Command Generating Device for Vibration-Free Positioning
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Solution Overview
Problem
Existing command generating devices for machines with low rigidity face issues such as increased command outgoing time, excitation of higher mode vibrations, unpredictable command shapes, residual vibrations, and inability to arbitrarily determine acceleration and deceleration times, leading to positioning delays and inaccuracies.
Innovation Solution
A command generating device that calculates an nth derivative command shape signal to ensure zero convolution with the impulse response of the machine's transfer function, integrating it n times to determine a position command that reaches the target position without delay or vibration, using a convolution of the velocity command and impulse response over the positioning time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Object-affected harmful factors
If a filter (such as a notch filter) is inserted into the command delivery path to suppress vibrations, then vibration suppression is improved, but the command outgoing time increases causing delay in positioning operation
Solution Approach 1:
The invention changes the parameters of the command signal by calculating an nth derivative command shape signal and integrating it n times to generate a position command that inherently suppresses vibrations without requiring external filters. This mathematical transformation of the command signal parameters achieves vibration suppression while maintaining timely positioning operation.
Solution Approach 2:
The invention replaces the mechanical filter system (notch filter insertion) with a computational approach (calculating nth derivative command shape signal and integrating n times). This substitution eliminates the need for physical or signal-processing filters that cause time delays, achieving vibration suppression through mathematical transformation instead.
2Object-affected harmful factors
If a notch filter is used to shape the command signal, then resonance frequency vibrations are suppressed, but the command signal develops steep changes that excite higher mode vibrations
Solution Approach 1:
The invention transforms the command signal parameters by calculating the nth derivative command shape signal and integrating n times, which smoothly shapes the signal to suppress resonance frequency vibrations without creating the steep changes that would excite higher mode vibrations. This parameter transformation inherently controls the signal's frequency content.
Solution Approach 2:
The invention converts the potential harm of steep signal changes into benefit by using mathematical integration to smooth the command signal. The integration process transforms what would be sharp transitions into gradual changes, turning the mathematical operation that could potentially create high-frequency content into a smoothing mechanism that suppresses all harmful vibrations.
3Object-affected harmful factors
If the acceleration command shape changes stepwise to suppress vibrations, then vibration suppression is improved, but the command signal contains many high-frequency components that excite higher mode vibrations
Solution Approach 1:
The invention changes the command signal parameters by calculating the nth derivative command shape signal and integrating it n times, which produces a smooth acceleration profile that suppresses vibrations without introducing high-frequency components. This continuous mathematical transformation avoids the stepwise changes that generate harmful high-frequency content.
4Measurement precision
If the number of conditions for the coefficient matrix is increased to improve positioning accuracy, then positioning precision is improved, but residual vibrations occur because end conditions cannot be satisfied strictly
Solution Approach 1:
The invention changes the approach by using nth derivative command shape signal calculation and n-time integration, which inherently satisfies all boundary conditions (position, velocity, acceleration, etc. at start and end) without requiring large numbers of conditions. This mathematical approach naturally produces smooth transitions that eliminate residual vibrations while achieving high positioning accuracy.
Data Source
AI summary
A command generating device includes a command shape calculating unit for calculating an nth derivative command shape which is a fixed multiple of the nth derivative with respect to time of a position command for causing a machine to reach a target position at a positioning time so that a convolution of a velocity command which is the first derivative with respect to time of the position command and the impulse response of a transfer function determined from the frequency of a vibration which occurs in the machine becomes equal to zero, the convolution being calculated over the time period from the positioning time onward, and an associating processing unit for integrating the nth derivative command shape n times with respect to time, and for multiplying the integral result by a constant which associates the position command at the positioning time with the target position so as to determine the position command.