WO2012014071A1 - Model construction apparatus - Google Patents
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- WO2012014071A1 WO2012014071A1 PCT/IB2011/001992 IB2011001992W WO2012014071A1 WO 2012014071 A1 WO2012014071 A1 WO 2012014071A1 IB 2011001992 W IB2011001992 W IB 2011001992W WO 2012014071 A1 WO2012014071 A1 WO 2012014071A1
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B17/00—Systems involving the use of models or simulators of said systems
- G05B17/02—Systems involving the use of models or simulators of said systems electric
Definitions
- the invention relates to a model construction apparatus.
- JP-A-2006-118428 describes a control apparatus.
- This control apparatus controls a plurality of objects to be controlled (to be referred to hereafter as "control objects") in an internal combustion engine using a pre -constructed model relating to an internal combustion engine that includes the respective control objects.
- control objects characteristics of the respective control objects of the internal combustion engine may vary over time. If the respective control objects of the internal combustion engine are controlled using the aforementioned pre-constmcted model in this case, it may be impossible to control a control amount of each control object to a target control amount, and as a result, the internal combustion engine may not exhibit an expected performance.
- an actual control amount (to be referred to hereafter as an "actual control amount") of each control object obtained during an operation of the internal combustion engine is compared with a control amount (to be referred to hereafter as a “theoretical control amount") of each control object obtained from the pre-constructed model, and when a difference exists between the actual control amount and the theoretical control amount, parameters of the pre-constructed model are re-identified such that the difference reaches zero.
- the pre-constructed model is then updated by applying the re-identified parameters to the pre-constructed model.
- the parameters of the model are re-identified such that the difference between the actual control amount and the theoretical control amount reaches zero without taking into account physical laws pertaining to the internal combustion engine. Accordingly, the physical laws pertaining to the internal combustion engine are not reflected in the model to which the re-identified parameters are applied.
- a re-identified parameter may be a parameter that should be constrained in accordance with the physical laws pertaining to the internal combustion engine. As a result, the re-identified parameter may take an inappropriate value.
- An object of the invention is to identify parameters of a model of a control object accurately and with a small calculation load.
- a first aspect of the invention relates to a model construction apparatus that identifies a parameter of a model equation of a control object and constructs a model of the control object by applying, to the model equation, a parameter value determined during parameter identification to be an optimum parameter value.
- the model construction apparatus obtains a constraint condition equation describing a condition of a parameter of the model equation that does not breach a constraint applied by a physical law pertaining to the control object, and identifies the parameter of the model equation within a range where the obtained constraint condition equation is satisfied.
- the parameter of the model equation is identified within a range where the constraint applied by the physical law pertaining to the control object is not breached.
- a parameter value that breaches the constraint applied by the physical law pertaining to the control object is excluded.
- a corresponding reduction in a calculation load required to identify the parameter is obtained.
- parameter values that breach the constraint applied by the physical law pertaining to the control object are not employed as the parameter value of the model equation, and therefore an appropriate parameter value is ultimately employed.
- the constraint condition equation may be described using a parameter of a physical model that describes the physical law pertaining to the control object.
- the model construction apparatus may obtain an evaluation function for identifying the parameter of the model equation, determine whether or not the constraint condition equation is satisfied while identifying the parameter of the model equation by solving an optimization problem of the obtained evaluation function, and employ an optimum solution obtained by solving the optimization problem of the evaluation function within the range where the constraint condition equation is satisfied, as the parameter value of the model equation.
- the model construction apparatus may obtain an evaluation function for identifying the parameter of the model equation, add the constraint condition equation to the obtained evaluation function, identify the parameter of the model equation by solving an optimization problem of the evaluation function to which the constraint condition equation has been added, and employ an optimum solution obtained by solving the optimization problem of the evaluation function to which the constraint condition equation has been added, as the parameter value of the model equation.
- the model construction apparatus constructs a model of a plant (to be referred to hereafter as a "plant model") including a plurality of objects to be controlled (to be referred to hereafter as "control objects").
- the plant model is a model of the internal combustion engine and the control objects are a fuel injection valve for supplying fuel to a combustion chamber, a spark plug that ignites the fuel in the combustion chamber, a throttle valve disposed in an intake passage to control an amount of gas introduced into the combustion chamber, a supercharger that is capable of raising and lowering a pressure of the gas introduced into the combustion chamber and includes a vane for controlling the degree by which the pressure of the gas is raised or lowered, an exhaust gas recirculation apparatus that leads exhaust gas discharged into an exhaust passage from the combustion chamber to the intake passage and includes an exhaust gas recirculation control valve for controlling the amount of exhaust gas led to the intake passage, and so on, for example.
- the control objects are a fuel injection valve for supplying fuel to a combustion chamber, a spark plug that ignites the fuel in the combustion chamber, a throttle valve disposed in an intake passage to control an amount of gas introduced into the combustion chamber, a supercharger that is capable of raising and lowering a pressure of the gas introduced into the combustion chamber and
- the physical laws are the law of conservation of momentum, the law of energy conservation, the first law of thermodynamics, Boyle-Charles' law, and so on, for example.
- the plant model constructed by the model construction apparatus is used to calculate a control amount of each control object or a control amount of the plant when a certain operation amount (to be referred to hereafter as a "control object operation amount”) is input into each control object, and determine, on the basis of the calculated control amount, a control object operation amount with which the control amount of each control object or the control amount of the plant can be aligned with a target control amount.
- a control object operation amount a certain operation amount
- the control amount is an amount of fuel supplied to the combustion chamber from the fuel injection valve, an amount of gas introduced into the combustion chamber, which is controlled by the throttle valve, the pressure of the gas introduced into the combustion chamber, which is controlled by the supercharger, the amount of exhaust gas led to the intake passage, which is controlled by the exhaust gas recirculation apparatus, an amount of emissions in the exhaust gas discharged from the combustion chamber, a torque output from the internal combustion engine, and so on.
- an optimum opening time of the fuel injection valve, an optimum ignition timing of the spark plug, an optimum opening of the throttle valve, an optimum opening of the supercharger vane, and an optimum opening of the exhaust gas recirculation control valve are determined from the plant model in accordance with operating conditions of the internal combustion engine.
- a map or a table storing the determined valve opening time, ignition timing, throttle valve opening, vane opening, and exhaust gas recirculation control valve opening is then created.
- the model construction apparatus obtains an evaluation function for identifying parameters of a model equation of the plant described in a specific description format, and obtains a constraint condition equation describing conditions of parameters of the model equation that do not breach constraints applied by the physical laws pertaining to the control objects and the plant.
- the constraint condition equation is described using parameters of a physical model that describes the physical laws pertaining to the control objects and the plant.
- the model construction apparatus determines whether or not the constraint condition equation is satisfied while identifying the parameters of the model equation by solving an optimization problem of the evaluation function.
- the model construction apparatus then employs an optimum solution obtained by solving the optimization problem of the evaluation function within a range where the constraint condition equation is satisfied as a parameter of the model equation.
- the model construction apparatus then constructs a plant model by applying the parameter value serving as the employed optimum solution to the model equation.
- the "physical model” is a "model satisfying a conservation law” that uses a conservation amount pertaining to mass, energy, momentum, molecular weight, or the like, for example, as a subject.
- the parameters of the model equation are identified within a range where constraints applied by the physical laws pertaining to the control objects and the plant are not breached.
- the parameters of the model equation are excluded.
- a corresponding reduction in a calculation load required to identify the parameters is obtained.
- parameter values that breach the constraints applied by the physical laws pertaining to the control objects and the plant are not employed as the parameter values of the model equation, and therefore appropriate parameter values are ultimately employed.
- the parameters of the physical model pertaining to the control objects and the plant are taken into account, and therefore, when the parameters of the plant model are identified using data in two different data groups for a specific purpose, for example, a situation in which two parameter values identified as optimum parameter values take greatly different values does not arise.
- the model construction apparatus identifies the parameters of the plant model while limiting the number of parameters of the plant model and the range in which the parameters of the plant model can be obtained using the constraint condition equation. As a result, redundancy in the parameters of the plant model is suppressed.
- the model construction apparatus identifies the parameters of the plant model using the constraint condition equation, which is described using the parameters of the physical model describing the physical laws pertaining to the control objects and the plant.
- the parameters of the plant model are identified such that a distance (or a divergence) between an identified parameter and a parameter value estimated from the physical mode] describing the physical laws pertaining to the control objects and the plant is reduced.
- the model construction apparatus determines whether or not the constraint condition equation is satisfied while identifying the parameters of the model equation by solving the optimization problem of the evaluation function.
- the invention may also be applied to a model construction apparatus that determines whether or not the constraint condition equation is satisfied separately from the process for identifying the parameters of the model equation by solving the optimization problem of the evaluation function.
- the invention may be applied to any model construction apparatus that identifies the parameters of the model equation within a range where the constraint condition equation is satisfied.
- Equation 1 When an output of a control object (i.e. the control amount of the control object) is represented by "y”, an input into the control object (i.e. the operation amount applied to the control object) is represented by “u”, a residual error is represented by “e”, a number of time steps is represented by “k”, and the model equation of the plant is described using an ARX model, the model equation of the plant may be described as shown in a following Equation 1. Note that in Equation 1, “a” and “b” are identified parameters, while “n” and “m” are positive integers.
- y(k) a l y(k - ⁇ ) + : - + a professiony(k - n) + b l u(k - ⁇ ) + - - + b m u(k ⁇ m) + e(k) - - (1)
- Equation 4 is obtained.
- x T (k) [y(k -l) + ⁇ - + y(k - n) + u(k - Y) - - - +u(k -m) ⁇ •••(2)
- 0 k +- + a medicine+V- +6 l _ ]
- y(k) x r (k)0 + e(k) - - -(4)
- Equation 9 by transforming Equation 5 using a matrix "Y” defined by Equation 6, a matrix "X” defined by Equation 7, and a matrix “E” defined by Equation 8, Equation 9 is obtained.
- Equation 10 an average value J of the square of the residual error e is ex ressed by Equation 10.
- Equation 10 When Equation 10 is transformed using the matrix E defined by Equation 8, on the other hand, Equation 11 is obtained.
- the matrix E from Equation 9 is expressed by Equation 12, and therefore, when Equation 11 is transformed using Equation 12, Equation 13 is obtained.
- Equation 13 is the evaluation function used by the model construction apparatus according to the first embodiment.
- Equation 14 the physical model based on the physical laws pertaining to the control objects and the plant may be described as shown in Equation 14. Note that in Equation 14, "p" is a scalar model parameter.
- Equation 15 is obtained.
- Equation 16 is a constraint condition equation. It may also be said that this constraint condition equation expresses a function with respect to a parameter variation range. Hence, by identifying a parameter ⁇ that minimizes Equation 13 using Equation 16 as the constraint condition equation, or in other words by solving the optimization problem of Equation 13 using Equation 16 as the constraint condition equation, the optimum parameter ⁇ (in other words, the optimum solution) is determined as a parameter of the plant model.
- the model construction apparatus determines whether or not the constraint condition equation is satisfied while identifying the parameters of the model equation by solving the optimization problem of the evaluation function.
- the model construction apparatus may solve the optimization problem of the evaluation function and determine whether or not the constraint condition equation is satisfied in the following manner.
- a model construction apparatus obtains the evaluation function for identifying the parameters of the model equation of the plant described in a specific description format, and obtains a constraint condition equation describing conditions of parameters of the model equation that do not breach constraints applied by the physical laws pertaining to the control objects and the plant.
- the constraint condition equation is described using parameters of a physical model that describes the physical laws pertaining to the control objects and the plant.
- the model construction apparatus then adds the constraint condition equation to the evaluation function, identifies the parameters of the model equation by solving an optimization problem of the evaluation function to which the constraint condition equation has been added, and employs an optimum solution obtained by solving the optimization problem of the evaluation function to which the constraint condition equation has been added as a parameter value of the model equation.
- the model construction apparatus then constructs a plant model by applying the parameter value serving as the employed optimum solution to the model equation.
- the parameters of the model equation are identified within a range where constraints applied by the physical laws pertaining to the control objects and the plant are not breached.
- the parameters of the model equation are excluded.
- redundancy in the parameters of the plant model is suppressed correspondingly, and a corresponding reduction in the calculation load required to identify the parameters is obtained.
- parameter values that breach the constraints applied by the physical laws pertaining to the control objects and the plant are not employed as the parameter values of the model equation, and therefore appropriate parameter values are ultimately employed.
- the parameters of the physical model pertaining to the control objects and the plant are taken into account, and therefore, when the parameters of the plant model are identified using data in two different data groups for a specific purpose, for example, a situation in which two parameter values identified as optimum parameter values take greatly different values does not arise.
- the model construction apparatus identifies the parameters of the plant model while limiting the number of parameters of the plant model and the range in which the parameters of the plant model can be obtained using the constraint condition equation. As a result, redundancy in the parameters of the plant model is suppressed.
- the model construction apparatus identifies the parameters of the plant model using the constraint condition equation, which is described using the parameters of the physical model describing the physical laws pertaining to the control objects and the plant.
- the parameters of the plant model are identified such that the distance (or the divergence) between an identified parameter and a parameter value estimated from the physical model describing the physical laws pertaining to the control objects and the plant is reduced.
- Equation 18 an evaluation function incorporating the constraint condition equation of Equation 17 (in other words, an evaluation function to which the constraint condition equation of Equation 17 has been added) can be expressed by Equation 18.
- the optimum parameter ⁇ (in other words, the optimum solution) is determined as a parameter of the plant model.
- model construction apparatus constructs a model of a plant in which a plurality of physical laws are established.
- the invention may also be applied to a model construction apparatus for constructing a model of a plant in which only one physical law is established.
- model construction apparatus constructs a model of a plant that includes a plurality of control objects.
- the invention may also be applied to a model construction apparatus for constructing a model of a plant that includes only one control object (in other words, a model of a single control object).
- the model construction apparatus constructs a plant model using a constraint condition equation describing conditions of parameters of a model equation that do not breach constraints applied by the physical laws pertaining to the control objects and the plant.
- the invention may also be applied to a model construction apparatus for constructing a plant model using a constraint condition equation describing conditions of parameters of a model equation that do not breach constraints applied by the physical laws pertaining to at least one of the control objects and the plant.
- a parameter value that breaches the constraints applied by the physical laws pertaining to the control objects and the plant denotes a parameter value having a large divergence from a parameter value estimated after taking into account the physical laws pertaining to the control objects and the plant, regardless of whether or not the parameter value is capable of aligning a control amount output from the constructed plant model with an actually output actual control amount.
Abstract
The invention relates to a model construction apparatus that identifies a parameter of a model equation of a control object and constructs a model of the control object by applying, to the model equation, a parameter value determined during parameter identification to be an optimum parameter value. The model construction apparatus according to the invention obtains a constraint condition equation describing a condition of a parameter of the model equation that does not breach a constraint applied by a physical law pertaining to the control object, and identifies the parameter of the model equation within a range where the obtained constraint condition equation is satisfied.
Description
MODEL CONSTRUCTION APPARATUS
BACKGROUND OF THE INVENTION
1. Field of the Invention
[0001] The invention relates to a model construction apparatus.
2. Description of Related Art
[0002] Japanese Patent Application Publication No. 2006-118428 (JP-A-2006-118428) describes a control apparatus. This control apparatus controls a plurality of objects to be controlled (to be referred to hereafter as "control objects") in an internal combustion engine using a pre -constructed model relating to an internal combustion engine that includes the respective control objects. Here, characteristics of the respective control objects of the internal combustion engine may vary over time. If the respective control objects of the internal combustion engine are controlled using the aforementioned pre-constmcted model in this case, it may be impossible to control a control amount of each control object to a target control amount, and as a result, the internal combustion engine may not exhibit an expected performance. Therefore, in the control apparatus described in JP-A-2006-118428, an actual control amount (to be referred to hereafter as an "actual control amount") of each control object obtained during an operation of the internal combustion engine is compared with a control amount (to be referred to hereafter as a "theoretical control amount") of each control object obtained from the pre-constructed model, and when a difference exists between the actual control amount and the theoretical control amount, parameters of the pre-constructed model are re-identified such that the difference reaches zero. The pre-constructed model is then updated by applying the re-identified parameters to the pre-constructed model.
[0003] Incidentally, in the control apparatus described in JP-A-2006-118428, the parameters of the model are re-identified such that the difference between the actual control amount and the theoretical control amount reaches zero without taking into
account physical laws pertaining to the internal combustion engine. Accordingly, the physical laws pertaining to the internal combustion engine are not reflected in the model to which the re-identified parameters are applied.
[0004] When the physical laws pertaining to the internal combustion engine are not taken into account while re-identifying the parameters, a calculation load required to re-identify the parameters increases, and in certain cases, values of the re-identified parameters may not be appropriate. In other words, when the physical laws pertaining to the internal combustion engine are not taken into account while re-identifying the parameters, the parameters are re-identified including parameters that should be constrained in accordance with the physical laws pertaining to the internal combustion engine. In this case, the calculation load required to re-identify the parameters increases in comparison with a case where the parameters are re-identified excluding the parameters that should be constrained in accordance with the physical laws pertaining to the internal combustion engine. Furthermore, since the physical laws pertaining to the internal combustion engine are not taken into account when re-identifying the parameters, a re-identified parameter may be a parameter that should be constrained in accordance with the physical laws pertaining to the internal combustion engine. As a result, the re-identified parameter may take an inappropriate value.
[0005] This applies likewise to a case in which a model is constructed for a single control object by identifying parameters of the model. More specifically, when physical laws pertaining to the control object are not taken into account while identifying the parameters of the model of the control object, the calculation load required to identify the parameters increases, and in certain cases, values of the identified parameters may not be appropriate.
SUMMARY OF THE INVENTION
[0006] An object of the invention is to identify parameters of a model of a control object accurately and with a small calculation load.
[0007] A first aspect of the invention relates to a model construction apparatus
that identifies a parameter of a model equation of a control object and constructs a model of the control object by applying, to the model equation, a parameter value determined during parameter identification to be an optimum parameter value. The model construction apparatus according to this aspect obtains a constraint condition equation describing a condition of a parameter of the model equation that does not breach a constraint applied by a physical law pertaining to the control object, and identifies the parameter of the model equation within a range where the obtained constraint condition equation is satisfied.
[0008] In the aspect described above, the parameter of the model equation is identified within a range where the constraint applied by the physical law pertaining to the control object is not breached. In other words, when identifying the parameter of the model equation, a parameter value that breaches the constraint applied by the physical law pertaining to the control object is excluded. By excluding parameter values on the basis of the constraint applied by the physical law pertaining to the control object in this manner, a corresponding reduction in a calculation load required to identify the parameter is obtained. Moreover, parameter values that breach the constraint applied by the physical law pertaining to the control object are not employed as the parameter value of the model equation, and therefore an appropriate parameter value is ultimately employed.
[0009] In the model construction apparatus according to the aspect described above, the constraint condition equation may be described using a parameter of a physical model that describes the physical law pertaining to the control object.
[0010] Further, the model construction apparatus may obtain an evaluation function for identifying the parameter of the model equation, determine whether or not the constraint condition equation is satisfied while identifying the parameter of the model equation by solving an optimization problem of the obtained evaluation function, and employ an optimum solution obtained by solving the optimization problem of the evaluation function within the range where the constraint condition equation is satisfied, as the parameter value of the model equation.
[0011] Further, the model construction apparatus may obtain an evaluation
function for identifying the parameter of the model equation, add the constraint condition equation to the obtained evaluation function, identify the parameter of the model equation by solving an optimization problem of the evaluation function to which the constraint condition equation has been added, and employ an optimum solution obtained by solving the optimization problem of the evaluation function to which the constraint condition equation has been added, as the parameter value of the model equation.
DETAILED DESCRIPTION OF EMBODIMENTS
[0012] An embodiment of a model construction apparatus according to the invention will now be described. The model construction apparatus according to this embodiment constructs a model of a plant (to be referred to hereafter as a "plant model") including a plurality of objects to be controlled (to be referred to hereafter as "control objects").
[0013] When the plant is an internal combustion engine, for example, the plant model is a model of the internal combustion engine and the control objects are a fuel injection valve for supplying fuel to a combustion chamber, a spark plug that ignites the fuel in the combustion chamber, a throttle valve disposed in an intake passage to control an amount of gas introduced into the combustion chamber, a supercharger that is capable of raising and lowering a pressure of the gas introduced into the combustion chamber and includes a vane for controlling the degree by which the pressure of the gas is raised or lowered, an exhaust gas recirculation apparatus that leads exhaust gas discharged into an exhaust passage from the combustion chamber to the intake passage and includes an exhaust gas recirculation control valve for controlling the amount of exhaust gas led to the intake passage, and so on, for example.
[0014] Further, a plurality of physical laws are established in relation to the plant for which the plant model is constructed by the model construction apparatus according to this embodiment. Here, the physical laws are the law of conservation of momentum, the law of energy conservation, the first law of thermodynamics, Boyle-Charles' law, and so on, for example.
[0015] Furthermore, the plant model constructed by the model construction apparatus according to this embodiment is used to calculate a control amount of each control object or a control amount of the plant when a certain operation amount (to be referred to hereafter as a "control object operation amount") is input into each control object, and determine, on the basis of the calculated control amount, a control object operation amount with which the control amount of each control object or the control amount of the plant can be aligned with a target control amount.
[0016] When the plant is an internal combustion engine, for example, the control amount is an amount of fuel supplied to the combustion chamber from the fuel injection valve, an amount of gas introduced into the combustion chamber, which is controlled by the throttle valve, the pressure of the gas introduced into the combustion chamber, which is controlled by the supercharger, the amount of exhaust gas led to the intake passage, which is controlled by the exhaust gas recirculation apparatus, an amount of emissions in the exhaust gas discharged from the combustion chamber, a torque output from the internal combustion engine, and so on.
[0017] Further, when the plant model constructed by the model construction apparatus according to this embodiment is used to determine the control object operation amounts input into the respective control objects of the internal combustion engine, for example, an optimum opening time of the fuel injection valve, an optimum ignition timing of the spark plug, an optimum opening of the throttle valve, an optimum opening of the supercharger vane, and an optimum opening of the exhaust gas recirculation control valve are determined from the plant model in accordance with operating conditions of the internal combustion engine. A map or a table storing the determined valve opening time, ignition timing, throttle valve opening, vane opening, and exhaust gas recirculation control valve opening is then created.
[0018] Next, a method of constructing a plant model using the model construction apparatus according to this embodiment (to be referred to as a "first embodiment" hereafter) will be described.
[0019] As described above, a plurality of physical laws are established in
relation to the plant for which the model construction apparatus according to the first embodiment constructs the plant model.
[0020] The model construction apparatus according to the first embodiment obtains an evaluation function for identifying parameters of a model equation of the plant described in a specific description format, and obtains a constraint condition equation describing conditions of parameters of the model equation that do not breach constraints applied by the physical laws pertaining to the control objects and the plant. Here, the constraint condition equation is described using parameters of a physical model that describes the physical laws pertaining to the control objects and the plant. The model construction apparatus according to the first embodiment determines whether or not the constraint condition equation is satisfied while identifying the parameters of the model equation by solving an optimization problem of the evaluation function. The model construction apparatus according to the first embodiment then employs an optimum solution obtained by solving the optimization problem of the evaluation function within a range where the constraint condition equation is satisfied as a parameter of the model equation. The model construction apparatus according to the first embodiment then constructs a plant model by applying the parameter value serving as the employed optimum solution to the model equation. Note that in this specification, the "physical model" is a "model satisfying a conservation law" that uses a conservation amount pertaining to mass, energy, momentum, molecular weight, or the like, for example, as a subject.
[0021] With the model construction apparatus according to the first embodiment, the following effects are obtained. Specifically, with the model construction apparatus according to the first embodiment, the parameters of the model equation are identified within a range where constraints applied by the physical laws pertaining to the control objects and the plant are not breached. In other words, when identifying the parameters of the model equation, parameter values that breach the constraints applied by the physical laws pertaining to the control objects and the plant are excluded. By excluding parameter values on the basis of the constraints applied by the physical laws pertaining to
the control objects and the plant in this manner, a corresponding reduction in a calculation load required to identify the parameters is obtained. Moreover, parameter values that breach the constraints applied by the physical laws pertaining to the control objects and the plant are not employed as the parameter values of the model equation, and therefore appropriate parameter values are ultimately employed.
[0022] Further, in a case where data relating to actual control amounts output from the plant are divided into two data groups and the parameters of the plant model are identified on the basis of the data in each data group, for example, two parameter values identified as optimum parameter values may take greatly different values if the parameters of the physical model pertaining to the control objects and the plant are not taken into account. In this case, it is impossible to determine which of the parameter values is the true optimum parameter value. With the model construction apparatus according to the first embodiment, however, the parameters of the physical model pertaining to the control objects and the plant are taken into account, and therefore, when the parameters of the plant model are identified using data in two different data groups for a specific purpose, for example, a situation in which two parameter values identified as optimum parameter values take greatly different values does not arise.
[0023] Further, the model construction apparatus according to the first embodiment identifies the parameters of the plant model while limiting the number of parameters of the plant model and the range in which the parameters of the plant model can be obtained using the constraint condition equation. As a result, redundancy in the parameters of the plant model is suppressed.
[0024] Furthermore, as described above, the model construction apparatus according to the first embodiment identifies the parameters of the plant model using the constraint condition equation, which is described using the parameters of the physical model describing the physical laws pertaining to the control objects and the plant. To put it another way, the parameters of the plant model are identified such that a distance (or a divergence) between an identified parameter and a parameter value estimated from the physical mode] describing the physical laws pertaining to the control objects and the
plant is reduced.
[0025] Note that the model construction apparatus according to the first embodiment determines whether or not the constraint condition equation is satisfied while identifying the parameters of the model equation by solving the optimization problem of the evaluation function. However, the invention may also be applied to a model construction apparatus that determines whether or not the constraint condition equation is satisfied separately from the process for identifying the parameters of the model equation by solving the optimization problem of the evaluation function. In other words, the invention may be applied to any model construction apparatus that identifies the parameters of the model equation within a range where the constraint condition equation is satisfied.
[0026] Next, a specific example of parameter identification performed by the model construction apparatus according to the first embodiment will be described.
[0027] When an output of a control object (i.e. the control amount of the control object) is represented by "y", an input into the control object (i.e. the operation amount applied to the control object) is represented by "u", a residual error is represented by "e", a number of time steps is represented by "k", and the model equation of the plant is described using an ARX model, the model equation of the plant may be described as shown in a following Equation 1. Note that in Equation 1, "a" and "b" are identified parameters, while "n" and "m" are positive integers.
y(k) = aly(k -\) + : - + a„y(k - n) + blu(k -}) + - - + bmu(k ~ m) + e(k) - - (1)
[0028] Here, when Equation 1 is transformed using "xT (k)" defined by Equation 2 and "Θ" defined by Equation 3, Equation 4 is obtained. xT(k) = [y(k -l) + ~ - + y(k - n) + u(k - Y) - - - +u(k -m)} •••(2) 0 = k +- + a„+V- +6l_ ] -(3) y(k) = xr(k)0 + e(k) - - -(4)
[0029] Then, by expressing the output y, the input u, and the residual error e
from k=l to k=N as a determinant, Equation 5 is obtained.
••(5)
[0030] Then, by transforming Equation 5 using a matrix "Y" defined by Equation 6, a matrix "X" defined by Equation 7, and a matrix "E" defined by Equation 8, Equation 9 is obtained.
E = - .(8)
e{k) y = Jfi + £ -(9)
[0031] Meanwhile, an average value J of the square of the residual error e is ex ressed by Equation 10.
[0032] When Equation 10 is transformed using the matrix E defined by Equation 8, on the other hand, Equation 11 is obtained. Here, the matrix E from Equation 9 is expressed by Equation 12, and therefore, when Equation 11 is transformed using Equation 12, Equation 13 is obtained. Equation 13 is the evaluation function used by the model construction apparatus according to the first embodiment.
Ε = Ϋ-ΧΘ - (12)
J = (9TXTXe- 2YTX9 + YTY) •••(13)
[0033] Meanwhile, the physical model based on the physical laws pertaining to the control objects and the plant may be described as shown in Equation 14. Note that in Equation 14, "p" is a scalar model parameter.
F(y(k), y(k - l - -, u{k),u{k - l),- -, p) = 0 - - (14)
[0034] Then, by simplifying Equation 14 using a first order Taylor series, Equation 15 is obtained.
a0y(k) + cc,y(k - \) + - ~ + fifiu(k) + p]u(k - \) + - + Y = 0 -- -(l 5)
[0035] Here, coefficients "α", "β", and "γ" are unknown variables, and therefore Equation 16 is satisfied.
}ιι(α0,αι,α2, · ·βΰ, β1, β2, -/) = 2 = 1,2, (16)
[0036] Here, Equation 16 is a constraint condition equation. It may also be said that this constraint condition equation expresses a function with respect to a parameter variation range. Hence, by identifying a parameter Θ that minimizes Equation 13 using Equation 16 as the constraint condition equation, or in other words by solving the optimization problem of Equation 13 using Equation 16 as the constraint condition equation, the optimum parameter Θ (in other words, the optimum solution) is determined as a parameter of the plant model.
[0037] Note that in reality, noise and the residual error must be taken into account, and therefore, by transforming Equation 16 into Equation 17 and identifying the parameter Θ that minimizes Equation 13 using Equation 17 as the constraint condition equation, or in other words by solving the optimization problem of Equation 13 using Equation 17 as the constraint condition equation, the optimum parameter Θ (in other
words, the optimum solution) is determined as a parameter of the plant model.
= 1,2, (17)
[0038] Incidentally, the model construction apparatus according to the first embodiment determines whether or not the constraint condition equation is satisfied while identifying the parameters of the model equation by solving the optimization problem of the evaluation function. However, the model construction apparatus according to the first embodiment may solve the optimization problem of the evaluation function and determine whether or not the constraint condition equation is satisfied in the following manner.
[0039] A model construction apparatus according to this embodiment (to be referred to hereafter as a "second embodiment") obtains the evaluation function for identifying the parameters of the model equation of the plant described in a specific description format, and obtains a constraint condition equation describing conditions of parameters of the model equation that do not breach constraints applied by the physical laws pertaining to the control objects and the plant. Here, the constraint condition equation is described using parameters of a physical model that describes the physical laws pertaining to the control objects and the plant. The model construction apparatus according to the second embodiment then adds the constraint condition equation to the evaluation function, identifies the parameters of the model equation by solving an optimization problem of the evaluation function to which the constraint condition equation has been added, and employs an optimum solution obtained by solving the optimization problem of the evaluation function to which the constraint condition equation has been added as a parameter value of the model equation. The model construction apparatus according to the second embodiment then constructs a plant model by applying the parameter value serving as the employed optimum solution to the model equation.
[0040] With the model construction apparatus according to the second embodiment, the following effects are obtained. Specifically, with the model
construction apparatus according to the second embodiment, similarly to the model construction apparatus according to the first embodiment, the parameters of the model equation are identified within a range where constraints applied by the physical laws pertaining to the control objects and the plant are not breached. To put it another way, when identifying the parameters of the model equation, parameter values that breach the constraints applied by the physical laws pertaining to the control objects and the plant are excluded. By excluding parameter values on the basis of the constraints applied by the physical laws pertaining to the control objects and the plant in this manner, redundancy in the parameters of the plant model is suppressed correspondingly, and a corresponding reduction in the calculation load required to identify the parameters is obtained. Moreover, parameter values that breach the constraints applied by the physical laws pertaining to the control objects and the plant are not employed as the parameter values of the model equation, and therefore appropriate parameter values are ultimately employed.
[0041] As described above in relation to the first embodiment, in a case where the data relating to the actual control amounts output from the plant are divided into two data groups and the parameters of the plant model are identified on the basis of the data in each data group, for example, two parameter values identified as optimum parameter values may take greatly different values if the parameters of the physical model pertaining to the control objects and the plant are not taken into account. In this case, it is impossible to determine which of the parameter values is the true optimum parameter value. With the model construction apparatus according to the second embodiment, however, the parameters of the physical model pertaining to the control objects and the plant are taken into account, and therefore, when the parameters of the plant model are identified using data in two different data groups for a specific purpose, for example, a situation in which two parameter values identified as optimum parameter values take greatly different values does not arise.
[0042] Further, the model construction apparatus according to the second embodiment identifies the parameters of the plant model while limiting the number of parameters of the plant model and the range in which the parameters of the plant model
can be obtained using the constraint condition equation. As a result, redundancy in the parameters of the plant model is suppressed.
[0043] Furthermore, as described above, the model construction apparatus according to the second embodiment identifies the parameters of the plant model using the constraint condition equation, which is described using the parameters of the physical model describing the physical laws pertaining to the control objects and the plant. To put it another way, the parameters of the plant model are identified such that the distance (or the divergence) between an identified parameter and a parameter value estimated from the physical model describing the physical laws pertaining to the control objects and the plant is reduced.
[0044] Next, a specific example of parameter identification performed by the model construction apparatus according to the second embodiment will be described.
[0045] When "η" denotes a relative weighting parameter equal to or greater than zero, an evaluation function incorporating the constraint condition equation of Equation 17 (in other words, an evaluation function to which the constraint condition equation of Equation 17 has been added) can be expressed by Equation 18.
J = ~∑<k)2 + η∑!ιι(αΰ,αι,α2,· - -β0,βι,β2,- - - )2 -(18)
[0046] By identifying the parameter Θ that minimizes Equation 18, or in other words by solving the optimization problem of Equation 18, the optimum parameter Θ (in other words, the optimum solution) is determined as a parameter of the plant model.
[0047] The following effects are obtained from this specific example of parameter identification performed by the model construction apparatus according to the second embodiment. Specifically, by solving the optimization problem of Equation 18, a parameter that brings the residual error close to zero (in other words, brings the first item on the right side of Equation 18 close to zero) and at the same time brings the constraint condition close to zero (in other words, brings the second item on the right side of Equation 18 close to zero) can be identified.
[0048] Note that the model construction apparatus according to the
embodiments described above constructs a model of a plant in which a plurality of physical laws are established. However, the invention may also be applied to a model construction apparatus for constructing a model of a plant in which only one physical law is established.
[0049] Further, the model construction apparatus according to the embodiments described above constructs a model of a plant that includes a plurality of control objects. However, the invention may also be applied to a model construction apparatus for constructing a model of a plant that includes only one control object (in other words, a model of a single control object).
[0050] The model construction apparatus according to the embodiments described above constructs a plant model using a constraint condition equation describing conditions of parameters of a model equation that do not breach constraints applied by the physical laws pertaining to the control objects and the plant. However, the invention may also be applied to a model construction apparatus for constructing a plant model using a constraint condition equation describing conditions of parameters of a model equation that do not breach constraints applied by the physical laws pertaining to at least one of the control objects and the plant.
[0051] Note that in the above embodiments, "a parameter value that breaches the constraints applied by the physical laws pertaining to the control objects and the plant" denotes a parameter value having a large divergence from a parameter value estimated after taking into account the physical laws pertaining to the control objects and the plant, regardless of whether or not the parameter value is capable of aligning a control amount output from the constructed plant model with an actually output actual control amount.
Claims
1. A model construction apparatus that identifies a parameter of a model equation of a control object and constructs a model of the control object by applying, to the model equation, a parameter value determined during parameter identification to be an optimum parameter value,
wherein the model construction apparatus obtains a constraint condition equation describing a condition of a parameter of the model equation that does not breach a constraint applied by a physical law pertaining to the control object, and identifies the parameter of the model equation within a range where the obtained constraint condition equation is satisfied.
2. The model construction apparatus according to claim 1, wherein the constraint condition equation is described using a parameter of a physical model that describes the physical law pertaining to the control object.
3. The model construction apparatus according to claim 1 or 2, wherein the model construction apparatus obtains an evaluation function for identifying the parameter of the model equation, determines whether or not the constraint condition equation is satisfied while identifying the parameter of the model equation by solving an optimization problem of the obtained evaluation function, and employs an optimum solution obtained by solving the optimization problem of the evaluation function within the range where the constraint condition equation is satisfied, as the parameter value of the model equation.
4. The model construction apparatus according to claim 1 or 2, wherein the model construction apparatus obtains an evaluation function for identifying the parameter of the model equation, adds the constraint condition equation to the obtained evaluation function, identifies the parameter of the model equation by solving an optimization problem of the evaluation function to which the constraint condition equation has been added, and employs an optimum solution obtained by solving the optimization problem of the evaluation function to which the constraint condition equation has been added, as the parameter value of the model equation.
5. A model construction method for identifying a parameter of a model equation of a control object and constructing a model of the control object by applying, "to the model equation, a parameter value determined during parameter identification to be an optimum parameter value, comprising:
obtaining a constraint condition equation describing a condition of a parameter of the model equation that does not breach a constraint applied by a physical law pertaining to the control object; and
identifying the parameter of the model equation within a range where the obtained constraint condition equation is satisfied.
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| CN104007663A (en) * | 2014-05-13 | 2014-08-27 | 南京航空航天大学 | Self-adaptation fault-tolerant control method of quadrotor posture with parameter nondeterminacy |
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| US20070100475A1 (en) * | 2005-10-25 | 2007-05-03 | Korchinski William J | Method and apparatus for applying reduced nonlinear models to optimization of an operation |
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