for complex track

Technical Field

The invention relates to a contour control method, in particular to a contour control method of a complex track.

Background

The existing methods for improving the track motion precision mainly comprise two methods: 1. the track profile error after the synthesis of each axis is indirectly reduced by respectively improving the servo tracking control performance of each single-axis track; 2. by means of coordination processing of single-axis servo dynamics, the control performance of the plane track profile is improved, the dynamic characteristics of the single-axis servo are considered, and errors of the plane track profile of two axes are directly reduced.

In general, profile control is closed-loop control for track tracking by sharing information among servo axes without changing a single-axis servo control structure, that is, by adopting a cross-coupling control strategy, additional profile error information is provided for each axis. The former is not used because: when one of the axes is affected by a disturbance, the other axes do not get corresponding feedback information, and are still considered to be working properly without taking effective compensation measures to reduce the deterioration of the profile performance. For different tracking tracks, such as non-linear profiles and large curvature angles, the influence of geometric characteristics on the track tracking process is not considered in the single-axis servo tracking control.

Cross-coupled control (CCC) based on a time-equivalent method proposed by Koren in 1980 is the most basic method for dealing with multi-axis coupling control. The method mainly includes the steps of obtaining tracking error information of each axis, estimating contour errors in real time, designing a coupling control law to perform feedback compensation on the contour errors, decoupling compensation quantities to each axis, and obtaining a linear calculation model epsilon = -C of the contour errors _x E _x +C _y E _y As shown in fig. 10 and 11. Due to the adoption of the P-type controller u _c ＝w _p Epsilon, which cannot control the non-linear profile. Koren et al then improved the P (proportional) type controller to propose variable gain nonlinear profile control, such as: and the circular arc adopts a linear approximation mode, and profile errors are decoupled and distributed according to different gain coefficients, so that each single axis is independently controlled. The basic cross coupling controller estimates the profile error of the tracking straight line or circular arc under a fixed coordinate system, the obtained profile error is the linear combination of the tracking errors of all axes, and the compensator adopts a P type or PID type controller with fixed parameters, so that the profile precision is greatly improved compared with the single-axis tracking control only under the condition of low speed or small curvature change.

In addition, in order to reduce the computational complexity of Contour motion coupling control, improve the stability of coupling control variable gain, and enhance the robustness of the coupling controller, t.c. chiu et al designed a control method based on a Contour Error Transfer Function (CETF) in 1998. The dynamic relation between the profile error generated by a coupled control system and the profile error generated by an un-decoupled system is described, so that the CETF is regarded as a transfer function of an equivalent system, and a cross-coupled controller is converted into an equivalent time-varying single-input single-output system for design.

The design of the cross coupling controller based on the profile error transfer function is essentially the systematic design method of the traditional cross coupling control, and the profile error gain C is obtained _x 、C _y Approximately in the range of-1,1]Within the range, an equivalent single-input single-output system is designed by adopting a Quantitative Feedback Technology (QFT), and the cross-coupling control compensator meeting the stability and the robustness of the cross-coupling gain change can be obtained.

In addition, in the 1999 Chin J.H., et al, the setting of the general contour error calculation based on the Cartesian coordinate system was changed, the system kinetic equation was transformed to the Task coordinate system (TCF for short), the dynamic characteristics of each axis were matched by adding the feedforward precompensator to each single-axis loop, so that the transfer function matrix of the system in the Task coordinate system was diagonalized, the contour error was approximated by the normal error component, and the design of the cross-coupled controller was simplified to the design of two independent single-loop controllers, thereby realizing the decoupling control of the normal error component and the tangential error component. The coupling controller is designed based on a frequency domain method, system characteristics are kept unchanged through coordinate transformation, and the method is limited to be used under a contour motion with low angular frequency and a piecewise linear reference contour on the assumption that a track contour is formed by micro-segment straight lines. The method is characterized in that the profile error is approximated by the normal component of the error on a task coordinate system, the bandwidth of the normal error component is emphatically improved, the influence of potential unstable factors of the system caused by the non-selected improvement of the bandwidth of one direction of each axis is avoided, the influence of the speed and the curvature direction is considered at the same time, and the normal error component is used as feedforward information of a controller to compensate the dynamic performance of the system, so that the profile performance of the system under high speed and large curvature can be improved. Besides straight lines and circles, TCF is established for a complex geometric characteristic plane curve with any curvature change, and the online calculation amount is large; the contour error is replaced by the normal error component approximation under the TCF frame, and the decoupling control of the contour error cannot be reliably realized; of course, the controller has a weak ability to handle uncertainty and external disturbances of the controlled object model.

Other methods applied to contour control, such as passive coupling controller design, are a multi-axis coordination control method in continuous trajectory motion realized by a CCC control law based on a Lyapunov function. The contour performance and the tracking performance are configured differently by adjusting the weight, a control law is designed by adopting an integral Backstepping technology, the control rate is actually time-varying PD control of speed acceleration information containing a reference track, the local stability can be realized, and the contour performance is improved at the expense of the tracking performance by increasing the weight.

Obviously, the essence of the passive CCC-based design is to introduce the concept of optimal energy control into the control target design, and adjust the weights of the set energy functions to adapt to different control requirements. In the practical application process, for a complex contour curve, an implicit expression mode of the complex contour curve is not easy to find, and when an error is close to zero, the contour performance is reduced due to discontinuous switching of a control rate, so that the application range of the complex contour curve is limited to a great extent.

The present invention provides a complete solution to the problem of contour control of planar or spatially complex trajectories and offers other advantages over the prior art.

Disclosure of Invention

The invention relates to a high-performance servo control algorithm for a complex track contour control process, which is designed to meet the field of plane/space contour control in industrial production and continuously improve the contour accuracy requirement and the reliable control stability requirement. The purpose is as follows: considering from two aspects of contour error and contour control stability, and based on the tracking control of the complex geometric feature trajectory, a high-precision and high-stability contour control method is provided.

The technical scheme for realizing the invention comprises the following specific steps:

(1) Modeling the position servo system, namely identifying the model of the position control system, determining the order of the model, obtaining the transfer function of the position control system, the linear regression data model and the model parameter J to be identified _eq 、B _eq ；

(2) Designing a PD-based position controller, determining a stable control pole according to the servo characteristics of the controlled object obtained by identification, and adjusting the parameters of the controller in real time to obtain a stable controller with micro-overshoot and no phase lag;

(3) The servo delay obtained by comparing the interpolation feed rate with the incremental position output value is input into a position controller to obtain the output of real-time control quantity;

(4) As shown in fig. 3, according to interpolation data stored in a hardware FIFO queue of a controller, a motion command queue output buffer mechanism is adopted, and a predictive feedforward input is generated based on the data model obtained by the identification in step (1); the adaptive predictive controller APC set by the invention processes the input quantity 301, the servo delay 302 and the control quantity 304, and obtains stable position output 308 under the condition that external disturbance 306 exists;

(5) As shown in fig. 13, the output position values of the servo axes are cross-coupled, a real-time coupling profile error 1330 is calculated, and the control quantity in the velocity loop is corrected once by the coupling compensation controllers 1350 and 1350'; decoupling calculation is performed at 1320 through the pre-estimated compensation gain processing which is set, and the calculation result is processed through v _kx 、v _ky Processing to realize real-time adjustment of the feed rate;

(6) Based on the step (5), in combination with the adaptive look-ahead controller realized in the step (4), as shown in fig. 14, the axis adaptive look-ahead controller 1410 controls the controlled variable U of each servo axis _x 、U _y The output is further adjusted. Improving the stable output of the real-time control quantity according to the historical position data and the external interference information; the inter-axis coordination control adopts a cross-coupling pre-compensation mechanism 1330, and simultaneously performs the front-end input feed rate 1315 and the control output U _x 、U _y And carrying out trimming treatment.

The specific implementation manner of the step (1) is as follows: as shown in fig. 1, a linear servo control model of the plane motion XY axis is established. Ignoring the electrical time delay, determining the identification order of the

motor servo systems

102 and 106 to be 2, and deducing a simplified linear system differential equation model:

wherein:

P

the screw pitch of the screw, y,

Respectively the displacement, speed and acceleration of the screw drive slide. If non-linear friction is not considered firstEraser item

And an external load T _l ', obtaining a transfer function from the servo input reference voltage u to the displacement output y, and J _eq 、 B _eq As are the parameters of the model to be identified,

wherein:

the sweep frequency identification experiment is to input continuous excitation sine sweep frequency signal to the u end of the system and collect the position information of the output end y, thus obtaining the output voltage from the reference voltageAnd linear identification model from input end to position output end. Fig. 2 shows a physical model of a vertical axis Z-axis, the movement of the Z-axis is a dynamic process of the simultaneous movement of the workpiece and the counterweight, the workpiece and the counterweight are transferred by a steel wire rope through two pulleys, and according to the analysis of the XY-axis, the dynamic model of the Z-axis can be obtained as follows:

after Laplace transformation, the following can be obtained:

wherein:

i.e. the model parameters to be identified.

The specific implementation manner described in the above step (2) is, as shown in fig. 3, to set the second-order controlled object 305:

wherein: y is _d Is a constant perturbation 306. With the PD controller 303, the closed-loop characteristic polynomial for pole allocation is assumed to be: a. The _m (z ^-1 ) The controller comprises an integration link, and the following steps are taken:

is provided with

The transfer function from fig. 4 is: f (z) ^-1 )u(k)＝H(z ^-1 )r(k)-G(z ^-1 ) y (k), 405 is calculated Fu (k), and therefore the expression u (k) of the available controlled variable 410 is:

see fig. 5, 303 after Z-transform, the PD controller 501 is obtained, whose output is 505. Wherein the amount to be solved is: f. of ₂ ，g ₀ ，g ₁ ，g ₂ Or f, K _P ，K _I ，K _D (ii) a Need to be full ofPole arrangement conditions of the foot: i.e. closed-loop characteristic polynomial a _m (z ^-1 ) Thus, there are: (AF + z) ^-1 BG)y(k)＝z ^-1 BHr (k), apparently characterized by the equation:

(AF+z ^-1 BG)＝A _m (z ^-1 ) Wherein: AF and z ^-1 BG are all 4 th degree polynomials, 4 independent equations can be obtained by comparing coefficients of the same power, and thus the unknown quantity f is solved ₂ ，g ₀ ，g ₁ ，g ₂ And reverse solving to obtain K _P ，K _i ，K _d . F (z) ^-1 ) Set to a quadratic polynomial, select Am (z) ^-1 ) Time fetch degA _m ＝2，A _m ＝1+a _m1 z ^-1 +a _m2 z ^-2 The corresponding continuous second order polynomial is:

by servoing controlled object characteristics xi, ω _n Value and set servo sampling period T ₀ Obtaining a of the quadratic polynomial _m1 ，a _m2 Satisfies the following equation:

at the moment, the self-adaptive characteristic is embodied in that F and G follow up simultaneously when A and B which reflect the characteristic of the controlled object model change; on the basis of online identification of the controlled object parameters, a stable control pole is configured, and the PD control parameters are self-adaptively set.

The specific implementation manner of the step (3) is as follows: the motion command FIFO queue transmission mechanism is realized, as shown in FIG. 6, the motion commands generated by the background program are sequentially stored (601) in the preset motion command buffer (i.e. the FIFO queue preset in the hardware memory area). Each command sequence is assigned an offset position by a pointer, a base address is set, interpolation position data is extracted (602) from the queue according to the offset address setting in a set servo period, and a motion function library is called to execute a corresponding servo motion task.

The specific implementation manner of the step (4) is as follows: the type I servo system obtained by identification gives the following quadratic weighted objective function,

wherein e (j) and u (j) are respectively servo tracking error and real-time control quantity, Q and H are weighting coefficient matrixes to be designed, and z is a control quantity calculation formula for adding an interference value, wherein the control quantity calculation formula comprises the following steps: u (k) = F _e ∑e(i)+F _x x(k)+F _pr (z)P(k)+F _pd (z) d (k), wherein:

the optimal predictive servo control system is constructed as shown in fig. 7. 715. 725 is the predicted feedforward target value and the predicted feedforward disturbance value. In a single-variable SISO control system, a feedback control 710 and a feedforward control matrix 715 are in one-dimensional time-invariant vectors, so that one term and two terms in a u (k) formula are the same as those of a typical servo control system, and three terms and four terms represent the characteristics of a predictive servo control system. F _pr (z) and F _pd (z) the process parameter to be identified is based on the input, output, M of the previous step _R (M _d ) The optimal predictive control action is made by the step-miss target value and the interference value. The biggest problem of applying the predictive servo control method to a real-time servo control system is to reasonably and effectively use the order of future information, the higher the information amount is, the higher the servo control precision is, but the more DSP processing resources are consumed, and theoretically, simulated data is as follows: it is not foreseen that exceeding the order 30 times will affect the performance of the servo control.Fig. 8 shows a specific algorithm implementation, in which 301, 308 are input/output of the system, 302 is servo delay,the predicted feedforward interference value 720 and the feedback control output 840 are jointly acted on the adaptive predictive controller 830, processed by the feedforward module 820, acted on the feedback controller 810, and the overall control output 850 is acted on the controlled object 710 to obtain the final predicted position output value. Fig. 9 shows a specific measurement and control flow under the servo control structure of fig. 1, where 910 is a semi-closed loop speed control mode fed back by a motor with an encoder, and 920 is a position control mode fed back by a linear scale installed on the linear servo mechanism.

The specific implementation manner of the step (5) is as follows: first, the real-time contour motion error is calculated, as shown in FIG. 10, 1010 is the tracking target track, y _d (k) And y _d (k-1) is two adjacent points on the tracked target track, y (k) and y (k-1) are the target points of the real-time tracking positions, and epsilon is in the geometric relationship in the figure _k And epsilon _k-1 1020 target track contour error, e _k And e _k-1 Target trajectory tracking error is 1030. Accordingly, in fig. 11, the coordinate system is transformed, and under the

tracking trajectory

1010', 1102 and 1105 are the tangential and normal tracking errors in the real-time task coordinate system, and 1130' is the tracking error, and 1102 can be regarded as the contour error of 1020. From this the geometrical relationship:

if the normal deviation 1102 is treated as a contour error, then:

wherein y (x) _m ，y _m )，y _d (x _r ，y _r ) Wherein:

i.e. the included angle between the tangent of the commanded position at that moment and the X-axis, f _x (k)、f _y (k) For the XY-axis feed rate in each servo period τ, the profile error ε can be approximated by: epsilon _k ＝e _ky cosθ-e _kx sin θ represents the relationship between the tracking error and the contour error. Speed control module by position control systemType I system speed following errorNamely:

the following error calculation formula of the speed loop can be obtained:

the rewritable profile error is generally calculated by the formula:

in addition, as in FIG. 12, the target trajectory curve is described by the geometry-valued point by the parametric vector function: r (u) = { x (u), y (u) }, order

Then: k is a radical of formula ₀ Is a curve at r ₀ Relative curvature of the points:

wherein: 1010"For arbitrary trace, trace type value point P _i The coordinates of (a) are:

the distance is as follows: d _i (s)＝[(X _i -X(s)) ² +(Y _i -Y(s)) ² ] ^1/2 Since the tracking error is 1230, the profile error 1220 of any plane curve can be calculated as:

on the basis of a path prediction compensation algorithm (PM) and cross coupling (CCC), the servo feed rate (primary pulse coarse interpolation value) and the control quantity output are modified. As shown in fig. 13, 1305 represents a coarse interpolation feed rate provided by a front end interpolator, 1310 represents an X-axis input command position, initial feed rates 1315 and 1315' of the coarse interpolation are obtained through a first differentiation link, a profile error calculation value 1330 is obtained according to servo outputs 1380 and 1380', the profile error calculation value is decoupled from input ends of feed rates 1315 and 1315' of the XY axes through a speed

loop adjustment coefficient

1360, 1325 trimming is performed on the profile error calculation value, and a reference command position input 1335 is obtained through a first integration link. Wherein 1340 is the controlled object of each axis, 1370 is the control interference component of each axis position; in addition, profile error calculation 1330 also makes one control adjustment to velocity inner ring 1350.

The specific implementation manner of the step (6) is as follows: let p be the current sampling point, e (k) = R (k) -y (k), y be the system output, R be the target value, e be the tracking error, u (k) be the input of the controlled object, let F _R ＝[F _R1 ，F _R2 ，...，F _Rj ，...，F _RM ]， F _d ＝[F _d0 ，F _d1 ，...，F _dj ，...，F _dM ]The control amount u (k) can be expressed as:

expressed in an incremental form as:

from the predictive control APC module of FIG. 8, the adjustable parameter F _Rj 、F _dj The adaptive control rate of (2) can be passed through J _p And solving the partial derivatives of the gradient data to enable the gradient data to descend along the direction of the negative gradient, and obtaining:

in the using process, the controlled object G _p (k) The linear identification model and the y (k)/u (k) model are stable and convergent, otherwise, output oscillation may be caused, as shown in fig. 14, the predictive control modules 1410 of each axis are added on the basis of the cross-coupling pre-compensation control of fig. 13, the cross-coupling pre-compensation control is used to modify the coarse interpolation primary feed rates 1315 and 1315 'and the outputs of the controllers 1345 and 1345', and the APC modules of each axis are used to modify the control quantity, so that the cross-coupling control process is more stableThe control result is more accurate.

Compared with the prior track tracking and contour control technology, the invention has the remarkable effects that:

(1) The position control data model is obtained through the linear identification of the servo system, and the parameters and the self-adaptation law of the online identification model are determined, so that accurate and stable predictive control output can be obtained. Compared with a common servo control system without a controlled object model, the method has the advantages that the output of the controlled quantity is more stable, and the output of the target position tracking is more accurate.

(2) The method for forecasting the adaptive control law and the cross-coupling precompensation control is particularly suitable for complex geometric characteristic contour control, and has good performance in reducing contour errors compared with a typical feedforward PD position tracking algorithm.

(3) The prediction self-adaptive real-time control method provided by the invention fully utilizes future and historical control information, adopts a quadratic optimal control method, and can obtain more stable control quantity output and more accurate profile precision by setting a proper self-adaptive prediction control rate compared with some track profile control algorithms proposed earlier.

The above features and other advantages of the present invention will be readily apparent from the following detailed description of the exemplary embodiments and by reference to the accompanying drawings.

Drawings

Fig. 1 shows a servo apparatus for performing a trajectory profile control experiment.

Fig. 2 is an analysis diagram about the Z-axis movement principle.

Fig. 3 shows a control block diagram for PD control using a pole configuration method.

FIG. 4 is a block diagram of a discrete control system with disturbances.

FIG. 5 shows a block diagram of a discrete control system with PID pole placement.

Fig. 6 shows a queue system for front-end interpolation data transmission.

Fig. 7 is a schematic diagram of predictive feedforward control.

Fig. 8 shows an adaptive predictive control block diagram with external disturbance.

Fig. 9 shows a flow chart of the measurement and control configuration based on fig. 1.

Fig. 10 shows the geometrical relationship of profile error and tracking error in a cartesian coordinate system.

Fig. 11 shows the profile error and tracking error geometry in a real-time task coordinate system.

Fig. 12 shows the arbitrary curve profile error and tracking error geometry with geometrically shaped value points.

FIG. 13 is a diagram of a typical control structure using a cross-coupled profile error pre-compensation mechanism.

Fig. 14 is a diagram of a cross-coupled profile error pre-compensation control scheme based on predictive control.

Detailed Description

One specific example embodiment is an example of planar complex trajectory tracking and contour control with reference to the actuator of fig. 1.

The servo control architecture diagram of fig. 1 shows the actual control platform that implements this example. 102 and 106 are XY axis linear motion guide rails respectively, are connected together in a mutually vertical mode and are fixed on a 101 mechanism platform support; the XY axle stroke position information is measured by the grating ruler, the moving part of 106 bears the actual work task; each motion axis is provided with a front and a back limit switch 104 and an origin point return switch. The linear motion part is driven by an alternating current servo motor 105 through a servo amplifier to drive a ball screw rod to transmit, speed information is returned by a motor encoder, and position information is obtained by a 103 (X axis) grating ruler (three axes are uniformly matched). The servo motion structure of vertical axis Z axle 109 is the same as XY axle, the epaxial motion part that carries on of linear motion, because vertical axis structure, then the stopping of Z axle leans on the motor band-type brake or installs front and back counter weight additional, 108 is the counter weight that this experimental apparatus installed additional promptly, 108 and Z axle motion part 207 are connected through being fixed in the coaxial line pulley 110 at Z axle top, 110' with rigid rope 203, counter weight 108 is by the restraint direction of motion of straight line optical axis guide arm, 206 is vertical axis transmission ball, 107 is fixed for the Z axle and supports and ride, 208, 209 are Z axle driving motor and encoder respectively. The motion mechanism is driven and controlled by a servo controller (DSP-Based), as shown in FIG. 9, the control system configuration can be according to the basic servo control mode, wherein the loop 910 is the velocity loop encoder information feedback, and the loop 920 is the position loop grating ruler information feedback.

The high-performance track contour control algorithm of the invention is realized by adopting a position control mode. Better control effect and contour control accuracy can be obtained according to the following control flow. The two-axis cross-coupling control block diagram shown in fig. 14 embodies the basic spirit of the present invention, and its core mainly embodies a real-time servo control algorithm based on a controlled object model.

The specific identification process for the controlled object of each axis is as follows:

firstly, a nominal model of each axis is constructed, and the structural dynamics of the contour control workbench are mainly expressed by a group of linear differential equations. Identifying a nominal model of a controlled object, needing to accurately know the electromechanical characteristics of a servo mechanism, and obtaining the most appropriate knowledge in the aspect by using empirical data/theoretical formula/measured data, wherein the information is used for determining the structure of the model and defining the parameters of the model;

then, the control performance index of the servo system is designed, so that the design of a control algorithm operated in the controller has feasibility and reaches optimization;

finally, the model is verified to ensure that the identified model is a robust control system model. It contains not only a theoretical model of the system dynamics but also an uncertainty description and a noise description. For the present invention, the model validation problem is formulated as a linear time invariant system with uncertainty of norm-bounded construction and experimental data, model validation is performed in the frequency domain, determining if the model matches the input-output data and if the controller matches the model.

Taking an X axis as an example, an identification model from an input reference voltage to an output position is identified by adopting a sine pulse frequency sweeping mode, a sine frequency sweeping signal with 0.1-500 Hz and an amplitude of 1.5V is continuously input at an input end of a controlled object, and the description is as follows:

k =0,1,2 \8230n, wherein: ts is the sampling period, k is the number of identification sampling points, omega is the input angular frequency, alpha is the input amplitude,

and acquiring the position information of the output end in real time for a friction torque compensation item, and performing off-line identification on the identification object by applying a least square method in a system identification tool box of Matlab/Simulink. A transfer function is obtained for each axis from a reference voltage input to a position output. For the identification of the Z axis of the vertical axis, because the Z axis has larger phase lag than the XY axis, a pure lag link is required to be added when the Z axis model structure is determined, a proper time constant is set, and a simplified model of the Z axis model in a low-frequency range can be obtained by the same method.

After obtaining the linear identification model of each motion axis, a real-time control model associated with the motion axis needs to be established. The invention adopts a pole configuration mode to set the real-time position control parameter.

Setting a second-order controlled object

Wherein, y _d For a constant disturbance, A _m (z ^-1 ) Namely, a characteristic polynomial for pole allocation is taken as:

then there are:

due to F (z) ^-1 )u(k)＝H(z ^-1 )r(k)-G(z ^-1 ) y (k), the available controlled quantity expression is:

it can be seen that proportional and integral control acts on the deviation signal and derivative acts on the output signal y (k). The real-time update amount of the corresponding control parameter is as follows:

the self-adaptive characteristic is embodied in that F and G follow up simultaneously when A and B of the controlled object model are changed. On the basis of determining the pole allocation PID parameter self-adaptive adjustment of the system, the steps of identifying the controlled object parameter on line and obtaining the controlled quantity u (k) are as follows:

(1) Setting an initial value of a control quantity, and reading input and output numerical values of a system;

(2) Estimating the controlled object data model translation operator coefficient according to the input control quantity u (k) and the output position value y (k) of the controlled object

(3) Solving F and G according to a pole allocation self-adaptive PID control algorithm and solving H;

(4) The value of u (k) in real time is solved.

Wherein,

the online identification method adopts an identification method of a linear parameter model of the LTI system. Finally, a forgetting factor method is used(RFF) model parameters can be identified in real time:

where Θ (k) and P (k) are intermediate variables, λ is a decimal close to 1 selected as a forgetting factor, and λ =1 indicates that the past data is handled equally.

Fig. 6 shows a functional flow diagram of the motion control command queue operation. The purpose of using queue operation in the invention is to place the interpolation calculation task in the background processing program of the DSP in order to solve the unbalanced interpolation iterative calculation time, thereby reducing the real-time servo control task and ensuring the hard real-time characteristic of the position servo control task. In the background processing program, each calculated position target point is transmitted to a servo command and stored as a motion control command in the FIFO (function call) for push, that is, 601 operation. When each servo cycle comes, a motion command is fetched from the FIFO to execute the servo operation, i.e. 602 operation, pop the stack. Since several tasks need to be managed in the background program, all hardware resources except for task management are allocated for interpolation calculation of complex curves. In order to ensure the continuity of motion, it is necessary to ensure that there is enough motion control command in the FIFO queue stack for servo call, and open up a space in the DRAM of the motion controller or the off-chip RAM, so as to implement the dynamic storage process of the motion command. Setting the upper limit and the lower limit of the memory space, firstly ensuring that the number of instructions not less than the lower limit capacity exists in the FIFO queue at the motion starting stage, starting the whole servo motion, regularly monitoring the stack content in the running process, stopping interpolation action once the memory capacity exceeds the upper limit, and providing a real-time motion control instruction only in each servo period. The determination of the upper limit and the lower limit of the FIFO queue stack and the length setting of the FIFO queue stack are determined according to the complexity of an interpolation calculation task, but the basic principle is that the supply of a motion instruction cannot be interrupted in the real-time servo control process. In the present invention, the FIFO stack capacity is set to 1K × 16 bytes, the upper limit is the stack top of the queue, and the lower limit is set to 25% of the queue capacity. If the motion control command size in the queue is less than the minimum tolerance, the interpolation period is increased to increase the motion command size.

For the trajectory contour control, the cross-coupling control method shown in fig. 13 is used to calculate a contour error 1330 in real time, and the calculated contour error is used as a feedback value to adjust the control amount. The compensation of the contour error feedback value is generally applied to the velocity loop feedback to correct the controlled amount of the controlled object, i.e. 1330 is applied to the output ends of the position controllers 1345 and 1345' through the coupling compensation controllers (fig. 13 only includes the proportional link) 1350 and 1350', 1345 and 1345' embody the servo dynamics of the motion axis and are simplified to the proportional link processing. The values of the coupling controllers 1350 and 1350 'are determined according to the matching characteristics of 1345 and 1345'. The calculation of the coupling profile error 1330 is obtained from the plane geometry shown in fig. 10 and fig. 11, and a more detailed theoretical derivation is performed in step (2) of the invention, and the specific embodiment adopts the formula:

or the formula:

the parameter specification may be compared to fig. 13. Proportional gain K of speed loop _px And K _py With reference to the aforementioned adaptive proportional gain coefficient K _p 、T _i 、T _d The method is obtained by adopting a trapezoidal integral approximation method through a general incremental PID control law

Thereby obtaining PID adaptive control law u (k) = u (k-1) + p of each motion axis ₁ e(k)+p ₂ e(k-1)+p ₃ e(k-2)。K _εx And K _εy The parameters are set according to the servo characteristics of different motion axes and the geometrical characteristics of the track profile.

If the profile error feedback value is compensated and acted on the position ring, a profile error pre-compensation mechanism can be applied to set pre-estimated decouplingA gain value 1360 for adjusting the coarse interpolation feed rate of each motion axis by each axis error decoupling calculation 1320, K _v The values can be set with reference to:

where ρ is the curvature.

Thus, the basic coupling compensation spirit of the present invention can be embodied.

Fig. 14 shows a cross-coupled pre-compensation motion control strategy that incorporates a look-ahead feed-forward control of individual motion axes. Converting the position control model identified in the step (1) into a state space model of a servo system,

wherein A is _x 、B _x 、C _x 、A _y 、B _y 、C _y May be determined according to a system linear transfer function. In the formula: d (k) is a known interference signal, when the controllability observability condition is satisfied, the target value signal is set to be R (k), and the error signal is: e (k) = R (k) -y (k), and the following error system equation is derived:

or X ₀ (k+1)＝φX ₀ (k)+GΔu(k)+G _R ΔR(k+1)+G _d Δ d (k), where φ is the coefficient to be identified { a } of the dynamic data model ₁ ，a ₂ ，…，a _m ；b ₁ ，b ₂ ，…，b _n The identification method refers to the forgetting factor method (RFF). Fig. 8 is a schematic diagram illustrating the application of the adaptive predictive controller to act on the feedback controller and the controlled object, under the input of the reference command position 301 and the external disturbance 725, the adaptive predictive controller 830, the predictive control module 820 and the feedback control module 810 act together with the controlled object 710 to obtain the predictive control output 308. With respect to FIG. 14, the adaptive control module 1410 outputs to further adjust the individual single-axis control values U _x 、U _y And cross-coupling controlThe controlled adjustments of the devices 1350, 1350' acting together on a single shaft to achieveTo a better control effect. Another aspect of each single axis adjustment is the feed rate modification to 1315 and 1315', the amount of modification being determined by the decoupling controller 1320, and the modified feed rates 1325, 1325' being output at the commanded position by an integrating element.

Thus, while a particular embodiment of the invention has been described with reference to a specific implementation flow incorporating various implementations. The determined nominal model of the controlled object is a data model subjected to linearization processing, and the uncertainty description of the model should cover the attribute information of the model structure and parameters to the maximum extent and provide an envelope around the nominal model. In the present embodiment, each motion axis servo loop includes a plurality of feedforward and feedback inputs and control amount adjustment, and therefore the control system configured by the method should employ a state space method.

It is to be understood that even though numerous implementation steps and implementations of methods of the invention have been set forth in the foregoing example embodiments, including control structures and specific functional details, this disclosure is illustrative only, and changes may be made in detail, especially in matters of structure and arrangement of parts within the principles of the present invention to the full extent indicated by the broad general meaning of the terms in which the appended claims are expressed. The particular application embodiment will vary depending on the particular drive type and implementation, while maintaining substantially the same type of functionality, without departing from the scope and spirit of the present invention.

Claims

1. A contour control method for a complex track comprises the following steps:

(2) Designing a PD-based position controller, determining a stable control pole according to the servo characteristics of the controlled object obtained by identification, adjusting the parameters of the controller in real time, and obtaining a micro-overshoot and phase lag-free stable controller;

(4) Generating a predictive feedforward input by adopting a motion command queue output buffer mechanism according to interpolation data stored in a hardware FIFO queue of the controller and based on the data model obtained by the identification in the step (1); processing the input quantity (301), the servo delay (302) and the control quantity (304) by an adaptive predictive controller to obtain a stable position output (308);

(5) Performing cross coupling processing on the output position values of the servo shafts, calculating a real-time coupling profile error (1330), and correcting the control quantity in the speed ring through coupling compensation controllers (1350 and 1350'); performing decoupling calculation through precompensation gain processing, and performing XY axial feed rate correction component v on the calculation result _kx 、v _ky Processing to realize real-time adjustment of the feed rate;

(6) Combining the adaptive foresight controller of the step (4) on the basis of the step (5), and controlling the control quantity U of each servo axis by each axis adaptive foresight controller (1410) _x 、U _y The output is further adjusted; improving the stable output of the real-time control quantity according to the historical position data and the external interference information; the inter-axle coordination control adopts a cross-coupling pre-compensation mechanism, and simultaneously inputs the feed rate (1315) and the control output U to the front end _x 、U _y And carrying out trimming treatment.

2. The method for contour control of a complex trajectory according to claim 1, wherein the determining of the stable control pole in step (2) is embodied by the following steps:

(a) Setting an initial value U of the control quantity U (k) _x 、U _y Reading input and output numerical values of the control system;

(b) Estimating the coefficients of the model translation operator in real time under the action of the adaptive model described in claim 1 according to the input control quantity u (k) and the output position y (k) of the current controlled object

(c) Adjusting characteristic parameters xi, omega obtained by identifying the controlled object according to the pole allocation algorithm _n Value and sampling period T ₀ Obtaining coefficients F and G of the polar point configuration characteristic polynomial and a feedforward module H thereof;

(d) Obtaining the value of the real-time control quantity u (k) according to the obtained intermediate variable;

3. the method according to claim 1, wherein the control process information available to the adaptive predictive controller in step (4) includes the current position target point, the future target point and the external disturbance variation, and a given weighting function is introduced within the range of the global control target so as to make the current position target point, the future target point and the external disturbance variation within the optimal controllable theoretical range; the method is realized by the following steps:

(a) Calculating real-time servo control delay, initializing control quantity, and setting a control objective function as a quadratic expression:

(b) The optimization model of the weighting coefficient matrixes Q and H can be obtained through related mathematical software;

(c) Setting a control increment value delta u (k), adding the influence of the interference future value on the control quantity, and obtaining a control quantity processing formula as follows:

u(k)＝F _e ∑e(i)+F _x x(k)+F _pr (z)P(k)+F _pd (z)d(k)；

(d) According to the input, output and M of the previous step _R (M _d ) Making optimal look-ahead actions on the future target values and the interference values, of which F _pr 、F _pd And carrying out vector coefficient identification.

4. The method for contour control of a complex trajectory according to claim 1, wherein the cross-coupling process of step (5) comprises the following two aspects:

(a) The cross-coupling precompensation control method is adopted to carry out one-time adjustment on the input feed rate of the front end of each single shaft, so that the input of the feed rate of the system not only comprises the geometrical characteristics of the track, but also comprises the dynamic characteristics of the shaft;

(b) Decoupling real-time profile error calculations of the real-time coupled profile error calculations (1330) by a coupling compensation controller (1350) to obtain U _x 、U _y The compensation is output as a control quantity.