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Numerical control system velocity planning method based on fractional calculus

A technology of fractional calculus and speed planning, which is applied in general control systems, control/regulation systems, digital control, etc., can solve problems such as sudden acceleration changes, complex programming, and severe vibration of machine tools, and achieve smooth results

Inactive Publication Date: 2015-09-30
HARBIN INST OF TECH
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

[0003] The purpose of the present invention is to solve the existing speed planning method that causes severe vibration of the machine tool, huge amount of calculation, complex programming, abrupt acceleration, and rigid impact, and proposes a numerical control system speed planning based on fractional calculus method

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  • Numerical control system velocity planning method based on fractional calculus
  • Numerical control system velocity planning method based on fractional calculus
  • Numerical control system velocity planning method based on fractional calculus

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specific Embodiment approach 1

[0024] Specific implementation mode one: a kind of speed planning method of numerical control system based on fractional calculus in this implementation mode is specifically prepared according to the following steps:

[0025] A numerical control system speed planning method based on fractional calculus uses the memory characteristics of fractional calculus to perform a fractional order integration on the predefined nominal acceleration to obtain a smooth acceleration and deceleration speed planning curve

[0026] Step 1, according to the controlled object motion time t, utilize the continuous function y=f(t) to derive the fractional derivative:

[0027] D t α c f ( t ) = lim h → 0 1 h α ...

specific Embodiment approach 2

[0040] Specific embodiment two: the difference between this embodiment and specific embodiment one is: in step one, according to the controlled object motion time t, utilize continuous function y=f (t), deduce the concrete process of fractional order derivative as:

[0041] (1) For the continuous function y=f(t), according to the classic derivation formula, the first-order derivation formula of the function y=f(t) is:

[0042] f ′ ( t ) = d f d t = lim h → 0 f ( t ) - f ( t - h ) ...

specific Embodiment approach 3

[0055] Specific embodiment three: the difference between this embodiment and specific embodiment one or two is: in step three, let α<0, the mathematical expression of the nominal acceleration defined in step two is:

[0056] a ( t ) = a 1 0 ≤ t t 1 a 2 t 1 ≤ t t 2 ...

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Abstract

The invention relates to numerical control system velocity planning methods, in particular to a numerical control system velocity planning method based on fractional calculus, and aims to solve problems that existing velocity planning methods cause violent vibration of a machine tool, are large in calculated amount and complex in programming, have sudden acceleration change and produce rigid impact. The method comprises steps as follows: 1, a continuous function y=f(t) is used for deducing a fractional derivative; 2, nominal acceleration corresponding to t1, t2 and t3 are solved to be a1, a2 and a3 respectively; 3, a required acceleration section velocity planning curve is acquired; 4, the total displacement increment is calculated; 5, the displacement is solved to be D(m) according to a formula (3); 6, a controlled object begins to decelerate from the ith step of a deceleration point until the velocity is 0 when not reaching the maximum velocity Vmax; 7, the controlled object begins to decelerate from the jth step of the deceleration point until the velocity is 0; 8, the controlled object decelerates to the velocity 0 according to an S-like curve and the like. The method is applied to the field of numerical control system velocity planning.

Description

technical field [0001] The invention relates to a numerical control system speed planning method, in particular to a numerical control system speed planning method based on fractional calculus. Background technique [0002] Speed ​​planning is the core technology of CNC system. Commonly used speed planning methods include trapezoidal speed planning method, S-curve speed planning method, exponential speed planning method, etc. Although the trapezoidal speed planning method has a small amount of calculation and simple programming, there is a phenomenon of sudden acceleration and deceleration during the acceleration and deceleration phase, resulting in severe vibration of the machine tool, which is not suitable for high-speed and high-precision machining. The commonly used S-curve speed planning method controls the sudden change of acceleration by limiting the jerk. However, the traditional S-curve speed planning method uses polynomial representation to divide the entire speed...

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Application Information

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IPC IPC(8): G05B19/416
CPCG05B19/416G05B2219/43065
Inventor 孙光辉刘小磊胡延旭周承邦郑辉吴庭丞杨玉梁许林杨
Owner HARBIN INST OF TECH
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