KR20200080997A - Controller comprising an auxiliary state variable calculation unit and a control method thereof - Google Patents

Abstract

Provided are a controller capable of more stably controlling a servo control system having disturbance and control input restrictions and a control method thereof. The controller is a controller which controls a control target through a control input limiting unit. The controller comprises: an auxiliary state variable calculation unit calculating a difference between a control input provided to the control input limiting unit from the controller and an output of the control input limiting unit and updating an auxiliary state variable based on the difference; a switching function calculation unit calculating an output of a switching function based on the auxiliary state variable; a disturbance compensation unit calculating an estimated disturbance value based on the output of the switching function; and a control input calculation unit calculating the control input based on the switching function output and the disturbance estimated value.

Description

A controller comprising an auxiliary state variable calculation unit and a control method thereof

The present invention relates to a controller including an auxiliary state variable calculating unit and a control method thereof, and more particularly, to a controller and a control method thereof that can more stably control a control system having disturbances and control input limitations.

[Explanation on national support R&D]

This study was conducted by the support of the World Class 300 (WC300) project of the Small and Medium Venture Business Department (development of a robot motion control solution for flexible response to smart machines/collaborative robots, task number: S2563339).

The servo motor control system is a feedback control system that generates a control current input using the input command and the encoder feedback output of the plant, and allows the encoder feedback value to follow the desired input command. The most widely used feedback control method is a proportional-integral-derivative control method, which is called PID control. The PID control method is a linear control method, easy to implement, and the parameter tuning method is intuitive. However, it is vulnerable to nonlinearity or disturbance of the model, and it is difficult to respond to load fluctuations during operation. For this reason, the PID control method has a disadvantage in that it has to go through a tuning process for each situation separately. Various auto-tuning methods have been proposed to overcome this disadvantage, but in general, such auto-tuning methods have a limitation in that the expected performance is lower than the manual tuning method.

On the other hand, the variable structure control method, which is a type of nonlinear control, is a robust control method having the advantage of ensuring the performance and stability of the system even within a certain range of disturbance sizes. The variable structure control method has significantly better tracking performance than the PID control method. In particular, when the variable structure control method and the disturbance compensation method are applied together, stability of the system against disturbance is secured more greatly, and chattering, a disadvantage of the variable structure control method The problem can be reduced.

However, a typical servo control system is limited in generating control inputs, that is, the size of control inputs. Due to the limitation of the control input, performance of the system may be significantly deteriorated, and a problem that stability is not guaranteed occurs. Particularly, in a control system using a variable structure control method, performance due to control input limitation is deteriorated and stability is not guaranteed.

Y. Eun, et al., “Discrete-time Variable Structure Controller with a Decoupled Disturbance Compensator and Its Application to a CNC Servomechanism,” IEEE Trans. on Control Systems Technology, vol. 7, no. 4, pp. 414-423, 1999.

The present invention has been devised to solve the above-mentioned problems, and provides a controller and a control method thereof that can solve problems in which performance degradation and stability are not guaranteed due to disturbance and control input limitation in a control system using a variable structure control method. do.

A controller according to an embodiment of the present invention is a controller that controls a control target through a control input limiting unit, calculates a difference between a control input provided from the controller to the control input limiting unit and an output of the control input limiting unit, and the difference An auxiliary state variable calculator that updates the auxiliary state variable based on the; A switching function calculator for calculating a switching function output based on the auxiliary state variable; A disturbance compensation unit to calculate a disturbance estimate based on the switching function output; And a control input calculating unit calculating a control input based on the switching function output and the disturbance estimation value.

A control method of a controller according to another embodiment of the present invention is a control method of a controller that controls a control target through a control input limiting unit, and a difference between a control input provided from the controller to the control input limiting unit and an output of the control input limiting unit Calculating; Updating an auxiliary state variable based on the difference between the control input and the output of the control input limiter; Calculating a switching function output based on the auxiliary state variable, and calculating a disturbance estimate based on the switching function output; And calculating a control input based on the switching function output and the disturbance estimate.

A computer program according to another embodiment of the present invention is stored in a medium to execute a control method of the controller in combination with hardware.

The controller according to an embodiment of the present invention and a control method thereof prevent the degradation of control performance by preventing the disturbance compensation value and the switching function output from being winded up even in a situation where disturbance exists and input control commands are limited. And stability can be secured.

In addition, while maintaining the robustness and excellent following performance structure, which are the advantages of the variable structure control method and the disturbance compensation unit, it can be equipped from the control input limit to the toughness.

1 is a block diagram of a control system including a controller according to an embodiment of the present invention.
2 is a block diagram of a controller according to an embodiment of the present invention.
3 is a graph showing an exemplary reference.
4 is a graph showing the results of inputting the reference of FIGS. 3A and 3B to a controller having a conventional control input limit and disturbance compensation.
5 is a graph showing the results of inputting the reference of FIGS. 3A and 3B to the controller according to an embodiment of the present invention.
6 is a flowchart of a control method of a controller according to another embodiment of the present invention.

For a detailed description of the present invention, which will be described later, reference is made to the accompanying drawings that illustrate, by way of example, specific embodiments in which the present invention may be practiced. These examples are described in detail enough to enable those skilled in the art to practice the present invention. The terminology used in the present specification is a general terminology that is currently widely used while considering functions, but this may be changed according to intentions or customs of technicians in the field or the appearance of new technologies. In addition, in certain cases, some terms are arbitrarily determined by the applicant, and in this case, their meanings will be described in the description of the corresponding specification. Therefore, the terms used in the present specification should be interpreted based on the actual meaning of the term and not the contents of the simple term, but the contents throughout the present specification.

1 is a block diagram of a control system including a controller according to an embodiment of the present invention. Referring to FIG. 1, the control system 10 includes a controller 110, a load unit 120, and a control input limiting unit 130.

)를 발생한다. 제어기(110)에서 발생한 제어 입력(

)는 부하부(120)에 전달된다. 부하부(120)는 전류 제어기(121), 제어 대상(122) 및 인코더(123)를 포함한다. 먼저, 제어기(110)로부터 전류 제어기(121)로 제어 입력(

)이 전달되면, 전류 제어기(121)는 제어 입력(

)에 상응하는 구동 전류를 제어 대상(122, 또는 부하)에 제공한다. 그리고, 인코더(123)는 예를 들어, 구동된 제어 대상(122)의 상태를 측정하여 피드백 정보(

)를 제어기(110)에 피드백으로서 제공한다. 제어기(110)는 이후의 서보 모터 제어시 수신된 피드백(

)을 참조한다. 여기서, 피드백 정보는 각변위를 기초로 생성될 수 있으나, 이에 한정되는 것은 아니며 제어 대상의 각변위(angular position) 및/또는 각속도(angular velocity)를 기초로 생성된 정보일 수도 있다. 전류 제어기(121), 모터(122) 및 인코더(123)의 구체적인 구성 및 동작 방법은 당해 기술 분야에 널리 알려져 있으므로, 여기서는 그에 대한 설명은 생략한다.The controller 110 is a control input for the control object 122 included in the load unit 120 (

). Control input generated from the controller 110 (

) Is transmitted to the load unit 120. The load unit 120 includes a current controller 121, a control target 122 and an encoder 123. First, the control input from the controller 110 to the current controller 121 (

) Is transmitted, the current controller 121 is a control input (

) Is provided to the control object 122 (or load) corresponding to the driving current. Then, the encoder 123 measures, for example, the state of the driven control object 122 to provide feedback information (

) To the controller 110 as feedback. The controller 110 receives feedback received during subsequent servo motor control (

). Here, the feedback information may be generated based on the angular displacement, but is not limited thereto, and may also be information generated based on an angular position and/or an angular velocity of a control target. Since the specific configuration and operation method of the current controller 121, the motor 122, and the encoder 123 are well known in the art, a description thereof will be omitted here.

)은 제어 입력 제한부(130)를 경유하여 부하부(120)에 제공된다. 제어 입력 제한부(130)는 부하부(120)에 인가되는 전류의 최대 크기를 제한하기 위한 모듈이다. 즉, 본 발명의 일 실시예에 따른 제어 시스템(10)은 제어 대상(122)에 입력되는 순간 전류의 크기가 허용 전류 이상으로 증가하지 못하도록 하는 제어 입력 제한부(130)를 포함한다.Control input generated from the controller 110 (

) Is provided to the load unit 120 via the control input limiting unit 130. The control input limiting unit 130 is a module for limiting the maximum amount of current applied to the load unit 120. That is, the control system 10 according to an embodiment of the present invention includes a control input limiting unit 130 that prevents the magnitude of the instantaneous current input to the control target 122 from increasing beyond the allowable current.

)(또는, 그것이 지시하는 전류의 크기)이 허용 전류를 초과하더라도, 제어 입력 제한부(130)는 허용 전류를 상한으로 하는 제한된 크기의 전류만이 제어 대상(122)에 전달되도록 전류 제어기(121)를 제어한다. 즉, 제어 입력 제한부(130)에 의해 제어 입력보다 작은 크기의 감축된 전류 명령(이하, 제한 전류)이 전류 제어기(121)로 전달된다. 따라서, 예측되는 모터의 출력과 실제로 발생된 모터의 출력 간에는 큰 차이가 발생하게 된다. 이 차이는 제어기(110)의 제어 값에 누적(또는, 적산(積算))되어, 제어시 큰 오버슈트(overshoot)를 야기하고 전체적인 반응 시간을 지연시킬 수 있다. 또한, 외란이 존재하고 입력 제어 명령이 제한되는 상황에서 외란 보상값과 절환 함수 출력은 특정 값으로 수렴하지 않고 발산할 수 있다. Control input provided from the controller 110 (

) (Or, the magnitude of the current indicated by it) exceeds the allowable current, the control input limiting unit 130 is the current controller 121 so that only the current of the limited size that limits the allowable current to the control target 122 ) Control. That is, the reduced current command (hereinafter, the limited current) having a size smaller than the control input is transmitted to the current controller 121 by the control input limiting unit 130. Therefore, a large difference occurs between the predicted motor output and the actually generated motor output. This difference is accumulated (or accumulated) in the control value of the controller 110, which may cause a large overshoot during control and delay the overall reaction time. In addition, the disturbance compensation value and the switching function output may diverge without converging to a specific value in the situation where the disturbance exists and the input control command is limited.

In order to perform system control in view of the above-described problems, the controller 110 of the present invention may additionally receive the output of the control input limiting unit 130, and the auxiliary state variable calculating unit 114 may be provided.

The auxiliary state variable calculating unit 114 calculates a difference between the control input and the output of the control input limiting unit 130, and receives the difference to update the auxiliary state variable. The controller 110 may generate a control input based on the auxiliary state variable provided by the auxiliary state variable calculator 114. Hereinafter, features of the auxiliary state variable calculating unit 114 together with the detailed configuration of the controller 110 will be described in more detail.

2 is a block diagram of a controller according to an embodiment of the present invention. Referring to FIG. 2, the controller 110 includes a switching function calculation unit 111, a control input calculation unit 112, a disturbance compensation unit 113, and an auxiliary state variable calculation unit 114.

The controller 110 according to the embodiments and each device or unit constituting the same may have aspects that are entirely hardware or partially hardware and partially software. For example, each component of the controller 110 of the present invention refers to a combination of hardware and software driven by the hardware. The hardware may be a data processing device including a central processing unit (CPU) or other processor. Also, software driven by hardware may refer to a running process, an object, an executable, a thread of execution, a program, or the like. For example, the switching function calculator 111 may refer to a combination of hardware and software for the same. In addition, each part constituting the controller 110 in the present specification is not intended to refer to separate components that are physically separated. That is, in FIG. 2, each part of the controller 110 is illustrated as a separate block that is separated from each other, but this is functionally divided by the operation executed by the controller 110. Depending on the embodiment, some or all of the above-described parts may be integrated in the same one device, or one or more parts may be implemented as separate devices physically separated from other parts. For example, each part may be components communicatively connected to each other under a distributed computing environment.

)를 추종하도록 제어 입력을 생성할 수 있다. 제어기(110)는 가변 구조 제어 방법 중 하나인 이산 시간 슬라이딩 모드(Discrete-time sliding mode control, DSMC) 제어 방법을 적용할 수 있다. 구체적으로, 본 발명의 일 실시예에 따른 제어 시스템(10)은 하기 수학식 1로 표현되는 이산 시간 상태 공간 방정식으로 정의된다.In the system environment of the discrete time state spatial equation according to Equation 1 below, the controller 110 receives the reference (

) To create a control input. The controller 110 may apply a discrete-time sliding mode control (DSMC) control method, which is one of the variable structure control methods. Specifically, the control system 10 according to an embodiment of the present invention is defined as a discrete time state space equation represented by the following equation (1).

[Equation 1]

는 상태 변수로 부하부(120)에서 제공되는 피드백 값이며,

는 제어기(110)로부터 제공되는 제어 입력,

는 일반화된 외란, A는 시스템 매트릭스로

로 정의되며, B는 입력 매트릭스로

로 정의되고, T는 샘플링 주기에 해당한다. A, B는 가제어성을 가지며, 외란의 변동치는 소정 값 미만이 되도록 가정(

)한다. 또한,

는 제어 입력과 제어 입력 제한부(130)의 출력의 차이로,

로 정의되고,

은 제어 입력 제한부(130)에 설정된 제어 입력 절대값의 최대 제한값이다.)(here,

Is a feedback value provided by the load unit 120 as a state variable,

Is a control input provided from the controller 110,

Is the generalized disturbance, A is the system matrix

Is defined as B is the input matrix

Defined as, T corresponds to the sampling period. A and B have controllability, and it is assumed that the fluctuation of disturbance is less than a predetermined value (

)do. Also,

Is the difference between the control input and the output of the control input limiting unit 130,

Is defined as,

Is the maximum limit value of the absolute value of the control input set in the control input limiter 130.)

)를 고려하여, 절환 함수 계산부(111) 및 외란 보상부(113)의 출력을 계산하고, 제어 입력(

)을 생성할 수 있다. 보조 상태 변수 계산부(114)에서 생성되는 보조 상태 변수(

)는 하기 수학식 2와 같이 정의된다.The controller 110 is an auxiliary state variable provided by the auxiliary state variable calculator 114 (

), the outputs of the switching function calculation unit 111 and the disturbance compensation unit 113 are calculated, and the control input (

). The auxiliary state variable generated by the auxiliary state variable calculator 114 (

) Is defined as in Equation 2 below.

[Equation 2]

는 보조 상태의 이득 파라미터로,

로 정의될 수 있으며,

는 절환 함수 관련 게인 매트릭스이다.)(here,

Is the auxiliary state gain parameter,

Can be defined as

Is a gain matrix related to the switching function.)

)를 고려하여, 현재 상태의 보조 상태 변수(

)를 업데이트할 수 있다. 보조 상태 변수 계산부(114)는 이전 상태의 제어 입력과 이전 상태의 제어 입력 제한부(130)의 출력의 차이(

)에 제1 값을 곱한 제2 값으로 조정할 수 있다. 여기서, 제1 값은 제어기(110)의 파라미터(GB)일 수 있다. 또한, 보조 상태 변수는 직전 상태의 보조 상태 변수값에 제3 값을 곱한 값과 상기 제2 값을 조합하여 현재의 보조 상태 변수 값을 업데이트할 수 있다. 여기서, 제3 값은 보조 상태의 이득 파라미터(

)에 해당한다. 보조 상태 변수는 상기 제어 입력 제한부로 제공되는 제어 입력과 상기 제어 입력 제한부의 출력의 차이 및 보조 상태 이득 파라미터를 기초로 업데이트될 수 있다.The auxiliary state variable calculating unit 114 is the difference between the control input of the previous state and the output of the control input limiting unit 130 of the previous state (

Considering ), the secondary state variable of the current state (

). The auxiliary state variable calculating unit 114 is the difference between the control input of the previous state and the output of the control input limiting unit 130 of the previous state (

) To the second value multiplied by the first value. Here, the first value may be the parameter GB of the controller 110. In addition, the auxiliary state variable may update the current auxiliary state variable value by combining the value of the auxiliary state variable of the immediately preceding state by a third value and the second value. Here, the third value is a gain parameter of the auxiliary state (

). The auxiliary state variable may be updated based on the difference between the control input provided to the control input limiter and the output of the control input limiter and an auxiliary state gain parameter.

)는 제어기(110)의 절환 함수 계산부(111)에 제공된다.The current auxiliary state variable updated by the auxiliary state variable calculator 114 (

) Is provided to the switching function calculator 111 of the controller 110.

)를 고려한 현재 상태의 절환 함수 출력(

)를 정의할 수 있다. 절환 함수 계산부(111)는 외부로부터 입력되는 레퍼런스(

), 피드백된 부하부의 상태 변수(

), 보조 상태 변수(

)로 구성된 절환 함수 출력(

)를 계산할 수 있다. 절환 함수 출력(

)은 하기 수학식 3과 같이 정의된다.The switching function calculation unit 111 is an auxiliary state variable of the updated current state (

Output of the switching function of the current state considering)

) Can be defined. The switching function calculation unit 111 is a reference input from the outside (

), the state variable of the feedback load part (

), secondary state variable (

Output of the switching function consisting of)

). Switching function output (

) Is defined as in Equation 3 below.

[Equation 3]

는 오차 함수로,

로 정의되고,

는 절환 함수 관련 게인 매트릭스이다.)(here,

Is the error function,

Is defined as,

Is a gain matrix related to the switching function.)

That is, the switching function output is defined based on the error of the reference variable input from the outside, the state variable output from the control object, and the auxiliary state variable.

)과 절환 함수 출력(

)에 기초하여 외란 추정 값(

)을 산출한다. 수학식 1의 상태 공간 방정식에서, 절환 함수 출력(

)를 0으로 만들기 위한, 외란 보상부(113)가 추정한 외란 추정 값(

)과, 제어 입력 계산부(112)의 제어 입력(

)가 정의된다. 외란 추정 값(

)은 하기 수학식 4와 같이 정의된다.Disturbance compensation unit 113 is a disturbance estimated gain (

) And switching function output (

Disturbance estimate based on)

). In the state-space equation of Equation 1, the switching function output (

The disturbance estimation value estimated by the disturbance compensation unit 113 to make) 0 (

) And the control input of the control input calculator 112 (

) Is defined. Disturbance estimate (

) Is defined as in Equation 4 below.

[Equation 4]

는 오차 함수(

)가 슬라이딩 매니폴드로 도달하는 속도를 결정하는 파라미터,

는 포화 함수(

)의 이득이며,

는 포화 함수의 경계층의 두께(boundary layer thickness)를 결정하는 파라미터,

는 외란 추정 이득,

는 외란 추정 값이다.)(here,

Is the error function (

) Is the parameter that determines the speed at which the sliding manifold reaches,

Is the saturation function (

)

Is a parameter that determines the boundary layer thickness of the saturation function,

Is the disturbance estimation gain,

Is the disturbance estimate.)

) 및 상기 외란 추정 값(

)에 기초하여 현재 상태의 제어 입력(

)을 계산한다. 현재 상태의 제어 입력(

)은 하기 수학식 5와 같이 정의된다.The control input calculator 112 outputs a switching function (

) And the disturbance estimated value (

Control input of the current state based on)

). Current state control input (

) Is defined as in Equation 5 below.

[Equation 5]

That is, the control input of the current state is defined based on the switching function output, the disturbance estimation value, a reference input from the outside, a state variable output from the control object, and the auxiliary state variable. The generated control input is provided to the control input limiting unit 130.

The control input calculator 112 may generate a control input such that the variable structure controller having Equation 5 as the control input makes the switching function output value to 0 on a sliding surface.

, 절환 함수:

, 외란 추정 방법:

, 제어 입력:

)의 외란 보상부에서 외란 추정 오차 다이나믹스(dynamics)를 나타낸 것이다. Equation 6 below is a conventional control system (discrete time state spatial equation:

, Switching function:

, Disturbance estimation method:

, Control input:

) Indicates the dynamics of the estimation error of the disturbance in the disturbance compensation unit.

[Equation 6]

는 실제 외란(

)과 추정 외란(

)의 차이를 의미한다.)(here,

Is the actual disturbance (

) And estimated disturbance (

) Means the difference.)

이고,

을 임의의 양수 M 및 모든 k에 대해 만족하는 경우(외란의 변화율이 M으로 바운드되면),

과 무관하게

을 만족하는 k가 반드시 존재하는 것이 증명된다. 즉, 제어 입력 제한을 받지 않는 제어 시스템의 외란 추정 오차 다이나믹스에서, 외란 추정 오차는

으로 안정화되는 것을 알 수 있다.

ego,

Is satisfied for any positive M and all k (if the rate of change of the disturbance is bound to M),

Irrespective of

It is proved that k satisfying k must exist. That is, in the disturbance estimation error dynamics of the control system that is not restricted by the control input, the disturbance estimation error is

It can be seen that it is stabilized.

Equation 7 below shows closed-loop sliding mode dynamics in the control input calculator 112 of the conventional control system assuming that the control input is not limited.

[Equation 7]

)는 안정하고 거의 0으로 수렴될 수 있다.That is, if there is no control input limit and the rate of change of the disturbance is sufficiently small, the switching function (

) Is stable and can converge to almost zero.

The results of Equations 6 and 7 mean that in a situation in which the input control command is not limited, the disturbance compensation value and the switching function do not diverge, and converge to a constant value to stabilize.

In this regard, the control system 10 according to an embodiment of the present invention may exhibit disturbance estimation error dynamics and closed-loop sliding mode dynamics in the same form as in Equations (6) and (7), even in a control input limit situation. The above-mentioned contents are verified through the following process.

The closed loop sliding mode dynamics of the present invention can be calculated as follows.

(1) 식이 도출될 수 있다. 그리고 수학식 1 및 수학식 2 및 상기 (1)식에 치환하여 정리하면 (2) 식이 도출되고, (2)식에 수학식 5를 치환하면 (3) 식이 도출되고, (3)식을 정리하면 (4)와 같은 폐루프 슬라이딩 모드 다이나믹스 결과가 도출된다.In Equation 3 above

(1) Equation can be derived. Then, by substituting Equation 1 and Equation 2 and Equation (1) above, Equation (2) is derived, and substituting Equation 5 by Equation (2) results in Equation (3) and Equation (3). When (4), the closed loop sliding mode dynamics result is obtained.

That is, the closed-loop sliding mode dynamics of the present invention may have the same result as the closed-loop sliding mode dynamics in a state in which there is no control input limit even if there is a control input limit.

으로부터 하기 수학식 8이 도출될 수 있다. Also, the

From Equation 8 below can be derived.

[Equation 8]

Substituting Equation 8 into Equation 4, the estimated disturbance value of the disturbance compensator 113 of the present invention is summarized as in Equation 9 below.

[Equation 9]

That is, the disturbance estimation error dynamics of the present invention may have the same result as the disturbance estimation error dynamics in a state in which there is no control input limit even if there is a control input limit.

The controller 110 according to an embodiment of the present invention generates a control input based on the auxiliary state variable provided by the auxiliary state variable calculator 114 to compensate for the disturbance even in a situation in which a disturbance exists and an input control command is limited. The value and the switching function value can be prevented from diverging. Accordingly, a decrease in control performance can be prevented and stability can be secured. Hereinafter, an embodiment of a controller according to an embodiment of the present invention will be described.

[Example]

)은 5.7A, 샘플링 주기(T)는 0.125 ms이다. 제어기의 각 파라미터는 하기 표 1과 같이 설정되었다. The control target is a 400W AC servo motor, mounted on an industrial ball-screw drive system. Maximum control input limit set in the control input limiter 130 (

) Is 5.7A, and the sampling period (T) is 0.125 ms. Each parameter of the controller was set as shown in Table 1 below.

[Table 1]

) 및 각속도(angular velocity,

)이다. 도 3는 예시적인 레퍼런스를 도시한 그래프이다. 도 3a는 각각 제어 대상의 각변위에 대한 레퍼런스, 도 3b는 제어 대상의 각속도에 대한 레퍼런스를 도시한 그래프이다.The reference of the control target is the angular position of the control target

) And angular velocity,

)to be. 3 is a graph showing an exemplary reference. 3A is a graph showing a reference to an angular displacement of a control object, and FIG. 3B is a graph showing a reference to an angular velocity of the control object.

4 is a graph showing the results of inputting the reference of FIGS. 3A and 3B to a controller having a conventional control input limit and disturbance compensation. 4A shows the angular displacement error, FIG. 4B shows the angular velocity, FIG. 4C shows the control input, and FIG. 4D shows the change in the disturbance estimation value.

5 is a graph showing the results of inputting the reference of FIGS. 3A and 3B to the controller according to the present embodiment. 5A shows the angular displacement error, FIG. 5B shows the angular velocity, FIG. 5C shows the control input, and FIG. 5D shows the change in the disturbance estimation value.

By comparing FIGS. 4 and 5, it can be seen that the angular displacement error of the controller according to the present embodiment is less, and it can be seen that the angular velocity of the reference is also more precisely followed. Also, it can be confirmed that the disturbance estimation value estimates only the disturbance component even in the control input saturation state. That is, the controller according to the present embodiment can provide stable servo control by preventing the disturbance compensation value and the switching function output from being winded up even when a disturbance exists and an input control command is limited. In addition, while maintaining the robustness and excellent following performance structure, which are advantages of the variable structure control method and the disturbance compensation unit, it is possible to provide from control input restriction to toughness.

Hereinafter, a control method of a controller according to another embodiment of the present invention will be described. The controller may be the controller 110 of FIGS. 1 to 5 described above, and FIGS. 1 to 5 may be referred to for description of the present embodiment.

Referring to FIG. 6, a control method of a controller according to another embodiment of the present invention is a control method of a controller that controls a control target through a control input limiting unit, control input and control provided from the controller to the control input limiting unit Calculating a difference in output of the input limiting unit (S100); Updating an auxiliary state variable based on the difference between the control input and the output of the control input limiter (S110); Calculating a switching function output based on the auxiliary state variable, and calculating a disturbance estimation value based on the switching function output (S120); And calculating a control input based on the switching function output and the disturbance estimate (S130).

First, the difference between the control input provided from the controller to the control input limiting unit and the control input and the output of the control input limiting unit is calculated (S100).

)을 추종하도록 제어 입력을 생성할 수 있다. 제어기(110)는 가변 구조 제어 방법 중 하나인 이산 시간 슬라이딩 모드(Discrete-time sliding mode control, DSMC) 제어 방법을 적용할 수 있다. In the system environment of the discrete time state spatial equation according to Equation 1, the controller 110 receives the reference command (

) To generate a control input. The controller 110 may apply a discrete-time sliding mode control (DSMC) control method, which is one of the variable structure control methods.

[Equation 1]

는 상태 변수로 부하부(120)에서 제공되는 피드백 값이며,

는 제어기(110)로부터 제공되는 제어 입력,

는 일반화된 외란, A는 시스템 매트릭스로

로 정의되며, B는 입력 매트릭스로

로 정의되고, T는 샘플링 주기에 해당한다. A, B는 가제어성을 가지며, 외란의 변동치는 소정 값 미만이 되도록 가정(

)한다. 또한,

는 제어 입력과 제어 입력 제한부(130)의 출력의 차이로,

로 정의되고,

은 제어 입력 제한부(130)에 설정된 제어 입력 절대값의 최대 제한값이다.)(here,

Is a feedback value provided by the load unit 120 as a state variable,

Is a control input provided from the controller 110,

Is the generalized disturbance, A is the system matrix

Is defined as B is the input matrix

Defined as, T corresponds to the sampling period. A and B have controllability, and it is assumed that the fluctuation of disturbance is less than a predetermined value (

)do. Also,

Is the difference between the control input and the output of the control input limiting unit 130,

Is defined as,

Is the maximum limit value of the absolute value of the control input set in the control input limiting unit 130.)

)를 계산할 수 있다.Specifically, the step (S100) of calculating the difference between the control input and the output of the control input limiting unit 130 may be performed by the auxiliary state variable calculating unit 114 of the controller 110. The auxiliary state variable calculating unit 114 is the difference between the control input of the previous state and the output of the control input limiting unit 130 of the previous state (

).

Next, an auxiliary state variable is updated based on the difference between the control input and the output of the control input limiting unit 130 (S110).

)를 고려하여, 현재 상태의 보조 상태 변수(

)를 업데이트할 수 있다. 보조 상태 변수(

)는 하기 수학식 2와 같이 정의된다. The step S110 may be performed by the auxiliary state variable calculator 114 of the controller 110. The auxiliary state variable calculating unit 114 is the difference between the control input of the previous state and the output of the control input limiting unit 130 of the previous state (

Considering ), the secondary state variable of the current state (

). Secondary state variable (

) Is defined as in Equation 2 below.

[Equation 2]

는 보조 상태의 이득 파라미터로,

로 정의될 수 있으며,

는 절환 함수 관련 게인 매트릭스이다.)(here,

Is the auxiliary state gain parameter,

Can be defined as

Is a gain matrix related to the switching function.)

That is, the auxiliary state variable may be updated based on the difference between the control input provided to the control input limiter and the output of the control input limiter and the auxiliary state gain parameter.

)는 제어기(110)의 절환 함수 계산부(111)에 제공된다.The auxiliary state variable of the current state updated by the auxiliary state variable calculator 114 (

) Is provided to the switching function calculator 111 of the controller 110.

Next, a switching function output is calculated based on the auxiliary state variable, and a disturbance estimation value is calculated based on the switching function output (S120).

)를 고려하여 현재 상태의 절환 함수 출력(

)을 계산할 수 있다. 절환 함수 계산부(111)는 외부로부터 입력된 현재 상태의 레퍼런스 명령(

), 피드백된 부하부의 상태 변수(

), 보조 상태 변수(

)로 구성된 절환 함수 출력(

)을 계산할 수 있다. 절환 함수 출력(

)은 하기 수학식 3과 같이 정의된다.The switching function calculator 111 is a secondary state variable of the current state (

Considering ), the current state of the switching function output (

). The switching function calculator 111 is a reference command of the current state input from the outside (

), the state variable of the feedback load part (

), secondary state variable (

Output of the switching function consisting of)

). Switching function output (

) Is defined as in Equation 3 below.

[Equation 3]

는 오차 함수로,

로 정의되고,

는 절환 함수 관련 게인 매트릭스이다.)(here,

Is the error function,

Is defined as,

Is a gain matrix related to the switching function.)

That is, the switching function output is defined based on the error of the reference variable input from the outside, the state variable output from the control object, and the auxiliary state variable.

)과 절환 함수(

)에 기초하여 외란 추정 값(

)을 산출한다. 외란 보상부(113)의 출력은 외란 추정 값일 수 있다. 수학식 1의 상태 공간 방정식에서, 절환 함수 출력(

)을 0으로 만들기 위한, 외란 보상부(113)가 추정한 외란 추정 값(

)과, 제어 입력 계산부(112)의 제어 입력(

)가 정의된다. 외란 추정 값(

)은 하기 수학식 4와 같이 정의된다.Disturbance compensation unit 113 is a disturbance estimated gain (

) And switching function (

Disturbance estimate based on)

). The output of the disturbance compensation unit 113 may be an estimated disturbance value. In the state-space equation of Equation 1, the switching function output (

The disturbance estimation value estimated by the disturbance compensation unit 113 to make) 0 (

) And the control input of the control input calculator 112 (

) Is defined. Disturbance estimate (

) Is defined as in Equation 4 below.

[Equation 4]

는 오차 함수(

)가 슬라이딩 매니폴드로 도달하는 속도를 결정하는 파라미터,

는 포화 함수(

)의 이득이며,

는 포화 함수의 경계층의 두께(boundary layer thickness)를 결정하는 파라미터,

는 외란 추정 이득,

는 외란 추정 값이다.)(here,

Is the error function (

) Is the parameter that determines the speed at which the sliding manifold reaches,

Is the saturation function (

)

Is a parameter that determines the boundary layer thickness of the saturation function,

Is the disturbance estimation gain,

Is the disturbance estimate.)

Finally, the control input is calculated based on the switching function output and the disturbance estimate (S130).

) 및 상기 외란 추정 값(

)에 기초하여 현재 상태의 제어 입력(

)을 계산한다. 제어 입력(

)은 하기 수학식 5와 같이 정의된다.The control input calculator 112 outputs the switching function calculator (

) And the disturbance estimated value (

Control input of the current state based on)

). Control input(

) Is defined as in Equation 5 below.

[Equation 5]

That is, the control input of the current state is defined based on the switching function output, the disturbance estimation value, a reference input from the outside, a state variable output from the control object, and the auxiliary state variable.

The control input calculator 112 may generate a control input such that the variable structure controller having Equation 5 as the control input makes the switching function 0 on a sliding surface.

The operation by the control method of the controller according to the above-described embodiments may be at least partially implemented in a computer program and recorded in a computer-readable recording medium. A program for implementing an operation by a control method of a controller according to embodiments is recorded and a computer-readable recording medium includes all types of recording devices in which data that can be read by a computer are stored. Examples of computer-readable recording media include ROM, RAM, CD-ROM, magnetic tape, floppy disks, and optical data storage devices. In addition, the computer readable recording medium may be distributed over network coupled computer systems so that the computer readable code is stored and executed in a distributed manner. In addition, functional programs, codes, and code segments for implementing the present embodiment will be readily understood by those skilled in the art to which this embodiment belongs.

Although described above with reference to embodiments, the present invention should not be construed as being limited by these embodiments or the drawings, and those skilled in the art will appreciate the spirit and scope of the present invention as set forth in the claims below. It will be understood that various modifications and changes can be made to the present invention without departing from the scope.

10: Control system
110: controller
111: switching function calculator
112: control input calculation unit
113: disturbance compensation department
114: auxiliary state variable calculation unit
120: load unit
121: current controller
122: control target
123: encoder
130: control input limiter

Claims (11)

A controller for controlling a control target through a control input limiting unit,
An auxiliary state variable calculator which calculates a difference between a control input provided from the controller to the control input limiter and an output of the control input limiter, and updates an auxiliary state variable based on the difference;
A switching function calculator for calculating a switching function output based on the auxiliary state variable;
A disturbance compensation unit to calculate a disturbance estimate based on the switching function output; And
And a control input calculator configured to calculate a control input based on the switching function output and the disturbance estimation value. According to claim 1,
And the auxiliary state variable is updated based on a difference between the control input provided to the control input limiter and the output of the control input limiter and an auxiliary state gain parameter. According to claim 1,
The switching function output is defined on the basis of the error of the reference variable input from the outside, the state variable output from the control target, and the auxiliary state variable. According to claim 1,
And the disturbance estimation value is defined based on the switching function output and the disturbance estimation gain. According to claim 1,
The control input is a controller characterized in that it is defined based on the switching function output, the disturbance estimation value, a reference input from the outside, a state variable output from the control target, and the auxiliary state variable. As a control method of a controller that controls a control target through a control input limiting unit,
Calculating a difference between a control input provided from the controller to the control input limiter and an output of the control input limiter;
Updating an auxiliary state variable based on the difference between the control input and the output of the control input limiter;
Calculating a switching function output based on the auxiliary state variable, and calculating a disturbance estimate based on the switching function output; And
And calculating a control input based on the switching function output and the disturbance estimation value. The method of claim 6,
And the auxiliary state variable is updated based on a difference between the control input provided to the control input limiter and the output of the control input limiter and an auxiliary state gain parameter. The method of claim 6,
The switching function output is defined on the basis of the error of the reference variable input from the outside, the state variable output from the control target, and the auxiliary state variable. The method of claim 6,
The disturbance estimation value is defined based on the switching function output and the disturbance estimation gain. The method of claim 6,
The control input is a control function of the controller characterized in that it is defined based on the switching function output, the disturbance estimation value, an external input reference, the state variable output from the control target, and the auxiliary state variable. A computer program stored in a medium to execute a control method of a controller according to any one of claims 6 to 10 in combination with hardware.

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