Servo Command Interpolation with Fifth-Order Jerk Control
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Solution Overview
Problem
Existing interpolation techniques for command values in numerically controlled machine tools face challenges in minimizing follow-up delay and jerk when command values are sequentially input, as they often require a large number of command values for generating interpolation functions, leading to increased acceleration.
Innovation Solution
A command value interpolation apparatus that generates a fifth-order interpolation function based on four command values, ensuring continuity of first and second derivatives, thereby reducing jerk and follow-up delay by matching function values and derivatives across time intervals.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Stability of the object's composition
If a large number of command values are used for generating an interpolation function, then the continuity of derivatives is improved, but the follow-up delay with respect to command increases
Solution Approach 1:
The patent divides the interpolation function generation into segments based on the number of command values available. When four or more command values are available, a fifth-order interpolation function is generated for high continuity. When fewer than four command values are available, a third-order interpolation function is generated instead, allowing the system to adapt the interpolation order to the available data, thus reducing follow-up delay while maintaining derivative continuity as much as possible with the given constraints.
Solution Approach 2:
The patent dynamically adjusts the order of the interpolation function based on the number of command values received. The system transitions between third-order and fifth-order interpolation functions depending on data availability, making the interpolation process adaptive rather than fixed. This dynamic adjustment allows the system to optimize between derivative continuity and response speed in real-time.
2Object-generated harmful factors
If a fifth-order interpolation function is generated based on four command values, then the jerk is reduced, but the complexity of the interpolation function increases
Solution Approach 1:
The patent changes the parameter of interpolation function order from the conventional third-order to fifth-order when four or more command values are available. This parameter change enables the generation of smoother trajectories with reduced jerk by ensuring continuity of second derivatives. The increased mathematical complexity is justified by the significant improvement in motion smoothness and reduction of harmful mechanical shocks.
Solution Approach 2:
The patent uses a standardized fifth-order interpolation function template with predefined mathematical structure. Instead of creating complex custom interpolation algorithms, the system applies a consistent fifth-order polynomial form: x(t) = a0 + a1*t + a2*t^2 + a3*t^3 + a4*t^4 + a5*t^5, where coefficients are calculated based on boundary conditions. This standardized approach manages complexity while achieving the desired jerk reduction.
3Loss of time
If the number of command values for interpolation is reduced, then the follow-up delay is reduced, but the smoothness of control operation deteriorates
Solution Approach 1:
The patent performs preliminary checks on the number of available command values before selecting the interpolation function order. When four or more command values are available, the system prepares and generates a fifth-order interpolation function in advance, ensuring smooth control operation. This preliminary assessment allows the system to optimize the interpolation approach before actual interpolation begins, balancing follow-up delay and smoothness based on available data.
Solution Approach 2:
The patent uses lower-order (third-order) interpolation functions as a temporary solution when fewer than four command values are available. These simpler, computationally cheaper interpolation functions are used only when necessary (when data is limited), accepting reduced smoothness in exchange for faster response. Once sufficient command values are accumulated, the system transitions to the more sophisticated fifth-order function for improved smoothness.
Data Source
AI summary
Provided is an interpolation technique in which command values chronologically input can be interpolated without increasing a jerk and with less follow-up delay with respect to a command. A control unit (10) of a servo driver (20) has a function of sequentially generating, on the basis of four command values from x(k−2) to x(k+1), a kth interpolation function for calculating command values in a kth (≥3) time interval and a function of generating, as the kth interpolation function, a fifth-order equation with respect to time in which function values at a start time and an end time of the kth time interval match x(k) and x(k+1), respectively, and in which a second derivative value at a start time of the kth time interval matches a second derivative value at an end time of a (k−1)th time interval corresponding to a (k−1)th interpolation function.