EP0433375B1
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Shaping command input to minimize unwanted dynamics
Assignee: Massachusetts Institute of Technology
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Filing: 1989-09-11
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Granted: 1996-10-23
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Expires: 2009-09-11
Abstract
Abstract A sequence of impulses is determined which eliminates unwanted dynamics of a dynamic system. This impulse sequence is convolved with an arbitrary command input to drive the dynamic system to an output with a minimum of unwanted dynamics. The input sequence is time optimal in that it constitutes the shortest possible command input that results in no unwanted dynamics of the system subject to robustness and implementation constraints. The preshaping technique is robust under system parameter uncertainty and may be applied to both open and closed loop systems.
Inventors
- 👤 Neil C. Singer
- 👤 Warren P. Seering
- 👤 Kenneth A. Pasch
Bibliographic Details
Application Number
—
Jurisdiction
EP
Data Source
google_patents
Last Synchronized
2026-10-30 14:54
CPC Classifications
G; G06; G06F; G06F17/00; G05; G05B; G05B19/00; G05B19/02; G05B19/18; G05B19/19; B; B25; B25J; B25J9/00; B25J9/16; B25J9/1628; B25J9/1635; G05B2219/00; G05B2219/30; G05B2219/41; G05B2219/41217; G05B2219/45; G05B2219/45083
Claims Analysis
Total Claims: 17
Claim 1
Independent Claim
74 words
Method for shaping an arbitrary command input to a dynamic physical system to reduce unwanted dynamics in the physical system comprising: determining an impulse or finite duration pulse sequence of greater than two impulses or finite duration pulses which eliminates unwanted dynamics of the physical system; convolving the sequence with the arbitrary command input to shape the input; and controlling the physical system based on the shape command input to the physical dynamic system.
Claim 2
Dependent Claim
72 words
The method of Claim 1 wherein the step of determining the impulse or finite duration pulse sequence comprises; establishing expressions quantifying the unwanted dynamics of the physical system; establishing first constraints bounding the available input to the physical system; establishing second constraints on variation in system response with variations in the physical system characteristics; and finding a solution which minimizes the value of the expressions while satisfying the first and second constraints.
Claim 3
Dependent Claim
20 words
The method of Claim 2 wherein the solution is a sequence of impulses or pulses that begin at specified intervals.
Claim 4
Dependent Claim
24 words
The method of Claim 2 wherein the solution is a sequence of impulses or pulses which are fixed in amplitude but variable in duration.
Claim 5
Dependent Claim
22 words
The method of Claim 2 wherein the solution is a sequence of pulses which are variable in amplitude but fixed in duration.
Claim 6
Dependent Claim
17 words
The method of Claim 1 wherein the impulse sequence is selected to improve robustness to system variability.
Claim 7
Dependent Claim
83 words
The method of claim 1 or claim 2 wherein the dynamic system has a single vibrational mode characterized by an undamped natural frequency ω 1 and a damping ratio ζ 1 and impulse sequences determined as the solution to the equations where B j = A j ω 1 √ 1-ζ 1 2 e -ζ 1 ω 1 t end -t j φ j = ω 1 √(1-ζ 1 2 )t j and A j is the amplitude of the jth impulse.
Claim 8
Dependent Claim
9 words
The method of claim 7 where N=3 and M=1
Claim 9
Dependent Claim
9 words
The method of Claim 7 where N=4 and M=2.
Claim 10
Dependent Claim
13 words
The method of Claim 7 where M is any integer value and N=M+2.
Claim 11
Dependent Claim
40 words
A method according to Claim 1, wherein the dynamic system has multiple vibrational modes, the method reducing end point vibration; and the impulse sequences which eliminate vibration of the dynamic system at the natural frequencies of its modes are determined.
Claim 12
Dependent Claim
53 words
A method according to Claim 1, wherein the dynamic system has p vibrational modes characterised by undamped natural frequencies ω i and damping ratios ζ i , i-1....p, the method reducing endpoint vibration; and p impulse sequences which eliminate vibration of the dynamic system at the natural frequencies of its modes are determined.
Claim 13
Dependent Claim
57 words
The method of Claim 2 wherein the dynamic system has p vibrational modes characterised by undamped natural frequencies ω 1 and damping ratios ζ i , i=1....p, establishing p sets of constraint equations, with the equations representing the first and second series of constraints and solving the p constraint equations simultaneously to yield a new input sequence.
Claim 14
Independent Claim
20 words
The method of any one of Claims 1 to 13 wherein impulses or pulses are allowed to assume negative values.
Claim 15
Dependent Claim
71 words
Apparatus for shaping an arbitrary command input to a dynamic physical system to reduce endpoint vibration comprising: computing apparatus for determining an impulse sequence of more than two impulses which eliminates vibration of the dynamic physical system at its natural frequencies; and apparatus for convolving the impulse sequence with the arbitrary command input; and apparatus for controlling the physical system based on the shaped command input to the dynamic physical system.
Claim 16
Dependent Claim
57 words
A method according to Claim 2 wherein the system has time varying characteristics; second constraints or variation in system response with variations in the system time varying characteristics are established; and a solution is found which minimizes the value of the expressions while satisfying the first and second constraints, whereby the solution tracks the time varying system.
Claim 17
Dependent Claim
21 words
A method according to Claim 1 further comprising the step of applying the shaped command input to the varying dynamic system.
References Cited (Backward Citations)
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