JP4301049B2 - Optimization method, optimization device, and optimization program - Google Patents

Description

  The present invention relates to an optimization method, an optimization apparatus, and an optimization program, and is particularly suitable for application to an optimization method for adapting an objective function to a target.

In a mechanical system including a conventional electric motor, an identification device for identifying an approximate model of the mechanical system is used, for example, as disclosed in Patent Documents 1 and 2, in order to optimize the control gain of the servo system. There is a way.
FIG. 3 is a block diagram showing a configuration of a conventional mechanical system identification apparatus.
In FIG. 3, the mechanical system identification device includes a first preprocessor 19, a second preprocessor 20, an actual response storage device 21, a simulation circuit 22, an evaluation function device 23, and a total adjustment device 24. The approximate model of the mechanical system 15 controlled by the real observer 16, the command generator 17, and the real controller 18 is identified.

The mechanical system 15 includes a load machine 11, a transmission mechanism 12 that transmits power, an electric motor 13 that drives the load machine 11 via the transmission mechanism 12, and an electric motor 13 based on the actual torque signal τM (t). It is comprised from the power converter device 14 which provides an electrical signal.
The actual observer 16 observes at least a part of the state quantity of the mechanical system 15 and generates an actual response signal θM (t). The command generator 17 generates an actual command signal θref (t). The actual controller 18 converts the actual torque signal τM (t) to the power conversion device based on the actual command signal θref (t) from the command generator 17 and the actual response signal θM (t) from the actual observer 16. 14 to provide.

The first preprocessor 19 converts the actual torque signal τM (t), which is a continuous signal, into an actual torque signal Tm (k), which is a discrete signal, at a constant sampling interval T, and the actual torque signal Tm of this discrete signal. (K) is stored in the actual response storage unit 21 as a data matrix.
The second preprocessor 20 converts the actual response signal θM (t), which is a continuous signal, into an actual response signal θm (k), which is a discrete signal, at a constant sample interval T, and calculates ωm (k). Then, θm (k) and ωm (k) are stored in the actual response storage unit 21 as two data matrices.

The simulation circuit 22 reads the actual torque signal Tm (k) from the actual response storage device 21 and generates a simulated position response signal θm ^ (k) and a simulated speed response signal ωm ^ (k) based on the simulation parameter Pi. .
The evaluation function unit 23 reads θm ^ (k) and ωm ^ (k) from the simulation circuit 22, and also reads θm (k) and ωm (k) from the actual response storage unit 21, thereby obtaining the evaluation value Ji. Is calculated and provided to the total adjustment device 24.

  The total adjustment device 24 adjusts the simulation parameter Pi by an adjustment method using a genetic algorithm so that the evaluation value Ji is optimized. That is, in the adjustment method using the genetic algorithm, when the optimization determination condition is satisfied, the simulation parameter Pi output from the total adjustment device 24 is the optimum simulation parameter for identifying the approximate model of the mechanical system 15. It becomes.

FIG. 4 is a block diagram showing a configuration of the simulation circuit 22 of FIG.
In FIG. 4, the simulation circuit 22 includes coefficient units 22b, 22f, and 22g, integrators 22c, 22d, 22h, and 22i, comparators 22a and 22e, and a simulation observer 22j. Then, the simulation circuit 22 updates the coefficients Jmi, JLi, and Kci of the coefficient units 22b, 22f, and 22g by using the given simulation parameter Pi, and the τM (k) stored in the actual response storage unit 21 is updated. Θm ^ (k) and ωm ^ (k) are calculated for the data and provided to the evaluation function unit 23.

Then, the total adjustment device 24 optimizes the evaluation value Ji by an adjustment method using a genetic algorithm, and when the optimization determination condition is satisfied, the simulation parameters Pi (including Jmi, JLi, and Kci) are: The identified optimal simulation parameter matrix is obtained.
JP 2001-8476 A JP 2002-351503 A

However, the conventional machine system identification apparatus is required to have a known structure of a mathematical model of the machine system. For this reason, the conventional machine system identification apparatus has a problem that the structure of the objective function to be optimized is fixed, and a machine system whose mathematical model structure is unknown cannot be identified.
Accordingly, an object of the present invention is to provide an optimization method, an optimization device, and an optimization program that can be applied to identification of a control target even when the structure of a mathematical model of the control target is unknown. .

In order to solve the above-described problem, according to the optimization method of claim 1, a step of setting an objective function represented by a transfer function expressed by a fractional polynomial simulating a control target; a method of assessing for all combinations of variables, on the basis of the evaluation results, obtained by repeating the process of changing the search point with the best value of the best values and populations at a plurality of search points before Symbol objective function And a step of setting the best value of the obtained group as an optimization result of the objective function.
This makes it possible to construct a system model to be controlled so that the objective function represented by the transfer function is optimized, and performs optimal control even if the structure of the system model to be controlled is unknown. It becomes possible.
In addition, when calculating each search point close to the best evaluation search point in the step of calculating the search point in the next step, the objective function can be brought close to the best evaluation search point.

According to the optimization method of claim 2, the step of setting an objective function expressed by a transfer function expressed by a fractional polynomial that simulates a controlled object ;
By evaluating all combinations of variables of the transfer function as an agent of the particle swarm Optimization, characterized in that it comprises a step of optimizing the structure of the objective function.
As a result, by using an algorithm with a simple concept, the objective function is brought closer to the structure of the best evaluation when calculating each search point close to the search point of the best evaluation at the stage of calculating the search point in the next step. It becomes possible.
For this reason, it is possible to optimize the structure of the objective function while maintaining a continuous variable, while reducing wasteful search, and even when the objective function takes a variable and continuous space, control is possible. It becomes possible to control the target at high speed and stably.

According to the optimization method of the third aspect, the control object is an electric machine system.
Thereby, even if the structure of the mathematical model of the motor machine system is unknown, it is possible to perform optimal control of the motor machine system.

Further, according to the optimization apparatus of claim 4 wherein at least one observation to the state observer means the actual state quantity based on the command signal of the control object system, expressed as a fraction polynomial simulating the control object system set the desired function represented by a transfer function, and the system model that outputs simulated state quantity based on the command signal, on the basis of the actual state amount and the simulated state variable, the response of the system model with respect to the command signal Based on the evaluation means to be evaluated and the evaluation result by the evaluation means, the process of changing the search point using the best value at the plurality of search points of the objective function set in the system model and the best value of the group is repeated. And optimizing means for using the best value of the group obtained as an optimization result of the objective function.
This makes it possible to evaluate the objective function while changing the search point of the objective function represented by the transfer function. For this reason, it is possible to construct a system model of the controlled system so that the objective function is optimized, and it is possible to perform optimal control even if the structure of the controlled system model is unknown. .
In addition, in the calculation of the search point in the next step, the calculation of bringing each search point close to the best evaluation search point makes it possible to bring the objective function close to the best evaluation search point.

According to the optimization apparatus of the fifth aspect, the control object is an electric machine system.
As a result, even if the structure of the system model of the motor machine system is unknown, it is possible to perform optimal control of the motor machine system.

According to the optimization program of claim 6, the step of setting an objective function represented by a transfer function expressed by a fractional polynomial simulating a controlled object and all combinations of variables of the transfer function are evaluated. a step of, based on the evaluation result, the best value of the best values and population obtained by repeating the process of changing the search point with the best value of a population at a plurality of search points before Symbol objective function the And a step of causing the computer to execute an objective function optimization result.
This makes it possible to construct a system model to be controlled so that the objective function represented by the transfer function is optimized by causing the computer to perform processing, and the structure of the system model to be controlled is unknown. Even so, optimal control can be performed.
In addition, when calculating each search point close to the best evaluation search point in the step of calculating the search point in the next step, the objective function can be brought close to the best evaluation search point.

As described above, according to the present invention, while changing the search point of the objective function represented by a transfer function, it is possible to evaluate with the objective function, as objective function is optimized Therefore, it is possible to construct a numerical model of the control target, and it is possible to perform optimal control even if the structure of the mathematical model of the control target is unknown.

Hereinafter, a case where iterative optimization according to an embodiment of the present invention is applied to identification of a mechanical system will be described with reference to the drawings.
FIG. 1 is a block diagram showing a schematic configuration of a control system according to an embodiment of the present invention.
In FIG. 1, the control system includes a mechanical system 1, a state observation unit 2, and an optimization system 6, and the optimization system 6 includes a mechanical system model 3, an evaluation unit 4, and an optimization unit 5. Yes.
Here, a command signal instructing the mechanical system 1 to perform a predetermined operation is input to the mechanical system 1. When the mechanical system 1 is an electric motor mechanical system, for example, electric power is supplied to the electric motor and the electric motor torque. It can be comprised with the electric power converter which controls this, and the machine driven by an electric motor.

The state observation unit 2 estimates or observes at least one state quantity of the mechanical system 1. Examples of the state quantity of the mechanical system 1 include the speed or position of the mechanical system 1.
The mechanical system model 3 simulates the mechanical system 1 by modeling the characteristics of the mechanical system 1 and outputs a simulated state quantity to the evaluation unit 4 as a response to the command signal.
Here, when the characteristic of the mechanical system 1 is numerically modeled, it can be expressed by an objective function having a variable structure, and the objective function having a variable structure is a transfer function expressed by a fractional polynomial expressed by the following equation: Can be used.

The evaluation unit 4 evaluates the response of the mechanical system model 3 to the command signal based on the actual state quantity output from the mechanical system 1 and the simulated state quantity output from the mechanical system model 3.
The optimization unit 5 optimizes the structure of the objective function set in the mechanical system model 3 based on the evaluation result by the evaluation unit 4.
Here, the optimization system 6 evaluates the response of the mechanical system model 3 to the command signal with respect to all combinations of the variables of the transfer function of the expression (1), and the variable that becomes the optimum evaluation result from the evaluation results. Can be extracted. That is, (1) the K, L, by identifying a _n and b _n, it is possible to the structure of the objective function and variable. Then, the number of a _n and b _n to be optimized can be determined by L, it is possible to determine the order of the denominator and numerator of the equation (1).

  This makes it possible to evaluate the structure of the objective function while changing the structure of the objective function, and to evaluate all structures of the objective function even when the structure of the objective function is unknown within the set range. Take possible. Therefore, it is possible to construct the mechanical system model 3 so that the structure of the objective function is optimized, and it is possible to perform optimal control even if the structure of the mechanical system model 3 is unknown.

Here, the operation performed in the optimization system 6 can be executed using an iterative search algorithm having a search space with multiple variables. As the iterative search algorithm, for example, particle swarm optimization can be performed. Can be used.
Particle swarm optimization is a modern heuristic (MH) method developed through simulation of a simplified social model, and represents the movement of a flock of birds in a two-dimensional space of continuous variables. Developed through.

  For particle swarm optimization, see J.A. Kennedy and R.K. “Particle Swarm Optimization” by Eberhart (Proc. Of IEEE International Conference on Neural Networks, Vol. IV, pp. 1942–1948, Perth, Australia, et al. "Study of Voltage Reactive Power Control Method by Swarm Optimization" (The Institute of Electrical Engineers of Japan B, Vol.119, No.12, December 1999), Japanese Patent Application Laid-Open No. 2000-11603 “Voltage Reactive Power Control Method” It is described in the “state estimation method”.

FIG. 2 is a flowchart showing an optimization operation of the control system of FIG. 1 when the particle swarm optimization is applied.
In FIG. 2, the initial values of the state variable s _i and the velocity v _i of each agent (search point) i in the particle swarm optimization are set (step S1). Note that the initial values of the state variable s _i and the speed v _i of each agent i can be determined randomly within a set range. The state variable s _i of node i, when using a transfer function (1) as an objective function of the mechanical system model 3 can be set by the following equation (2).

Note that (1) the variable a _n and b _n of formula is required by the maximum value L _max of the search range L previously given.
Next, the value of the state variable s _i of the agent i is substituted into the expression (1), and the response of the mechanical system model 3 to the command signal is obtained for all combinations of the variables of the expression (1). Then, the evaluation unit 4 evaluates the mechanical system model 3 by comparing the simulated state quantity of the mechanical system model 3 with the actual state quantity of the mechanical system 1 (step S2).
Incidentally, the variable a _n and b _n of agent i, unless L is not the maximum value, considering molecules, the denominator may have _{(L max} · C L) ² or a combination. The evaluation formula for evaluating the mechanical system model 3 is the sum of squares of the differences between the actual state quantity of the mechanical system 1 and the simulated state quantity of the mechanical system model 3 as shown in the following expression (3). be able to.

However,
Xr (n): actual state quantity data Xe (n) of the mechanical system 1 observed by the state observing unit 2: simulated state quantity data W (n) of the mechanical system model 3: weighting function F for data points: evaluation result is there.
Next, among the evaluation results of the state variable s _i of the agent i for all combinations of variables, the combination with the best evaluation is set as the extraction matrix h _i (step S3).
For example, when L _max = 2, the combination of variables of agent i can be expressed by the following equation (4).

Here, when L = 1 and the combination of variables having the best evaluation is a ₁ and b ₂ , the extraction matrix h can be expressed by the following equation (5).

Next, in order to obtain the variable of each agent i in the next step, the speed v _i ^{k + 1} of each agent i is obtained by the following equation (6) (step S4).
v _i ^{m + 1} = w × v _i ^m + c ₁ × rand () × k _pi (pbest _i −s _i ^m )
+ C ₂ × rand () × _kg (gbest−s _i ^m ) (6)
However,
v _i ^m : velocity of agent i rand (): uniform random number s _i ^{m from} 0 to 1: position of search for agent i at the mth time (search point)
pbest _i : variable of the best evaluation of the objective function so far in search of agent i gbest: the best of the group among pbest _i w: weight function for agent speed c ₁ , c ₂ : weight coefficient for each term k _pi : extraction matrix h of pbest _i
k _g : gbest's extraction matrix h
It is.

Here, the value of the new agent i obtained in the next step is drawn to pbest _i and gbest, but by using the extraction matrix h in equation (6), only the variables that were valid in the evaluation of step S2 are obtained. It can be drawn.
When the velocity v _i ^{m + 1} of the agent i is obtained by the equation (6), the state variable s _i ^{m + 1} of the new agent i for the next step is obtained by the following equation (7) (step S5). .
s _i ^{m + 1} = s _i ^m + v _i ^{m + 1} (7)

Then, when the processes of steps S2 to S5 are performed for a predetermined number of repetitions (step S6), the value of gbest can be set as the optimization result of the objective function (step S7).
As a result, by using an algorithm with a simple concept, the objective function is brought closer to the structure of the best evaluation when calculating each search point close to the search point of the best evaluation at the stage of calculating the search point in the next step. It becomes possible.
For this reason, it becomes possible to optimize the structure of the objective function while maintaining the continuous variable while reducing the useless search, and the objective function of the mechanical system model 3 takes a variable and continuous space. Even in this case, the mechanical system 1 can be controlled at high speed and stably.

In addition, particle swarm optimization is a multipoint search having a plurality of search points as in the genetic algorithm, and each search point is probabilistic using the best value pbest of each search point and the best value gbest of the group By changing to, a global optimum solution (best solution) can be obtained.
In addition, in particle swarm optimization, a global search (first term on the right side of equation (2)) that tries to maintain the current speed and a local search that tries to approach these using the best values pbest and gbest. (The second and third terms on the right side of equation (2)) can be performed in a well-balanced manner.

Furthermore, in particle swarm optimization, it is necessary to evaluate the objective function at each step, but since the number of evaluations is only the number of agents regardless of the scale of the problem, it can be easily applied to large-scale problems. be able to.
In the above-described embodiment, the expression (3) for evaluating the agent can be freely set according to the purpose. For example, a deviation from an ideal response may be evaluated.

Further, since the mechanical system model 3, the evaluation unit 4 and the optimization unit 5 can all be processed in the computer, the mechanical system model 3 is stored by storing information such as the state observation unit 2 and command signals in the memory. The evaluation unit 4 and the optimization unit 5 may be separated in hardware.
In the above-described embodiment, the mechanical system model 3, the evaluation unit 4, and the optimization unit 5 may be realized by a plurality of computers and communication means. For example, data transmission / reception is performed between computers connected to a network. While performing, you may make it implement | achieve the operation | movement of the mechanical system model 3, the evaluation part 4, and the optimization part 5. FIG.

  In the above-described embodiment, the method of operating the mechanical system model 3, the evaluation unit 4, and the optimization unit 5 by using an optimization algorithm to which particle swarm optimization is applied has been described. An iterative search algorithm such as may be used. For example, in addition to particle swarm optimization, the structure of the objective function may be optimized by evaluating all combinations of variables of the objective function using an algorithm having a search space with multiple variables. .

It is a block diagram showing a schematic structure of a control system concerning one embodiment of the present invention. It is a flowchart which shows the optimization operation | movement of the control system of FIG. 1 at the time of applying particle | grain swarm optimization. It is a block diagram which shows the structure of the identification apparatus of the conventional mechanical system. FIG. 4 is a block diagram showing a configuration of a simulation circuit 22 in FIG. 3.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Mechanical system 2 State observation part 3 Mechanical system model 4 Evaluation part 5 Optimization part 6 Optimization system

Claims (6)

Setting an objective function represented by a transfer function expressed by a fractional polynomial that simulates a controlled object;
Evaluating all combinations of variables of the transfer function;
Based on the evaluation results, the optimum of the objective function the best value before Symbol the objective function optimum value and population obtained by repeating the process of changing the search point with the best value of a population at a plurality of search points An optimization method comprising: a step of generating a conversion result. Setting an objective function represented by a transfer function expressed by a fractional polynomial that simulates a controlled object ;
By evaluating all combinations of variables of the transfer function as an agent of the particle swarm Optimization, optimization how to characterized in that it comprises a step of optimizing the structure of the objective function. The optimization method according to claim 1, wherein the control object is an electric machine system . State observing means for observing at least one actual state quantity based on the command signal of the controlled system ;
A system model that sets an objective function represented by a transfer function expressed by a fractional polynomial that simulates the system to be controlled, and outputs simulated state quantities based on the command signal for all combinations of variables of the transfer function When,
On the basis of the actual state amount and the simulated state variable, and evaluating means for evaluating the response of the system model with respect to the command signal,
Based on the evaluation result by the evaluation means, the best of the group obtained by repeating the process of changing the search point using the best value of the plurality of search points of the objective function set in the system model and the best value of the group An optimization device comprising: optimization means for setting a value as an optimization result of the objective function. The optimization apparatus according to claim 4, wherein the controlled object is an electric machine system. Setting an objective function represented by a transfer function expressed by a fractional polynomial that simulates a controlled object;
Evaluating all combinations of variables of the transfer function;
Based on the evaluation results, the optimum of the objective function the best value before Symbol the objective function optimum value and population obtained by repeating the process of changing the search point with the best value of a population at a plurality of search points An optimization program characterized by causing a computer to execute a step as a result of optimization.

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