KR100841455B1 - Method for controlling irregular disburstment using real time stochastic controller and Recording medium thereof - Google Patents

Abstract

Disclosed are a method of controlling irregular disturbance using a real-time probability controller and a recording medium recording the same.

The present invention includes calculating a state equation in a time domain for a system to be controlled, and performing a probability analysis on the time equation in the time domain to convert information of irregular disturbances in the time domain into a constant of power spectral density. Transforming, obtaining an approximate solution of a probability density function for the system in which the probability analysis is performed, designing a probability controller using the approximation solution, and controlling the control gain of the probability controller in the time domain Converting to a signal and applying the control signal to a control signal for controlling the irregular disturbance in the system.

According to the present invention, it is possible to design a new type of controller that can achieve the optimal control effect while securing the robustness of the system against irregular disturbances, and adopts a method of solving the probability density function and a real-time application algorithm of the irregular signal generator. As a result, it is possible to provide a robust control method capable of overcoming a problem in real-time implementation that has emerged as a problem of the conventional hur-probability controller.

Description

Method for controlling irregular disburstment using real time stochastic controller and recording medium

1 is a conceptual diagram of a conventional probability control method.

2 is a conceptual diagram of a real-time probability control apparatus according to the present invention.

3 is a block diagram of a real-time probability control apparatus according to an embodiment of the present invention.

4 is a flowchart of a design method of a real-time probability controller according to another embodiment of the present invention.

5 is a detailed flowchart of the controller design process of FIG. 4.

6 is a graph showing the time response according to the design method of the real-time probability controller according to the present invention.

7 is a graph showing the time response of the mean of the square according to the design method of the real-time probability controller according to the present invention.

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a system that requires noise reduction due to exposure to irregular disturbances, and more particularly, to a design method of a real time probability controller, a recording medium thereof, and a real time probability control device.

The probability control method considers information on irregular disturbances inside and outside the system in the probability domain.

Many techniques have been proposed for the control of systems exposed to irregular disturbances. In addition, there are LQG, LQR, Kalman method, and hur-probability control method for probabilistic analysis. However, methods such as LQG, LQR, and Kalman do not systematically utilize irregular disturbance information.

On the other hand, the "Hur-Probability Control Method" invented in 2002 is a revolutionary method that utilizes the information systematically and collectively for the first time by converting information about irregular disturbance into a constant.

1 is a conceptual diagram of a conventional probability control method.

The conventional probability control method using the hur-probability controller is a method of designing a controller in a probability domain by converting irregular disturbance information such as noise or disturbance into a constant through probability analysis of a system exposed to irregular disturbance. to be.

In the probability control method of FIG. 1, the system equation in the time domain is performed through a Fokker-Planck-Kolmogorov (F-P-K) equation (hereinafter referred to as "colmogorov-poker-plank equation"). The probability system constructed as a result of the probability analysis performed in this way converts the information of irregular disturbance in the real physical time domain into a constant. The controller is designed by using the transformed constant, and the designed control gain value is a breakthrough probability control concept proven through simulation and experiments, such as using as a control signal in the time domain.

In the conventional "Hur-probability controller", the system is configured using the Colmogorov-poker-Plank equation, and a time delay occurs in the process of feedback and generation of control signals. However, there are some constraints such as the analytical solution of the probability density function that can be used.

The conventional "her-probability control method" converts a dynamic moment equation in the probability domain using the Colmogorov-Poker-Planck equation to interpret the system in the time domain in the probability domain. The controller is designed using the transformed dynamic moment equation and used as a probability control signal in the time domain.

However, since the exact solution of the Colmogorov-Poker-Planck equation cannot be found, we construct and use the dynamic moment equation. In addition, when the system is transformed into a dynamic moment equation in the time domain, the order of the system increases. For this reason, the conventional "her-probability control method" is difficult to apply in real time. That is, it is not easy to apply the probability controller in real time, such as the construction of the Colmogorov-poker-Planck equation, which is necessary, and requires a lot of manual effort and time in applying the same.

Therefore, the conventional probability control method has a problem that the order of the system is excessively increased and it is not easy to control in real time.

Therefore, the first technical problem to be achieved by the present invention is to secure a method for solving the probability density function by systematically and rationally utilizing all the information of irregular disturbances and to increase the order of the system in the "permissibility control method". It is to provide a design method of a real-time probability controller that can solve the problem.

A second technical object of the present invention is to provide a computer-readable recording medium having recorded thereon a program for executing the design method of the real-time probability controller on a computer.

The third technical problem to be achieved by the present invention is to provide a real-time probability control apparatus to which the design method of the real-time probability controller is applied.

In order to achieve the first technical problem, the present invention includes calculating a state equation in the time domain for a system to be controlled, and performing random analysis in the time domain on the state equation, thereby causing irregular disturbances in the time domain. Transforming the information into a constant of the power spectral density, obtaining an approximation solution of a probability density function for the system of the time domain where the probability analysis is performed, and designing a probability controller using the approximation solution, and And converting a control gain value into a control signal in the time domain and applying the control signal as a control signal for controlling the irregular disturbance in the system.

In order to achieve the second technical problem, the present invention provides a computer-readable recording medium having recorded thereon a program for executing the design method of the real-time probability controller on a computer.

In order to achieve the third technical problem, the present invention provides a state equation calculation unit for calculating a state equation in a time domain for a system to be controlled, and performing a probability analysis in the time domain on the state equation in a time domain. Probability analysis unit for converting the information of irregular disturbances into a constant of the power spectral density, a controller for calculating an approximation solution of the probability density function for the system of the time domain in which the probability analysis is performed, and designing a probability controller using the approximation solution Provides a real-time probability control device including a design unit and a real-time probability control unit for converting the control gain value of the probability controller to a control signal in the time domain and applying the control signal as a control signal for controlling the irregular disturbance in the system do.

The present invention provides a design method and an implementation method which makes practical use of the conventional "her-probability controller" without taking much of the effort and time described above by approximating a probability density function.

According to the present invention, in order to control a system subject to irregular disturbances of the "Hur-probability control method," a method for solving the probability density function as a method for real-time application while securing robustness and real-time "Hur- Design of the probability controller "is possible.

Hereinafter, with reference to the drawings will be described a preferred embodiment of the present invention. However, embodiments of the present invention illustrated below may be modified in many different forms, and the scope of the present invention is not limited to the embodiments described below.

2 is a conceptual diagram of a real-time probability control apparatus according to the present invention.

The algorithm of FIG. 2 is an algorithm that generates a probability control signal in the time domain using a solution of the Colmogorov-Poker-Planck equation after performing a probability analysis in the time domain, rather than applying a control method in the probability domain.

In FIG. 2, first, state equations in the time domain are constructed (210).

Next, the random disturbance information is converted into a constant through probability analysis using the Colmogorov-Poker-Planck equation (220).

When the information of the random disturbance is converted into a constant, an approximate solution of the probability density function of the Colmogorov-poker-Planck equation is obtained (230).

Next, a random system is constructed using a random variable obtained through an approximate solution and a controller is designed in a random domain (240).

The control gain value of the above-described probability system is converted into a control signal in the time domain and used (250).

According to this, it is possible not only to apply in real time, but also to solve the problem of the conventional "license-probability controller" such as an increase in system order.

3 is a block diagram of a real-time probability control apparatus according to an embodiment of the present invention.

The state equation calculating unit 310 calculates a state equation in the time domain for the system to be controlled.

The probability analysis unit 330 performs probability analysis in the time domain on the state equation to convert information of irregular disturbance in the time domain into a constant of the power spectral density. Preferably, the probability analysis unit 330 may perform a probability analysis by the Colmogorov-poker-Plank equation in the time domain with respect to the state equation.

The controller design unit 340 obtains an approximate solution of the probability density function for the system of the time domain in which the probability analysis is performed, and designs the probability controller using the approximated solution. Preferably, the controller design unit 340 can solve the Colmogorov-poker-Plank equation for the controller design.

The real-time probability controller 350 converts the control gain value of the probability controller into a control signal in the time domain and applies the control signal as a control signal for controlling irregular disturbance in the system.

For the design of a real-time high probability controller for a general system, the following example is given.

를 받을 때에 이를 제어하고자 한다.As in Equation 1, an external disturbance in the form of irregular random noise in which a second-order system has a constant power spectral density (PSD) in the form of white noise

You want to control this when you receive it.

와

은 시스템 변수이며,

는 불규칙 교란이고 평균이 0이며, 백색잡음이다.here,

Wow

Is a system variable,

Is an irregular disturbance with an average of 0 and white noise.

The controller design is carried out through the following process.

The F-P-K process is one of the methods for analyzing the behavior of the probability density function of a system that is exposed to internal, external and mutually influenced random disturbances. This solution of the Colmogorov-poker-Planck equation provides the stochastic behavior of the system's response. Two basic assumptions are needed to derive the Colmogorov-Poker-Planck equation.

First, the irregular input must always be small enough so that disturbed motion can be represented in the form of a continuous trajectory as a superposition of the first order small value of the irregular variation.

Second, the random process should be a Markov process that is not affected in the past. A general form of Colmogorov-Poker-Planck equation composed of a floating (first incremental moment) coefficient and a diffusion (second incremental moment) coefficient is given by Equation 2 below.

는 부유계수이고

는 확산계수이다. 즉,

이고,

이다.here,

Is the coefficient of suspension

Is the diffusion coefficient. In other words,

ego,

to be.

The Colmogorov-Poker-Planck equation can only be used for irregular disturbances in the form of white noise. The solution to the equation represents the stochastic behavior of the response. However, it is known in the art that in most cases it is almost impossible to derive the analytical solution of the Colmogorov-Poker-Plank equation for the target physical system in an analytical manner.

를 일반적인 좌표계

에 대한 응답이라고 하면 다음의 수학식 3과 같이 표현된다.Many studies have focused on the moment response instead of solving the stationary or non-stationary probability density function of the Colmogorov-Poker-Planck equation in the probability domain. Looking at the interpretation of the conventional Colmogorov-Poker-Planck equation

Common coordinate system

Speaking for the response to is expressed by the following equation (3).

차 모멘트는 다음의 수학식 4와 같이 표현된다.

The difference moment is expressed as in Equation 4 below.

이다. 동적모멘트 미분방정식은 콜모고로프-포커-플랑크 방정식의 양변에

를 곱하여

영역에 대해 적분을 하면 얻을 수 있다. here,

to be. The dynamic moment differential equation is applied to both sides of the Colmogorov-Poker-Planck equation.

Multiply by

Integrate over an area to get it.

In other words,

이다.

to be.

In addition, the general dynamic moment equation is shown in Equation 5 below.

The dynamic moment equation consists of mean (first moment) and autocorrelation coefficients, cross-correlation coefficients (secondary moment, cross-correlation), power spectral density (PSD) values, and system constants. In dynamic moment equations, fluctuations in system parameters caused by irregular disturbances are represented by constant or simple functional power spectral density (PSD) values, and system variables in the time domain are transformed into moments. These moment and power spectral density values are useful values for understanding the behavior of the system in the probability domain. Therefore, the dynamic moment equation describes the behavior of the system in the probability domain. In other words, the dynamic moment equation can grasp the stochastic dynamic characteristics of the system.

값을 대입해서 적분과정을 직접 손으로 풀어야 가능했고 계산과정 또한 복잡하다. 따라서 종래의 '허-확률 제어기"는 불규칙한 교란을 제어할 수 있는 획기적인 개념이기는 하지만 실시간 제어가 곤란하고 시스템 차수(system order) 또한 증가하는 문제가 있다.However, in the calculation process, as seen above, the conventional method

It was possible to solve the integration process by hand by assigning a value, and the calculation process is complicated. Therefore, although the conventional 'per-probability controller' is a breakthrough concept for controlling irregular disturbances, it is difficult to control in real time and also increases the system order.

The present invention provides a method for approximating the Colmogorov-Poker-Planck equation instead of using the complex response moment as before. In addition, the present invention deals with the difficult part to calculate using numerical analysis.

The solution of the Colmogorov-Poker-Planck equation shows the behavior of the system probability density function. Hereinafter, a method for obtaining an approximate solution of the Colmogorov-poker-Plank equation will be described. If Equation 2 is rearranged from the probability differential equation of Ito using a diffusion coefficient and a floating coefficient, it is expressed as Equation 6 below.

을 취해주면 다음의 수학식 7과 같다.On both sides

If you take the following equation (7).

The approximate solution of the probability density function PDF is assumed to be typical, as shown in Equation 8 below.

시스템 파라미터이다. Here, in a system that receives white noise

System parameter.

는 다음의 수학식 9를 만족한다.Probability Density Function of Stationary Response of Random System (PDF)

Satisfies Equation 9 below.

에 정확하게 만족하지 않는다. 그 이유는

는 단지 근사해이기 때문이다. 위의 과정을 통하여 다음의 수학식 10을 구한다.In general, the Colmogorov-Poker-Planck equation is

Not exactly satisfied with The reason is that

Is just an approximation. Through the above process, the following Equation 10 is obtained.

,

이다.here

,

to be.

Therefore, the final solution of the probability density function that went through the above process is taken as Equation 11 below.

는 상수 값,

는 대상계의 시스템 파라미터(Parameter)이다. 위에서 구한 확률밀도 함수의 해를 이용하여 확률해석을 수행하며 이를 시스템의 상태변수와 결합하여 제어기를 설계한다.here

Is a constant value,

Is a system parameter of the target system. Probability analysis is performed using the solution of the probability density function obtained above, and the controller is designed by combining it with the state variables of the system.

4 is a flowchart of a design method of a real-time probability controller according to another embodiment of the present invention.

First, a state equation in the time domain for a system to be controlled is calculated (step 410). This process (step 410) is a process of obtaining a governing equation in the time domain, and is a process of obtaining a governing equation in the time domain for a system to be controlled. The governing equations of the obtained system can be expressed in the form of state equations.

Next, a probability analysis is performed in the time domain on the state equation to convert information of irregular disturbance in the time domain into a constant of the power spectral density (step 420). That is, the probability analysis of the governing equations in the time domain is performed. In the time domain governing equations, external, internal, or interactive disturbances applied to the system appear in the form of indeterministic time series with various noise forms in the real physical system. It can also be excited. The irregular disturbance information in the time domain is converted into a constant of the power spectral density (PSD) through probability analysis.

When the information of the random disturbance is converted into a constant of the power spectral density, an approximation solution of the probability density function is obtained for the system of the time domain where the probability analysis is performed, and a probability controller is designed using the approximation solution (step 430). In this step (430), the probability controller can be designed using the solution of the probability density function for the time domain system in which the probability analysis is performed using the Colmogorov-poker-Plank equation. When the solution of the probability density function is used, the order of the system does not increase, and it is converted into a system that can be applied in real time.

This transformed system can be used in conventional time-domain control methods (Purge, Linear-Quadratic-Gaussian, LQG), Linear-Quadratic-Regulator (LQR), Reinforcement Learning, or Artificial Intelligence in the non-probability domain. Etc.) has an advantage that can be easily linked to configure the algorithm.

In addition, through the probability analysis, the information on the irregular disturbance becomes a constant so that the controller can be easily configured.

Finally, the control gain value of the probability controller is converted into a control signal in the time domain and the control signal is applied as a control signal for controlling irregular disturbances in the system (step 440). In this process (440), the obtained power spectral density (PSD) value of the control input may be used as a control signal.

The control input value obtained through the probability analysis is applied as the power spectral density (PSD) value and used as the control signal to control the irregular disturbance applied to the system.

Preferably, in order to use as a control signal it is possible to generate a control signal in the time domain by applying the Monte-Carlo method. The irregular signal generator can also minimize the time delay problem practically according to the algorithm for real time application.

FIG. 5 is a detailed flowchart of the controller design process 430 of FIG. 4.

First, an approximate solution of the probability density function is calculated (step 531). In this case, the approximate solution may be in the form of Equation 11.

Next, a probability state variable is constructed using the approximated solution of the calculated probability density function (step 532).

Finally, a probability controller is designed using the probability state variable (step 533).

The real-time hur-probability control method according to the present invention confirmed the possibility through numerical simulation (Simulation). In addition, through a physical experiment, when the real-time probability control method according to the present invention is implemented in a system that receives irregular disturbances, it can be seen that control is possible in real time.

을 도시한 그래프이다. 도 7은 본 발명에 따른 실시간 확률 제어기의 설계 방법에 따른 제곱평균의 시간응답

을 도시한 그래프이다.6 is a time response according to a design method of a real-time probability controller according to the present invention.

Is a graph. 7 is a time response of a root mean square according to a design method of a real-time probability controller according to the present invention.

Is a graph.

As shown in FIG. 6 and FIG. 7, the case where the dotted line is displayed, that is, when the real-time probability control according to the present invention is not applied (Uncontrolled Respose) has a large response variation with time, while applying the real-time probability control according to the present invention. In other words, when the solid line is displayed, it can be seen that the response deviation with time is small.

The real-time probability controller according to the present invention is designed through the above steps. In addition, we design the controller by introducing the most suitable optimal control method according to the situation for the system obtained through probability analysis. This results in a new type of controller design that ensures the optimal control effect while securing the robustness of the system against irregular disturbances. In addition, the present invention provides a robust control method capable of overcoming the problem of real-time implementation, which has emerged as a problem of the conventional hur-probability controller, by adopting a method for solving a probability density function and a real-time application algorithm of an irregular signal generator. can do.

Preferably, a program for executing the design method of the real-time probability controller of the present invention on a computer may be recorded and provided on a computer-readable recording medium.

The invention can be implemented via software. When implemented in software, the constituent means of the present invention are code segments that perform the necessary work. The program or code segments may be stored on a processor readable medium or transmitted by a computer data signal coupled with a carrier on a transmission medium or network.

The computer-readable recording medium includes all kinds of recording devices in which data is stored which can be read by a computer system. Examples of computer-readable recording devices include ROM, RAM, CD-ROM, DVD ± ROM, DVD-RAM, magnetic tape, floppy disks, hard disks, optical data storage devices, and the like. The computer readable recording medium can also be distributed over network coupled computer devices so that the computer readable code is stored and executed in a distributed fashion.

Although the present invention has been described with reference to one embodiment shown in the drawings, this is merely exemplary, and it will be understood by those skilled in the art that various modifications and variations can be made therefrom. However, such modifications should be considered to be within the technical protection scope of the present invention. Therefore, the true technical protection scope of the present invention will be defined by the technical spirit of the appended claims.

As described above, according to the present invention, it is possible to design a new type of controller that can achieve the optimal control effect while securing the robustness of the system against irregular disturbances, and to solve the probability density function and the method of the irregular signal generator. By adopting a real-time application algorithm, there is an effect that can provide a robust control method that can overcome the problems of the real-time implementation that emerged as a problem of the conventional hur-probability controller.

Claims (11)

In the random disturbance control method using a real-time probability controller, Calculating a state equation in a time domain for a system to be controlled, and performing probability analysis on the state equation to convert information of irregular disturbances in the time domain into a constant of power spectral density; Obtaining an approximation solution of a probability density function for the system of the time domain in which the probability analysis is performed, and calculating a control gain value in a probability controller using the approximation solution; And Converting the control gain value into a control signal in the time domain and controlling the irregular disturbance according to the control signal, Approximate solutions of the probability density functions are system parameters of a secondary system to which irregular disturbance of white noise is applied.

ego,

Is a constant,

Irregular disturbance control method using a real-time probability controller, characterized in that expressed in the form of. The method of claim 1, Converting the power spectral density into a constant And performing a probabilistic analysis of the state equation by the Colmogorov-poker-Plank equation in the time domain. The method of claim 1, Computing the control gain value of the probability controller A method of controlling irregular disturbances using a real-time probability controller, comprising: solving a Colmogorov-poker-Planck equation. The method of claim 1, Computing the control gain value of the probability controller Constructing a probability state variable using an approximation solution of the probability density function; And And designing a probabilistic controller using the probabilistic state variable. The method of claim 1, Computing the control gain value of the probability controller Configuring the system in conjunction with any one of fuzzy, linear-quadratic-gaussian (LQG), linear-quadratic-regulator (LQR), reinforcement learning, or artificial intelligence. An irregular disturbance control method using a real-time probability controller. delete delete A non-transitory computer-readable recording medium having recorded thereon a program for executing the method of claim 1. delete delete delete

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