JP2001286170A - Two-freedom degree torque control method of two-inertia torsion shaft system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To realize torque control of a two-inertia torsion shaft system superior in both disturbance characteristic and instruction follow-up characteristic without using a torque meter. SOLUTION: In the torque control of a two-inertia torsion shaft system, a disturbance observer is provided in inside an electric motor to input motor torque and electric motor speed, estimated shaft torque is calculated with the disturbance observer, a PID controller is provided to input the deviation between the torque instruction and the estimated shaft torque, and a feed forward proportional compensator inputting the torque instruction is also provided, the sum of the output of the PID controller and the output of the feed forward proportional compensator takes a means for controlling the shaft torque as the motor torque, the disturbance suppression characteristic is improved by the PID controller, and the instruction follow-up characteristic is improved by the feed forward proportional compensator.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a two-degree-of-freedom torque control method for a two-inertia torsion shaft system in which a motor and a load are connected by a low-rigidity elastic shaft.

[0002]

2. Description of the Related Art Generally, in a motor drive system for an industrial plant or an industrial robot, if a motor and a load are connected by an elastic shaft having a low rigidity, a mechanical resonance system is generated, and a torsional vibration is generated. Sometimes. The outline will be described with reference to FIGS. FIG. 2 shows a two inertia torsion shaft system, 11 is an electric motor, 12 is a load, 13
Is an elastic axis. When the mechanical system is coupled by the elastic shaft 13 in this manner, a shaft torsional vibration mode exists in the mechanical system, and the mechanical system is a two-mass torsion shaft system. FIG. 3 is a block diagram showing the two-inertia torsion axis system of FIG. However, _{T m} is motor torque, _{T c} is the axial torque, _{T L} is the disturbance torque on the load side, omega _m is motor speed, omega _L is the load speed, _{K c} is the spring constant of the shaft, _{D c} is the viscosity coefficient of the shaft , _Jm is the motor inertia, J
_L is the load inertia. In FIG. 3, the open loop transfer function G _L (s) from the disturbance torque _TL to the shaft torque _Tc and the motor torque T _m are shown as torque transmission characteristics of the open loop system.
The open-loop transfer function G _m (s) from to the shaft torque _Tc is given by the equations (1) and (2) shown in Equation 1, respectively.

[0003]

(Equation 1)

Where s is a Laplace operator, ω ₀ and ζ ₀
Is a natural resonance frequency and a damping coefficient of the two-mass torsion axis system, and are expressed by Expressions (3) and (4) shown in Expression 2, respectively.

[0005]

(Equation 2)

In the two-inertia torsion axis system torque control, the control performance to be considered can be divided into a disturbance suppression characteristic (feedback characteristic) and a command following characteristic (target value following characteristic). First, from the disturbance suppression characteristics, in order to suppress the torsional vibration of the shaft due to the application of the disturbance torque _TL , the frequency response gain of the open-loop transfer function G _L (s) as shown by the dotted line (A) in FIG. It is necessary to suppress characteristic peaks. FIG. 4B shows a phase characteristic corresponding to the gain characteristic shown in FIG. On the other hand, from the command following characteristic, in order to make the shaft torque _Tc follow the torque command T ^* quickly and without vibration, a closed loop transfer function Ф ^* (s) from the torque command T ^* to the shaft torque _Tc is shown in FIG. It is necessary to have a desirable frequency response gain characteristic as shown by the solid line (f) in FIG. That is, from the 0 frequency to the resonance frequency ω ₀
The gain characteristic is always a constant 0
Must have a value close to dB. FIG. 5B shows a phase characteristic corresponding to the gain characteristic shown in FIG.

[0007]

In general, the viscosity coefficient D of a shaft
_c is a very small value, (4) As can be seen from the equation, since the damping factor zeta ₀ is small, the open-loop system of the frequency response gain characteristic | G _L (j [omega]) │ and | G _m (j [omega]) │ is look like the dotted dashed, respectively, in FIG 4 (a) (a) and FIG. 5 (a) (g), at the resonance frequency omega _0, resulting high peak in the gain characteristics, torsional resonance frequency omega ₀ Are likely to occur, and both the disturbance suppression characteristic and the command following characteristic are not good. Conventionally, PID (proportional-integral-derivative) control has been used for the torque control of such a two-inertia torsion shaft system. However, with the development of modern control theory in recent years, there has been a demand for shaping the frequency response of the control system. As a theory, H∞ control and control in combination with PID have been widely studied.
However, both the conventional PID control and the recent H∞ control described above often use the shaft torque detected by the torque meter for feedback control, and therefore, such as a system without a torque meter, is used. If the shaft torque cannot be detected, it is impossible to apply these control methods. Further, even if there is a torque meter, it is often impossible to use it for control due to the installation location or the influence of noise.

The present invention has been made in view of the above-mentioned problems of the prior art, and has as its object to improve a disturbance suppression characteristic and a command following characteristic without using a torque meter. As shown, the two-degree-of-freedom torque control of a two-inertia torsion shaft system is provided by using the shaft torque _Tce estimated by a disturbance observer including a filter for feedback control.

[0009]

According to a first aspect of the present invention, there is provided a two-inertia torsion shaft torque control for transmitting a driving torque from an electric motor to a load via an elastic shaft. without using the meter, the provided disturbance observer 3 that receives the motor torque T _m and motor speed omega _m, to calculate the estimated shaft torque T _ce with the disturbance observer, the torque command T ^* and the estimated shaft torque T _ce Deviation ΔT
Is provided, and a feed-forward proportional compensator 2 is provided with a torque command T ^* as an input, and the sum of the output of the PID controller and the output of the feed-forward proportional compensator is obtained. 2 constitutes a degree of freedom torque control system, a proportional gain of the PID controller from the disturbance suppression characteristic of the torque control system (K _p), integral gain to the sum and the motor torque T _m of a 2-mass torsional shafting 4 (K _i) , Differential gain (K _d ), approximate differential time constant (T _d ), and the gain (K _ff ) of the feedforward proportional compensator from the command following characteristics of the torque control system to determine the disturbance suppression characteristics and the command following of the control system. Improve properties.

[0010]

DESCRIPTION OF THE PREFERRED EMBODIMENTS In order to achieve the object of improving the above-described disturbance suppression characteristics and command follow-up characteristics without using a torque meter, the present invention uses a disturbance observer attached to an electric motor to obtain a shaft. An object of the present invention is to solve the problem by suppressing peaks in the gain characteristics of the frequency responses G _L (jω) and G _m (jω), which are the causes of torsional vibration, and providing a controller having good command follow-up characteristics. The details of these means will be described below with reference to the drawings. Figure 1 is a block diagram for describing the present invention, the disturbance observer 3 that receives the motor torque T _m and motor speed omega _m the motor side
And the disturbance observer estimates the shaft torque T
Calculate _ce . In order to improve the disturbance suppression characteristics, as shown in FIG. 1, a PID controller 1 is provided which _receives a deviation ΔT between a torque command T ^* and a shaft torque _Tce estimated by the disturbance observer as an input to follow the torque command. In order to improve the characteristics, a feedforward proportional compensator 2 having a torque command T ^* as an input is provided, and the sum of the output of the PID controller and the output of the feedforward proportional compensator is obtained. with the motor torque T _m of a system 4 constitute a two-degree-of-freedom torque control system of the two-inertia torsional axis system.

The shaft torque _Tce estimated by the disturbance observer attached to the motor can be expressed by the following equation (5).

[0012]

(Equation 3)

Where J _mn is a nominal value of the motor inertia J _m , T _f is a time constant of a disturbance observer filter, and s is a Laplace operator. Here, for the sake of simplicity, assuming that the nominal value J _mn of the motor inertia is the same as the motor inertia J _m (that is, J _mn = J _m ), the estimated shaft torque T _ce is further expressed by the following equation (6). It is obtained as in the formula.

[0014]

(Equation 4)

The transfer function F ₁ of the PID controller ₁
(S) can be expressed as in the following equation (7).

[0016]

(Equation 5)

Where K _p , K _i and K _d are P
ID controller proportional gain, integral gain and derivative gain, T
_d is an approximate differential time constant, and s is a Laplace operator.

Here, in order to easily design the controller parameters, the shaft viscosity coefficient is set to D _c = 0, and the disturbance observer 3 is provided with the nominal value J _mn of the motor inertia and the motor inertia J _m.
When the disturbance observer 3 and the PID controller 1 are applied to the two-inertia torsion axis system 4, the characteristic polynomial Δ (s) of the closed loop system is obtained as shown in the following equation (8).

[0019]

(Equation 6)

As can be seen from equation (8), if the filter time constant (T _f ) of the disturbance observer 3 and each constant (K _p , K _i , K _d , T _d ) of the PID controller 1 are determined, Each coefficient (a _i ) of the characteristic polynomial Δ (s) is determined, and the arrangement of the poles of the closed loop system is determined. In order to quickly estimate the shaft torque, the disturbance observer filter time constant _Tf must be increased. However, if _Tf is too small, the influence of noise tends to increase. Therefore, from a practical point of view, the filter time constant _{Tf is set} to _Tf ≧ 10 [ms]
ec]. The determination of the constants ( _Kp , _Ki , _Kd , _Td ) of the PID controller can be performed, for example, by a Manabe polynomial based on a coefficient diagram. For a detailed explanation of the coefficient projection and the Manabe polynomial, see Manabe's "Unified Interpretation of Classical Control, Optimal Control, and H∞ Control."
(Journal of the Society of Measurement and Control, October 1991, 30-10) and Mr. Manabe, "Design of a Two-Inertia Resonant System Controller Using Coefficient Diagrams"
And is publicly known. Here, the outline of the coefficient 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 Δ (s) is given to an n-order closed-loop system as in Expression (9) shown in Expression 7.

[0022]

(Equation 7)

The stability index γ _i indicating the stability and response speed of the control system and the equivalent time constant τ are shown in the following equation (10).
Equation (11) and Equation (11) are defined.

[0024]

(Equation 8)

In the coefficient map method, the standard form recommended by Mr. Manabe is represented by the following equation (12), which is called a Manabe polynomial.

[0026]

(Equation 9)

Hereinafter, a method of determining each constant of the PID controller by the Manabe polynomial of the coefficient diagram will be described in detail. For the closed-loop characteristic polynomial in equation (8),
The stability index γ _i (i = 1 to 4) and the equivalent time constant τ of the coefficient diagram are expressed by the following equation (13). However, in the case of the fifth-order system, γ _{4 of the} stability index is γ ₄ = 1.25.

[0028]

(Equation 10)

[0029] if decided in advance the disturbance observer filter time constant _{T f,} from (13) the gamma ₄ Section obtained as shown in Expression 11 to approximate differentiation time constant _{T d} (14) below.

[0030]

[Equation 11]

Using T _d determined by equation (14),
As a solution of the expression (13), each gain ( _Kp , _Ki , _Kd ) of the PID controller is determined by the expression (15) shown in Expression 12.

[0032]

(Equation 12)

However, p _ij and q _i are determined by the equation (16) shown in Expression 13 as a function of the mechanical constant of the two-mass torsion axis system.

[0034]

(Equation 13)

The PID designed by equations (15) and (16)
When the controller is applied to torque control of a two inertia torsion axis system,
As shown by the solid line (a) in FIG._L
From shaft torque T_cClosed-loop transfer function up to Ф_L(S)
The frequency response gain characteristic is the original open-loop gain characteristic (Fig.
Higher peaks are suppressed lower than (a) (dotted line (a)).
And the disturbance torque T_LShaft torsional vibration caused by
It can be seen that it can be suppressed. Also, the broken line in FIG.
As shown in FIG.^*From shaft torque T _c
Closed-loop transfer function up to Ф^*Frequency response gain of (s)
The peak is also kept low as seen in the characteristics,
, The torsional vibration can be suppressed. However,
The in characteristic is 0 to ω₀Greater than 0dB in low frequency band
And the desired frequency gain characteristic indicated by the solid line (f) in FIG.
Command follow-up characteristics are not good because there is a large difference between the command follow-up characteristics.

Therefore, in order to improve the command follow-up characteristic, a feedforward proportional compensator 2 is used together with the PID controller 1 as shown in FIG. 1 to constitute a two-degree-of-freedom torque control system. According to the control theory, since the feedforward compensation does not affect the disturbance suppression characteristics, the feedforward proportional compensator 2 may be designed only by improving the command following characteristics.

[0037] In the structure of the two-degree-of-freedom torque control system of FIG. 1, the torque command ^{T *} torque command from tracking error [Delta] T ^* (= ^{T *} -
The transfer function _{ｅ e} (s) up to T _c ) is obtained as in the following equation (17).

[0038]

[Equation 14]

Here, F ₁ (s) and F ₂ (s) are transfer functions of the PID controller 1 and the feedforward proportional compensator 2, respectively, and G _m (s) is the motor torque T _m to the shaft torque T _c. The open loop transfer function up to here,
When emphasizing only the improvement of the command following characteristic in the low frequency range of the control band, F ₂ (s) may be designed so that Ф _e (0) = 0. As a result, F ₂ (s) is obtained as a proportional compensator as shown in the following equation (18).

[0040]

(Equation 15)

When the two-degree-of-freedom torque control using the feedforward proportional compensator 2 in combination with the PID controller 1 is applied to the two-inertia torsion axis system shown in FIG. 1, the frequency response characteristic of a closed loop system expressing the command following characteristic is obtained. Ф ^* (jω) is shown in FIG.
(A), the gain characteristic curve | Ф ^* (jω) | takes a value close to 0 dB in the low frequency band of ₀ to ω ₀ , as shown by the solid line (f) in FIG. Since it is close to the desired frequency response gain characteristic, it can be seen that the command follow-up characteristic is well improved while maintaining good disturbance suppression characteristics.

As described above, according to the two-degree-of-freedom torque control method of the two-inertia torsion shaft system of the present invention, the torque control system is attached to the motor without using a torque meter as shown in FIG. Disturbance observer 3 and PID controller 1
(F ₁ (s)) and the feedforward proportional compensator 2 (F
₂ (s)) constitutes a two-degree-of-freedom control, and the PID controller 1
(F ₁ (s)) can be designed from the disturbance suppression characteristic, and the feedforward proportional compensator 2 (F ₂ (s)) can be designed from the command following characteristic.

Hereinafter, specific embodiments of the present invention will be further described with reference to numerical examples. The mechanical constants of a two-inertia torsion shaft system as a numerical example are as follows: Motor inertia J _m , load inertia J _L , shaft spring constant K _c , and shaft viscosity coefficient D _c are shown in Equation 16 below (1).
9) Each constant K of the two-degree-of-freedom torque control when the value of the equation is used.
An example of determining _p , _Ki , _Kd , _Td, and _Kff will be described.

[0044]

(Equation 16)

The two inertia torsion axis system having the above mechanical constant is as follows:
The frequency response characteristics G _L (s) and G _m (s) of the open-loop system expressing the disturbance suppression characteristic and the command following characteristic are shown in FIG.
As shown by dotted lines (a) and (sa) in FIG. 6, the gain characteristic has a peak at the resonance frequency ω ₀ (= 77.3 [rad / sec]).

In the torque control of the above two inertia torsion shaft system,
A disturbance observer 3 having a motor torque T _m and a motor speed ω _m as inputs is provided on the motor side, and J _mn and T _f are respectively set as parameters of the disturbance observer, J _mn = J _m =
If 0.0786 and T _f = 20 [msec] are set, the respective constants of the PID controller are T _d = 0.0185 and K _p = − from equations (14) and (15). 0.92
_07, K _{i = 5.9017,} a K d = -0.0075. When the above-described disturbance observer 3 and PID controller 1 are applied to a two-inertia torsion axis system torque control, a closed-loop system frequency response characteristic _{Ｌ L} (jω) expressing a disturbance suppression characteristic is shown in FIG.
As shown by the solid line (a) shown in FIG. 5, no peak is generated in the gain characteristic, and it is understood that the torsional vibration of the shaft can be suppressed and a good disturbance suppression characteristic can be obtained. However, the closed-loop frequency response characteristic （ ^* (jω) expressing the command following characteristic is
The gain characteristic in the low frequency band from ₀ to ω ₀ is significantly higher than 0 dB, and the command following characteristic of the shaft torque is not good, as shown by the broken line (S) shown in FIG.

In order to improve the command following characteristic of the one-degree-of-freedom torque control, the two-degree-of-freedom control of the present invention is applied to a torque control system, and feedforward proportional compensation for amplifying a torque command T ^* by a gain K _ff. vessel 2 Add the _(F 2 _(s)), the sum of the output of the feedforward proportional compensator 2 and output the PID controller 1 and the motor torque T _m of a said 2-mass torsional shafting 4. If calculated by the above equation (18), the value of the feedforward proportional gain K _ff is K _ff = 1.6379. When this two-degree-of-freedom compensator (combination of the PID controller 1 and the feedforward proportional compensator 2) is applied to the above-described two-inertia torsion axis system torque control, a closed-loop system frequency response characteristic Ф ^* ( jω) is as shown by the solid line (s) shown in FIG. 6, and the gain characteristic in the low frequency band from ₀ to ω ₀ is closer to 0 dB than the broken line (s) in FIG. 6, but is still larger than 0 dB. Therefore, in order to obtain better tracking characteristics, (18)
What is necessary is just to adjust the value calculated by the formula in the smaller direction. As an example, when the value 1.6379 is adjusted to 1.1, the gain characteristic of the frequency response becomes as shown by a broken line (c) in FIG. 6, indicating that the command following characteristic is further improved.

FIG. 7 shows a step-like torque command T ^* (1
0Nm) and step-like disturbance torque _TL (4Nm)
5 shows the time response of the shaft torque _{Tc to} the time. However, a dotted line (T), a dashed line (H), and a solid line (T) in the figure are an open-loop system, one-degree-of-freedom control (ie, when only the PID controller 1 is applied), and two-degree-of-freedom control (ie, , The case where a feedforward proportional compensator with F ₂ (s) = 1.1 is added to the one-degree-of-freedom control described above. As can be seen from the time response, the two-degree-of-freedom control achieves a better response to the rise of the torque command following while having the same disturbance suppressing characteristic as the one-degree-of-freedom controlling, and has the disturbance suppressing characteristic and the command following characteristic. It can be understood that the two-degree-of-freedom torque control can be performed in both cases.

[0049]

As described above, according to the invention of the present application, the torque control system of the two-inertia torsion shaft system includes the disturbance observer 3 attached to the motor side, the PID controller 1, and the feedforward proportional compensation. Disturbance control characteristics and command tracking characteristics by designing each constant of the PID controller from the disturbance suppression characteristics and designing the feed-forward proportional compensator gain from the command tracking characteristics. Can provide two-degree-of-freedom torque control of a good two-inertia torsion shaft system.

[Brief description of the drawings]

FIG. 1 is a block diagram for explaining the present invention.

FIG. 2 is a diagram showing a two inertia torsion shaft system.

FIG. 3 is a block diagram of a two inertia torsion axis system.

FIG. 4 is a diagram showing frequency response characteristics for explaining a disturbance suppression effect of the present invention.

FIG. 5 is a diagram showing a frequency response characteristic for explaining a command following effect of the present invention.

FIG. 6 is a specific example showing a frequency response characteristic for explaining a command following effect of the present invention.

FIG. 7 is a diagram showing a time response of the present invention.

[Explanation of symbols]

REFERENCE SIGNS LIST 1 PID controller 2 feedforward proportional compensator 3 disturbance observer 4 2 inertia torsion axis system having elastic axis 11 motor 12 load 13 elastic axis J _m motor inertia J _mn nominal value of motor inertia J _L load inertia Kc spring constant of axis D Viscosity coefficient of _c- axis T ^* Torque command _Tm Motor torque T _C- axis torque T _E- axis torque estimated value _TL Disturbance torque on load side ΔT Deviation between torque command and estimated value of shaft torque ΔT ^* Torque command and transmission of the deviation value omega _m motor speed omega _L load speed F ₁ (s) PID controller with the shaft torque function K _p PID controller proportional gain K _i PID controller integral gain K _d PID controller of differential gain T proportional transmission of _d PID controller of approximate differentiation time constant F ₂ (s) feedforward proportional compensator function K _ff feedforward proportional compensator In T _f disturbance observer filter time constant omega _{0 2} inertial torsion axis system natural resonance frequency zeta _{0 2} stability index of equivalent time constant gamma _i coefficients projection of the damping coefficient τ coefficient projection of the inertial torsional shafting .PHI ^{* (s)} Closed-loop transfer function from T ^* to _{Tc Ｌ L} (s) Closed-loop transfer function from _TL to _Tc Ф _e (s) Transfer function from T ^* to ΔT ^* G _m (s) From _Tm to _Tc Open-loop transfer function _GL (s) Open-loop transfer function from _TL to _Tc

Continued on front page F-term (reference) JJ30

Claims (1)

[Claims] In a two-inertia torsion axis system torque control for transmitting a driving torque from an electric motor to a load via an elastic shaft, a disturbance observer (3) having a motor torque T _m and an electric motor speed ω _m as inputs is provided. calculating the estimated shaft torque T _ce with the disturbance observer, PID controller which receives the difference ΔT between the estimated shaft torque T _ce a torque command T ^* and (1) is provided, and inputs the torque command T ^* , A sum of the output of the PID controller and the output of the feedforward proportional compensator is obtained, and the sum is used as the motor torque T of the two-inertia torsion shaft system (4). _m , a two-degree-of-freedom torque control system is constructed, and a proportional gain ( _Kp ), an integral gain ( _Ki ), and a differential gain ( _Ki ) of the PID controller are obtained from the disturbance suppression characteristics of the torque control system.
_d ), an approximate differential time constant (T _d ) is determined, and a gain (K _ff ) of the feedforward proportional compensator is determined from a command following characteristic of a torque control system. Torque control method.