Method and apparatus for minimizing unwanted dynamics in a physical system
AssigneeConvolve, Inc.
InventorsWilliam E. Singhose, Neil C. Singer, Stephen J. Derezinski, III, Bert W. Rappole, Jr., Kenneth Pasch
Life of this patent
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Abstract
Method and apparatus for minimizing unwanted dynamics in a physical system response. Constraints on the input and on the unwanted dynamics are established, and an impulse sequence which satisfies the constraints is determined. The impulse sequence is convolved with an arbitrary command input to produce a shaped input which is used to drive physical system, thereby minimizing unwanted dynamics. The constraints on the input and on the unwanted dynamics may be selected to achieve shaped inputs and residual unwanted dynamics of various characteristics.
Claims130
A method for controlling a physical system by generating an input to the system to minimize unwanted dynamics in the system response comprising;
- establishing expressions quantifying the unwanted dynamics;
- establishing first constraints bounding an available input to the dynamic system;
- establishing second constraints bounding the unwanted dynamics;
- finding a solution which allows maximum variations in physical system characteristics and is used to generate the input while still satisfying the first and second constraints;
- and
- controlling the physical system based on the input to the physical system whereby unwanted dynamics are minimized.
A method for controlling a physical system by generating an input to the system to minimize unwanted dynamics in the system response comprising;
- establishing expressions quantifying the unwanted dynamics;
- establishing first constraints bounding an available input to the dynamic system;
- establishing second constraints bounding the unwanted dynamics;
- finding a minimum length solution which is used to generate the input while satisfying the first and second constraints;
- and
- controlling the physical system based on the input to the physical system whereby unwanted dynamics are minimized.
A method for controlling a physical system by generating an input to the system to minimize unwanted dynamics in the system response comprising;
- establishing expressions quantifying the unwanted dynamics;
- establishing first constraints bounding an available input to the dynamic system;
- establishing second constraints on variation in system response with variations in the physical system characteristics;
- finding a minimum length solution which is used to generate the input while satisfying the first and second constraints;
- and
- controlling the physical system based on the input to the physical system whereby unwanted dynamics are minimized.
A method for controlling a physical system by generating an input to a dynamic system with p vibrational modes characterized by undamped natural frequencies .omega. and damping ratios .zeta..sub.i, i=1 . . . p, to minimize unwanted dynamics in the physical system response comprising:
- defining a sequence of n=2p+1 impulses by the equations ##EQU73## for each of the p vibrational modes, ##EQU74##
- t.sub.1 =0
- A.sub.i .gtoreq.0
- where A.sub.i are the amplitudes of the impulses and t.sub.i are the locations of the impulses;
- approximating the solution to the defining equations;
- and
- controlling the physical system based on the generated input to the physical system whereby unwanted dynamics are minimized.
A method for controlling a physical system by generating an input to the system to minimize unwanted dynamics in the system response comprising;
- establishing first constraints on a sequence of impulses which minimize the unwanted dynamics;
- determining a first sequence of impulses which satisfies the first constraints;
- determining a second sequence of impulses, which is discretized in locations and is used to generate the input, by determining the number of impulses and the locations of the impulses of the second sequence based on the first sequence;
- determining the amplitudes of the second sequence to satisfy second constraints based on the first constraints;
- and
- controlling the physical system based on the input to the physical system whereby unwanted dynamics are minimized.
A method for controlling a physical system by generating an input to a dynamic physical system to reduce the deviation between the shape of a trajectory traversed by a point in the physical system and a pre-selected shape comprising:
- establishing constraints on the available inputs to the dynamic system to define a group of possible inputs;
- determining an impulse sequence which eliminates unwanted dynamics in the physical system;
- convolving the impulse sequence with each input in the group of possible inputs to determine a group of shaped inputs;
- determining the shaped input which minimizes the deviation between the shape of the actual trajectory and the pre-selected shape;
- and
- controlling the physical system based on the shaped input which minimizes the deviation between the shape of the actual trajectory and the pre-selected shape, whereby the deviation is minimized.
A method for controlling a physical system by generating an input to a dynamic system to minimize unwanted dynamics in the physical system response comprising:
- establishing expressions quantifying the unwanted dynamics;
- establishing first constraints on the available inputs to the dynamic system to define a group of possible inputs;
- expressing each input in the group of possible inputs as a combination of one or more primitive input trains;
- determining the combination which minimizes the unwanted dynamics;
- controlling the physical system based on the input in the group of possible inputs which corresponds to the combination which minimizes the unwanted dynamics, whereby unwanted dynamics are minimized.
A method for shaping an arbitrary command input to a dynamic physical system to reduce unwanted dynamics in the physical system comprising:
- determining a first parameterization for the arbitrary command input;
- determining an impulse sequence which eliminates unwanted dynamics in the physical system;
- determining a second parameterization to express the convolution of the impulse sequence with the arbitrary command input;
- and
- controlling the input to the physical system based on the second parameterization, whereby unwanted dynamics in the physical system are minimized.
An apparatus for controlling a physical system by reducing the deviation between the shape of a trajectory traversed by a point in a dynamic physical system and a pre-selected shape comprising:
- computing apparatus for determining an impulse sequence which eliminates unwanted dynamics in the physical system;
- apparatus for selecting an input from a group of possible inputs which, when convolved with the impulse sequence, minimizes the deviation between the shape of the actual trajectory and the pre-selected shape;
- and
- apparatus for controlling the physical system based on the convolution of the impulse sequence with the selected input whereby the deviation between the shape of the actual trajectory and the pre-selected shape is minimized.
An apparatus for controlling a physical system by shaping an arbitrary command input to a physical system in order to minimize unwanted dynamics in a physical system response comprising:
- a sensor for measuring the unwanted dynamics;
- computing apparatus for determining natural frequencies of the unwanted dynamics based on the measurement of the unwanted dynamics;
- apparatus for determining a sequence of impulses, a sequence of pulses, or a trajectory which minimizes the unwanted dynamics at the natural frequencies;
- apparatus for convolving the sequence of impulses with the arbitrary command input to produce a shaped command input;
- and
- apparatus for controlling the physical system based on the shaped command input whereby the unwanted dynamics are minimized.
An apparatus for minimizing unwanted dynamics in a physical system response comprising:
- computing apparatus for expressing each input in a group of possible inputs as a combination of impulse sequences and a step function;
- apparatus for determining which of the combinations of impulse sequences minimizes the unwanted dynamics;
- apparatus for controlling the physical system based on the input which corresponds to the combination of impulse sequences which minimizes unwanted dynamics.
Apparatus for controlling a physical system by shaping an input to a dynamic physical system to reduce unwanted dynamics in the physical system comprising:
- apparatus for determining a command which eliminates unwanted dynamics in the physical system;
- computing apparatus for splitting the command into an impulse sequence and an input such that the command is obtained if the input and the impulse sequence are convolved together;
- apparatus for convolving the sequence of impulses with an arbitrary command input to produce a shaped output;
- and
- apparatus for controlling the physical system based on the shaped input whereby unwanted dynamics are minimized.
An apparatus for reducing unwanted dynamics in a physical system response of a closed loop dynamic system comprising:
- a first filter which is based on an impulse sequence which eliminates unwanted dynamics in the physical system response and which is located in a feed-forward branch of the closed loop system;
- and
- a second filter which is based on an inverse of the first filter and which is located in the feed-back branch of the closed loop system, whereby unwanted dynamics are minimized.
A method for reducing unwanted dynamics in a physical system response of a closed loop dynamic system comprising:
- determining an impulse sequence which eliminates unwanted dynamics in the physical system response;
- inserting a first filter based on the impulse sequence in a feed-forward branch of the closed loop system;
- and
- inserting a second filter based on an inverse of the first filter in the feed-back branch of the closed loop system whereby unwanted dynamics are minimized.
A method for controlling a physical system by generating an input to a dynamic system to minimize unwanted dynamics in a physical system response comprising:
- establishing expressions quantifying the unwanted dynamics;
- establishing first constraints bounding an available input to the dynamic system;
- establishing desired values for the unwanted dynamics at pre-selected values of a physical system characteristic;
- establishing an error measure based on the differences between the desired values for the unwanted dynamics and the expressions quantifying the unwanted dynamics when evaluated at the pre-selected values of the physical system characteristic;
- finding a solution which minimizes the error measure and is used to generate the input while still satisfying the first constraints;
- and
- controlling the physical system based on the input to the physical system whereby unwanted dynamics are minimized.
Dependencies are inferred from the claim text.