JP2002325471A - Pid speed control method in motor drive system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To realize stable speed control in a motor drive system, using only PID control, regardless of the existence of a nonlinear element, such as backlashes in the motor drive system. SOLUTION: When the speed control of a motor drive system is carried out by PID control, sufficient conditions for the stability of a control system are introduced, and a measure which can set respective constants of a PID controllers so as to satisfy the sufficient conditions for stability is taken. With such a constitution, the stable control can be realized, regardless of the existence of a nonlinear element, such as backlashes in the motor drive system.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a PID speed control method for a motor drive system.

[0002]

2. Description of the Related Art Generally, in a motor drive system of an industrial plant or an industrial robot, when a motor and a load machine are connected by a gear (or a coupling) and an elastic shaft, the motor drive system becomes a multi-inertia motor drive system, and a backlash occurs. Vibration and torsional vibration may occur, which may be a problem. The outline will be described with reference to FIGS. FIG. 7 is an external view showing a three-inertia motor drive system as a representative example of the motor drive system.
Denotes a motor, 12 denotes a load machine, 13 denotes a gear, and 14 denotes an elastic shaft. In FIG. 7, the gear 13 and the elastic shaft 14
When this mechanical system has three inertia consisting of motor inertia, gear inertia and load machine inertia,
A three-inertia motor drive system in which the gear backlash vibration mode and the shaft torsional vibration mode coexist. FIG. 7 is a block diagram showing a three-inertia motor drive system as shown in FIG. Where ω
_m is the motor speed, ω _g is the gear speed, ω _L is the load machine speed,
The T _m is motor torque, _{T g} is Giatoruku, _{T c} is the axial torque, _{T L} is the disturbance torque of the load-side, _{K g} is the spring constant of the gear, _{K c} is the spring constant of the shaft, _{D g} is the viscosity coefficient of the gear , D _c
The viscosity of the shaft, [delta] is a gear backlash width, J _m is the motor inertia, J _g is the gear inertia, J _L is the load machine inertia, s is a Laplace operator. In FIG. 8, as an open-loop transfer characteristic of the three-inertia motor drive system, an open-loop transfer function G _3m (s) from the motor torque T _m to the motor speed ω _m is given by the following equation (1). However, the viscosity coefficient D _g
And _Dc are very small values, and are omitted.

[0003]

(Equation 1)

Here, ω _h1 is a natural anti-resonance frequency corresponding to the shaft torsional vibration mode, ω _h2 is a natural anti-resonance frequency corresponding to the gear backlash vibration mode, ω ₀₁ is a natural resonance frequency corresponding to the shaft torsional vibration mode, ω ₀₂ is a natural resonance frequency corresponding to the gear backlash vibration mode, and is represented by the following equations (2) to (5), respectively.

[0005]

(Equation 2)

FIG. 9 is a characteristic diagram showing a frequency response of the open-loop transfer function G _3m (s). FIGS. 9A and 9B show a gain characteristic and a phase characteristic, respectively. FIG. 9 (a)
The two peaks in the gain characteristics correspond to the torsional vibration mode and the gear backlash vibration mode, respectively.
Also, the phase characteristic of FIG. 9B is ΔG _{3m in} all frequency bands.
(Jω) ≧ −90 °. Similarly, for a multi-inertia system with three or more inertia, ΔG _nm (jω) ≧ −9
There is a feature of 0 °. However, the subscript n means the number of inertia.

Here, conventional PID speed control designed with a two-inertia motor drive system will be described, and problems in applying to a three-inertia motor drive system will be described. In a motor drive system, the spring constant of the gear is generally much higher than the spring constant of the shaft (ie, K _g >> K _c ), so that the motor inertia (J
_m ) and the gear inertia (J _g ) are merged into the motor equivalent inertia (J
_mg = J _m + J _g ), the original three inertia motor drive systems (J _m , J _g , J _L ) are replaced with the two inertia motor drive systems (J
_It is common to design PID speed control as _mg , J _L ). FIG. 6 shows a PID controller 1 having a two-inertia motor drive system 3.
Is a block diagram applied to FIG. The open-loop transfer function G _2m (s) of the two-inertia motor drive system 3 from the motor torque T _m to the motor speed ω _m can be expressed by the following equation (6).

[0008]

[Equation 3]

Where s is the Laplace operator and J _mg is J
motor equivalent inertia is calculated in _{mg = J m + J g,} ω h and ω
₀ is the anti-resonance frequency and the resonance frequency of the two inertial motor drive system 3, respectively, and is expressed by the following equations (7) and (8).

[0010]

(Equation 4)

The transfer function F ₁ of the PID controller ₁
(S) can be expressed as in the following equation (9).

[0012]

(Equation 5)

Where K _p , K _i and K _d are the proportional gain, integral gain and differential gain of the PID controller 1, _Td is the time constant of differentiation, and s is the Laplace operator.

Here, in order to facilitate the analysis,
The transfer function F ₁ (s) of the PID controller 1 is represented by a quadratic equation such as the following equation (10).

[0015]

(Equation 6)

However, each constant (K _p ,
K _i , K _d , T _d ) are the respective coefficients (l ₀ ,
l ₁ , l ₂ , T) is obtained as shown in the following equation (11).

[0017]

(Equation 7)

Here, when the shaft viscosity coefficient is set to D _c = 0 and the PID controller 1 is applied to the two-inertia motor drive system 3 so that the controller parameters can be easily designed, the closed-loop system characteristic polynomial Δ (S) is obtained as in the following equation (12).

[0019]

(Equation 8)

Here, l ₂ = J _mg + l ₂ is an intermediate variable.

As can be seen from equation (12), the PID
Each coefficient (l ₀, L₁, L₂,
T), each coefficient (a) of the characteristic polynomial Δ (s) is determined.
_i) Is determined, and the pole arrangement of the closed loop system is determined.
And Each coefficient of the quadratic expression of the PID controller 1
(L₀, L₁, L₂, T), for example,
It can be performed by a numerical projection. Detailed explanation of CDM
"Manabe's unification of classical control, optimal control and H∞ control
Interpretation ”(Journal of the Society of Instrument and Control Engineers, October 1991, 30-10)
Mr. Manabe said, “Installation of a two-inertial-resonant-system controller using the coefficient diagram method.
Total "(January 1998, IEEJ Industrial Applications Section, 118-
D-1) and is publicly known. Where the coefficient
An outline of the projection will be briefly described.

The coefficient diagram method is a kind of algebraic design method on a polynomial ring, and is characterized in that a characteristic polynomial and a controller are simultaneously designed using a coefficient diagram with the appropriateness of the form as a measure. The various mathematical relationships used in the CDM are listed below. It is assumed that a characteristic polynomial △ (s) is given to an n-order closed-loop system as in the following equation (13).

[0023]

(Equation 9)

Also, a stability index γ _i indicating the stability of the control system.
And the equivalent time constant τ indicating the control system response speed are defined as in the following equations (14) and (15), respectively.

[0025]

(Equation 10)

In the coefficient map method, the standard form stability index recommended by Mr. Manabe is represented by the following equation (16).

[0027]

(Equation 11)

According to the coefficient diagram method, the sufficient and stable conditions of the control system are as follows (17)
Equation (18) is obtained.

[0029]

(Equation 12)

Hereinafter, the above-mentioned P
Each constant of the ID controller 1 is determined. For the closed-loop characteristic polynomial of the above equation (12), the stability index γ
_i (i = 1 to 4) and the equivalent time constant τ are expressed by the following equation (19).

[0031]

(Equation 13)

Γ ₁ γ ₂ γ ₃ γ ₄ , γ ₃ γ ₄ , γ ₁ , γ ₄
Therefore, the coefficients (l ₀ , l ₁ , l ~ ₂ , T) of the quadratic expression of the PID controller 1 have the relationship of the following expression (20).

[0033]

[Equation 14]

Here, k ₀ , k ₁ , and k ₂ are intermediate variables and are defined by the following equation (21).

[0035]

(Equation 15)

From the simultaneous equations of the above equation (20), PID
Each coefficient (l ₀, L₁, L ~₂,
Although it takes time to find T), the solution procedure is as follows:
First, l₀, And from the expression of the second term, l ~
₂From the third term equation₁And finally the expression in the first term
Find T. From equation (20), l₀Is shown below (2
2) It is obtained as a solution of a quadratic equation such as the equation.

[0037]

(Equation 16)

However, the coefficients a, b and c are as follows (2
3) It is defined as in the following equation.

[0039]

[Equation 17]

Since the solution l ₀ (= K _i ) of the equation (22) is a real number solution, the following equation (24) is obtained from b ² −4ac ≧ 0.
A limiting condition such as the equation is obtained.

[0041]

(Equation 18)

For example, the standard form stability index (γ₁= 2.5; γ
₂= γ₃= γ₄= 2.0), use the above equation (24)
Inertia ratio K_JIs K_JLimited to ≤3.0. On the other hand, K
_JIf> 3.0, the fourth term γ of the stability index₄The standard form
γ₄= 2.0 to non-standard form γ₄≧ (1 + K_J) / 2
Can be changed to There are two answers to the above equation (22).
But l₀(= K_i) Is the integral gain of PID control
So only positive values can be used. Also, l₁The answer is correct
There are two negative ones, as can be seen from the first term of equation (20)
So, l₁l^~ ₂The sign of the value of the time constant T
Since the time constant T can only use a positive value from the physical point of view,
l ₁The sign of the value of is l^~ ₂Must match the sign of the value of
No.

[0043] When the inertia ratio K _J large, regardless of the 2 inertial or 3 inertial motor drive system, applying the PID controller 1 designed in the standard form stability index, as described above, either may control characteristic obtained If used, but small inertia ratio _{K J,}
When the PID controller 1 designed with the standard stability index as described above is applied to speed control of a two-inertia motor drive system, FIG.
0, a good time response characteristic can be obtained. However, if a non-linear element of backlash exists in the motor drive system, and the two-inertia motor drive system becomes a three-inertia motor drive system, the backlash vibration as shown in FIG. Occurs, and stable control cannot be performed.

PID designed with the above standard form stability index
When the controller 1 is applied to a three-inertia motor drive system, the control system
Is stable if the loop frequency response (G_3m(J
ω) F ₁(Jω)) from the phase margin analysis. Inertia ratio
K_JIs large, P designed by the standard form stability index
ID controller 1 uses K_dPID system with differential gain> 0
Become an instrument. Such a PID controller is connected to a three-inertia motor drive.
When applied to a dynamic system, its loop frequency response (G_3m(J
ω) F₁(Jω)) means that there is a phase margin in all frequency bands
Thus, the control system is stable. However, the inertia ratio K_JSmall
In case, PID controller 1 designed by standard form stability index
Is K_d<0 differential gain and fast differential time constant T_dhave
It becomes a PID controller. Such a PID controller has three inertia
When applied to a motor drive system, its loop frequency response (G
_3m(Jω) F₁(Jω)) is high as shown in FIG.
Phase margin in frequency band is Ф_m3<0 °, that is,
Since there is no margin, the control system responds as shown in FIG.
The answer diverges and becomes unstable.

[0045]

As described above [0006] in general is a spring constant K _g gear much higher than the spring constant K _c of the shaft, i.e., K _g >> K _c, since a motor inertia (J _m) The gear inertia (J _g ) is _reduced to one equivalent inertia (J _mg = J _m + J
_g ) (hereinafter, J _mg is referred to as motor equivalent inertia), so that the original three inertia motor drive systems (J _m , J _g , J _L ) are replaced with the two inertia motor drive systems (J _mg , J _L ). Equivalently, it is common to design a speed control system. Conventionally, PID (proportional-integral-
Differential) control has been used, but with the recent development of modern control theory, resonance ratio control based on a disturbance observer, H や control as a theory relating to shaping of frequency response of a control system, and the like have been widely studied. However, the ratio between the load unit inertia and the motor equivalent inertia _{(K J = J L / J} mg, and later, the _{K J} is referred to as inertia ratio) when is small, conventional PID as described above
The control also requires a fast differential time constant (T _d ) while having a negative differential gain (K _d <0) in order to suppress the torsional vibration of the two inertial motor drive system. However, the realization of fast differentiation not only requires a high-speed controller, but also the presence of non-linear elements such as backlash in the motor drive system makes it possible for the two-inertia motor drive system to drive three or three or more inertia motors. When switching to the system, backlash vibration is induced, and the control system may become unstable. Similarly,
When the inertia ratio is small, a recent disturbance ratio control also requires a fast disturbance observer time constant (T _f ). Therefore, the two-inertia motor drive system is changed to a three-inertia or multi-inertia motor drive system with three or more inertia. Sometimes, backlash vibration is induced and the control system may become unstable.

The present invention has been made in view of the above-described problems of the prior art, and aims at achieving stable speed control without backlash vibration. Is applied only to the PID control, but a speed control method is adopted in which the constants of the PID control are determined so as to satisfy a sufficient condition for stability of the control system.

[0047]

In order to achieve the above object, there is provided a speed control method in a multi-inertia motor drive system according to claim 1, wherein a PID having a deviation between a speed command and a motor speed as an input is used. when the controller controls the speed of the motor drive _system, the _{K d + T d K p ≧} 0, K d + 8T d K i ≧ 0 , however, _{K d} derivative gain, _{T d} differential time constant, _{K p} proportional gain , _Ki integral gain. Is derived as a sufficient control system stability condition, and by setting each constant of the PID controller so as to satisfy the sufficient stability condition of the control system, even when the inertia ratio is small, the multi-inertia motor drive system includes PI that can achieve stable speed control regardless of the presence or absence of nonlinear elements such as backlash
This is a D speed control method.

[0048]

Figure 1 DETAILED DESCRIPTION OF THE INVENTION is a block diagram for explaining a PID speed control method of the present invention, in FIG. 1, and inputs the deviation △ omega between the speed command omega ^* and the motor speed omega _m the provided PID controller 1, the output of the PID controller 1 by a motor torque T _m of a said 3 inertial motor drive system 2 constitute a speed control system of the motor drive system.
The design of the constants of the PID controller 1 is similar to the conventional technique, it is performed by the equivalent of 3 inertial motor drive system 2 inertial motor drive system, the motor regardless of the magnitude of the inertia ratio K _J By deriving a sufficient stability condition for stabilizing the drive system and setting each constant of the PID controller 1 so as to satisfy the sufficient stability condition, two inertia due to the presence of a nonlinear element such as backlash in the motor drive system can be obtained. Even if the motor drive system is changed to a three-inertia motor drive system, the control system can be stabilized. In order to derive the sufficient stability condition, the transfer function F ₁ (s) of the PID controller 1 is rewritten as shown in (25) below.

[0049]

[Equation 19]

[0050] However, L (s) (= 1 / (T d s + 1))
Is a first-order lag element, and F ^~ (s) is a fully differential PID controller. K ^~ _p , K ^~ _i , and K ^~ _d are the proportional gain, integral gain, and derivative gain of the full differential PID controller F ^~ (s), respectively, and are defined as (26) shown below.

[0051]

(Equation 20)

From equation (25), the PID controller F₁(s) is
Fully differential PID controller F^~(s) (= K^~ _p+ K^~ _i/ s + K^~
_ds) and the first-order lag element L (s) (= 1 / (T_ds + 1))
It seems to be composed of a series. Then (1): complete
Total derivative gain K^~ _d> 0 (ie, K_d+ T_dK_p
≧ 0), frequency response F^~(jω) is as shown in FIG.
In addition, the phase characteristic changes from -90 ° to + 90 ° as ω increases.
Become On the other hand, the frequency response L (jω) of the first-order lag element
The phase characteristic changes from 0 ° to -90 ° as ω increases
And F^~The phase change rate (increase rate) of (jω) is the first-order lag element
Is higher than the absolute value of the phase change rate (decrease rate) of
d (∠F^~(jω)) / dω ≧ | d (∠L (jω)) / dω
|), PID controller F₁(jω) phase characteristic ∠F₁(J
ω) (= ∠F^~(jω) + ∠L (jω)) is the entire frequency band
∠F₁(Jω) ≧ −90 °, 3 inertia motor drive
Even if applied to the system,_nm(Jω) ≧ -90 °
The loop frequency response has a phase margin in all frequency bands.
(∠ (G_nm(Jω) F₁(Jω)) ≧ −180 °),
It can be expected that the control system will not become unstable. But,
(2): Complete differential gain K^~ _d<0 (ie, K_d+
T_dK_p<0), frequency response F^~(jω) is shown in FIG.
As shown in the figure, in the high frequency band, F^~(Jω)
Phase characteristics converge to -90 °. On the other hand, the first-order lag element
L (jω) also converges to -90 ° in the high frequency band
When applied to a three-inertia motor drive system,
The phase characteristic of the loop frequency response in several bands is ∠ (G_nm(J
ω) F₁(Jω)) |_{ω → ∞}→ -270 °, phase
There is a possibility that the margin may be lost, and the control system may become unstable.
There is.

Hereinafter, the stable and sufficient conditions of the multi-inertia motor drive system to which the PID control is applied are as follows: K _d + T _d K _p ≧ 0 and K _d +8
It derives that T _d K _i ≧ 0. Here, in order to simplify the derivation of the stable and sufficient conditions, F ^~ rate of change of phase ^{(jω) (d (∠F ~} (jω)) / dω) the absolute value of the phase change rate of the primary delay element ( Introduce a function f (ω) related to comparison with | d (∠L (jω)) / dω |). However, if f (ω) ≧ 0, the function f (ω) is d (∠F ^~ (jω)) /
dω ≧ | d (∠L (jω)) / dω | Then, (1) PID control of K _d ≧ 0 and (2) K _d <
The PID control of 0 is divided, and a sufficient condition for stabilizing the control system is found by analyzing the function f (ω). (25)
From the equation, the frequency expression of the transfer function F ^~ (jω) and L (jω)
Are expressed by the following equations (27) and (28), respectively.

[0054]

(Equation 21)

The phase characteristic of F ^~ (jω) and the phase characteristic of L (jω) are expressed by the following equations (29) and (30), respectively.

[0056]

(Equation 22)

[0057] d (arctanx) / dx = by the differentiation law of ^{1 / (1 + x 2)} , F ~ phase rate of change d (∠F ^~ (j of (jω)
ω)) / dω and the absolute value of the phase change rate of L (jω) | d (∠
L (jω)) / dω | are (31) and (3)
It is obtained as in equation 2).

[0058]

(Equation 23)

From the expressions (31) and (32), the function f
(Ω) is defined as in the following equation (33).

[0060]

(Equation 24)

Here, A, B and C are intermediate variables.
From equation (33), if f (ω) ≧ 0, then d (∠F ^~ (j
ω)) / dω ≧ | d (∠L (jω)) / dω |. Also, the proportional gain K _p > 0 and the integral gain K _i >
Since it is 0, the coefficient C becomes C> 0 in the equation (33).

(1) K_d≧ 0 PID control Inertia ratio K_JIs large, the differential gain K_d≧ 0
Therefore, the coefficient B becomes B> 0 in the equation (33). If the coefficient
A is A ≧ 0 (ie, K_d≤T_d ²K_i), The function
f (ω) is f (ω)> 0 in the entire frequency band, so that P
ID controller F₁(jω) phase characteristic ∠F₁(Jω) (= ∠
F^~(jω) + ∠L (jω)) is ∠F over the entire frequency band.
₁(Jω) ≧ −90 °. Therefore, three inertia motor drive
Even when applied to a dynamic system, the control system can be stabilized. one
On the other hand, if the coefficient A is A <0 (ie, K _d> T_d ²K_i)
, The function f (ω) is a fourth-order function with the maximum value at the vertex.
Frequency ω which becomes the object function and reaches its vertex_t1Is d
From (f (ω)) / dω = 0, the following equation (34) is obtained.
Required.

[0063]

(Equation 25)

[0064] (33) from the equation, f (0) = C> 0 , so, to the frequency band of the 0~ω _t1 function f (ω) is f (ω)
It can be seen that> 0. Further, at the frequency omega _t1, phase characteristic ∠F of the full differential PID controller F ^~ (s)
^~ (jω _t1 ) is expressed as ∠F ^~ (j
ω _t1 )> 0 °.

[0065]

(Equation 26)

From equation (31), when K _d ≧ 0, F
^~ (J [omega]) phase change rate d of ^{(∠F ~ (jω)) /} dω> 0 , and the words, since ∠F ^{~ (jω)} is a function of monotonically increasing, ∠ in the frequency band of omega> omega _t1 F ^~ (jω)> ∠F ^~ (j
ω _t1 )> 0 °. Therefore, FID of the PID controller
₁ phase characteristics of (j [omega]) is the ∠F ₁ (jω) ≧ -90 ° over the entire frequency band of 0~ω _t1 ~ + ∞. Therefore, in summary, even if the PID control with the differential gain K _d ≧ 0 is applied to the three-inertia motor drive system, the control system does not become unstable.

[0067] ₍₂₎ When the small _K d <0 PID control inertia ratio _{K J,} derivative gain _K and since ^d <0, _T d 2 to the coefficient A of the equation (33) _K i _-K d> 0
It becomes. If there is a condition of ^{_{K ~ d = K d + T}} d K p ≧ 0, coefficient A is A> 0 become. Furthermore, if (3)
If the coefficient B of the equation 3) is B ≧ 0, the function f (ω) ≧ 0 holds for all frequencies ω (that is, ∠F
₁ (jω) ≧ −90 °). Therefore, here, A> 0 and B
In the case of <0, it is considered that a condition that also satisfies the function f (ω) ≧ 0 should be derived. If A> 0 and B <0,
The function f (ω) is a fourth-order parabolic function with the minimum value at the vertex, and the frequency ω _t2 reaching the vertex is d (f (ω))
From / dω = 0, it is obtained as in the following equation (36).

[0068]

[Equation 27]

Function value f (ω _t2 ) as vertex (minimum value)
Is obtained as in the following equation (37).

[0070]

[Equation 28]

From equation (37), if K _d + 8T _d K _i ≧ 0, then the minimum value of the function f (ω) is f (ω _t2 ) ≧ 0, so the above assumption K _d + T _d K _p ≧ 0, K
_{When d} <0, the sufficient conditions for stability of the control system are as follows (3.
It is derived as in equation 8).

[0072]

(Equation 29)

If K _d ≧ 0, equation (38) always holds, so that (1) the PID control of K _d ≧ 0 and (2) K _d <
By combining PID control of 0, equation (38) can be set as a sufficient condition for the stability of the control system. Also, usually, 8K _i >
Since the case of K _p is almost considered to be using only the first term expression (38) below as a stable sufficient condition.

From the above, when the inertia ratio is large,
Since K _d ≧ 0, the sufficient stability condition of the equation (38) is always satisfied. However, when the inertia ratio is small, K _d <0
Therefore, it is understood that in order to satisfy the sufficient stability condition of the equation (38), it is necessary to design a PID control having a slow differential time constant T _d (that is, a large value T _d ). Therefore, hereinafter, to satisfy the sufficient stability condition of the equation (38),
By adjusting the stability index γ _i , the slow differential time constant T of the present invention is obtained.
Design a PID control with _d .

In order to design the PID control so as to satisfy the sufficient stability condition of the equation (38), it is first necessary to clarify the factors that determine the differential time constant _Td . When the total inertia _{J t} of the motor drive system 2 inertia is defined as _{J t = J mg + J L} , shown below _{T d} from (20) (39)
It can be expressed like an equation.

[0076]

[Equation 30]

[0077] by a different _{K J} and _{γ i, l 0, l 1} ,
The value of l ^~ ₂ changes, intuitively, is proportional and derivative time constant T _d is the inertia ratio K _J, as the inertia ratio K _J is small, the differential time constant T _d decreases, i.e., as described above , if small inertia ratio _{K J,} PID by standard form stability index
Designing the control requires a fast differential time constant _Td .
Further, T _d is inversely proportional with the stability index gamma _i, is set smaller than the standard form of gamma _i, it can be seen that it is possible to increase the T _d. However, from the equation (18) for the sufficient condition of instability of the control system and the equation (24) for the existence condition of the real number solution of l ₀ , the stability index γ _i is set as shown in the following equation (40). There are some restrictions.

[0078]

[Equation 31]

Therefore, for a two inertia motor drive system,
Due to the restriction of equation (40), γ _i smaller than the standard form stability index
Is set, and if the PID control having a slow differential time constant is designed so as to satisfy the equation (38) of a sufficiently stable condition, it can be understood that stable control can be performed even when applied to a three-inertia motor drive system. FIGS. 4 and 5 show a loop frequency response and a time response in which the PID control designed as described above is applied to a three-inertia motor drive system. Since the equation (38) of the sufficient stability condition is satisfied, the phase characteristic of the loop frequency response in FIG.
Since there is a phase margin even in a high frequency band, the control system is stable, and it can be seen that stable control without backlash oscillation in the time response of FIG. 5 was performed.

In summary, the motor drive of the present invention
The PID speed control method in the system is as follows.
As shown, the PID controller 1 (F₁(S)) only
And the PID controller 1 (F₁(S)) control system stability
K_d+ T_dK_p≧ 0 and K _d+ 8T_dK_iSatisfies ≧ 0
If designed so that the motor drive system has backlash etc.
Of the two inertia motor drive system due to the presence of
Stable without backlash vibration
Speed control is possible. Also, a multi-inertia motor drive with three or more inertia
The dynamic system has its open-loop transfer function G_nm(S) frequency
Response phase characteristic is ∠G in all frequency bands._nm(Jω) ≧ −
Since the angle is 90 °, the PI that satisfies the sufficient stability conditions of the present invention is
Apply D speed control to multi-inertia motor drive system with 3 or more inertia
However, stable speed control can be realized.

Hereinafter, the present invention will be described with reference to numerical examples.
The physical form will be further described. Three inertia motors as numerical examples
The mechanical constant of the drive system is the motor inertia J_m, Gear inertia J _g,
Load machine inertia J_L, Gear spring constant K_g, Shaft spring constant K_c,
Gear viscosity coefficient D_g, Shaft viscosity coefficient D_c, And gear back
PI when the lash width δ is the value of the following equation (41)
Each constant K of D controller 1_p, K_i, K_d, T_dIn the decision example of
explain about.

[0082]

(Equation 32)

[0083] 3 inertial motor drive system with the machine constants, Giabane constant is much greater than the axial spring constant, i.e., K _g >> K _c So motor inertia J _m and gear inertia J _g
And the motor inertia J _mg (= J _m + J _g ), a PID speed control system can be designed as a two inertia motor drive system as shown in FIG. K _J = J _L /
Since it is a two inertia motor drive system having a small inertia ratio of J _mg = 0.5, the standard form stability index (γ ₁ = 2.5; γ ₂ = γ ₃ = γ ₄ =
When the PID controller F ₁ (s) is designed according to (2.0), the PID controller ₁ satisfies K _d <0 as shown in the following equation (42).

[0084]

[Equation 33]

When the PID control having the value of the equation (42) is applied to the two-inertia motor drive system shown in FIG. 6, the time response becomes as shown in FIG. It turns out that was completed. However, in the presence of a gear backlash to the motor drive system, if the two-inertia motor drive system is changed to 3 inertial motor drive system, calculated by the value of equation (42), and _{K d + T d K p =} -0.4948 <0 Therefore, the sufficient condition for stabilizing the control system of the equation (38) is not satisfied. As shown in FIG. 12, the loop frequency response G _3m (jω) F ₁ (jω) has a phase margin of Ф _m3 <in the high frequency band.
Since it is 0 °, the speed control of the three inertia motor drive system becomes unstable. The time response is as shown in FIG. 11, and continuous backlash vibration occurs. Then, (3
8) The stability index γ _i of the coefficient projection is set to γ ₁ = 2.5, γ ₂ = 1.3333, γ ₃ = 2.0, so that the sufficient stability condition of the equation is satisfied.
When the non-standard form of γ ₄ = 1.25 is set, the PID controller F ₁
Each constant of (s) is obtained as in the following equation (43).

[0086]

(Equation 34)

K _d + T _d K _p = 0.1494> 0 and K _d + 8T
_{Since d} K _i = 1.7491> 0, the control system is stable.
As shown in FIG. 4, the loop frequency response G _3m (jω) F ₁ (jω) has a phase margin even in a high frequency band (Ф _m3 >
0 °), and the time response is as shown in FIG. 5, indicating that stable speed control without backlash vibration was achieved.

[0088]

As described above, according to the invention of the present application, the speed control system of the motor drive system is constituted only by the PID control, and K _d + T _d K _p ≧ 0 and K _d satisfying the sufficient condition of the control system stability.
By setting the constants of the PID control so that + 8T _d K _i ≧ 0 is satisfied, stable speed control can be realized regardless of the presence or absence of a non-linear element such as a backlash in the motor drive system. Is extremely useful.

[Brief description of the drawings]

FIG. 1 is a block diagram showing one embodiment of the present invention.

2 is a frequency response diagram of the PID controller having a complete differentiation (for derivative gain K ^~ _d> 0).

3 is a frequency response diagram of the PID controller having a complete differentiation (for derivative gain K ^~ _{d <0).}

FIG. 4 is a three-inertia motor drive system loop frequency response characteristic diagram to which PID control having a slow differential time constant is applied.

FIG. 5 is a time response characteristic diagram of a three-inertia motor drive system to which PID control having a slow differential time constant is applied.

FIG. 6 is a block diagram of a two-inertia motor drive system to which PID control is applied.

FIG. 7 is an external view of a three-inertia motor drive system.

FIG. 8 is a block diagram of a three inertia motor drive system.

FIG. 9 shows an open-loop transfer function G _{3m of a} three-inertia motor drive system.
It is a frequency response characteristic figure of (s).

FIG. 10 is a time response characteristic diagram of a two inertial motor drive system to which PID control having a fast differential time constant is applied.

FIG. 11 is a time response characteristic diagram of a three-inertia motor drive system to which PID control having a fast differential time constant is applied.

FIG. 12 is a diagram showing a loop frequency response characteristic of a three-inertia motor drive system to which PID control having a fast differential time constant is applied.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 PID controller 2 3 inertia motor drive system which has a gear and an elastic axis 3 2 inertia motor drive system which has an elastic axis 11 motor 12 load machine 13 gear 14 elastic axis J _m motor inertia J _g gear inertia J _mg motor equivalent inertia J _L load machine inertia K _g gear spring constant D _g deviation of the gear of the viscosity coefficient K _c axis of the spring constant D _c axis of the viscosity coefficient δ gear backlash width omega ^* speed command omega _m motor speed Δω speed command and the motor speed ω _g gear speed ω _L load machine speed T _m motor torque T _g gear torque T _c- axis torque _TL disturbance torque on the load machine side F ₁ (s) Transfer function of PID controller 1 K _p Proportional gain of PID controller 1 K _i PID controller 1 integral gain K _d PID controller 1 differential gain T _d differential time constant of the PID controller 1 F ^~ (s) completely derivative PID controller transfer function K ^~ _p complete Min PID controller proportional gain K ^~ i fully differential PID controller integral gain K ^~ _d fully differential PID controller of differential gain L (s) transfer function ∠F ^~ primary delay element (jω) F ^~ (jω) L (jω) Phase characteristic of L (jω) Relational function between the phase change rate of f (ω) F ^~ (jω) and the absolute value of the phase change rate of L (jω) ω _h 2 Inertia motor drive Natural anti-resonance frequency of the system ω ₀ natural resonance frequency of the two inertial motor drive system ω _h1 natural anti-resonance frequency of the three inertial motor drive system (corresponding to the torsional vibration mode) ω _h2 natural anti-resonance frequency of the three inertial motor drive system (backlash) Ω ₀₁ The natural resonance frequency of the three-inertia motor drive system (corresponding to the torsional vibration mode) ω ₀₂ The natural resonance frequency of the three-inertia motor drive system (corresponds to the backlash vibration mode) τ Equivalent time constant of coefficient diagram γ _i Person in charge Projection of stability index G _3m (s) 3 inertial motor drive system of the motor torque _{T m}
-Loop transfer function G _2m (s) from ω _m to motor speed ω _m Motor torque T _m of two inertia motor drive system
-Loop transfer function from _nm to motor speed ω _m G _nm (s) Open-loop transfer function from motor torque T _m to motor speed ω _m of a multi-inertia motor drive system with three or more inertia

Claims (1)

[Claims] In a speed control of a multi-inertia motor drive system that transmits a drive torque from a motor to a load machine via a backlash, an elastic shaft, or the like, a PID controller that receives a deviation between a speed command and a motor speed as an input. When performing the speed control of the motor drive system, the constants of the PID controller are adjusted to the sufficient and sufficient conditions of the control system K _d + T _d K _p ≧ 0 and K _d + 8T _d K _i ≧ 0 where K _d differentiation Gain, _Td derivative time constant, _Kp
Proportional gain, _Ki integral gain. A PID speed control method characterized by realizing stable speed control irrespective of the presence or absence of a non-linear element such as a gear backlash in the multi-inertia motor drive system by setting to satisfy the following.