CN105929791B - The direct contour outline control method of plane rectangular coordinates kinematic system - Google Patents

Abstract

The invention discloses a direct contour control method of a Cartesian coordinate motion system, which is completed through 11 modular logic processing calculations, and the specific steps are as follows: motion planning; contour state monitoring; speed reverse transformation; tangential velocity generation; tangential Speed control; contour error control; forward transformation of control quantity; characteristic matching of X and Y axes; and single-axis control of X and Y axes. The method can monitor the motion state of the contour in real time, and calculate the real contour error according to the actual position and the analytical formula of the programmed contour. The contour error direction realizes the double closed-loop control of the contour error and the contour error speed, conforms to the physical law of the Cartesian coordinate motion system, and improves the contour control effect. Cartesian coordinates and contour coordinates match the real-time transformation of speed and control amount and the characteristics of the coordinate axes, so that each Cartesian coordinate axis is coordinated when performing contour movements in different directions. It can fully reduce the contour error and realize high-precision contour control.

Description

Direct Contour Control Method for Plane Cartesian Coordinate Motion System

technical field

The invention belongs to the field of numerical control machining, and in particular relates to a computer numerical control technical method for planar Cartesian coordinate contour movement.

Background technique

In the process of CNC machining, contour error is an important index to evaluate the accuracy of multi-axis motion control system. At present, the basic principle of computer digital control of the Cartesian coordinate motion control system is that the control system performs data sampling interpolation on the contour moving path, interpolates to obtain the coordinates in the Cartesian coordinate system at each time, and then distributes the interpolation coordinates to The servo system of each moving axis is used as the position command of the servo system of each moving axis. The servo system of each axis follows the position command, and compares the data of the axis position with the command position output by interpolation at that time in each servo cycle to obtain the position error (that is, the following error of the axis). Then, according to the position error and according to a certain control law, the control quantity at this moment is calculated as the control output. Repeat the above work of measurement, comparison, calculation and output every fixed servo cycle, and then the servo motor and transmission mechanism of the axis can be driven to follow the time sequence of the position command output by the interpolator for continuous motion. The actual contour motion trajectory is obtained by synthesizing the motion of each axis of the Cartesian coordinate motion mechanism.

Because in the motion control, the following error of each axis always exists, so there is also an error in the synthetic contour motion, which leads to the deviation between the actual motion contour and the command contour. On the other hand, due to the different response characteristics of each axis to commands, as well as the different states of nonlinear friction and load disturbance on each axis, the motion of each axis cannot be fully coordinated, and contour errors will also occur. To reduce contour errors, current motion control systems employ two different strategies. The first is to reduce the single-axis following error, including the use of position/speed/current three closed-loop control, feedforward control, disturbance observation and compensation, etc. The disadvantage of this method is that due to the response characteristics, unknown disturbances, parameter changes, and model accuracy, it is impossible to completely eliminate the following error, so the ability to reduce the contour error is limited. In addition, since each axis is controlled independently of the position, the mismatch between the tracking errors of each axis is not considered, resulting in uncoordinated multi-axis linkage, which causes a large deviation between the actual motion profile and the ideal profile. In order to improve the coordination of multi-axis linkage and reduce the contour error, a second control strategy to reduce the contour error - cross-coupling control has been proposed in recent years. The cross-coupling contour control generates a compensation control quantity by estimating the direction and size of the contour error in real time. After coordinate transformation, the contour compensation control output is superimposed on the control output of the original single-axis controller. By correcting the actual synthetic motion, its motion coordination is improved to reduce contour errors. But this method is still based on the traditional single-axis position tracking. The controllers of each axis need to take into account the reduction of position following error and contour error at the same time, and trade off the two indicators by setting different control gains. Since the control commands of these two aspects are not orthogonal in Cartesian coordinates, there is a coupling between position tracking and contour error control. The position tracking control amount will weaken the contour error control amount, so it is still possible to generate a large contour error, which is more obvious on the high-speed, high-curvature motion path. In addition, in this kind of controller, because the controller gains of position following control and contour control are coupled and restrained, it is difficult to adjust, so it cannot be widely used in CNC machining technology.

Contents of the invention

The purpose of the present invention is to provide a direct contour control method for a plane Cartesian coordinate motion system, which can solve the problems of low precision and difficult adjustment of the existing control methods.

In order to solve the above problems, the proposed direct contour control method of the planar Cartesian coordinate motion system is completed through 11 modular logic processing calculations. The specific steps are as follows:

(1) Motion planning: generate contour motion tangential speed command planning; according to the programming contour input by the user Plan the contour motion process with the motion planning constraints, and generate the relational function f between the contour motion tangential velocity command v _tc and the contour curve parameter u, v _tc = f(u), for the subsequent real-time control link.

(2) Contour status monitoring: According to the actual position P _x , P _y of the current XY axis and the programmed contour Real-time calculation of contour error e _c and contour error direction The parameter u of the programming contour curve corresponding to the current actual position, and the tangential movement direction corresponding to the actual position in are unit direction vectors.

(3) Speed reverse transformation: According to the XY two-axis speed V _x , V _y and the current Calculate the actual tangential velocity v _ta and the profile error direction velocity v _ca along the programmed profile.

(4) Tangential speed generation: calculate the current tangential feed speed; calculate the current tangential feed speed command v _tc in real time according to the curve parameter u calculated by the contour state monitoring module and f generated by the motion planning module.

(5) Tangential speed control: calculate the tangential control output; calculate the tangential speed error e _vt according to the commanded tangential speed v _tc and the actual tangential speed v _ta , where e _vt = v _tc - v _ta , and then by e _vt calculates the tangential control output according to the feedback control law.

(6) Contour error control: Calculate the contour error direction control output U _C according to the feedback control law based on the e _c calculated by the contour state monitoring and the v _ca calculated by the reverse speed transformation.

(7) Forward transformation of control quantity: calculated according to the current contour state monitoring module Transform the tangential control quantity U _T and the contour error direction control quantity U _C into the control quantity U _x of the X-axis and the control quantity U _y of the Y-axis in Cartesian coordinates.

(8) X-axis control characteristic matching: Compensate the input/output characteristics of the X single-axis control module to match the characteristics of the XY axis; U _x is processed by this module to generate the actual X-axis control amount

(9) X-axis single-axis control: according to the X-axis control amount After signal processing and power amplification, it is converted into the torque output of the servo motor, and drives the X-axis movement in the XY rectangular coordinates through the mechanical transmission link;

(10) Y-axis control characteristic matching: Compensate the characteristics of the input/output of the Y single-axis control module to match the characteristics of the XY-axis; after U _y is processed by this module, the actual Y-axis control amount is generated

(11) Y-axis single-axis control: according to the Y-axis control amount After signal processing and power amplification, it is transformed into the torque output of the servo motor, and drives the Y-axis movement under the X-Y rectangular coordinates through the mechanical transmission link.

In each servo control cycle, the motion control system repeats the process of the above steps (2) to (11), that is, continuous high-precision contour motion can be realized.

The control of the contour error in the above step (6) adopts double closed-loop feedback control in the direction of the contour error, the outer loop is the contour error control loop; the inner loop is the contour error speed control loop. Step (6) can be further decomposed into the following steps:

(6-1) Contour error feedback control: Calculate the speed command v _cc in the direction of the contour error according to the e _c calculated by contour state monitoring.

(6-2) Calculate the velocity error in the direction of the contour error: Calculate the velocity error e vc _in the direction of the contour error according to v _cc and v _ca calculated by the inverse transformation of the velocity, where e _vc =v _cc -v _ca .

(6-3) Contour error speed feedback control: Calculate the contour error direction control output U _C according to e _vc .

Advantage of the present invention and the beneficial effect that produce are:

(1) It can directly monitor the motion state of the planar rectangular coordinate contour in real time, and calculate the real contour error according to the actual position and the analytical formula of the programmed contour, with high precision. The contour error direction realizes the double closed-loop control of contour error and contour error speed, which conforms to the physical law of the plane Cartesian coordinate motion system and improves the contour control effect. Cartesian coordinates and contour coordinates match the real-time transformation of speed and control amount and the characteristics of the coordinate axes, so that the X-Y axes of Cartesian coordinates are coordinated in different directions for contour movement. Therefore, this method can sufficiently reduce the contour error and realize high-precision contour control.

(2) The method of the present invention no longer performs contour control indirectly through X-Y axis position tracking. After canceling the position tracking link, there is no contour error component caused by two-axis tracking errors, thereby improving the contour control accuracy.

(3) From the orthogonality between the error direction of the plane contour and the tangential direction of the contour motion, it can be seen that the control variables U _C and U _T are orthogonal, the control variables do not affect each other, the tangential motion and the contour error control part can be adjusted independently, and The control parameters have clear physical meaning, which simplifies the adjustment process of the system.

(4) In occasions such as numerical control machining, the tangential velocity of the contour motion has an important influence on the surface processing quality. The traditional controller cannot directly perform closed-loop control on the tangential velocity. The incoordination of each axis and the position tracking lag lead to poor accuracy of the tangential velocity, especially in high-speed movements with large curvature and corner positions. The method of the invention can acquire the real-time tangential speed command quickly and with high precision according to the tangential speed planning function f and the real-time detected curve parameter u. And through the closed-loop control of the tangential speed control, the accuracy of the tangential speed is improved.

(5) The implementation of the method of the present invention can be based on the existing motion control system hardware facilities, and can be implemented without adding hardware, which facilitates the upgrading of the existing motion control system and reduces the cost.

Description of drawings

Fig. 1 is a block diagram of logical processing and calculation of the direct contour control method in the present invention.

Fig. 2 is a schematic diagram of contour state monitoring in the present invention.

Fig. 3 is a schematic diagram of the motion planning module in the present invention.

Fig. 4 is a diagram of the transformation relationship between the control variable vector and the speed vector in the present invention.

Fig. 5 is a schematic diagram of tangential speed control in the present invention.

Fig. 6 is a schematic diagram of contour error control in the present invention

Detailed ways

The implementation steps of the method of the present invention will be further described below in conjunction with the accompanying drawings and examples. It should be noted that the following examples are illustrative, not limiting, and the content covered by the present invention is not limited to the following examples.

The direct contour control method of the planar Cartesian coordinate motion system is completed through the following 11 modular logical processing calculations. The specific steps are as follows:

(1) Motion planning: generate contour motion tangential speed command planning; according to the programming contour input by the user Plan the contour motion process with the motion planning constraints, and generate the relational function f between the contour motion tangential velocity command v _tc and the contour curve parameter u, v _tc = f(u), for the subsequent real-time control link.

(2) Contour status monitoring: According to the actual position P _x , P _y of the current XY axis and the programmed contour Real-time calculation of contour error e _c and contour error direction The parameter u of the programming contour curve corresponding to the current actual position, and the tangential movement direction corresponding to the actual position in are unit direction vectors.

(3) Speed reverse transformation: According to the XY two-axis speed V _x , V _y and the current Calculate the actual tangential velocity v _ta and the profile error direction velocity v _ca along the programmed profile.

(4) Tangential speed generation: calculate the current tangential feed speed; calculate the current tangential feed speed command v _tc in real time according to the curve parameter u calculated by the contour state monitoring module and f generated by the motion planning module.

(5) Tangential speed control: calculate the tangential control output; calculate the tangential speed error e _vt according to the commanded tangential speed v _tc and the actual tangential speed v _ta , where e _vt = v _tc - v _ta , and then by e _vt calculates the tangential control output U _T according to the feedback control law.

(6) Contour error control: Calculate the contour error direction control output U _C according to the feedback control law based on the e _c calculated by the contour state monitoring and the v _ca calculated by the reverse speed transformation.

(7) Forward transformation of control quantity: calculated according to the current contour state monitoring module Transform the tangential control quantity U _T and the contour error direction control quantity U _C into the X-axis control quantity U _x and the Y-axis control quantity U _y in Cartesian coordinates.

(8) X-axis control characteristic matching: Compensate the input/output characteristics of the X single-axis control module to match the characteristics of the XY axis; after U _x is processed by this module, the actual X-axis control amount is generated

(9) X-axis single-axis control: according to the X-axis control amount After signal processing and power amplification, it is converted into the torque output of the servo motor, and drives the X-axis movement under the XY rectangular coordinates through the mechanical transmission link.

(10) Y-axis control characteristic matching: Compensate the input/output characteristics of the Y single-axis control module to match the characteristics of the X-Y axis; after U _y is processed by this module, the actual Y-axis control amount is generated

(11) Y-axis single-axis control: according to the Y-axis control amount After signal processing and power amplification, it is transformed into the torque output of the servo motor, and drives the Y-axis movement under the X-Y rectangular coordinates through the mechanical transmission link.

In each servo control cycle, the motion control system repeats the process of the above steps (2) to (11), that is, continuous high-precision contour motion can be realized.

The control of the contour error in the above step (6) adopts double closed-loop feedback control in the direction of the contour error, the outer loop is the contour error control loop; the inner loop is the contour error speed control loop. Step (6) can be further decomposed into the following steps:

(6-1) Contour error feedback control: Calculate the speed command v _cc in the direction of the contour error according to the e _c calculated by contour state monitoring.

(6-2) Calculate the velocity error in the direction of the contour error: Calculate the velocity error e vc in the direction of the contour error according to v _cc and v _ca calculated by the inverse transformation of the velocity, where _{e vc =} v _cc -v _ca .

(6-3) Contour error speed feedback control: Calculate the contour error direction control output U _C according to e _vc .

Figure 1 shows the logical relationship between the operation of the contour control system. The planar Cartesian coordinate motion mechanism of this embodiment includes two vertical control axes of X-Y.

In Fig. 1, the single-axis control module is composed of the driver of the servo motor of each X-Y motion axis, the servo motor, the transmission mechanism, and the position and speed feedback device. The other modules in Figure 1 can be realized in the form of real-time digital control program on the microprocessor of the contour motion controller, and the signals in the control program are transmitted in the form of program variables. The microprocessor communicates with the single-axis control module through electrical signals and interface circuits.

In this embodiment, the X and Y axes adopt AC synchronous servo motors and their drivers, and the drivers work in the torque control mode. According to the control amount of each axis (wherein, i=x, y, the same below), after signal processing and power amplification, it is transformed into the torque output of the servo motor. Then through the coupling, ball screw pair and guide rail pair, it drives the XY table to move to complete the contour movement. The position and speed sensors installed on the X and Y axes can obtain the respective actual position and speed signals of the X and Y axes in real time.

The principle of motion planning is shown in Figure 3. The user's programming profile is stored in the form of a parameter equation inside the control system. Suppose the parametric equation of the programmed profile curve being processed is The parameter range is [u _s , u _e ], then the curve parameter corresponding to the start position of the movement is u _s , and the curve parameter corresponding to the movement end position is u _e . The constraints of motion planning include the initial velocity v _s , the maximum velocity v _max , the maximum end velocity v _emax , the maximum acceleration a _max and the maximum jerk J _{max of} tangential motion. The result of planning requires the generation of the relationship function f between the contour motion tangential velocity command v _tc and the contour curve parameter u.

The specific implementation is to generate the relationship f _t between v _tc and time t and the relationship S _t between contour curve displacement S and time t under the constraint conditions according to the conventional planning method, and at the same time according to The relationship function S _u between S and u can be obtained. According to f _t , S _t and _Su , the planning f _t in the time domain can be mapped to the curve parameter domain by spline interpolation method, and the motion planning f expressed by spline function with u as an independent variable can be obtained. Since f can be obtained before motion, motion planning does not occupy the time resources of the microprocessor during real-time motion control.

The principle of contour state monitoring is shown in Figure 2. Due to disturbance etc., the actual motion profile will deviate from the programmed profile. At some point in the motion, assume the current actual position read by the position feedback device Can be based on and Solve the contour motion state of the positional relationship. Since the magnitude of the contour error e _c is defined as arrive The shortest distance of , so the point corresponding to this shortest distance on the programmed curve can be found can know at the same time The direction of is coincident with the contour error direction.

On the other hand, from the curve parameter equation can be calculated in Derivative vector at but The direction of is the tangent direction of the curve. According to the definition of contour error, the point The tangent direction of the curve at vertical, so the equation By solving this equation, the parameter u of the corresponding programming contour curve can be obtained. Further, the absolute value of the contour error can be obtained The unit vector of the tangential motion direction corresponding to the actual position

Contour error direction unit vector defined as Rotate 90 degrees counterclockwise, then The symbol for e _c is defined as and Negative in the same direction, and Positive when reversed.

Refer to the left side of Figure 4 for the principle of speed inverse transformation. V _x and V _y are the actual speeds of the X and Y axes measured by the single-axis control module of the X and Y axes respectively, so the synthetic speed vector can be obtained Will respectively projected to and direction, get the actual tangential velocity v _ta along the programmed contour and the contour error direction velocity v _ca . According to the definition of vector inner product, we can get and

The generation of tangential speed is based on the curve parameter u calculated by the contour state monitoring module and f generated by the motion planning module, and the tangential feed speed command v _tc at the current moment is calculated, that is, v _tc =f(u) (see Figure 3 ).

The tangential speed control adopts the feedback control law to calculate the control quantity output U _T , as shown in Figure 5. Calculate the tangential velocity error e _vt =v _tc -v _ta according to the commanded tangential velocity v _tc and the actual tangential velocity v _ta . In this embodiment, the feedback control rate adopts PI (proportional + integral) control to reduce the steady-state error. Let the proportional and integral gains be K _PT and K _IT respectively, then

Contour error control adopts double closed-loop feedback control law (see Figure 6), the outer loop is the contour error control loop, and the inner loop is the contour error speed control loop.

In this embodiment, the outer loop adopts P (proportional) control, and the speed command v _cc in the direction of the contour error is calculated from the contour error e _c to compensate the contour error. Assuming that the proportional gain of the outer loop is K _PCO , then v _cc =K _PCO e _c . The inner loop adopts PI (proportional + integral) control, and calculates the speed error e _vc in the direction of the contour error according to v _cc and v _ca calculated by the speed inverse transformation module = v _cc -v _ca . Set the proportional and integral gains of the inner loop as K _PCI and K _ICI respectively, then the control output

Refer to the right side of Figure 4 for the principle of the forward transformation of the control quantity. In order to transform U _T and U _C to the Cartesian coordinates of the XY plane, project U _T and U _C on the X and Y axes respectively, and then superimpose the control components projected on each axis. because Both are unit vectors, so U _x = U _T T _x + U _C N _x , U _y = U _T T _y + U _C N _y .

Coordinate axis control characteristic matching—used to compensate the input/output characteristics of the single-axis control module to match the characteristics of each axis and improve the coordination of multi-axis linkage control. In this embodiment, the X and Y axis control characteristic matching modules are all proportional links, and the proportional gain is K _Mi , then in Fig. 1 Assuming that the output torque M _i of single-axis control is relative to the control signal The gain of the load is K _ai , and the moment of inertia of the load is J _i . When ignoring the dynamic characteristics of the axes and factors such as friction and disturbance, in order to realize the coordination of motion, it is hoped that the total gains of each axis are equal, that is, satisfying Therefore, by setting K _Mi of each axis, the requirements of the above formula can be met, and the response to the contour control signal U _T and U _C is consistent when moving in each direction.

According to the logic flow in Fig. 1, after motion planning, each real-time computing module is called according to the signal processing sequence in each servo cycle, so as to realize the direct contour control method and complete continuous high-precision contour motion.

Claims (2)

1. the direct contour outline control method of plane rectangular coordinates kinematic system, it is characterised in that the control method passes through 11 moulds The logical process of block calculates to complete, and is as follows：

(1) motion planning：Generate the instruction planning of contour motion tangential velocity；According to programming profile input by userAnd movement Plan constraint condition plans contour motion process generation contour motion tangential velocity instructs v_tcWith contour curve parameter u Relation function f, v_tc=f (u) is used for follow-up controlling unit in real time；

(2) profile Stateful Inspection：According to current X-Y axis physical location P_x、P_yAnd programming profileProfile errors are calculated in real time e_c, profile errors directionThe parameter u of the corresponding programming contour curve of current actual positions, the corresponding tangential fortune of physical location Dynamic directionWhereinIt is unit direction vector；

(3) speed transformation by reciprocal direction：According to two axle speed V of X-Y_x、V_yAnd currentCalculate actually cutting along programming profile To speed v_taWith profile errors direction speed v_ca；

(4) tangential velocity generates：Calculate current time tangential admission speed；Joined according to the curve that profile state monitoring module calculates The number u and f of motion planning module generation calculates the speed command v of current time tangential admission in real time_tc；

(5) tangential velocity controls：Calculate the output of Tangents Control amount；According to instruction tangential velocity v_tcWith practical tangential velocity v_taIt calculates Tangential velocity error e_vt, wherein e_vt=v_tc-v_ta, then by e_vtTangents Control amount output U is calculated according to Feedback Control Law_T；

(6) profile errors control：The e calculated according to profile Stateful Inspection_cAnd the v that speed transformation by reciprocal direction calculates_ca, controlled according to feedback Rule processed calculates profile errors direction controlling amount output U_C；

(7) controlled quentity controlled variable positive-going transition：It is calculated according to current outline state monitoring moduleBy Tangents Control amount U_TAnd wheel Wide direction of error controlled quentity controlled variable U_C, it is transformed into the controlled quentity controlled variable U of X-axis under rectangular co-ordinate_xWith the controlled quentity controlled variable U of Y-axis_y；

(8) X-axis control characteristic matches：The characteristic of X single shaft control module input/output is compensated, makes the characteristics match of X-Y axis；U_xThrough After crossing the resume module, practical X-axis controlled quentity controlled variable is generated

(9) X-axis single shaft control：According to X-axis controlled quentity controlled variableThe torque of servo motor is converted to by signal processing and power amplification Output drives the X-axis under X-Y rectangular co-ordinates to move by machine driving link；

(10) Y-axis control characteristic matches：The characteristic of Y single shaft control module input/output is compensated, makes the characteristics match of X-Y axis；U_y After the resume module, practical Y-axis controlled quentity controlled variable is generated

(11) Y-axis single shaft control：According to Y-axis controlled quentity controlled variableTurning for servo motor is converted to by signal processing and power amplification Square exports, and the Y-axis under X-Y rectangular co-ordinates is driven to move by machine driving link,

Within each SERVO CONTROL period, kinetic control system repeats the above steps the processes of (2)~(11), can realize continuous High-accurate outline movement.

2. the direct contour outline control method of plane rectangular coordinates kinematic system described in accordance with the claim 1, it is characterized in that：It is described Profile errors control in step (6) is controlled in profile errors direction using Dual-loop feedback control, and outer shroud is profile errors control ring； Inner ring is profile errors speed control ring；Step (6) further can be analyzed to following steps：

(6-1) profile errors feedback control：The e calculated according to profile Stateful Inspection_cCalculate the speed command in profile errors direction v_cc；

(6-2) calculates the velocity error in profile errors direction：According to v_ccAnd the v that speed transformation by reciprocal direction calculates_ca, calculate profile errors The velocity error e in direction_vc, wherein e_vc=v_cc-v_ca；

(6-3) profile errors speed feedback control：According to e_vcCalculate profile errors direction controlling amount output U_C。