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Method and apparatus for creating time-optimal commands for linear systems
| Details |
Inventors: Tuttle, Timothy D.; Seering, Warren P.;
Assignee: Massachusetts Institute of Technology (Cambridge, MA)
Primary Examiner: Grant; William
Assistant Examiner: Garland; Steven R.
Attorney, Agent or Firm: Choate, Hall & Stewart
The system described herein determines an input command profile for a dynamic system that can be modeled as a linear system, the input command profile for transitioning an output of the dynamic system from one point to another point. The system identifies characteristics of the dynamic system, and then selects a command profile which defines an input to the dynamic system based on the identified characteristics. The command profile comprises one or more pulses which rise and fall at switch times, and the command profile is useable with substantially any dynamic system that can be modeled as a linear system. The system then imposes a plurality of constraints on the dynamic system, at least one of the constraints being defined in terms of the switch times, and determines the switch times for the input to the dynamic system based on the command profile and the plurality of constraints. |
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DETAILED DESCRIPTION The present invention addresses the foregoing needs by providing a new and practical approach for deriving time-optimal and time-efficient command profiles for virtually all types of linear systems.
The invention is general enough to apply to a wide class of systems, yet simple enough to allow for quick and effective solutions.
The general solution framework can be summarized in the following three steps.
Step 1: Select a candidate command profile.
Time-optimal and time-efficient commands represent a special subclass of optimal command profiles designed to move systems rapidly from one point to another.
As a result, they all have similarities in structure that can be leveraged to better find a solution.
Specifically, as above, time-optimal and time-efficient commands are typically comprised of a staircase or pulse train with a finite number of discontinuities.
In some cases, namely for systems that have zeros, this pulse train or staircase can be followed by a tail made up of a sum of exponential terms.
Due to this unique construction, the profile of these commands can typically be described completely by a small number of parameters.
The solution space of these parameters, then, outlines the entire family of solutions for the optimal command profile.
As is illustrated below, navigating the solution space of possible command profiles using a small number of command parameters greatly reduces the computational complexity of this problem.
As a result, solutions for time-optimal and time-efficient commands are easy to identify and implement.
Step 2: Impose the problem constraints.
Given a parameterized analytic expression for a candidate command profile, the next step toward finding an optimal solution is imposing the problem constraints.
Typically, the problem statement, such as the time-optimal and time-efficient control problem statements outlined above, specifies the exact nature of the constraints required for a specific problem.
These constraints, however, are most commonly expressed as conditions on the system performance in response to an input command
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