CN108319228B - Acceleration and deceleration control method in numerical control system trajectory planning - Google Patents

Acceleration and deceleration control method in numerical control system trajectory planning Download PDF

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CN108319228B
CN108319228B CN201810134489.XA CN201810134489A CN108319228B CN 108319228 B CN108319228 B CN 108319228B CN 201810134489 A CN201810134489 A CN 201810134489A CN 108319228 B CN108319228 B CN 108319228B
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acceleration
time
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numerical control
deceleration
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朱其新
费清琪
刘红俐
蒋全胜
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Suzhou University of Science and Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/416—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control of velocity, acceleration or deceleration
    • G05B19/4163—Adaptive control of feed or cutting velocity
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/36—Nc in input of data, input key till input tape
    • G05B2219/36521—Select by combination of detected force, acceleration, speed, work rate

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Abstract

The invention provides a speed increasing and reducing control method in numerical control system track planning, which assumes the processing of a numerical control systemThe total operation time is T, and the total operation time is divided into seven time segments which are respectively 0-T1、t1～t2、t2～t3、t3～t4、t4～t5、t5～t6、t6～t7Defining a time interval of T for each time segmenti(i is 1,2,3 … …,7), then T1The corresponding time period is 0 to t1，T2Corresponding to a time period of t1～t2，T3Corresponding to a time period of t2～t3，T4Corresponding to a time period of t3～t4,T5Corresponding to a time period of t4～t5,T6Corresponding to a time period of t5～t6,T7Corresponding to a time period of t6～t7The algorithm expression used in planning the acceleration and deceleration curve model is
Figure DDA0001575855930000011
Where j (t) is a function of jerk with respect to time t, jmaxIs the jerk maximum during operation,
Figure DDA0001575855930000012
the acceleration and deceleration control method in the numerical control system track planning provided by the invention is intersected with the prior art, the control algorithm model is simpler, the acceleration curve is smoother, and the start and stop of the numerical control system are directly reduced.

Description

Acceleration and deceleration control method in numerical control system trajectory planning
Technical Field
The invention relates to the field of servo system motion control, in particular to an acceleration and deceleration control method in numerical control system trajectory planning.
Background
The traditional linear acceleration and deceleration control is widely applied due to the fact that positioning time is optimal under the conditions of given position, speed and acceleration, but discontinuous acceleration at the turning point of the traditional linear acceleration and deceleration control often causes overtravel and oscillation when a machine reaches an end point with expected accuracy. Compared with the linear acceleration and deceleration control, the exponential acceleration and deceleration control has relatively higher smoothness and motion precision. However, the control algorithm is complex and takes long time, and acceleration sudden change still exists at the starting and ending points of acceleration and deceleration, so that certain impact is generated on the machine tool.
The currently used S-curve acceleration/deceleration control algorithm is shown in fig. 1, and ideally, the S-curve acceleration/deceleration control algorithm realizes continuous change of acceleration, but the step-change acceleration still causes large shock and oscillation of the system. A Jerk continuous sine function square curve acceleration and deceleration algorithm research (158-. However, the acceleration and deceleration control method still has the defects that: in the uniform acceleration section, although the Jerk curve of the speed change section and the uniform acceleration section (uniform deceleration section) is continuous, the Jerk curve at the turning point is still not smooth enough, which may cause the numerical control system to still be in a state of abrupt acceleration or abrupt deceleration at this point.
Disclosure of Invention
The invention provides a speed increasing and reducing control method in numerical control system track planning, which is used for solving the problems.
In order to achieve the purpose, the invention provides a speed reduction control method in numerical control system track planning, which is characterized in that the total operation time of the numerical control system during processing is assumed to be T, and the total operation time is divided into seven time periods which are respectively 0-T1、t1～t2、t2～t3、t3～t4、t4～t5、t5～t6、t6～t7Defining a time interval of T for each time segmenti(i is 1,2,3 … …,7), then T1The corresponding time period is 0 to t1，T2Corresponding to a time period of t1～t2，T3Corresponding to a time period of t2～t3，T4Corresponding to a time period of t3～t4,T5Corresponding to a time period of t4～t5,T6Corresponding to a time period of t5～t6,T7Corresponding to a time period of t6～t7The algorithm expression used in planning the acceleration and deceleration curve model is
Figure BDA0001575855910000021
Where j (t) is a function of jerk with respect to time t, jmaxIs the jerk maximum during operation,
Figure BDA0001575855910000022
preferably, T is1＝T3＝T5＝T7。
Preferably, the arithmetic expression of acceleration in the acceleration and deceleration curve model is
Figure BDA0001575855910000031
Wherein a ismaxIs the maximum acceleration.
Preferably, the arithmetic expression of the speed in the acceleration and deceleration curve model is
Figure BDA0001575855910000032
Wherein VmaxMaximum speed, v, allowed for numerical control system machining1,v2,v5,v6When t is equal to t1,t2,t5,t6The instantaneous speed of the time.
Preferably, the arithmetic expression of the displacement in the acceleration and deceleration curve model is
Figure BDA0001575855910000033
Wherein s is1,s2,s3,s4,s5,s6When t is equal to t1,t2,t3,t4,t5,t6The displacement of time.
Preferably, the numerical control system generates a during processingmaxOr-amaxAnd defining the target displacement when the numerical control system is processed as L, when t is t7When the displacement is S7；S7Less than or equal to L.
The acceleration and deceleration control method in the numerical control system track planning provided by the invention has the following advantages:
1. compared with the existing exponential acceleration and deceleration control algorithm, the control algorithm model is simpler, and more algorithm compiling time can be saved in the practical system application.
2. Compared with the existing Jerk continuous sine function square curve acceleration and deceleration control method, the acceleration curve of the method is smoother, the start and stop of the numerical control system are directly reduced, and therefore the impact and oscillation of the change of the acceleration on the numerical control system in the acceleration and deceleration process are reduced.
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FIG. 1 is a prior art S-curve acceleration and deceleration control algorithm curve;
FIG. 2 is a prior art Jerk continuous sine function square curve acceleration and deceleration control method curve;
FIG. 3 is a modified sine function square curve acceleration and deceleration model curve provided by the present invention;
FIG. 4 is a graph of an acceleration/deceleration model provided by the present invention when the maximum speed and the maximum acceleration cannot be achieved;
fig. 5 is a curve of an acceleration/deceleration model capable of achieving the maximum speed and the maximum acceleration according to the present invention.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.
The invention aims to provide an improved sine function square curve acceleration and deceleration control method applied to high-precision servo system track planning. FIG. 3 shows a modified sine function square curve acceleration and deceleration curve model, wherein jmaxIs the maximum jerk during operation, amaxAt maximum acceleration, VmaxThe maximum speed is allowed for machining. The whole acceleration and deceleration curve can be divided into 7 symmetrical stages from 0 to t1Are all acceleration phases, t1～t2In the stage of uniform acceleration, t2～t3To reduce the acceleration phase, t3～t4At a constant speed stage, t4～t5Is an acceleration and deceleration stage, t5～t6At the stage of uniform deceleration, t6～t7For deceleration phases, defining the time interval of each phase as TiI is 1,2,3 … …,7 (e.g. 0-t)1Segment T1, T1～t2Segment is T2By analogy), and because of the symmetry of the entire velocity curve, we can conclude that: t is1＝T3＝T5＝T7. Defining total operation time as T, and the functions of jerk, acceleration, speed and displacement with respect to time T as J (T), A (T), V (T) and S (T), respectively, and making T0The expression of jerk as a function of time t is first given below at 0:
Figure BDA0001575855910000051
(1) the method comprises the following steps:
Figure BDA0001575855910000052
by sequentially integrating the expression (1), the expressions of acceleration, speed and displacement can be obtained as shown in the expressions (2), (3) and (4), wherein v1、v2、v5、v6When t is equal to t1、t2、t3、t4、t5、t6Instantaneous speed of time; s1、s2、s3、s4、s5、s6When t is equal to t1、t2、t3、t4、t5、t6The displacement of time.
Figure BDA0001575855910000061
Figure BDA0001575855910000062
Figure BDA0001575855910000063
(1) And (4) is a mathematical expression of the accelerated speed, the speed and the displacement of the improved sine function square curve acceleration and deceleration curve.
The above equation satisfies such boundary conditions:
1. the maximum acceleration or deceleration can be achieved during acceleration and deceleration.
2. Defining the target displacement as L, when t is t ═ t7When the displacement is S7；S7Less than or equal to L. Then, from equation (2):
Figure BDA0001575855910000064
namely:
Figure BDA0001575855910000065
Figure BDA0001575855910000072
T＝4T1+2T2+T4 (7)
in the actual trajectory planning, speed planning under different control conditions is required, and the following formula (3) can be obtained:
Figure BDA0001575855910000071
defining the actual motion displacement in the process of planning the track as L and the target displacement as S7The simulation parameters are selected as follows S70.0245m 2450 counts, 2000Hz sampling frequency, maximum speed vmaxAt 600mm/s, the planning can be divided into the following two cases:
(1) when L < S7At this time, the actual moving speed cannot reach the maximum speed, the acceleration cannot reach the maximum acceleration, and the simulation result is shown in fig. 4, where L is set to 0.0145 m.
(2) When L is more than or equal to S7At this time, the actual moving speed can reach the maximum speed, the acceleration can reach the maximum acceleration, L is set to 0.0345m, and the simulation result is shown in fig. 5.
The acceleration and deceleration control method in the numerical control system track planning provided by the invention has the following advantages:
1. compared with the existing exponential acceleration and deceleration control algorithm, the control algorithm model is simpler, and more algorithm compiling time can be saved in the practical system application.
2. Compared with the existing Jerk continuous sine function square curve acceleration and deceleration control method, the acceleration curve of the method is smoother, the start and stop of the numerical control system are directly reduced, and therefore the impact and oscillation of the change of the acceleration on the numerical control system in the acceleration and deceleration process are reduced.
It will be apparent to those skilled in the art that various changes and modifications may be made in the invention without departing from the spirit and scope of the invention. It is intended that the present invention cover the modifications and variations of this invention provided they come within the scope of the appended claims and their equivalents.

Claims (6)

1. A speed-up and speed-down control method in numerical control system track planning is characterized in that the total operation time of a numerical control system during processing is assumed to be T, and the total operation time is divided into seven time periods which are respectively 0-T1、t1～t2、t2～t3、t3～t4、t4～t5、t5～t6、t6～t7Defining a time interval of T for each time segmenti(i is 1,2,3 … …,7), then T1The corresponding time period is 0 to t1，T2Corresponding to a time period of t1～t2，T3Corresponding to a time period of t2～t3，T4Corresponding to a time period of t3～t4,T5Corresponding to a time period of t4～t5,T6Corresponding to a time period of t5～t6,T7Corresponding to a time period of t6～t7The algorithm expression used in planning the acceleration and deceleration curve model is
Figure FDA0001575855900000011
Where j (t) is a function of jerk with respect to time t, jmaxIs the jerk maximum during operation,
Figure FDA0001575855900000012
2. the acceleration-deceleration control method in numerical control system trajectory planning as recited in claim 1, wherein T is1＝T3＝T5＝T7。
3. The acceleration and deceleration control method in the numerical control system trajectory planning as recited in claim 1, wherein the arithmetic expression of the acceleration in the acceleration and deceleration curve model is
Figure FDA0001575855900000013
Wherein a ismaxIs the maximum acceleration.
4. The acceleration-deceleration control method in numerical control system trajectory planning as recited in claim 3, wherein the arithmetic expression of the velocity in the acceleration-deceleration curve model is
Figure FDA0001575855900000021
Wherein VmaxMaximum speed, v, allowed for numerical control system machining1,v2,v5,v6When t is equal to t1,t2,t5,t6The instantaneous speed of the time.
5. The acceleration-deceleration control method in numerical control system trajectory planning of claim 4, characterized in that the arithmetic expression of the displacement in the acceleration-deceleration curve model is
Figure FDA0001575855900000022
Wherein s is1,s2,s3,s4,s5,s6When t is equal to t1,t2,t3,t4,t5,t6The displacement of time.
6. The method for controlling acceleration and deceleration in numerical control system trajectory planning as recited in claim 5, wherein a occurs when the numerical control system is processingmaxOr-amaxAnd defining the target displacement when the numerical control system is processed as L, when t is t7When the displacement is S7；S7Less than or equal to L.
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CN110134065B (en) * 2019-05-30 2020-08-18 西安交通大学 Machine tool machining track motion planning method based on sine square acceleration forward-looking
CN111158318B (en) * 2020-01-16 2022-10-18 江南大学 Flexible acceleration and deceleration planning method for asymmetric quartic curve
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