KR101849464B1 - Automatic Tuning Method for PID controllers - Google Patents

Abstract

The present invention provides a PID gain automatic tuning method capable of automatically and systematically selecting a gain of a PID controller. The present invention also provides a PID gain automatic tuning method capable of automatically updating PID control gains if only the slope parameters of the sliding surface for describing the control period (sampling time L) of the control system and the desired error dynamics are set will be.
To this end, a PID controller according to an embodiment of the present invention includes a parameter setting unit for setting a slope of a sliding mode and a control period of the system; A gain automatic adjustment unit for automatically adjusting a gain using the slope of the sliding mode and the control period of the system; And a control input calculation unit for calculating a control input through the controlled gains. Wherein the gain automatic adjustment unit adjusts the gain using Equation (1), and the control input calculation unit calculates the control input using Equation (2). ≪ EMI ID = An automatic tuning method is disclosed.

Description

PID Gain Automatic Tuning Method for PID controllers [

The present invention relates to a PID gain automatic tuning method. More particularly, the present invention relates to a PID gain automatic tuning method capable of automatically and systematically selecting a gain of a PID controller.

The PID controller (Proportional Integral Derivative Controller) is one of the controllers widely used in the industrial field in the control system field. The PID controller has a simple structure consisting of proportional, integral, and derivative parts. The gain of the PID controller has a clear physical meaning, such as corresponding to position error, speed error and integral error, respectively, but rather than tuning the gain of the PID controller to be adjusted by the engineer, It is difficult to be sure that the final gain is the best gain.

In particular, tuning the PID gain needed to control a multivariable nonlinear system such as a robot requires a great deal of time and effort. Therefore, in order to set a gain by a user without expert knowledge, a procedure and a tuning algorithm for automatically tuning the gain are required.

There are many techniques for gain design of PID controllers. For example, the Ziegler-Nichols method is simple and can adjust the PID gain easily, but it is said to be unsatisfactory in nonlinear systems. In general, many studies on PID controllers show good performance in linear systems, but performance in nonlinear systems can be difficult or often inadequate to predict.

In Patent Document 10-1640931, when an initial value is determined by an equation and the differential gain is increased to satisfy the condition, a value obtained by multiplying the differential gain by 0.8 is defined as a new differential gain value, the differential gain is fixed, and the proportional gain is increased And the PID control is performed. When the condition is satisfied, the value obtained by multiplying the proportional gain by 0.8 is fixed to a new proportional gain value, the derivative gain is increased again, and the derivative gain with which the figure of merit is minimized is set as a new differential gain value , The proportional gain which minimizes the figure of merit by fixing the differential gain and raising the proportional gain again is set as a new proportional gain value. Finally, PID control is performed by increasing the integral gain after fixing the proportional gain and differential gain, and finally tuning. In the conventional PID gain tuning of the patent 10-1640931, tuning of the differential gain, tuning of the proportional gain, tuning of the differential gain again, and tuning of the proportional gain are repeated using the trial-and-error method To gain access to the gain. Therefore, it includes issues such as whether the optimum figure of merit is coming up or when the iterative process should be stopped, and the gain tuning steps are many and complicated.

In the patent document 10-1242678, a PID parameter is generated using an approximate model using RBF (Radial Basis Function). Reinforcement learning is used to correct errors and correct errors in operation and improve overall performance. This method has improved performance compared to the existing PID control method, but it is difficult to use because of the complexity of application. For example, this method needs to calculate a Gaussian function that requires a lot of weights, a discount rate, and a large amount of computation, and it is necessary to calculate errors, average values of kernel functions, and standard deviations. Parameter setting and tuning. Also, because of the use of advanced functions, a large amount of computation is required and its application is complicated.

The present invention provides a PID gain automatic tuning method capable of automatically and systematically selecting a gain of a PID controller.

The present invention also provides a PID gain automatic tuning method capable of automatically updating PID control gains if only the slope parameters of the sliding surface for describing the control period (sampling time L) of the control system and the desired error dynamics are set will be.

It is to be understood that both the foregoing general description and the following detailed description of the present invention are exemplary and explanatory and are not intended to limit the invention to the precise form disclosed. It can be understood.

A PID controller according to an embodiment of the present invention includes a parameter setting unit for setting a slope of a sliding mode and a control period of the system; A gain automatic adjustment unit for automatically adjusting a gain using the slope of the sliding mode and the control period of the system; And a control input calculation unit for calculating a control input through the controlled gains. Wherein the gain automatic adjustment unit adjusts the gain using Equation (1), and the control input calculation unit calculates the control input using the following Equation (2).

[Equation 1]

는 실수 범위에서 정해지는 대각 게인 행렬이다.)(Where K, T _I , and T _D are the gains in the discrete space, λ is the sliding slope of the target sliding mode dynamics,

Is a diagonal gain matrix that is determined by the real number range.

&Quot; (2) "

(Where L is the control period, u (k) is the control input corresponding to the kth control period, and e (k) is the kth error.)

는 하기 [수학식 3]을 이용하여 정의될 수 있다.In addition,

Can be defined using the following equation (3).

&Quot; (3) "

,

는 사용자에 의해 결정되는 상수이고, S는 슬라이딩 변수이며,

는

에 대한 변화율이다.)(Where,

,

Is a constant determined by the user, S is a sliding variable,

The

.)

Further, the sliding parameter S may be defined using Equation (4) below.

&Quot; (4) "

은 오차의 변화율,

는 추종오차이다.)(here,

The rate of change of error,

Is the tracking error.)

(실수 범위에서 정해지는 대각 게인 행렬)를 정의하는 단계; 상기

로, 게인(K, T_I, T_D)을 조절하는 단계; 상기 게인(K, T_I, T_D)으로 제어입력(u(k))을 계산하는 단계; 및 상기 제어입력을 시스템에 입력하는 단계를 포함하고, 상기 게인(K, T_I, T_D)은 하기 [수학식 1]을 이용하여, 조절되고, 상기 제어 입력은 하기 [수학식 2]을 이용하여, 계산되고, 상기

는 하기 [수학식 3]을 이용하여 정의될 수 있다.Meanwhile, a PID gain automatic tuning method according to an embodiment of the present invention includes setting a slope of a sliding mode and a control period of the system; Using error

(A diagonal gain matrix determined in real range); remind

, Adjusting the gains (K, T _I , T _D ); Calculating a control input u (k) with said gains (K, T _I , T _D ); And inputting the control input to the system, wherein the gain (K, T _I , T _D ) is adjusted using Equation (1) Is calculated using the equation

Can be defined using the following equation (3).

 [Equation 1]

는 실수 범위에서 정해지는 대각 게인 행렬이다.)(Where K, T _I , and T _D are the gains in the discrete space, λ is the sliding slope of the target sliding mode dynamics,

Is a diagonal gain matrix that is determined by the real number range.

&Quot; (2) "

(Where L is the control period, u (k) is the control input corresponding to the kth control period, and e (k) is the kth error.)

&Quot; (3) "

,

는 사용자에 의해 결정되는 상수이고, S는 슬라이딩 변수이고,

는

에 대한 변화율이다.)(Where,

,

Is a constant determined by the user, S is a sliding variable,

The

.)

Further, the sliding parameter S may be defined using Equation (4) below.

&Quot; (4) "

은 오차의 변화율,

는 추종오차이다.)(here,

The rate of change of error,

Is the tracking error.)

The PID gain automatic tuning method according to the present invention can automatically and systematically select the gain of the PID controller.

Also, the PID gain automatic tuning method according to the present invention can automatically update the PID control gains if only the slope parameters of the sliding surface for describing the control period (sampling time L) of the control system and the desired error dynamics are set .

It should be understood, however, that the effects obtained by the present invention are not limited to the above-mentioned effects, and other effects not mentioned may be clearly understood by those skilled in the art to which the present invention belongs It will be possible.

와 슬라이딩 변수의 응답 관계를 나타낸 그래프이다.
도 5는 본 발명의 일 실시예에 따른

와 슬라이딩 변수의 상관 궤적(Phase portrait)을 나타낸 그래프이다.
도 6은 본 발명의 일 실시예에 따른 제어 오차와 제어입력을 나타낸 그래프이다.
도 7은 본 발명의 일 실시예에 따른 PID 게인 자동 튜닝 방법을 나타내는 블록다이어그램이다.BRIEF DESCRIPTION OF THE DRAWINGS The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate preferred embodiments of the invention and, together with the description, And shall not be interpreted.
1 is a block diagram schematically showing a PID controller according to an embodiment of the present invention.
2 is a flowchart illustrating a PID gain automatic tuning method according to an embodiment of the present invention.
3 is a graph illustrating a path to follow in accordance with an embodiment of the present invention.
Figure 4 is a graphical representation of time-

And sliding variables.
FIG. 5 is a block diagram of an embodiment of the present invention,

And Phase correlation of sliding variables.
6 is a graph illustrating control errors and control inputs according to an embodiment of the present invention.
7 is a block diagram illustrating a PID gain automatic tuning method according to an embodiment of the present invention.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings.

The embodiments of the present invention are described in order to more fully explain the present invention to those skilled in the art, and the following embodiments may be modified into various other forms, It is not limited to the embodiment. Rather, these embodiments are provided so that this disclosure will be more faithful and complete, and will fully convey the scope of the invention to those skilled in the art.

Also, in the following drawings, each configuration is exaggerated for convenience and clarity of description, and the same reference numerals denote the same elements in the drawings. As used herein, the term " and / or " includes any and all combinations of any of the listed items.

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.

As used herein, the singular forms "a," "an," and "the" include singular forms unless the context clearly dictates otherwise. Also, " comprise " and / or " comprising " when used herein should be interpreted as specifying the presence of stated shapes, numbers, steps, operations, elements, elements, and / And does not preclude the presence or addition of one or more other features, integers, operations, elements, elements, and / or groups.

FIG. 1 is a block diagram schematically showing a PID controller according to an embodiment of the present invention, and FIG. 2 is a flowchart illustrating a PID gain automatic tuning method according to an embodiment of the present invention.

정의 단계(S20), 게인 조절 단계(S30), 제어입력 계산 단계(S40) 및 제어입력 입력 단계(S50)를 포함한다.1 and 2, a PID controller 100 according to an embodiment of the present invention includes a parameter setting unit 110, an automatic gain control unit 120, and a control input calculation unit 130, The PID gain automatic tuning method used includes a parameter setting step (S10)

A definition step S20, a gain adjustment step S30, a control input calculation step S40, and a control input step S50.

In the parameter setting step (S10), parameters for automatically tuning the PID gain are set through the parameter setting unit (110).

Here, the parameter includes a control period (Sampling time, L) and a slope (?) Of a sliding surface for describing a desired error dynamics.

These parameters may be suggested by the user at any value.

정의 단계(S20)에서는 상기 단계(S10)에서 설정된 파라미터들과 오차를 통해

의 값을 정의한다.Then,

In the defining step S20, through the parameters and the error set in the step S10,

Is defined.

는 실수 범위에서 정해지는 대각 게인 행렬이다.here,

Is a diagonal gain matrix determined in the real number range.

은 다음의 수학식에 의해 연산된다.In this step S20

Is calculated by the following equation.

,

는 사용자에 의해 결정되는 상수이고, S는 슬라이딩 변수이고,

는

에 대한 변화율을 나타낸다.Here,

,

Is a constant determined by the user, S is a sliding variable,

The

Lt; / RTI >

Further, the sliding parameter S is defined by the following equation.

은 오차의 변화율,

는 추종오차이다.)(here,

The rate of change of error,

Is the tracking error.)

는 자동 게인 튜닝을 위한 파라미터로서 α는 슬라이딩 변수의 크기가 클 때

를 증가시키는 역할을 하며,

는 Leakage Term으로서 슬라이딩 변수가 0에 가까워(즉, 에러가 작을 때) 목표 오차에 가까울 때에

가 줄어드는 속도를 결정해준다. 따라서

는 오차가 크면 커지려고 하는 경향이 있으며, 오차가 작으면 자동으로 줄어들게 된다. 이에 따라

의 크기가 자동적으로 적절하게 조절되게 된다. That is,

Is a parameter for automatic gain tuning and α is the magnitude of the sliding variable

, And the number

Is a Leakage Term and when the sliding variable is close to zero (ie, when the error is small)

Determines the rate at which it declines. therefore

Tend to increase if the error is large, and decrease automatically if the error is small. Accordingly

So that the size of the lens is automatically adjusted appropriately.

의 입력의 상한이

에서 포화되며, 입력의 하한이

에서 포화될 수 있다.here,

The upper limit of the input of

, And the lower limit of the input

. ≪ / RTI >

은 [

,

]의 구간에 있게 된다.

와

는

의 파라미터 입력 범위(parameter search space)를 정해주는 것으로, 사용자가 대략적으로

의 범위를 지정할 수 있는 것이다. In other words,

Is [

,

].

Wow

The

The parameter search space of the user,

Can be specified.

는 아주 작은 양의 값(예: 0.0000001)을 선택한다.Here, generally,

Selects a very small amount of value (for example, 0.0000001).

,

및 L을 통해, 자동으로 다음 수학식과 같이 PID 게인 들을 유도한다.Thereafter, in the gain adjustment step S30,

,

And L, it automatically derives the PID gains as follows:

Here, K, T _I , and T _D represent gains in the discrete space.

Thereafter, in the control input calculation step S40, the control input calculation unit 130 calculates the control input u (k) through the following equation.

Here, u (k) is the control input corresponding to the kth control period, e (k) is the kth error, e (k-1) .

Thereafter, in the control input step S50, the control input value obtained through the above-described step is input to the plant and operated.

The above-described PID gain automatic tuning method is shown in a block diagram as shown in FIG.

<Examples>

Hereinafter, the result of controlling the robot arm through the control input obtained using the PID gain automatic tuning method will be described as an embodiment.

와 슬라이딩 변수의 응답 관계를 나타낸 그래프이며, 도 5는 본 발명의 일 실시예에 따른

와 슬라이딩 변수의 상관 궤적(Phase portrait)을 나타낸 그래프이고, 도 6은 본 발명의 일 실시예에 따른 제어오차와 제어입력을 나타낸 그래프이다.FIG. 3 is a graph illustrating a path to follow in accordance with an embodiment of the present invention. FIG.

And FIG. 5 is a graph showing a response relationship of the sliding variable according to an embodiment of the present invention

FIG. 6 is a graph illustrating a control error and a control input according to an exemplary embodiment of the present invention. Referring to FIG.

First, referring to FIG. 3, it is possible to confirm the route to follow.

은 아주 작은 값에서 급속히 증가하면서 일정 값 이상으로 가면

가 다시 줄어드는 것을 알 수 있다. 또한, 로봇이 운동방향이 바뀔 때(급격한 쿨롱마찰을 경험할 때)에는

가 커지고, 오차가 적을 때에는

가 줄어 드는 것을 알 수 있다. 또한 위치오차가 커질 때 슬라이딩 변수(S)가 커지고 따라서

가 커지는 것을 확인할 수 있다.4,

Increases rapidly from a very small value and goes above a certain value

Is reduced again. Also, when the robot changes its direction of motion (when experiencing rapid Coulomb friction)

When the error is small,

Can be reduced. In addition, when the position error increases, the sliding parameter S increases,

.

과 슬라이딩 변수(S)의 상관 궤적(Phase portrait)을 통해서도 확인할 수 있다.5,

And the phase correlation between the sliding parameter S and the sliding parameter S.

Referring to FIG. 6, the tracking error e and the control input u (k) of the PID controller of the present invention can be confirmed from the tracking control error e and the control input u (k). It can be seen that the control error (e) is close to 0 and slightly increases due to the influence of Coulomb friction at the time when the direction of the robot arm changes, and then converges to 0 at a high speed.

Also, it can be seen that the control input u (k) is generated in the opposite direction at the time when the motion direction of the robot arm changes. This is to compensate Coulomb friction.

That is, it can be confirmed that PID auto-tuning is possible by the PID gain automatic tuning method of the present invention based on the above-described data, and satisfactory results can be obtained through the PID controller of the present invention performing autotuning.

As described above, the present invention is not limited to the above-described embodiment, and the present invention is not limited to the above-described embodiments, It will be understood by those of ordinary skill in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention.

100: PID controller 110: Parameter setting section
120: automatic gain control unit 130: control input calculation unit

Claims (5)

A PID controller for a non-linear system,
A parameter setting unit for setting a slope of the sliding mode and a control period of the system;
A gain automatic adjustment unit for automatically adjusting a gain using the slope of the sliding mode and the control period of the system; And
A control input calculation unit for calculating a control input through the controlled gains; Lt; / RTI &gt;
The gain automatic adjustment unit adjusts the gain using Equation (1) below,
Wherein the control input calculating unit calculates the control input using Equation (2) below.
[Equation 1]

(Where K, T _I , and T _D are the gains in the discrete space, λ is the sliding slope of the target sliding mode dynamics,

Is a diagonal gain matrix that is determined by the real number range.
&Quot; (2) &quot;

(Where L is the control period, u (k) is the control input corresponding to the kth control period, and e (k) is the kth error.)
The method according to claim 1,
remind

Is defined using Equation (3) below. &Quot; (3) &quot;
&Quot; (3) &quot;

(Where,

,

Is a constant determined by the user, S is a sliding variable,

The

.)
3. The method of claim 2,
Wherein the sliding parameter S is defined using Equation (4) below.
&Quot; (4) &quot;

(here,

The rate of change of error,

Is the tracking error.)
A method for automatically tuning a PID gain of a nonlinear system,
Setting a slope of the sliding mode and a control period of the system;
Using error

(A diagonal gain matrix determined in real range);
remind

, Adjusting the gains (K, T _I , T _D );
Calculating a control input u (k) with said gains (K, T _I , T _D ); And
Inputting the control input to the system,
The gains (K, T _I , T _D ) are adjusted using Equation (1) below,
The control input is calculated using the following equation (2)
remind

Is defined using Equation (3) below. &Lt; EMI ID = 3.0 &gt;
[Equation 1]

(Where K, T _I , and T _D are the gains in the discrete space, λ is the sliding slope of the target sliding mode dynamics,

Is a diagonal gain matrix that is determined by the real number range.
&Quot; (2) &quot;

(Where L is the control period, u (k) is the control input corresponding to the kth control period, and e (k) is the kth error.)
&Quot; (3) &quot;

(Where,

,

Is a constant determined by the user, S is a sliding variable,

The

.)
5. The method of claim 4,
Wherein the sliding parameter (S) is defined using Equation (4).
&Quot; (4) &quot;

(here,

The rate of change of error,

Is the tracking error.)

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