Method and system for vibration avoidance for automated machinery
First Claim
1. A method of producing a space-time contour to be followed by at least one actuator forcing at least one machine element, based upon a series of concatenated polynomial segments that are functions of time where their dependent variable is a time-derivative of at least the first order of a physical variable to be controlled, each polynomial segment comprising a duration and at least one coefficient;
- the method comprising;
a) optimizing the durations and coefficients of the series of concatenated polynomial segments, such that the following constraints are met;
i) energy that would be introduced into at least one machine element by an actuator following a space-time contour created by time-integrating the series of concatenated polynomial segments, is suppressed for at least one frequency, andii) a space-time contour created by time-integrating the series of concatenated polynomial segments, is constrained within at least one limitation of the physical variable; and
b) time-integrating, at least once, the series of concatenated polynomial segments to form a space-time contour in the physical variable to be controlled;
c) commanding an actuator to follow the space-time contour.
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Abstract
A method for vibration avoidance in automated machinery produces actuator space-time contours that meet design objectives of the machinery while suppressing energy content at frequencies in the space-time contour, by concatenating multiple space-time contour segments together in such a way as to be mostly free of energy at the frequencies of interest while meeting other specified design goals. The segments used to construct these frequency-optimized-contours are a series of concatenated polynomial segments, the independent variable t being time. These segments can define the variable to be controlled (e.g. speed or distance) versus time, or define one of the controlled variable'"'"'s time-derivatives (e.g., the slope of the speed vs. time, etc.). When these frequency-optimized-contours are fed as a command to a machine controller through an actuator or actuators, the energy at the frequencies of interest is low enough to avoid deleterious vibration from occurring while still meeting the machine performance objectives.
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Citations
22 Claims
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1. A method of producing a space-time contour to be followed by at least one actuator forcing at least one machine element, based upon a series of concatenated polynomial segments that are functions of time where their dependent variable is a time-derivative of at least the first order of a physical variable to be controlled, each polynomial segment comprising a duration and at least one coefficient;
- the method comprising;
a) optimizing the durations and coefficients of the series of concatenated polynomial segments, such that the following constraints are met; i) energy that would be introduced into at least one machine element by an actuator following a space-time contour created by time-integrating the series of concatenated polynomial segments, is suppressed for at least one frequency, and ii) a space-time contour created by time-integrating the series of concatenated polynomial segments, is constrained within at least one limitation of the physical variable; and b) time-integrating, at least once, the series of concatenated polynomial segments to form a space-time contour in the physical variable to be controlled; c) commanding an actuator to follow the space-time contour. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11)
- the method comprising;
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12. A method of producing a space-time contour to be followed by at least one actuator forcing at least one machine element, based upon a series of concatenated polynomial segments that are functions of time, in which a dependent variable of each segment is a physical variable to be controlled, and each polynomial segment comprises a duration and a coefficient, forming a space-time contour in the physical variable, the method comprising:
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a) optimizing the durations and coefficients of the series of concatenated polynomial segments such that the following constraints are met; i) the energy that would be introduced into at least one machine element by an actuator following the space-time contour is suppressed for at least one frequency, and ii) the space-time contour is constrained within at least one limitation of the physical variable; and c) commanding an actuator to follow the space-time contour. - View Dependent Claims (13, 14, 15, 16, 17, 18, 19, 20, 21, 22)
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Specification