JPS61138314A - Deadbeat control method of servo motor - Google Patents

Abstract

PURPOSE:To apply the deadbeat control directly to a servo motor control system using an actual electronic computer by setting feedback coefficients in consideration of the operation time of the electronic computer. CONSTITUTION:In the positioning digital control of the servo motor using the electronic computer, when a target value thetar, a position theta(n) and a speed theta'(n) at the sampling time, and a speed theta(n-1) preceding the speed at the speed sampling time are used to control a speed controlled variable (m) in accordance with an equation m=k{thetar-theta(n)}-Kvtheta'(n)-Ketheta'(n-1), feedback coefficients are obtained approximately in accordance with equations K=1/{1-Exp(-Ts/ Tm)}Ts, Kv={1+Exp(-Ts/Tm)}/{1-Exp(-Ts-Tm)}, and Ke=Tm/Ts where Ts is the sampling time and Tm is the time constant of the motor, thus performing the control in consideration of the dead time of the electronic computer.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a digital control method for positioning a servo motor in the shortest possible time using an electronic computer.

[Prior art]

The control method related to the finite settling of the minimum time is called deadbeat control, and conventionally, this control method has been mainly studied from a theoretical perspective. In the theoretical analysis, the servo model is idealized and the influence of dead time such as the calculation time of the microcomputer is not considered.

The details of the control will be explained below.

Deadbeat control is described in the literature (Strange translation: "Deadbeat control", Measurement and Control, Vo 1.22. A7.1983)
It can be determined from the relationship shown below. The discrete-time model of the control system is given by the following equation.

z (n+1) =Aar(n)-)-B! (n)
+・−・(11 When state feedback ω(n)=Fz(n) is applied to system+11, the following equation is obtained.

2(n+1)==(A soil BF):H(n)=Cz(n
) -------・(1)' The characteristic equation of this system is given by the following equation, where λ is the eigenvalue.

1λm-c1=o Song...(2) However, ■ is a unit matrix.

Deadbeat control corresponds to the case of having an eigenvalue of λ=0 and is reduced to the problem of finding a feedback coefficient giving λ-0 from equation (2).

FIG. 3 shows a positioning servo system using an ultrasonic distance sensor, and FIG. 4 shows a block diagram thereof. Further, FIG. 5 shows the input/output relationship when the calculation time is very small compared to the sampling time.

In Fig. 3, 1 is an ultrasonic distance sensor, 2 is a servo motor, 3 is an object, 4 is a signal processing circuit, 5 is a servo amplifier, 6 is a speed feedback gain, 7 is a feedback generator, and 8 is a microcomputer. .

When the mechanical time constant Tm of the system is very small compared to the sampling time Ts, the equation of state of the system is given by the following equation.

θ(n+1)=6)1-KnTs19(n+1)'
−...(31 At this time, formula +31. f4)
The characteristic equation of is given by the following equation.

λ and 1−KT s −((v )λ+(−(1−KT
s) KV-→XvTs)=O...-(5) Equation (5) is λ
In order to have a root of =0, the following relationship is required. However, K=K p K m K n.

KTs=1. KV=0”-・(
6) Using the feedback coefficient K given by the above relational expression, the step response of the servo system shown in FIG. 3 was determined and the results are shown in FIG. The relationship between the feedback coefficient of this result and the sampling time T8 is KT s=0.97
This almost satisfies the result of equation (6).

However, as shown in this result, the step response does not result in deadbeat control, but results in a large overshoot. This is because the influence of calculation time on an actual microcomputer is not considered.

[Problem that the invention seeks to solve]

In the conventional control method described above, the actual timing of the input/output relationship is different from that shown in FIG. 6 and is close to that shown in FIG. 7. This is because, in an actual microcomputer, the calculation time required to perform computer processing on input information and output it is so large that it cannot be ignored compared to the sampling time.

Therefore, conventional theoretical analysis results cannot be directly applied to actual cases.

[Means for solving problems]

The control method of the present invention solves the above-mentioned conventional problem by setting the feedback coefficient in consideration of the calculation time of the electronic computer.

Therefore, in the control method of the present invention, the position θ(n) and the speed θ(
n), and the previous velocity θ(
n-1), and set the speed control amount m to m=1((θr-θ
(n))-Kvθ(n)-Keθ(n-1) When performing control to give te, let the sampling time be T6 and the motor time constant be Tm, then the respective feedback coefficients are θ=Tm/TB. It is characterized by giving values in the vicinity.

〔Example〕

Embodiments of the present invention will be described below with reference to FIGS. 1 and 2. Note that descriptions of parts similar to those of the conventional example described above will be omitted.

First, as can be seen from Figure 7 above, it is affected. For this reason, feedback as an amount of feedback is also required. The equation of state at this time is u(n) = 71
Considering the term (n −1), it is given by the following equation.

θ(n+1)=Decoration)+KnTa Fortune))KnTm(1
−B7cp (−Tsβm))*(u(n)−θ(n)
) Keu(n)]'+(I Exp(7Ts/Tm))
u (n+1) = θ(n)
......(7) However, K p' =
KpKllll.

Here, α==Ezp(Ts/Tm), β=1−Ex
1/-Ts/Tm), the characteristic equation of equation (7) can be rearranged into the form of the following equation.

λ3−(αr−KVp+1)λ2+[(α−Kvβ)−
1- to β(Ts-Tmβ) 10Keβ]λ+(KTmβ'
−((eβ)=0 (8) Deadbeat control is to have only a root of λ=0, so that equation (8) is 7
Each feedback coefficient when the root of 'J,=O is given by the following equation.

An example in which a specific servo system is constructed using the feedback coefficient of equation (9) will be described below. Assuming that the sample and time 'f s = 50 m s, the time constant 'l'm used in the embodiment is = 20 m5, so each feedback coefficient is given by the following equation from equation (9).

Km21.8 (17B), Kv=-1,18,I
(e=0.4 (IQ) Using the above feedback coefficient, a specific feedback method is performed according to the procedure shown in FIG. 1.

This procedure is performed by the microcomputer 8 in FIG. 3, and feedback is provided to the servo amplifier 5 in the form of a command voltage E. To use the invention in the form of a command voltage E, the following modifications are necessary.

The second equation of equation (7) is expressed by the following equation using command voltage E.

arn+1)=θ(n)Exp(Ts/Tm)+Er(
m(1-Exp(-Ts/Tm))...aυ However, the command voltage E is expressed in the following form.

B=KP (19r-19(nD = shi(n)-!
-shi(n-1)Km Km -K(θr-θ(n■-J(n)-Keb(n-1)
−”7 Here, k4fr4C/KmKn, Kv−
Kv/I(m, gg'Yoe/r(m).

The feedback gains Km and Kn used in this embodiment are given by the following equations.

Km=50 Orpm/V, Kn=1.58-A
pm ・−・−・+132H, (Lυ, a3 is used to set the feedback coefficient of the command voltage E to [v, [e
can be determined.

As in the procedure shown in Fig. 1, position θ(n) and velocity θ
(The thin information is input to the microcomputer, the speed information &(n-1) stored in the microcomputer is also used, and the command voltage E is calculated using the feedback coefficient given by 2α. Sampling time Ts Deadbeat control can be performed by calculating the command voltage at each time and applying the command voltage to the servo amplifier.

In addition, if the speed of the servo motor completely follows the command voltage, there is no need to sample the speed information, and the past command voltage information can be stored in the microcomputer, and the following formula, which is a modification of the formula α, can be used. The command voltage can be given by

E(n) =K(θiθ(n)) −KvE(n-1)
-KeE(n-2) = (14) Find a finitely stable waveform by changing each coefficient in the vicinity of the feedback coefficient of H,
FIG. 2 shows a case that provides the most ideal response waveform. In this case, each feedback coefficient is =20,[v==1
．． 0, I (e = 0.4, and K and Kv are slightly lower values than the theoretical values shown in formula Oa. As shown in Figure 2, using the present invention, almost no overshoot phenomenon occurs. It can be seen that it is possible to realize an ideal step response and deadbeat control.

〔Effect of the invention〕

As explained above, the put-beat control method for a servo motor according to the present invention is a dead-beat control method that takes into account the dead time of calculation time of an electronic computer, so it can be directly applied to a servo motor control system using an actual microcomputer. can do.

[Brief explanation of drawings]

Fig. 1 is an explanatory diagram of the calculation procedure of the microcomputer when implementing the control method of the present invention, Fig. 2 is a step response diagram according to the control method of the present invention, and Fig. 3 is a positioning servo using an ultrasonic distance sensor. Schematic diagram of the system, Part 4
The figure is a block diagram of the servo system in Figure 3, Figure 5 is an ideal input/output timing diagram of the microcomputer in the servo system in Figure 3, and Figure 6 is the theoretical step of the servo system in Figure 3. The response diagram, FIG. 7, is a realistic input/output timing diagram of the servo system microcomputer shown in FIG. 1... Ultrasonic distance sensor, 2... Servo motor, 3... Target object, 4... Signal processing circuit, 5... Servo amplifier, 6...
...Velocity feedback gain, 7...Feedback gain, 8...Yaikuro computer. Figure 1

Claims (1)

[Claims] In positioning digital control of a servo motor using an electronic computer, a target value θr, a position θ(
n), the speed ■(n), and the previous speed ■(n-1) at the time of speed sampling to calculate the speed control amount m.
m=K(θr−θ(n))−Kv■(n)−Ke■(
n-1), where the sampling time is Ts and the motor time constant is Tm, the respective feedback coefficients are K=1/{[1-Exp(-Ts/Tm)]Ts}, K
v=[1+Exp(-Ts/Tm)]/[1-Exp(
-Ts/Tm)], a deadbeat control method for a servo motor characterized by giving a value near Tm/Ts.