Calibrating method and system, recording medium for this method
AssigneeCommissariat A L'energie Atomique Et Aux Energies Alternatives
InventorSuzanne Lesecq
Life of this patent
Estimating the term…
Abstract
A method for calibrating coefficients of an observer of a variable state of a physical system from measurements of physical quantities of the system, at different instants includes measuring a variable of the physical system at several instants, the variable being a function of a system state variable, and determining a vector of coefficients that minimizes a sum of the number of measurements of a square of a norm of a vector that is the difference between the measured variable and a function of the system state variable and the vector of coefficients. The minimization is subject to a constraint that the trajectory of the measured variable be within a corridor of uncertainty on either side of a trajectory of its estimate, at least for the measurement instants.
Claims9
A method for calibrating coefficients of an observer of a variable state xk of a physical system from measurements yk of physical quantities of the system, wherein index k identifies an instant of measurement, the method comprising causing a sensor to measure a variable zk of the physical system at N different instants, the variable zk being a function of a state variable xk, and causing a computer to determine a vector p of coefficients that minimizes the following criterion in complying with a predetermined set Δ of one or more constraints:
- f
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- p
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- wherein {circumflex over (x)}kis an estimation of the variable xk built by the observer calibrated with the coefficients of the vector p at the instant k, φ is a known function that links the estimation {circumflex over (x)}k to an estimation {circumflex over (z)}k of the variable zk, ∥ . . . ∥2 is a norm of the difference between zk and φ({circumflex over (x)}k, p), and the one or more constraints of the predetermined set Δ dictate that a trajectory of the variable zk be included in a corridor of uncertainty situated on either side of a path of the estimation {circumflex over (z)}k at least for a majority of the instants k.
A manufacture comprising a non-transitory computer-readable medium having encoded thereon software for calibrating coefficients of an observer of a variable state xk of a physical system from measurements yk of physical quantities of the system, wherein index k identifies an instant of measurement, the software comprising instructions for causing a sensor to measure a variable zk of the physical system at N different instants, the variable zk being a function of a state variable xk, and causing a computer to determine a vector p of coefficients that minimizes the following criterion in complying with a predetermined set Δ of one or more constraints:
- _
-
- f
-
- (
- p
- )
- =
- ∑
- k
- =
- 1
- N
-
-
-
- z
- k
- -
- (
- x
- ^
- k
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- p
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- 2
- wherein {circumflex over (x)}k is an estimation of the variable xk built by the observer calibrated with the coefficients of the vector p at the instant k, 100 is a known function that links the estimation {circumflex over (x)}k to an estimation {circumflex over (z)}k of the variable zk, ∥ . . . ∥2 is a norm of the difference between zk and φ({circumflex over (x)}k, p), and the one or more constraints of the predetermined set Δ dictate that a trajectory of the variable zk be included in a corridor of uncertainty situated on either side of a path of the estimation {circumflex over (z)}k at least for a majority of the instants k.
An apparatus for calibrating coefficients of an observer of a state variable xk of a physical system from measurements yk of physical quantities of the system, wherein index k identifies an instant of measurement, the apparatus comprising:
- at least one sensor capable of measuring a variable zk of the physical system at N different instants, the variable zk being a function of a state variable xk, and a computer capable of determining a vector p of coefficients that minimizes the following criterion in complying with a predetermined set Δ of one or more constraints:
- f
-
- (
- p
- )
- =
- ∑
- k
- =
- 1
- N
-
-
-
- z
- k
- -
- (
- x
- ^
- k
- ,
- p
- )
-
- 2
- wherein {circumflex over (x)}kan estimation of the variable xk built by the observer calibrated with the coefficients of the vector p at the instant k, φ is a known function that links the estimation {circumflex over (x)}kto an estimation {circumflex over (z)}kof the variable zk, ∥ . . . ∥2 is a norm of the difference between zk and φ({circumflex over (x)}k, p), and the one or more constraints of the predetermined set Δ dictate that a trajectory of the variable zk be included in a corridor of uncertainty situated on either side of a path of the estimation {circumflex over (z)}kat least for a majority of the instants k.
Dependencies are inferred from the claim text.