JP7635515B2 - Inertia estimation device and motor control device - Google Patents

Description

The present invention relates to a technology for estimating the inertia of a mechanical drive system that is configured by connecting a mechanical load to a speed-controllable motor.

In order to perform good speed control of a motor connected to a mechanical load, it is necessary to know the inertia of the entire mechanical drive system including the motor and the mechanical load and to reflect this inertia in the speed control conditions.
When a mechanical load with unknown inertia is connected to a motor to drive it, the inertia is often estimated using information on the torque and speed during operation. In this case, it is possible to estimate the inertia offline using data within a certain time range, and online estimation using the recursive least squares method or the like has already been put to practical use.

When a motor drives a mechanical load, in addition to the acceleration torque due to inertia x acceleration, load torques such as Coulomb friction and viscous friction are generally generated. In order to prevent erroneous inertia estimation due to these load torques, for example, in Non-Patent Document 1, instead of using the relationship between the torque applied by the motor and the acceleration as is, online estimation is performed using the relationship between the torque change and the acceleration change from the previous time, thereby realizing inertia estimation that removes the influence of certain disturbances.
In relation to this, Patent Document 1 discloses an online estimation means that reduces an estimation gain during detection of vibration of a mechanical load, thereby reducing an inertia estimation error.

Furthermore, Non-Patent Document 2 discloses a means for estimating inertia together with Coulomb friction and viscous friction coefficient under the premise that the load torque is expressed by the sum of Coulomb friction of a sign function type independent of speed and viscous friction proportional to speed. In this document, a periodic signal with symmetric positive and negative values is given as a speed command, and as shown in Fig. 6 (Fig. 4 in Non-Patent Document 2), the signals τ _e , q ₀ , q ₀ ^' , and q ₁ based on the torque command u and the angular velocity ω are multiplied together to obtain the elements φ ₁₁ , φ ₁₃ , φ ₂₂ , φ ₂₃ , and φ ₃₃ of the matrix Φ and the elements v ₁ , v ₂ , and v ₃ of the vector V, and then a calculation Φ ^-1 V is performed to identify parameters including inertia.

Patent No. 3796261 ([0009] to [0013], etc.)

Yoichi Hori and Hiroaki Kamei, "High-Performance Control of Servo Motors Using Low-Precision Encoders - Instantaneous Speed Observer and Identification of Moment of Inertia -", Transactions of the Institute of Electrical Engineers of Japan, Vol. 114, No. 4 (1994), pp. 424-431 Ichiro Awaya et al., "Parameter Identification Method for Mechanical Motion Systems with Coulomb Friction", Transactions of the Japan Society of Mechanical Engineers (Series C), Vol. 59, No. 567 (1993), pp. 108-114

According to the methods described in Non-Patent Document 1 and Patent Document 1, even if the influence of a certain disturbance can be removed, when a load torque that is highly speed-dependent occurs, a non-negligible inertia estimation error occurs unless the acceleration torque is sufficiently large relative to the load torque.
Furthermore, according to the method described in Non-Patent Document 2, although there is an advantage in that other parameters are also estimated along with the inertia, it is premised on providing a speed command as a periodic signal, and in addition, when the load torque shows a non-linear dependency on the speed, there is a risk that correct values, including the inertia, will not be estimated.
Furthermore, while it is desirable to estimate inertia as accurately as possible, there are also cases where it is desired to estimate it in a short period of time. However, with conventional estimation methods, it was difficult to achieve both improved estimation accuracy and reduced estimation time.

Therefore, an object of the present invention is to provide an inertia estimation device that can correctly estimate the inertia of a mechanical drive system even when the load torque shows a nonlinear dependency on the speed, and a motor control device that controls a motor using the inertia estimation result.

In order to solve the above problem, the inertia estimation device according to claim 1 comprises:
An apparatus for estimating inertia of a mechanical drive system including a motor and a mechanical load driven by the motor, comprising:
a means for storing the speed of the motor as an estimated inertia start speed when a first condition is satisfied that an absolute value of the speed of the motor exceeds a predetermined threshold speed, and a second condition is satisfied that an elapsed time since the motor was started or the direction was reversed exceeds a predetermined threshold time;
a means for starting a numerical integration including at least the torque and acceleration of the motor in an integrand function when the first condition and the second condition are satisfied;
means for terminating the numerical integration when the absolute value of the speed of the motor is reduced and falls below the estimation start speed;
Equipped with
The inertia estimation value of the mechanical drive system is obtained from the calculation result of the numerical integration during the acceleration/deceleration period of the motor.

The inertia estimation device according to claim 2 is the inertia estimation device according to claim 1,
The inertia estimated value _J1 is expressed as _follows :
The calculation is performed by using the acceleration a(t) and torque T(t) of the motor at time t during the acceleration/deceleration period according to Equation A.
[Formula A]
J ₁ =∫T(t)a(t)dt/∫{a(t)} ² dt

The inertia estimation device according to claim 3 is the inertia estimation device according to claim 1,
The inertia estimated value _J1 is expressed as _follows :
The calculation is performed according to Equation B using the acceleration a(t), torque T(t), and speed v(t) of the motor at time t during the acceleration/deceleration period, and an estimated load torque T _Lest (v(t)) estimated based on a load model.
[Formula B]
J ₁ =∫{T(t)−T _Lest (v(t))}a(t)dt/∫{a(t)} ² dt

The inertia estimation device according to claim 4 is the inertia estimation device according to claim 2 or 3,
a means for determining the estimated inertia value _J1 for each acceleration/deceleration period of the motor and calculating a weight _W1 =∫{a(t)} ^2dt ;
a means for updating an estimated inertia average value _J2 and an integrated weight _W2 stored before the acceleration/deceleration period using the estimated inertia value _J1 and the weight _W1 , and outputting the updated estimated inertia average value _J2 as an estimated inertia result;
The present invention is characterized by comprising:

The inertia estimation device according to claim 5 is the inertia estimation device according to claim 4,
The inertia estimated average value _J2 and the integrated weight _W2 are updated each time the inertia estimated value _J1 and the weight _W1 are newly obtained by adding the current value _W1 to the previous value _W2 , and limiting the result by a predetermined upper limit value _Wmax as the current value _W2 , and then:
The inertia estimated average value _J2 is updated as a current value _J2 by using formula C.
[Formula C]
_J2 current value = _J2 previous value + ( _W1 current value / _W2 current value) x ( _J1 current value - _J2 previous value)

The inertia estimation device according to claim 6 is the inertia estimation device according to claim 4 or 5, characterized in that the inertia estimation average value _J2 and the integrated weight _W2 are stored in a non-volatile memory and can be initialized from the outside.

The motor control device according to claim 7 is characterized in that it controls the motor using an inertia estimation value obtained by the inertia estimation device described in any one of claims 1 to 6.

According to the present invention, the inertia of a mechanical drive system can be correctly estimated even when the load torque exhibits a nonlinear dependency on the speed .

1 is a block diagram showing a main part of a motor control device according to an embodiment of the present invention; FIG. 2 is a block diagram showing a first embodiment of the inertia estimation device in FIG. 1 . FIG. 3 is a block diagram of an integration start/end determination unit in FIG. 2 . FIG. 3 is a block diagram of an inertial estimation averaging unit in FIG. 2 . FIG. 2 is a block diagram showing a second embodiment of the inertia estimation device in FIG. 1 . FIG. 1 is an explanatory diagram showing a main part of Non-Patent Document 2 as a conventional technique.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
First, FIG. 1 shows a main part of a motor control device for controlling a motor connected to a mechanical load.
1, a speed control unit 100 generates torque T(t) so that motor speed v(t) coincides with a speed command, and this torque T(t) is applied to a motor and a mechanical load 200 to drive the motor. An inertia estimation device 300 receives at least the motor speed v(t), torque T(t), and a reset command as inputs and calculates an estimated inertia average value _J2 . Here, torque T(t) may be either the torque command or a torque estimate obtained by detecting a current passed through the motor to apply torque.
The estimated inertia average value _J2 output from the inertia estimation device 300 is used to adjust the speed control gain in the speed control section 100, for example, to control the speed and torque of the motor.

2 is a block diagram showing a first embodiment of the inertia estimation device 300. Here, the inertia estimation device is designated by the reference numeral 300A.
The motor speed v(t) is input to an integration start/end determination unit 302 and a differential calculation unit 303 via a low-pass filter 301 .
An integration start/end determination unit 302 determines the start and end of integration calculation using a function described later, and outputs integration start/end commands, as well as outputting update commands to a division means 309 and an inertia estimation averaging unit 310. A differential calculation unit 303 differentiates the motor speed v(t) to calculate acceleration a(t), which is input to multiplication means 304 and 307. The output of the multiplication means 304 is input to an integration means 305.
On the other hand, the torque T(t) is input to a multiplication means 307 via a low-pass filter 306 having the same time constant as the low-pass filter 301 , and the result of multiplication by the acceleration a(t) is input to an integration means 308 .
It should be noted that the low-pass filters 301 and 306 are intended to remove white noise and the like contained in the input signal, but are not essential components of the present invention.

The integrating means 305 calculates ∫{a(t)} ^2dt , and the integrating means 308 calculates ∫T(t)a(t)dt, and the outputs of these integrating means 305 and 308 are input to the dividing means 309. The output of the integrating means 305, ∫{a(t)} ^2dt , is input to the inertia estimation averaging unit 310 as a weight _W1 . The dividing means 309 calculates ∫T(t)a(t)dt/∫{a(t)} ^2dt to find an inertia estimation value _J1 , and this inertia estimation value _J1 is input to the inertia estimation averaging unit 310.

Here, the start and end timings of calculations in the integrating means 305, 308 follow the integration start/end commands output from the integration start/end determining section 302. Also, the division means 309 performs division according to the update command output from the integration start/end determining section 302, and outputs the latest inertia estimated value _J1 and weight _W1 as their current values to the inertia estimation averaging section 310, which performs an update calculation, described later, according to the update command every time the inertia estimated value _J1 and weight _W1 are input, and outputs the inertia estimation average value _J2 .

Next, the configuration of the integration start/end determination unit 302 will be described with reference to FIG.
First, the motor speed v(t) is input to an absolute value calculation unit 302a, where the speed absolute value |v(t)| is calculated. This speed absolute value |v(t)| is input to a zero speed determination unit 302b, where it is determined whether the motor is stopped or not, and the determination signal is sent to a delay unit 302c in the next stage. The zero speed determination unit 302b and the delay unit 302c are means for determining whether the time during which the motor is not stopped, that is, the time elapsed from the time when the motor is started or the direction is reversed, has exceeded a predetermined threshold time. When the threshold time has elapsed, a "High" level signal is input from the delay unit 302c to one end of a logical product calculation unit 302e. In FIG. 3, the output signal of the zero speed determination unit 302b is inverted and input to the delay unit 302c consisting of an on-delay circuit, but the output signal of the zero speed determination unit 302b may be input to the delay unit consisting of an off-delay circuit without being inverted.

Furthermore, the speed absolute value |v(t)| is compared with a threshold speed in a comparison unit 302d, and when the speed absolute value |v(t)| exceeds the threshold speed, a "High" level signal is input to the other end of a logical product calculation unit 302e. The output signal of the logical product calculation unit 302e is input to a start instruction unit 302f, and the start instruction unit 302f outputs an integration start instruction and an estimated start speed storage instruction.
Furthermore, the speed absolute value |v(t)| is input to a storage unit 302g for adjusting the speed control gain at a given time, and the estimation start speed detected in accordance with an estimation start speed storage command is input to a comparison unit 302. This comparison unit 302h outputs an integration end command and an update command when the speed absolute value |v(t)| falls below the estimation start speed during deceleration of the motor.

Next, the significance of configuring the inertia estimation device 300A in FIG. 2, and particularly the integration start/end determination unit 302 therein, as shown in FIG. 3, will be described.
The load torque generated when driving a mechanical load may show a nonlinear dependency on the speed, but in most cases, except for the vicinity of zero speed, it is uniquely determined with respect to the speed, regardless of whether it is accelerating or decelerating. Therefore, if the load torque T _L (v(t)) generated from time _t1 to time _t2 while the motor is being driven is multiplied by the acceleration dv/dt and integrated, we get
∫T _L (v(t))(dv/dt)dt=∫T _L (v)dv,
If we integrate so that the velocity at the integration start time and integration end time is the same, we get
_∫TL (v(t))(dv/dt)dt=0.

For this reason, when estimating inertia J based on the equation of motion: T(t) = J(dv/dt) + T _L (v(t)), the influence of the load torque T _L is removed by multiplying both sides of the equation of motion by a = dv/dt and integrating under the condition that the speeds during acceleration and deceleration are equal, and the inertia J is estimated by the following equation 1.
[Formula 1]
J=∫T(t)a(t)dt/∫{a(t)} ² dt
It should be noted that the above formula 1 is substantially the same as the above formula A.

When driving a mechanical load, a load torque with hysteresis often occurs near zero speed. To correctly estimate inertia using Equation 1, it is necessary to exclude the hysteresis region from the integration interval. One method for doing this is to set the condition for starting integration when the absolute value of the motor's speed exceeds a predetermined threshold speed. Furthermore, even mechanical systems that can be regarded as a one-inertia system during normal operation may behave in an oscillatory manner immediately after startup, and in order to correctly estimate inertia, it is desirable to start integration after this oscillation has decayed.

Therefore, in order to start the integration of the numerator and denominator in Equation 1, it is effective to set the conditions as follows: first, the absolute speed value of the motor exceeds the above-mentioned predetermined threshold speed; and second, the acceleration time after the motor leaves the zero speed state exceeds a predetermined threshold time. When these first and second conditions are satisfied, the integration is started and the absolute speed value at that time is stored as the estimation start speed. When the motor decelerates and the absolute speed value falls below the estimation start speed, the integration is terminated and the inertia _J1 during a series of acceleration and deceleration periods is determined.

In the integration start/end determination unit 302 in FIG. 3, the logical product calculation unit 302e determines whether the above first and second conditions are met and sends a signal to the start instruction unit 302f to generate an integration start command and an estimated start speed storage command, and the temporary storage unit 302g, comparison unit 302h, and end instruction unit 302i operate to output an integration end command and update commands for the inertia estimate value _J1 and weight _W1 (and the inertia estimate average value J2 _and integrated weight _W2 described below).

Next, the inertia estimation averaging unit 310 provided at the final stage in FIG. 2 and receiving the inertia estimation value _J1 and weight _W1 will be described with reference to FIG.
When the inertia is small and the acceleration is small, even if the above calculation method is used, it is possible that the inertia cannot be estimated with sufficient accuracy by only one acceleration/deceleration operation. When the same acceleration/deceleration operation is repeated, the estimation accuracy can be improved by applying a simple moving average to the inertia estimation value obtained for each acceleration/deceleration operation, but when trying to improve the estimation accuracy during a non-repeated operation, the reliability of each inertia estimation differs for each acceleration/deceleration operation. Therefore, in this embodiment, the reliability of the inertia estimation can be improved by using the inertia estimation averaging unit 310 shown in FIG. 4.
The configuration and operation of the inertial estimation averaging unit 310 will now be described.

That is, in addition to the estimated inertia value _J1 and weight _W1 for each acceleration/deceleration motion, an estimated inertia average value _J2 and integrated weight _W2 are defined, and every time _J1 and _W1 are newly obtained, _J2 and _W2 are updated as follows.
In Fig. 4, the _W2 previous value output from the previous value holding unit 310c is input to the adding means 310a via the switching unit 310d and added to the _W1 current value. The result of this addition is limited to a predetermined upper limit value (maximum value) _Wmax by the limiting unit 310b to obtain the _W2 current value. In addition, the division means 310e calculates the _W1 current value/ _W2 current value.
Meanwhile, the previous value of the estimated inertia average value _J2 output from the previous value holding unit 310i is input to a subtraction means 310f via a switching unit 310j and subtracted from the current value of _J1 to obtain (current value of _J1 -previous value of _J2 ).
Then, the multiplication means 310g calculates ( _W1 current value/ _W2 current value) x ( _J1 current value- _J2 previous value), and the resultant value and the previous value of _J2 are added by the addition means 310h, and the result is output as the current value of the inertia estimated average value _J2 .
The above process can be expressed by the following equation 2. Note that this equation 2 is substantially the same as the above-mentioned equation C.
[Formula 2]
_J2 current value = _J2 previous value + ( _W1 current value / _W2 current value) x ( _J1 current value - _J2 previous value)

4, _J2 and _W2 can be initialized by switching the switching units 310j and 310d to the "0" side in response to an external reset command. Specifically, _J2 and _W2 are initialized when the mechanical load is replaced, and thereafter, J2 and W2 are updated while being stored in the non-volatile memory. Then, when the system is restarted, the values _{of J2} and _W2 can be read from _the non-volatile memory before the system is operated.

The above-mentioned update process of J ₂ and W ₂ will be further explained.
In FIG. 4, even after the adding means 310a adds the _W1 current value to the _W2 previous value, if the sum remains below the upper limit value _Wmax , then Equation 3 holds.
[Formula 3]
_J2 current value = _J2 previous value + {( _W1 current value / ( _W2 previous value + _W1 current value)} × ( _J1 current value - _J2 previous value)
By rearranging the formula 3, the formula 4 is obtained.
[Formula 4]
_J2 current value = ( _J2 previous value x _W2 previous value + _J1 current value x _W1 current value) / ( _W2 previous value + _W1 current value)
This is equivalent to estimating inertia using all data from past acceleration/deceleration driving, and since the weight is reduced for acceleration/deceleration driving, which is more difficult to achieve accurate estimation, a highly reliable inertia estimation average value _J2 can be obtained.

However, if operation continues without introducing a limit by the upper limit value _Wmax , _W2 will eventually reach infinity, and _J2 will not be updated even if new acceleration or deceleration occurs. Therefore, by limiting _W2 to a predetermined upper limit value _Wmax using the limiting unit 310b, the latest operation result will be reflected in the estimated inertia average value _J2 even if the motor continues to operate.

Here, instead of defining weights as in this embodiment, for example,
[Formula 5]
_J2 current value = _J2 previous value + constant x ( _J1 current value - _J2 previous value) (0 < constant < 1)
The case where the calculation is performed as above will be compared with this embodiment.
Even when the current value of _J2 is calculated using Equation 5, the accuracy of the inertia estimation increases as the number of acceleration and deceleration movements increases. However, in this case, _J2 becomes smaller than the true value until the number of acceleration and deceleration movements reaches about (3/constant) (in other words, before it reaches about (3/constant)). In addition, in the case of this calculation, even if low acceleration or short-term acceleration and deceleration driving that is not suitable for inertia estimation is performed, the inertia estimation value is updated with the result, just like other movements.
In contrast, in this embodiment, by initializing _J2 and _W2 when the mechanical load is changed, it is possible to obtain estimated values close to the true value even when the number of acceleration/deceleration movements is small. In addition, since the estimated inertia average value J2 is updated with a weight proportional to ∫{a(t)} ^2dt , the estimated inertia average value _J2 is less likely to be disturbed for driving that is not suitable for inertia estimation.

5 shows an inertia estimation device 330B according to a second embodiment of the present invention. The main parts of the motor control device other than the inertia estimation device 330B are configured in the same manner as in FIG.
In this inertia estimation device 330B, assuming that the speed dependency T _Lest (v) of the load torque is known, a load torque estimation unit 311 estimates the load torque T _Lest (v(t)) based on the speed v(t) at each time t, inputs it to a subtraction means 312, and calculates an estimated inertia value _J1 using Equation 6.
[Formula 6]
J ₁ =∫{T(t)−T _Lest (v(t))}a(t)dt/∫{a(t)} ² dt
The above formula 6 is substantially the same as the above formula B.

By performing the calculation in this manner, the integrand function of the numerator becomes a value close to J{a(t)} ² , so that the calculation error can be reduced. T _Lest (v) may be, for example, of the form D×v+T _f ×sign(v), and the parameters D and T _f may be identified using the method disclosed in the above-mentioned non-patent document 2, or the like.

100: Speed control unit 200: Motor and mechanical load 300, 300A, 300B: Inertia estimation device 301, 306: Low-pass filter 302: Integration start/end determination unit 302a: Absolute value calculation unit 302b: Zero speed determination unit 302c: Delay unit 302d, 302h: Comparison unit 302e: Logical product calculation unit 302f: Start instruction unit 302g: Temporary storage unit 302i: End Completion instruction section 303: Differential calculation section 304, 307: Multiplication means 305, 308: Integration means 309: Division means 310: Inertia estimation averaging section 310a, 310h: Addition means 310b: Restriction Sections 310c, 310i: Previous value holding sections 310d, 310j: Switching section 310e: Division means 310f: Subtraction means 310g: Multiplication means 311: Load torque estimation section 312: Subtraction means

Claims (7)

An apparatus for estimating inertia of a mechanical drive system including a motor and a mechanical load driven by the motor, comprising:
a means for storing the speed of the motor as an estimated inertia start speed when a first condition is satisfied that an absolute value of the speed of the motor exceeds a predetermined threshold speed, and a second condition is satisfied that an elapsed time since the motor was started or the direction was reversed exceeds a predetermined threshold time;
a means for starting a numerical integration including at least the torque and acceleration of the motor in an integrand function when the first condition and the second condition are satisfied;
means for terminating the numerical integration when the absolute value of the speed of the motor is reduced and falls below the estimation start speed;
Equipped with
An inertia estimation device, comprising: a controller for estimating an inertia of the mechanical drive system from a result of the numerical integration during an acceleration/deceleration period of the motor; 2. The inertia estimation device according to claim 1,
The inertia estimated value _J1 is expressed as _follows :
3. An inertia estimation device comprising: an inertia estimation unit for performing calculations according to Equation A using the acceleration a(t) and torque T(t) of the motor at time t during the acceleration/deceleration period.
[Formula A]
J ₁ =∫T(t)a(t)dt/∫{a(t)} ² dt 2. The inertia estimation device according to claim 1,
The inertia estimated value _J1 is expressed as _follows :
An inertia estimation device characterized by performing calculations using equation B using the acceleration a(t), torque T(t), and speed v(t) of the motor at time t during the acceleration/deceleration period, and an estimated load torque T _Lest (v(t)) estimated based on a load model.
[Formula B]
J ₁ =∫{T(t)−T _Lest (v(t))}a(t)dt/∫{a(t)} ² dt 4. The inertia estimation device according to claim 2,
a means for determining the estimated inertia value _J1 for each acceleration/deceleration period of the motor and calculating a weight _W1 =∫{a(t)} ^2dt ;
a means for updating an estimated inertia average value _J2 and an integrated weight _W2 stored before the acceleration/deceleration period using the estimated inertia value _J1 and the weight _W1 , and outputting the updated estimated inertia average value _J2 as an estimated inertia result;
An inertia estimation device comprising: 5. The inertia estimation device according to claim 4,
The inertia estimated average value _J2 and the integrated weight _W2 are updated each time the inertia estimated value _J1 and the weight _W1 are newly obtained by adding the current value _W1 to the previous value _W2 , and limiting the result by a predetermined upper limit value _Wmax as the current value _W2 , and then:
The inertia estimation device is characterized in that the inertia estimation average value _J2 is updated as a _J2 current value by using formula C.
[Formula C]
_J2 current value = _J2 previous value + ( _W1 current value / _W2 current value) x ( _J1 current value - _J2 previous value) 6. The inertia estimation device according to claim 4 or 5,
The inertia estimation device, characterized in that the inertia estimation average value _J2 and the integration weight _W2 are stored in a non-volatile memory and can be initialized externally. A motor control device that controls the motor using an inertia estimation value obtained by the inertia estimation device described in any one of claims 1 to 6.

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