KR100275907B1 - On-line pid tuner for dc motor - Google Patents

Abstract

PURPOSE: An on-line Proportional-Integral-Derivative (PID) study tuner is provided to enable automatic adjustment of PID gains and reduce endeavors for adjusting the PID gains by using PID gain adjusting means and a reverse model study process. CONSTITUTION: A subtracter(11) subtracts an output of a DC motor(16) from the reference input to output an error signal. An adjustment block(13) receives the error signal from the subtracter(11) to adjust control gains from a PID controller(14). The PID controller(14) performs PID control in response to the control gains adjusted by receiving the error signal, and outputs the first control signal for controlling a DC synchronizing signal. A study block(12) receives the error signal from the subtracter, and performs reverse study to output the second control signal for controlling the DC motor(16). An adder(15) adds the second control signal with the first signal to output the sum.

Description

On-line PID learning tuner of DC motor

The present invention relates to an on-line PID learning tuner of a position control system using a DC motor. On-line PID learning tuner.

If the DC motor's model parameters, external load torque, and disturbance are well known, it is possible to apply the existing PID controller only to DC motor control. However, the parameters of a typical DC motor system are often used to control loads that change and change over time.

If the system's parameters or operating conditions are uncertain or unknown, the time-variable PID controller designed assuming that all conditions are known has a problem that does not guarantee such good performance. In addition, since the parameters of the actual system cannot be obtained accurately, even a stable general PID controller designed to see that all conditions are known may be unstable when applied in practice due to inaccurate modeling, and there is a problem of retuning according to operating conditions.

An object of the present invention for solving the above problems is to provide an on-line PID learning tuner of a DC motor control system that overcomes such adverse effects such as fluctuations in system parameters, fluctuations in external load torque, and disturbance.

Another object of the present invention is to provide an on-line PID learning tuner that can be stably applied to a DC motor system in which operating conditions such as model parameters are unknown.

It is still another object of the present invention to provide an on-line PID learning tuner that can be applied to a small microprocessor by designing a controller having a small amount of computation.

1 is a block diagram illustrating a configuration of an on-line PID learning tuner of a DC motor according to the present invention.

2 is a control system diagram showing an embodiment of the present invention using a personal computer (PC).

3 is a graph showing an output when the reference input of the PID learning tuner according to the present invention is stepped and there is no disturbance.

4 is a graph showing an output when the reference input of the PID learning tuner according to the present invention is sine pie and there is no disturbance.

5 is a graph showing the output when the reference input of the PID learning tuner according to the present invention is stepped and there is a sine wave disturbance.

6 is a graph showing the output when the reference input of the PID learning tuner according to the present invention is sinusoidal and disturbance.

* Description of the symbols for the main parts of the drawings *

11 ... Subtractor 12 ... Learner

13 ... Regulator 14 ... PID Controller

15 ... adder 16 ... DC motor

The present invention for achieving the above object,

)를 출력하는 피아이디 제어부와, 감산부의 에러신호(e)를 입력받아서 역모델 학습을 하여 직류전동기를 제어하는 제2 제어신호(v_l)를 출력하는 학습부와, 학습부의 제2 제어신호(v_l)와 피아이디 제어부의 제1 제어신호(v_fb)를 가산하여 그 합(v_a= v_fb+ v_l)을 직류전동기에 출력하는 가산부를 구비한다. 그리하여 본 발명은 직류전동기의 모델을 구하고 이를 설계한 입력에 맞게 변형하여 상태공간표현으로 나타내며 상태공간표현에 맞고 안정성이 증명된 학습제어규칙을 적용한다.Output (θ) of the direct-current electric motor on a direct current electric motor for controlling so that the follower to the reference input (θ _d) - In-line blood ID (PID) learning tuner, the output (θ) of the direct current motor at the reference input (θ _d) Subtract the error signal ( e = θ _d -θ ), The output type for the subtraction unit, and a subtracting unit error signal (e) receiving an input control for adjusting a control gain (K _D, K _P, K ₁₎ of the blood ID control unit and a subtraction unit error signal (e) of The first control signal for controlling the DC motor by performing the PID control according to the received control gain (K _D , K _P , K ₁ )

), A learner for outputting a second control signal (v _l ) for controlling a DC motor by receiving an error signal (e) of the subtractor and performing reverse model learning. and an adder for adding (v _l ) and the first control signal v _fb of the PID control unit and outputting the sum (v _a = v _fb + v _l ) to the DC motor. Thus, the present invention obtains a model of a DC motor and transforms it according to the designed input to represent a state space representation, and applies a learning control rule that has been proved to be suitable for state space representation.

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

First, consider the permanent magnet DC motor model of Equation 1.

In Equation 1, input and output variables, state variables, and electrical and mechanical parameters are defined as follows.

v _a Input voltage i _a Armature current θ Rotation angle T _a Output torque T _l Unknown load torque L Unknown armature inductance R Unknown armature resistance K _a Unknown torque constant K _b Unknown back EMF constant K _c Unknown modulus of elasticity J Unknown motor inertia B Unknown friction coefficient

In this DC motor, a problem to be solved in the present invention is to construct a robust on-line PID learning tuner in which a DC motor system having unknown parameters and disturbance torque follows the target position trajectory θ _d .

To this end, first, assume that the electrical time constant in Equation 1 is sufficiently smaller than the mechanical time constant (LAPPROX0) and rewrite Equation 1 as in Equation 2.

으로 치환하고 수학식 2를 정리하면 수학식 3을 얻는다.now,

Substituting the equation and arranging Equation 2 gives Equation 3.

Define _a voltage v _a consisting of the learning control input and the PID controller as shown in Equation 4.

이고 v_l은 아래에서 정의될 학습입력이다. 수학식 4를 사용하여 수학식 3을 다시 정리하면 수학식 5를 얻는다.here

And v _l is the learning input defined below. Using Equation 4 to rearrange Equation 3, Equation 5 is obtained.

와 같이 정의된다. 수학식 5에서 a₀=dK_D+a, b₀=dK_P+b, c_o=dK_I를 정의하고 치환하면 수학식 6을 얻는다.Where V _d is

Is defined as: In Equation 5, a ₀ = dK _D + a, b ₀ = dK _P + b, and c _o = dK _I are defined and replaced with Eq.

Now assume that the coefficients {a ₀ ^* , b ₀ ^* , c ₀ ^* } and the PID gain {K _P ^* , K _I ^* , K _D ^* } satisfying the error response lets do it. {a ₀ ^* = dK _D ^* + a, b _o ^* = dK _P ^* + b, c _o ^* = dK _I ^* }. Equation 6 may then be written as Equation 7.

If we rearrange Equation 7,

이고,

이다.here

ego,

to be.

Now, in order to facilitate the implementation and verification of the PID learning controller, Equation (8) is expressed as Equation (9).

이다.here,

to be.

Since matrix A is Hurwitz, output vector C defines system {A, B, C} to satisfy the SPR (Strictly Positive Real) condition. That is, the system {A, B, C} satisfies Equation (10).

A ^T P + PA = -Q

C = B ^T P

Where P and Q are positive symmetric matrices.

Now, the learning rule of the PID gain and the auxiliary control input v ₁ is defined as shown in Equation (11).

Where pr (·) is projection and learning gains Λ ₁ and Λ ₂ are positive finite matrices and constants with diagonal elements, respectively.

1 is a block diagram showing the configuration of an embodiment according to the present invention, as shown here a subtractor 11 and a subtractor 11 for subtracting an output θ from a reference input θ _d of a reference input terminal. A learner 12 for inverse model learning based on the output of the controller, a controller 13 for adjusting the PID gain based on the output of the subtractor 11, and a PID controller using the gains adjusted by the controller 13. (14), a closed loop composed of an adder (15) for adding the outputs of the learner (12) and the PID controller (14), and a DC motor (16) driven by the output (v _a ) of the adder (15). Control system.

In FIG. 1, the total control input of the DC motor is composed of a control input output from the PID controller and a learning control input output from the learner. After learning is sufficiently performed, the control input output from the PID controller decreases its role while the learner learns. The learning control input outputted from EK achieves the purpose of tracking and eliminating disturbance by approximating the inverse model of the system.

This role-sharing in transient and steady state is one of the main features of PID learning controller, and it is also different from general PID tuner and adaptive control scheme.

The PID learning controller consisting of the error system Equation 4 and the learning rule Equation 5 for the PID gain and auxiliary learning input converge gradually.

When configuring the DC motor control system, the controller proposed in the present invention can be used to reduce the effort to match the PID gains, and to change the system parameters, external loads, and disturbances that may occur due to aging or environmental changes of the system. Even if this exists, the desired location tracking performance can be obtained.

2 illustrates an embodiment in which the controller proposed in the present invention is implemented using a PC. In FIG. 2, the experimental apparatus is roughly divided into four parts: the main computer 21, the interface board 22, the motor controller 23, and the motor driver 24. First, the main computer 21 is connected to the motor controller from the interface board 22. It receives the encoder pulse 26 input passed by (23) and uses it as a feedback input to obtain a learning control input and output it. The interface board 22 serves as a path for controlling the flow of input / output signals between the main computer 21 and the motor controller 23 through the FIFO memory. As the motor controller 23, for example, an Intel 80C196KC can be used. The motor controller 23 reads the control input value calculated by the main computer 21 from the interface board 22 and outputs the result to the motor driver 24. Then, the encoder input is up-down counted and output to the interface board 22. A linear amplifier having stable output characteristics was used as the motor driver 24. The linear amplifier uses an 8-bit latch, a DAC, and an OP-AMP to output an 8-bit output of the input motor controller 23. The motor 25 is driven by changing the signal between -12V and +12. In addition, the motor driver 24 has a current control loop composed of hardware ID control and adjusts the torque of the motor 25 according to the magnitude of the input signal.

The motor 25 used in the embodiment of the present invention is a 40W DC motor and supplies ± 24V to the motor power source. The motor shaft is connected to an encoder with 600 pulse / revolution resolution and connected to an external load drive shaft via a 12.5: 1 reduction gear. That is, 12.5 * 600 pulses are output from the encoder when the axis passing through the reduction gear rotates one turn. In this embodiment, the gear shaft has an inertia load of 11 cm in diameter and a weight of 100 g, and the reference trajectory indicates the value of the wheel in radians.

The input voltage v _a is scaled from -127 to +127 using an 8-bit DAC, the sampling period is 1ms, and the input value of the encoder is scaled in radians for each sampling period. Calculate and pass to motor drive input.

3 to 6 are response diagrams of the on-line PID learning tuner obtained through the embodiment of the present invention shown in FIG. 2.

In the embodiment, in the PID learning rule having the form of Equation 5, the constraints of the PID gains are set to 0≤K ₁ ≤50, 0≤K _P ≤100, and 0≤K _D ≤10.

Decided.

The three terms of the output vector C are composed of the matrix A of equation 9 after finding the {a ₀ ^* , b ₀ ^* , c ₀ ^* } so that the characteristic equation of the left-hand equation of Equation 8 satisfies the desired response. In this case, the matrix A and the matrix B of Equation 9 satisfy SSP conditions of Equation 10.

으로 주고, 전동기입력에 더해지는 외란으로 함수 10sin(πt)를 사용한다. 도면에서 나타난 응답을 보면 파라미터가 알려지지 않은 직류전동기에 대한 응답이었음에도, 우수한 위치추적성능과 부하변동이나 외란에 대한 강인성을 갖는다는 것을 알 수 있다.Also from Fig. 63 by the characteristic equation (s + 1) have ² (s + 100) = 0 when using the two calculated _{^{h 0 = 5.0x10 -3, h 1}} = 7.5x10 -3 h 2 = 4.975x10 -3 a It is a response of time. The response of the on-line PID learning tuner is shown by dividing the DC motor when there is no disturbance and when there is a fluctuating disturbance. The required trajectory is 1rad in the calculation form and sinusoidal form

Use the function 10sin (πt) as the disturbance added to the motor input. The response shown in the figure shows that although the parameter was a response to an unknown DC motor, it has excellent position tracking performance and robustness against load variation or disturbance.

In addition, the on-line PID learning tuner has a simple learning rule, which leads to fast calculation time. Even if a good algorithm takes a long time to compute, you will have to use a processor that is fast enough to actually implement it. The present invention has a simple learning rule for learning and compensating automatic tuning of PID control gain, dynamics, disturbance, etc. in a general PID controller and can be mounted on small microprocessors currently used for control.

According to the present invention as described above, by adjusting the PIA gain automatically according to the unique PID gain adjusting means according to the present invention, through the inverse model learning process, it is possible to reduce the effort to match the PID gains Even if there are fluctuations in system parameters, external loads, and disturbances that may occur due to aging of the system or changes in the environment, there is a special effect to obtain the desired location tracking performance.

Claims (1)

In the on-line PID learning tuner of the DC motor which controls the output θ of the DC motor to follow the reference input θ _d , Subtraction means for subtracting the output (θ) of the DC motor from the reference input (θ _d ) and outputting an error signal (e = θ _d −θ); Modeling formula of the DC motor Modeling formula of the DC motor

Equation (a, b, f, d are variables of DC motor)

The coefficients {a ₀ ^* , b ₀ ^* , c ₀ ^* } and PID gain {K _P ^* , K _I ^* , K _D ^* } to have this target response characteristic are a ₀ ^* = dK _D ^* + a, b Assume that ₀ ^* = dK _P ^* + b, c ₀ ^* = dK _I ^*

(here

ego,

And a state-space representation of the generated expression, i.e.

Output vector C is A ^T P + PA = -Q, C = B ^T P (where P, Q is obtained by a positive symmetric matrix), and y (t) is obtained from the state space representation, so that the output of the adjusting means is K (t) = pr _l [K (tT)] + Λ _l xy (t (Where pr (·) is projection and learning gain Λ _l is a positive limiting matrix with diagonal elements), and receives the error signal e of the subtraction means to control the PID control. Adjusting means for adjusting the control gain (K _D , K _P , K _l ) for; A first control voltage signal for controlling the DC motor by performing PID control according to the control gains K _D , K _P , K _l received by receiving the error signal e of the subtraction means.

ID control means for outputting; Modeling formula of the DC motor

Equation (a, b, f, d are variables of DC motor)

The coefficients {a ₀ ^* , b ₀ ^* , c ₀ ^* } and PID gain {K _P ^* , K _I ^* , K _D ^* } to have this target response characteristic are a ₀ ^* = dK _D ^* + a, b Assume that ₀ ^* = dK _P ^* + b, c ₀ ^* = dK _I ^*

Generates an expression, and the state of the generated expression

Is obtained by A ^T P + PA = -Q, C = B ^T P (where P and Q are positive symmetric matrices), and y (t) is obtained from the state-space representation. The output of the inverse model learning means is equal to v _l (t) = pr [v _l (tT)] + Λ ₂ y (t) (pr (·) is projection and Λ ₂ is constant as learning gain). Inverse model learning means determined by an equation and outputting a second control voltage signal v _l for receiving the error signal e of the subtracting means and controlling the DC motor through reverse model learning; And The second control voltage signal v _l of the learning means and the first control voltage signal v _fb of the PID control means are added to output the sum (v _a = v _fb + v _l ) to the DC motor. On-line PID learning tuner of the DC motor, characterized in that it comprises an addition means.

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