JP7491190B2 - Two-inertia system simulator - Google Patents

Description

The present invention relates to a two-inertia system simulator that simulates an entire system comprising a first motor driven by a motor control device and a second motor connected to the first motor via a coupling unit so that the entire system behaves as a two-inertia system when viewed from the motor control device side, and more specifically, to technology that can be applied to the development and operation verification of motor control devices such as servo systems.

One of the issues when driving a mechanical load with a motor is the vibration problem of the motor and the mechanical load. In motor control devices such as servo amplifiers, in addition to adjusting the position/speed feedback control gain and the filter in the feedback control loop as a means of suppressing vibration, methods of generating and processing command values that do not induce vibration are often used.

When developing a motor control device with such a vibration suppression function, it is common to go through a process of performing simulations at an early stage and then performing actual verification. In actual verification of driving equipment including a motor and a mechanical load, there are cases where a mechanical load is actually driven and tested, and cases where an electronically controlled load machine is used for testing, with the latter being often used for verification involving steady-state load torque. When accelerating and decelerating a mechanical load, a torque proportional to inertia is also added, but to perform an acceleration/deceleration test of a mechanical load that can be considered a one-inertia system, in addition to accelerating and decelerating the actual mechanical load, it is also possible to use a device that simulates inertia.
Many simulation devices and methods for a single-inertia system have been proposed and put to practical use, such as the inertia simulator disclosed in Japanese Patent Application Laid-Open No. 2003-233691.

On the other hand, as a conventional technique for simulating a two-inertia system, for example, as disclosed in Patent Document 2, an electric inertia control device is applied to an engine power measurement system, and is provided in a dynamometer control unit that controls a dynamometer via an inverter to simulate mechanical inertia as electrical inertia. The axial torque of the dynamometer is detected and input to a two-inertia model in which a first electrical inertia and a second electrical inertia are connected by an electric spring, and a torque command is generated for the inverter to realize the behavior of the two-inertia model.

Patent No. 2884698 (Figure 1, etc.) Patent No. 4946495 ([0018] to [0020], Figs. 1 to 3, etc.)

The conventional technology disclosed in Patent Document 2 requires a shaft torque meter for detecting the shaft torque of the dynamometer and calculations using the detected shaft torque value, which results in a problem that the overall system configuration is relatively large-scale and expensive.
In addition, since the shaft torque meter itself has inertia, it is not easy to perform a proper test using a motor with a relatively small inertia that cannot be ignored.
If the shaft torque is not detected, it is necessary to calculate the torque command for the inverter based on the speed detection value or the differential value of the position detection value to simulate a two-inertia system, but this calculation involves a delay, which may cause the operation to become unstable. Even if it is possible to simulate a system that is less likely to become unstable and has large damping, it is difficult to reproduce the speed of damping.

The problem to be solved by the present invention is to provide a two-inertia system simulator that can simulate a two-inertia system stably and at low cost without the need for shaft torque detection means and calculation processing using the detected values as described in Patent Document 2.

In order to solve the above problem, the invention according to claim 1 comprises:
a dummy load control device that couples a rotary shaft of a second motor via a coupling unit to a rotary shaft of a first motor driven by a motor control device, and controls the second motor by receiving a speed signal v of the second motor or the first motor as an input so that the second motor outputs a torque T;
The simulated load control device includes:
the inertia of a portion assumed to move integrally with the rotation shaft of the first motor is defined as a first simulated inertia _J1 , and assuming that a portion exists downstream of the coupling unit that has a lower rigidity than the rotation shaft of the first motor and moves while weakly coupled to the first simulated inertia _J1 , the inertia of the portion is defined as a second simulated inertia _J2 , and the first simulated inertia _J1 , the second simulated inertia _J2 , an elastic constant K and a damping coefficient C between the first simulated inertia _J1 and the second simulated inertia _J2 , and an actual total inertia _Jr of the first motor, the second motor, and the coupling unit are included as setting items;
The torque T output by the second motor is
The setting items, a transfer function H(s) having a compensated damping coefficient C'=C+C _cmp , which is obtained by adding a compensating damping coefficient C _cmp for compensating for a phase delay caused by control simulating a two-inertia system to the damping coefficient C, as a constant, and a transfer function of a low-pass filter are given to the velocity signal v by calculation.

The invention according to claim 2 is the two-inertia system simulator according to claim 1,
The transfer function H(s) is given by the following formula A (s is the Laplace operator).

The invention according to claim 3 is the two-inertia system simulator according to claim 1 or 2,
The compensating damping coefficient C _cmp is given so that, at a gain crossover frequency ω _G where the absolute value of the product of the transfer function H(s) and the transfer function of the low-pass filter is 1, a phase ∠H(s) when the transfer function H(s) is calculated as a compensated damping coefficient C'=C _cmp is equal to a phase lag Δθ generated by a delay time from when the calculation by the low-pass filter and the calculation of the torque T are performed until when the speed changed due to the application of the torque T is reflected in the speed signal v.

The invention according to claim 4 provides the two-inertia system simulator according to any one of claims 1 to 3,
The resonant frequency of the two-inertia system to be simulated is limited to a frequency lower than the cutoff frequency of the low-pass filter.

The invention according to claim 5 provides a two-inertia system simulator according to any one of claims 1 to 4,
The speed signal v is provided as a detected speed value or an estimated speed value of the second motor or the first motor, or as a speed command value when the motor control device controls the speed of the first motor.

The present invention makes it possible to simulate a two-inertia system stably and at low cost without detecting the shaft torque, which can be useful for developing motor control devices such as servo systems and verifying their operation.

1 is a configuration diagram of a two-inertia system simulator according to a first embodiment of the present invention. FIG. 2 is a control block diagram when simulating a two-inertia system by the simulated load control device of FIG. 1 . FIG. 2 is a block diagram of a two-inertia system corresponding to Equation 2 in the first embodiment of the present invention. 1 is a flowchart showing a simulation procedure for a two-inertia system. FIG. 11 is a waveform diagram showing a simulation result when a two-inertia load having the parameters of Table 1 is driven under the motor control conditions of Table 2. FIG. 11 is a waveform diagram showing the actual measurement results when the motor control conditions in Table 2 are set in an actual motor control device and a simulated load set to simulate a two-inertia system having the parameters in Table 1 is driven. FIG. 5 is a configuration diagram of a two-inertia system simulator according to a second embodiment of the present invention. FIG. 11 is a configuration diagram of a two-inertia system simulator according to a third embodiment of the present invention. FIG. 9 is a control block diagram of the two-inertia system simulator shown in FIG. 8 . FIG. 11 is a configuration diagram of a two-inertia system simulator according to a fourth embodiment of the present invention.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
Fig. 1 is a configuration diagram of a two-inertia system simulator according to a first embodiment of the present invention. In Fig. 1, the rotating shaft of a first motor _M1 and the rotating shaft of a second motor _M2 driven by a motor control device 10 are connected by a highly rigid coupling unit 20, and the total inertia of these motors _M1 , _M2 and the coupling unit 20 can be regarded as _Jr.
Here, the inertia of the part assumed to move integrally with the rotating shaft of the first motor _M1 is defined as a first simulated inertia (motor-side inertia) _J1 , and it is assumed that there exists a part downstream of the coupling portion 20 that has a lower rigidity than the rotating shaft of the first motor _M1 and moves weakly coupled with the first simulated inertia _J1 , and the inertia of that part is defined as a second simulated inertia (load-side inertia) _J2 .

The dummy load control device 30 calculates a torque command T _* based on a speed signal of the second motor M2, for example, a detected speed value of the second motor _M2 , so that the operation is equivalent to driving a two-inertia system when viewed from the motor control device 10 ^side which directly drives the first motor _M1 , and supplies a current corresponding to this torque command T ^* to the second motor _M2 .

2 is a control block diagram for simulating a two-inertia system by the dummy load control device 30. This control block is composed of a transfer function (1/Jrs) for obtaining a deviation between the torque _T1 generated by the first motor _M1 and the torque (torque for simulating a two-inertia system) T generated by the second motor _M2 by an adding/subtracting means 31a and obtaining a speed signal v such as a detected speed value of the second motor _M2 from the deviation thus obtained, a low-pass filter LPF to which the speed signal v is input, and an open-loop transfer function H ₍ s) for converting the output of the low-pass filter LPF into the torque T generated by the second motor _M2 .

That is, the dummy load control device 30 calculates the torque T output by the second motor _M2 so that the relationship between the torque _T1 and the speed due to the first motor _M1 becomes equal to the relationship between the torque and the speed in the two-inertia system to be simulated, and feedback controls this torque T with respect to the torque _T1 due to the motor _M1 .
Here, the order of the low-pass filter LPF to which the speed signal v is input may be first order when the speed of the second motor _M2 is directly detected, but it must be second order or higher when the detected speed value is substituted by the numerical differentiation of the detected position value. In the following, a case will be described in which a second order low-pass filter LPF is used to obtain the detected speed value by numerically differentiating the detected position value of the second motor _M2 , and in particular, the transfer function is calculated in the form of 1/(τ _f s) ^2. Here, τ _f is the time constant of the filter, and s is the Laplace operator.

数式１において、第１の模擬慣性Ｊ_１は、前述した全慣性Ｊ_ｒに対してＪ_１≧Ｊ_ｒという関係にあるものとする。また、Ｋは第１の模擬慣性Ｊ_１と第２の模擬慣性Ｊ_２との間の弾性定数、Ｃは同じく減衰係数である。 First, the transfer function H(s) in FIG.

In the formula 1, the first simulated inertia _J1 has a relationship of _J1 ≧ _Jr with respect to the total inertia _Jr described above. Furthermore, K is an elastic constant between the first simulated inertia _J1 and the second simulated inertia _J2 , and C is a damping coefficient.

（ただし、Ｊ_μ＝Ｊ_１Ｊ_２／（Ｊ_１＋Ｊ_２） とした。） Assuming that the effects of the low-pass filter LPF and dead time can be ignored, the feedback control shown in FIG. 2 causes the speed signal v of the second motor _M2 to change with respect to the torque _T1 of the first motor _M1 as shown in Equation 2.

(where J _μ = J ₁ J ₂ /( J ₁ + J ₂ ).)

The above formula 2 is equal to an equation expressing the speed signal v of the second motor M2 when a torque _T1 is applied to a two-inertia system consisting of a first simulated inertia _J1 and a second simulated inertia _J2 coupled by an elastic constant K and a damping coefficient _C , as shown in the block diagram of Fig. 3. Therefore, in an ideal control system without dead time delay, etc., a desired two-inertia system can be simulated by having the second motor _M2 output a torque T obtained by calculating H(s) for the speed signal v, for example, the detected speed value.

Next, a case in which the influence of the low pass filter LPF and the dead time is taken into consideration will be described.
2, the phase lag at frequency _ω , which is the sum of the low pass filter LPF and the dead time _τd , is _2arctanωτf + _ωτd . When the damping coefficient C is close to zero, the two-inertia resonant system is originally at the stability limit, so that the two-inertia system cannot be stably simulated by feedback control including a phase lag.
Therefore, the damping coefficient C is increased to compensate for the phase delay caused by the feedback control, a compensated damping coefficient C' is obtained, and this damping coefficient C' is applied to the transfer function H(s) for feedback control, thereby stabilizing the two-inertia system simulation.
The specific method will be described below.

At the beginning,
Let J _a = J ₂ (J ₁ - J _r )/(J ₁ + J ₂ - J _r ), ω ₁ = √(K/J ₂ ), and ω ₂ = √(K/J _a ).
When the damping coefficient C is close to 0, H(jω) moves from −∞ to 0 in the range of ω ₁ < ω < ω _2. At the angular frequency ω = ω _G (gain crossover frequency) where the absolute value of the product of the transfer function H(s) and the transfer function of the low-pass filter LPF is 1, Equation 3 holds when the Cs term in Equation 1 is ignored.

数式４を用いて数式３を整理すると、数式５となる。

Next, ω _z , η, q, r, and x are defined by the following formula 4: where ω _z is the anti-resonance frequency of the simulated two-inertia system.

When Equation 3 is rearranged using Equation 4, Equation 5 is obtained.

As a result, x defined in Equation 4 can be obtained by Equation 6.

Further, the gain crossover frequency ω _G can be obtained as ω _G =ω _z √x from the definition of x in Equation 4 and Equation 6.
At this gain crossover frequency _ωG , a compensating damping coefficient C _cmp is introduced as a damping coefficient in the transfer function H(s) so as to compensate for a phase delay caused by the low-pass filter LPF or dead time. When simulating a two-inertia system having a damping coefficient C, a compensated damping coefficient C' obtained by increasing the damping coefficient C by C' = C + C _cmp is given to the open loop transfer function H(s).
That is, as in Formula A recited in claim 2, the torque T output by the second motor M2 is calculated by performing feedback control using a transfer function H(s) to which a compensated damping coefficient C' = C + _{C cmp} is applied, instead of the damping coefficient C in Formula 1.

The compensating damping coefficient C _cmp can be obtained as a solution to the following equation 7.

This compensating damping coefficient C _cmp can be found by numerical calculation, but since a small phase delay is the issue here, it can be found using the approximation formula of Equation 8.

Next, FIG. 4 is a flow chart showing the procedure of the above-mentioned two-inertia simulation.
First, the parameters _J1 , _J2 , K, and C of the two-inertia system to be simulated, and the total inertia _Jr including the motors _M1 and _M2 and the coupling unit 20 are set (step S1). Next, the gain crossover frequency _ωG at which the absolute value of the product of the transfer function H(s) and the transfer function of the low-pass filter LPF becomes 1 is calculated (step S2).
Then, a compensating damping coefficient C _cmp necessary for compensating for the phase delay at ω = ω _G is calculated (step S3), a compensated damping coefficient C' where C' = C + C _cmp is used to determine a transfer function H(s) (step S4), and feedback control is performed using this transfer function H(s) (step S5).
This makes it possible to stably simulate a two-inertia system without the need for shaft torque detection as in Patent Document 2. However, it is desirable to limit the resonance frequency of the two-inertia system to be simulated to a frequency lower than the cutoff frequency of the low-pass filter LPF.

In the first embodiment, the transfer function of the low-pass filter LPF is calculated as 1/(τ _f s) ^2. However, this form is not essential. A phase delay at an open-loop gain of 1 can be estimated according to the transfer function of the low-pass filter, a compensating damping coefficient C _cmp for compensating for this phase delay can be calculated, and this can be added to the damping coefficient C of the two-inertia system to be simulated to obtain a compensated damping coefficient C', which can then be applied to the open-loop transfer function H(s).
In the first embodiment, the speed detection value of the second motor _M2 is input to the dummy load control device 30. However, since the motors _M1 and _M2 are regarded as a single inertial body, the speed detection value of the first motor _M1 may be input instead of the speed detection value of the second motor M2, provided that this does not impede the operation of the motor control device ₁₀ which directly drives the first motor _M1 .

Next, the results of an experiment simulating a two-inertia system according to this embodiment will be described.
In FIG. 1, motors M ₁ and M ₂ , each of which has an inertia _Jm of 1.35×10 ⁻⁵ [kgm ² ], were coupled by a coupling portion 20 with an inertia of 1.84×10 ⁻⁵ [kgm ² ], and the following experiment was performed with a total inertia _Jr of 4.54×10 ⁻⁵ [kgm ² ].
As simulated load control conditions for the two-inertia system to be simulated, which are set in the simulated load control device 30, parameters for conditions 1 to 3 are prepared as shown in Table 1. Note that the first inertia value and the second inertia value in Table 1 are ratios ( _J1 / _Jm , _J2 / _Jm ) to the inertia _Jm (=1.35× ^10-5 [ ^kgm2 ]) of the motors _M1 and _M2 alone, respectively.

The transfer function of the low-pass filter LPF in the simulated load control is 1/(1+τ _f s) ² , and the filter constant τ _f =0.8 [ms]. The dead time delay in the control is estimated to be 0.2 [ms]. Using these and each parameter in Table 1, the compensation damping coefficient C _cmp is calculated by the above-mentioned formula 8, and the open loop transfer function H(s) is determined using the compensated damping coefficient C' where C' = C + C _cmp , and the simulated load control is implemented by the calculation shown in Figure 2.

In addition, after setting each parameter as shown in Table 1, motor _M1 was operated with trapezoidal acceleration/deceleration under the motor control conditions shown in Table 2, and the speed and torque of motor _M1 were monitored, thereby confirming that the load as viewed from the motor control device 10 behaves as the two-inertia system that was being simulated.
The feedback control is a proportional control of position that includes a minor loop of speed control using proportional-integral control. In order to confirm that the motor behaves as a two-inertia system, the motor control conditions are deliberately set to inappropriate position control gain and proportional control gain (which tend to cause vibration at the anti-resonance frequency).

Fig. 5 shows the simulation results (speed and torque waveforms of motor _M1 ) under each condition when a two-inertia load having the parameters shown in Table 1 is driven under the motor control conditions in Table 2. As the control gains given are too high for the conditions of driving these two-inertia loads, as is clear from Fig. 5, the simulation results show significant vibration in the torque waveform.

Next, the control conditions shown in Table 2 were set in an actual motor control device, and a simulated load set to simulate a two-inertia system with the parameters shown in Table 1 was driven by the motor control device. The actual measurement results are shown in Figure 6. As can be seen from Figure 6, the actual measurement results when the simulated load was driven were almost the same as the simulation results in Figure 5, in which the two-inertia load itself was driven, and it was confirmed that this embodiment can accurately simulate a two-inertia system.

Next, FIG. 7 is a configuration diagram of a two-inertia system simulator according to a second embodiment of the present invention.
The second embodiment differs from the first embodiment in that the speed signal v input to the simulated load control device 30 is obtained from a motor control device 10 that drives a motor _M1 . Since the motors _M1 and _M2 are coupled by a coupling unit 20 and move integrally, even if the speed detection value of the motor _M1 is obtained from the motor control device 10 instead of the speed detection value of the motor _M2 , a two-inertia system can be simulated in the same manner as in the first embodiment.
When the speed of motor _M1 is controlled by motor control device 10, the speed command value of motor _M1 may be used instead of the detected speed value of motor _M1 as speed signal v. If the speed control gain is high and the actual speed value of motor _M1 is close to the speed command value, the torque _T1 commanded by motor control device 10 to achieve that speed will be equal to the torque for driving the two-inertia system to be simulated, which is equivalent to simulating a two-inertia system.

Fig. 8 is a block diagram of a two-inertia system simulator according to a third embodiment of the present invention. Fig. 9 is a control block diagram of a simulated load controller 30, in which 32 denotes a speed observer, G _ob denotes an observer gain, and 31 a, 31 b, and 31 c denote addition and subtraction means.
In the third embodiment, as shown in FIG. 9, the torque _T1 generated by the motor _M1 and the detected speed value of the motor _M2 are input to a speed observer 32 having an observer gain G _ob to calculate an estimated speed value of the motor _M2 , and control is performed so that the motor _M2 outputs a torque T based on this estimated speed value.
Although the control of this embodiment is slightly more complicated than that of the first or second embodiment, the high frequency noise contained in the estimated speed value is smaller than the high frequency noise contained in the detected speed value, so that the time constant _τf of the low pass filter LPF can be reduced.

Further, FIG. 10 is a configuration diagram of a two-inertia system simulator according to a fourth embodiment of the present invention.
The fourth embodiment differs from the third embodiment in that the detected speed value of motor _M1 is input to the dummy load control device 30 together with torque _T1 instead of the detected speed value of motor _M2 , but the subsequent control is the same as in the third embodiment.
In the fourth embodiment, a means for transmitting the detected speed value of the motor _M1 to the dummy load control device 30 is required, but even if the speed of the motor _M2 cannot be detected directly, it is possible to simulate a two-inertia system.

The present invention can be used in the development and verification of motor control devices and drive equipment, including servo systems, and can also be used as an educational and training tool for those who use these devices to adjust drive systems.

10: Motor control device 20: Coupling section 30: Dummy load control devices 31a to 31c: Addition and subtraction means 32: Speed observer M ₁ : First motor M ₂ : Second motor LPF: Low pass filter

Claims (5)

a dummy load control device that couples a rotary shaft of a second motor via a coupling unit to a rotary shaft of a first motor driven by a motor control device, and controls the second motor by receiving a speed signal v of the second motor or the first motor as an input so that the second motor outputs a torque T;
The simulated load control device includes:
the inertia of a portion assumed to move integrally with the rotation shaft of the first motor is defined as a first simulated inertia _J1 , and assuming that a portion exists downstream of the coupling unit that has a lower rigidity than the rotation shaft of the first motor and moves while weakly coupled to the first simulated inertia _J1 , the inertia of the portion is defined as a second simulated inertia _J2 , and the first simulated inertia _J1 , the second simulated inertia _J2 , an elastic constant K and a damping coefficient C between the first simulated inertia _J1 and the second simulated inertia _J2 , and an actual total inertia _Jr of the first motor, the second motor, and the coupling unit are included as setting items;
The torque T output by the second motor is
a transfer function H(s) having as a constant a compensated damping coefficient C'=C+C _cmp obtained by adding a compensating damping coefficient C _cmp for compensating for a phase delay caused by control simulating a two-inertia system to the damping coefficient C, and a transfer function of a low-pass filter, which are applied to the velocity signal v by calculation; In the two-inertia system simulator according to claim 1,
A two-inertia system simulator, characterized in that the transfer function H(s) is given by the following formula A (s is the Laplace operator).

In the two-inertia system simulator according to claim 1 or 2,
The compensating damping coefficient C _cmp is given so that a phase ∠H(s) when the transfer function H(s) is calculated as a compensated damping coefficient C'=C _cmp becomes equal to a phase lag Δθ caused by a delay time from when the calculation by the low-pass filter and the calculation of the torque T are performed until when the speed changed due to the application of the torque T is reflected in a speed signal v at a gain crossover frequency _ωG where the absolute value of the product of the transfer function H(s) and the transfer function of the low-pass filter is 1. In the two-inertia system simulator according to any one of claims 1 to 3,
A two-inertia system simulator, characterized in that the resonant frequency of the two-inertia system to be simulated is limited to a frequency lower than the cutoff frequency of said low-pass filter. In the two-inertia system simulator according to any one of claims 1 to 4,
A two-inertia system simulator characterized in that the speed signal v is provided as a speed detection value or a speed estimate value of the second motor or the first motor, or as a speed command value when the motor control device controls the speed of the first motor.

Images