JP4359736B2 - Position control device - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a position control device that positions a control object, and more particularly to a position control device that positions a motor.
[0002]
[Prior art]
FIG. 12 is a control block diagram showing a configuration of a conventional position control device. As shown in FIG. 12, the conventional position control device includes a position controller 1, a speed controller 2, a motor 4, and a differentiator 5. This conventional position control device controls the position θ [rad] of the motor 4 whose inertia is J [N · m · s ² ]. Normally, a torque controller is provided for driving the motor 4 by inputting the generated torque command and generating the torque. However, the response of the torque controller is assumed to be fast enough to be ignored. Omitted from inside.
[0003]
For the sake of simplicity, it is assumed here that the controlled object is a rigid body and that the total inertia of the controlled object and the motor 4 can be J.
[0004]
The motor 4 is provided with an encoder (not shown) so that the position θ of the motor 4 can be detected by the encoder. A position deviation between the position command θ _r issued from a host device (not shown) and the position θ of the motor 4 is input to the position controller 1 and the differentiator 5. The position controller 1 is a proportional controller that outputs a value obtained by multiplying the deviation by K _p by a proportional gain K _p [1 / s]. The differentiator 5 outputs a value obtained by differentiating the position deviation between the position command θ _r and the position θ of the motor 4. Speed controller 2 is a proportional controller that outputs a value K _d multiplying the value obtained by a differentiator 5 by derivative gain K _d [1 / s]. The conventional position control apparatus is for to follow the position theta of the motor 4 to the position command theta _r, the position theta of the motor 4, the position response to the position command theta _r.
[0005]
The torque for controlling the motor 4 in this conventional position control device is a torque that is not shown in the figure, using a value obtained by adding the values output from the position controller 1 and the speed controller 2 as a torque command. Generated by the controller.
[0006]
FIG. 13 shows another conventional position control device in which an integrator 6 and an integration controller 3 are newly provided in addition to the conventional position control device shown in FIG.
[0007]
The integrator 6 integrates the position deviation between the position command θ _r and the position of the motor 4 and outputs the value. Integral controller 3 amplifies and outputs a value obtained by the integrator 3 by the integral gain K _i.
[0008]
The torque for controlling the motor 4 in this conventional position control device is obtained by adding a value obtained by adding the values output from the position controller 1, the speed controller 2 and the integral controller 3 as a torque command. It is generated by a torque controller not shown.
[0009]
In the conventional position control apparatus as shown in FIGS. 12 and 13, in order to exhibit desired performance in the response of θ to the position command θ _r , the response of θ to the disturbance T _d, etc., gains K _p , K _d, it is necessary to an optimum value by adjusting the value of K _i. This adjustment can be easily obtained from the control theory when the controlled object (the total of the actuator and the machine connected to the actuator) is an ideal rigid body, but the actual controlled object has friction and spring elements. Therefore, the adjustment is generally performed by trial and error. Therefore, parameter adjustment has been a laborious work.
[0010]
FIG. 14 and FIG. 15 show a conventional position control device for solving such a problem. FIG. 14 is obtained by adding amplifiers 7 and 8 to the conventional position control device shown in FIG. 12, and FIG. 15 shows amplifiers 7 and 8 added to the conventional position control device shown in FIG. 8 and 9 are added.
[0011]
The amplifier 7 amplifies the value output from the position controller 1 by a value K _g ^{2 obtained} by squaring the adjustment gain K _g and outputs the amplified value. Amplifier 8 amplifies and outputs the output value from the speed controller 8 by adjusting the gain K _g. The amplifier 9 amplifies the value output from the integration controller 3 by a value K _g ³ that is the third power of the adjustment gain K _g and outputs the amplified value.
[0012]
In such a conventional position control system, a proportional element, differential element, introducing the parameters K _g for changing the integral element at the same time, once, the proportional gain K _p, derivative gain K _d, by determining the integral gain K _i if, it is possible to simply gain adjustment while keeping the balance changing the adjustment gain K _g is the one parameter, it could be easily realized the required response characteristic.
[0013]
However, the conventional position control device shown in FIGS. 14 and 15 has a problem when a disturbance response is taken into consideration. For example, in the conventional position control device shown in FIG. 15, a command response that is a response of the position deviation θ ₁ to the position command θ _r and a disturbance response that is a response of the position deviation θ ₂ to the disturbance T _d are calculated. As shown in FIG. In such a control system, even if K _p , K _d , K _i , and K _g are adjusted in an attempt to reduce the position deviation θ ₂ due to the influence of the disturbance T _d , the position command θ _r to the position deviation θ ₁ Since the transfer function depends only on the same parameter, the position deviation θ ₁ in the command response also changes with the position deviation θ ₂ in the disturbance response. That is, in such a configuration, since it is a so-called one-degree-of-freedom control system, adjustment cannot be performed with only the adjustment gain K _g on the feedback side.
[0014]
[Problems to be solved by the invention]
In the conventional position control device described above, even if the adjustment gain is used to adjust the gain of the feedback control system with one parameter, it is difficult to realize the required response characteristics when adjusting the disturbance response. There was a problem that there was.
[0015]
An object of the present invention is to provide a position control device that can easily realize a required response characteristic even when adjusting a disturbance response.
[0016]
[Means for Solving the Problems]
In order to achieve the above object, a position control device of the present invention includes a position control means for amplifying a position deviation between a position command issued from a host device and a position to be controlled by a proportional gain,
First amplifying means for amplifying and outputting the value output from the position control means by a value obtained by squaring the adjustment gain;
Differentiating means for differentiating the position deviation between the position command and the controlled object;
Speed control means for amplifying and outputting the value obtained by the differentiating means with a differential gain;
Second amplifying means for amplifying and outputting the value outputted from the speed control means by the adjustment gain;
By adding a value obtained by amplifying the position command twice with a first feedforward gain and a value obtained by amplifying the position command with a second feedforward gain and the adjustment gain. Feedforward control means for outputting the obtained value;
A torque controller configured to set a value obtained by adding the values output from the first and second amplifying means and the feedforward means as a torque command, and to drive the control object based on the torque command; ing.
[0017]
According to the present invention, the feed-forward control means is provided so that the control system is a two-degree-of-freedom system, and the gain of the feed-forward control means and the gain of the feedback system can be adjusted by an adjustment gain that is one parameter. Therefore, the gain adjustment for determining the required response characteristic can be simplified.
[0018]
Further, in the present invention, in addition to the above configuration, an integration unit that integrates the position deviation between the position command and the control target, an integration control unit that amplifies and outputs a value obtained by the integration unit by an integral gain, You may make it further provide the 3rd amplification means which amplifies and outputs the value output from the integral control means by the value which raised the said adjustment gain to the cube.
[0019]
Further, according to the present invention, in addition to the above-described configuration, the second differential means for differentiating the position deviation between the position command and the controlled object twice, and the value obtained by the second differential means is amplified by the acceleration gain. You may make it provide the acceleration control means to output.
[0020]
DETAILED DESCRIPTION OF THE INVENTION
Next, embodiments of the present invention will be described in detail with reference to the drawings.
[0021]
(First embodiment)
FIG. 1 is a block diagram showing the configuration of the position control apparatus according to the first embodiment of the present invention. In FIG. 1, the same components as those in FIG. 14 are denoted by the same reference numerals, and the description thereof will be omitted.
[0022]
The position control apparatus of this embodiment is provided with a feedforward controller 10 in addition to the conventional position control apparatus shown in FIG. is obtained as associated with adjustment gain K _g is a common parameter of the feedback system.
[0023]
The feed-forward controller 10 amplifies the value obtained by differentiating the position command θ _r twice with the feed forward gain K _ff1 and the value obtained by differentiating the position command θ _r once with the feed forward gain K _ff2 and the adjustment gain K _g. The value obtained by adding the value amplified by the above is output.
[0024]
In the present embodiment, the torque for controlling the motor 4 is a torque controller (not shown) using a value obtained by adding the values output from the amplifiers 7 and 8 and the feedforward device 10 as a torque command. Is generated by
[0025]
The transfer function in the position control apparatus of the present embodiment shown in FIG. 1 is as shown in FIG. 2, and at this time, the disturbance response is determined only by the denominator of the transfer function from the disturbance T _d to θ _2. . If this is _Gd , it can be expressed by the following equation (1). However, for simplicity of explanation, J = 1.
[0026]
G _d = S ² + K _g · K _d · S + K _g ² · K _p (1)
Here, the stability of the control system is determined by the root of the characteristic equation G _d = 0, that is, the poles ρ ₊ and ρ ₋ of the control system.
[0027]
From equation (1),
ρ ₊ = −K _g {K _d − (K _d ² −4K _p ) ^0.5 } / 2 (2)
ρ ₋ = −K _g {K _d + (K _d ² −4K _p ) ^0.5 } / 2 (3)
If K _d and K _p are once determined here, changing K _g will change only the time scale in the pole placement and not the overshoot quantity.
[0028]
To explain this in a commonly used form,
G _d = (S ² + 2ζωS + ω ² ) (4)
After all,
ω = K _g (K _p ) ^0.5 (5)
ζ = K _d / (2K _p ^0.5 ) (6)
It can be seen that only ω is related to K _g .
[0029]
The pole arrangement at this time is as shown in FIG. 3, and once K _p and K _d are determined, the overshoot amount does not change due to K _g , so the balance of the response waveform does not change, and the time direction (that is, ω ) Only change.
[0030]
On the other hand, the command response is determined by a transfer function from the position command θ _r to the position deviation θ ₁ . The transfer function in this case is set as G = G ₁ / G ₂ . Since the numerator in addition to the denominator changes depending on the control gain, the response of the control system is the root of the characteristic equation G ₂ = 0, that is, the poles ρ ₊ and ρ _{− of the} control system and the root of the characteristic equation G ₁ = 0. That is, it is determined by the zero point of the control system.
[0031]
With respect to the pole, since G ₂ = G _d , Equations (1) to (6) are similarly applied as they are, so the zero point will be described here. However, for simplicity of explanation, J = 1.
[0032]
G ₁ = K _ff1 · S ² + K _g (K _d + K _ff2 ) S + K _g ² · K _p = 0 (7)
In other words, the zeros z ₊ and z ₋ are determined by solving the equation (7).
[0033]
From the formula (7), the following formulas (8) and (9) are obtained.
_{z + = -K g {(K} d + K ff2) - ((K d + K ff2) 2 -4K ff1 · K p) 0.5} / (2K ff1) ····· (8)
_{z - = -K g {(K} d + K ff2) + ((K d + K ff2) 2 -4K ff1 · K p) 0.5} / (2K ff1) ····· (9)
Here, even if K _d and K _p that determine the pole are once determined, the response can be changed by K _ff1 and K _ff2 . That is, the control system can be determined independently of the disturbance response. On the other hand, once K _d , K _p , K _ff1 , and K _ff2 are determined, only the scale related to time changes with K _g , and the amount related to overshoot does not change.
[0034]
To explain this in a commonly used form,
G ₁ = K _ff1 (S ² + 2ζ ₁ ω ₁ S + ω ₁ ² ) (10)
After all,
ω ₁ = K _g (K _p / K _ff1 ) ^0.5 (11)
ζ ₁ = (K _d + K _ff2 ) / {2 (K _ff1 · K _p ) ^0.5 } (12)
It can be seen that only ω ₁ is related to K _g .
[0035]
The pole arrangement at this time is as shown in FIG. 4. Once K _d , K _p , K _ff1 , and K _ff2 are determined, the balance does not change according to K _g , and the time direction (that is, ω ₁ ) You can see that it only changes.
[0036]
The response waveform in this embodiment is shown in FIG. FIG. 5 shows the response waveform when K _g = 0.5 to K _g = 1.5, but the overall waveform is not changed and is increased only by the response speed. _{However, K d = 40, K p} = 800, K ff1 = 0, K ff2 = -16, J = 1, the position command theta _r is the maximum speed = 200 (rad / s), acceleration time, deceleration time = 0. 05 (sec), command payout time is 0.1 (sec).
[0037]
In this way, once K _d and K _p are determined, the response characteristics of the command response are determined by one parameter K _g .
[0038]
In order to compare the effect obtained by the position control device of the present embodiment with that of the conventional example, the feedforward gain K _ff1 = K _ff2 = 0 in the present embodiment is changed to K _g = 0.5 to 1.5. FIG. 6 shows the response waveform in the case of the above. By setting K _ff1 = K _ff2 = 0, the response waveform of FIG. 6 becomes the response waveform of the conventional position control device shown in FIG.
[0039]
When the response waveform of FIG. 6 which is a response waveform of a conventional position control device not provided with the feedforward controller 10 is compared with the response waveform shown in FIG. 5, the response waveform of the conventional position control device overshoots. It can be seen that the amount is increasing.
[0040]
In the position control device according to the present embodiment, by which is adapted to connection with a common parameter adjustment gain K _g of the feedback system the gain of the feedforward controller 10, the adjustment of the response characteristics by a single parameter called adjustment gain K _g It is possible. That is, when a feedforward controller is simply provided for the conventional position control device and the adjustment gain _Kg is not included in the gain of the feedforward controller, it is difficult to adjust the response characteristics. Such an effect cannot be obtained. To illustrate this, a 1 _{K g} in the feed-forward controller 10 of FIG. 1 _shows the response waveform when changing to K g = 0.5 to 1.5 in FIG. Referring to FIG. 7, the command response, it can be seen that adjusting the waveform is greatly changed according to the adjustment gain K _g has become difficult. In the position control apparatus of the present embodiment, the feedforward gains K _ff1 and K _ff2 can be set independently of the feedback control system. Further, both the feedback control system and the feedforward control system have K _g ² in the position term. Since the speed term (one-time differential term) is multiplied by K _g , once the response waveform is determined, only the adjustment gain K _g is adjusted to operate while maintaining the response waveform. Only the time can be changed.
[0041]
That is, in the position control device of the present embodiment, the feedforward controller 10 is provided so that the control system is a two-degree-of-freedom system, and the gain of the feedforward controller 10 and the gain of the feedback system are adjustment gains which are one parameter. Since the adjustment can be made by K _g, the gain adjustment for determining the required response characteristic can be simplified.
[0042]
(Second Embodiment)
Next, a position control device according to a second embodiment of the present invention will be described. FIG. 8 is a block diagram showing the configuration of the position control apparatus according to the second embodiment of the present invention.
[0043]
The position control apparatus of this embodiment is provided with a new feedforward controller 11 with respect to the conventional position control apparatus shown in FIG.
[0044]
Feedforward controller 11, amplified by the position command θ and values obtained by amplifying a differential value twice a _r a feedforward gain K _ff1, position command θ feed forward gain differential value of the _r K _ff2 and adjusting the gain K _g And a value obtained by adding the value obtained by amplifying the position command θ _r by a value K _g ² obtained by squaring the feed forward gain K _ff3 and the adjustment gain K _g is output.
[0045]
In the present embodiment, the torque for controlling the motor 4 is a torque that is not shown in the figure, using a value obtained by adding the values output from the amplifiers 7, 8, 9 and the feedforward device 11 as a torque command. Generated by the controller.
[0046]
In the position control device of the present embodiment, the feedforward controller 11 is provided so that the control system is a two-degree-of-freedom system, and the gain of the feedforward controller 11 and the gain of the feedback system are adjustment gains K _g that are one parameter. Therefore, the gain adjustment for determining the required response characteristic can be simplified as in the case of the position control device of the first embodiment.
[0047]
(Third embodiment)
Next, a position control device according to a third embodiment of the present invention will be described. FIG. 10 is a block diagram showing the configuration of the position control apparatus according to the third embodiment of the present invention.
[0048]
The position control device of this embodiment is such that a second-order differentiator 12 and an acceleration controller 13 are newly provided in the position control device of the third embodiment shown in FIG.
[0049]
The second differentiator 12 differentiates the position deviation between the position command θ _r and the control target twice. Acceleration controller 13 outputs a value obtained by twice differentiator 12 is amplified by an acceleration gain K _i.
[0050]
In this embodiment, the torque for controlling the motor 4 is obtained by adding the values output from the amplifiers 7, 8, 9, the acceleration controller 13, and the feedforward unit 11 as torque commands. Generated by a torque controller (not shown).
[0051]
In the position control device of the present embodiment, the feedforward controller 11 is provided so that the control system is a two-degree-of-freedom system, and the gain of the feedforward controller 11 and the gain of the feedback system are adjustment gains K _g that are one parameter. Therefore, the gain adjustment for determining the required response characteristic can be simplified as in the case of the position control device of the first embodiment.
[0052]
【The invention's effect】
As described above, according to the present invention, it is possible to adjust the response waveform by adjusting both the gains of the feedback control system and the feedforward control system by adjusting only one parameter. Even when the response is adjusted, the required response characteristic can be easily realized.
[Brief description of the drawings]
FIG. 1 is a block diagram showing a configuration of a position control device according to a first embodiment of the present invention.
FIG. 2 is a diagram for explaining a response of the position control device of FIG. 1;
3 is a pole layout diagram for explaining the operation of disturbance response in the position control device of FIG. 1; FIG.
4 is a pole layout diagram for explaining the operation of command response in the position control device of FIG. 1; FIG.
In the position control device of FIG. 5 FIG. 1 is a graph showing changes in response waveform when changing the value of the adjustment gain K _g.
FIG. 6 is a diagram showing a change in response waveform when feed forward gains K _ff1 and K _ff2 are set to zero.
7 is a graph showing changes in response waveform when a 1 to adjust the gain K _g in the feed-forward controller 10.
FIG. 8 is a block diagram showing a configuration of a position control device according to a second embodiment of the present invention.
9 is a diagram for explaining a response of the position control device of FIG. 8;
FIG. 10 is a block diagram showing a configuration of a position control apparatus according to a third embodiment of the present invention.
11 is a diagram for explaining a response of the position control device of FIG. 10;
FIG. 12 is a block diagram showing a configuration of a conventional position control device.
FIG. 13 is a block diagram showing a configuration of another conventional position control device.
14 is a block diagram showing a configuration of a position control device that can adjust the gain with an adjustment gain K _g with respect to the conventional position control device of FIG. 12;
15 is a block diagram showing a configuration of a position control device that can adjust the gain with an adjustment gain K _g with respect to the conventional position control device of FIG. 13;
16 is a diagram for explaining a response of the position control device of FIG. 15;
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 Position controller 2 Speed controller 3 Integration controller 4 Motor 5 Differentiator 6 Integrator 7, 8, 9 Amplifier 10, 11 Feed forward controller 12 Double differentiator 13 Acceleration controller

Claims (3)

Position control means for amplifying the position deviation between the position command issued from the host device and the position of the controlled object by a proportional gain,
First amplifying means for amplifying and outputting the value output from the position control means by a value obtained by squaring the adjustment gain;
Differentiating means for differentiating the position deviation between the position command and the controlled object;
Speed control means for amplifying and outputting the value obtained by the differentiating means with a differential gain;
Second amplifying means for amplifying and outputting the value outputted from the speed control means by the adjustment gain;
By adding a value obtained by amplifying the position command twice with a first feedforward gain and a value obtained by amplifying the position command with a second feedforward gain and the adjustment gain. Feedforward control means for outputting the obtained value;
A torque controller configured to set a value obtained by adding the values output from the first and second amplifying means and the feedforward means as a torque command, and to drive the control object based on the torque command; Position control device. Position control means for amplifying the position deviation between the position command issued from the host device and the position of the controlled object by a proportional gain,
First amplifying means for amplifying and outputting the value output from the position control means by a value obtained by squaring the adjustment gain;
Differentiating means for differentiating the position deviation between the position command and the controlled object;
Speed control means for amplifying and outputting the value obtained by the differentiating means with a differential gain;
Second amplifying means for amplifying and outputting the value outputted from the speed control means by the adjustment gain;
Integrating means for integrating a position deviation between the position command and the controlled object;
Integration control means for amplifying and outputting the value obtained by the integration means by an integral gain;
A third amplifying means for amplifying and outputting the value output from the integral control means by a value obtained by cubeing the adjustment gain;
A value obtained by amplifying a value obtained by differentiating the position command twice by a first feedforward gain, a value obtained by amplifying a value obtained by differentiating the position command by a second feedforward gain and the adjustment gain, and the position command Feedforward control means for outputting a value obtained by adding a third feedforward gain and a value amplified by squaring the adjustment gain;
A torque controller that uses a value obtained by adding the values output from the first, second and third amplifying means and the feedforward means as a torque command, and drives the control object based on the torque command. And a position control device. Position control means for amplifying the position deviation between the position command issued from the host device and the position of the controlled object by a proportional gain,
First amplifying means for amplifying and outputting the value output from the position control means by a value obtained by squaring the adjustment gain;
Differentiating means for differentiating the position deviation between the position command and the controlled object;
Speed control means for amplifying and outputting the value obtained by the differentiating means with a differential gain;
Second amplifying means for amplifying and outputting the value outputted from the speed control means by the adjustment gain;
Integrating means for integrating a position deviation between the position command and the controlled object;
Integration control means for amplifying and outputting the value obtained by the integration means by an integral gain;
A third amplifying means for amplifying and outputting the value output from the integral control means by a value obtained by cubeing the adjustment gain;
A twice differentiating means for differentiating a position deviation between the position command and the controlled object twice;
Acceleration control means for amplifying and outputting the value obtained by the second differentiation means by an acceleration gain;
A value obtained by amplifying a value obtained by differentiating the position command twice by a first feedforward gain, a value obtained by amplifying a value obtained by differentiating the position command by a second feedforward gain and the adjustment gain, and the position command Feedforward control means for outputting a value obtained by adding a third feedforward gain and a value amplified by squaring the adjustment gain;
A value obtained by adding the values output from the first, second and third amplifying means, the acceleration control means, and the feedforward means is used as a torque command, and the control object is based on the torque command. And a torque controller for driving the position controller.

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