JP3672713B2 - Rotating body drive control method - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a rotating body drive control method.
[0002]
[Prior art]
For example, in a color copying machine or a color printer using a drum-shaped photoconductor, the peripheral speed (linear velocity) of the photoconductor is constant in order to improve image quality with little positional deviation when writing image data. It is required to be stable. In addition to the photosensitive member, there are many rotating members that are required to have a constant peripheral speed and be stable. However, in reality, it is not easy to rotate the rotating body at a constant peripheral speed due to factors such as eccentricity of the rotating shaft of the rotating body such as the photoconductor, and various countermeasures have been taken conventionally.
[0003]
As a typical example, there is a rotating body drive control device as disclosed in JP-A-6-175427, for example. According to the publication, in consideration of eccentricity of the rotation shaft, a rotary encoder is attached to the rotation shaft of the photosensitive drum, the rotation angular velocity is detected, and the rotation speed of the motor is controlled so that this rotation angular velocity is constant. Thus, the eccentricity of the rotary encoder is removed. In other words, the amount of eccentricity is detected, and the eccentricity is removed by adjusting the axis (that is, the rotation center) of the photosensitive drum based on the detection result.
[0004]
[Problems to be solved by the invention]
However, the control method of the publication is a speed control method. Therefore, the position deviation increases with time, or the delay at the time of rising cannot be absorbed. In particular, as in a color copying machine, when color toners of black, yellow, magenta, and cyan are sequentially developed on a photosensitive member and superimposed on a transfer belt, color misregistration occurs. Further, in the 4-drum system such as the tandem system, when a difference in speed of each drum occurs due to disturbance or the like, the color shift is caused as it is. That is, after the speed difference is generated, the state is shifted.
[0005]
Also, according to the same publication method, when the transfer characteristics of the control system change due to changes over time, temperature changes, etc., and sufficient phase margin and gain margin cannot be obtained, sufficient phase margin can be obtained by switching control parameters. A margin and a gain margin can be secured, and the speed control of the rotating body can always be performed with high accuracy. However, it is described that the round transfer function G (s) · H (s) is obtained automatically by the CPU at the start of operation or based on a user instruction. Here, s is a Laplace operator. In order to obtain the frequency characteristics, it is necessary to perform processing / operation such as s = j · ω (j; √ (−1), ω: angular frequency) and sweeping in the frequency band in which the angular frequency ω is desired. Yes, it can't be easy. In addition, the environment of temperature change may not be predicted by an unspecified number of users, and it is necessary to always obtain transfer characteristics.
[0006]
Accordingly, a first object of the present invention is to detect the amount of eccentricity in association with the rotational position, even if the rotating body is eccentric, so that the amount of movement per unit time at the circumferential position of the rotating body, That is, it is to provide a rotating body drive control method capable of making the peripheral speed constant.
[0007]
In addition, the second object of the present invention is stable even if the transfer characteristics of the control system fluctuate due to changes with time, temperature, etc., that is, even if there are parameter fluctuations and disturbances between the rotating body and the drive source. It is to provide a rotating body drive control method capable of performing position control.
[0008]
The third object of the present invention is to achieve the target value even when the moment of inertia, the motor torque constant, the armature resistance, and the inductance are multiplicatively perturbed with respect to the specification values due to manufacturing variations, changes over time, temperature changes, and the like. It is an object of the present invention to provide a rotating body drive control method capable of stably following.
[0009]
The fourth object of the present invention is to make the amount of movement per unit time at the circumferential position of the rotating body, that is, the rotation that can make the peripheral speed constant by accurately following the target value even if there is an eccentric disturbance or the like. It is to provide a body drive control method.
[0010]
A fifth object of the present invention is to provide a rotating body drive control method that can be controlled by a general-purpose low-cost microcomputer without using an expensive digital signal processor or the like by reducing the amount of calculation.
[0011]
A sixth object of the present invention is to provide a rotator drive control method that allows a robust control system designed as a continuous system to follow a target value with high accuracy without being affected by the sampling time as compared with a case where it is directly calculated by a CPU. Is to provide.
[0012]
A seventh object of the present invention is to provide a rotating body drive control method capable of suppressing a target position tracking delay and a steady deviation caused by a frictional force.
[0013]
[Means for Solving the Problems]
According to the first aspect of the present invention, the amount of eccentricity of the rotating body that is rotationally driven by the drive source is detected corresponding to the rotational position, and the peripheral speed of the rotating body is determined based on the detected amount of eccentricity and the corresponding rotational position. The target rotational position of the rotating body is variably adjusted so as to be constant. Therefore, even if the rotating body is eccentric, the amount of eccentricity is detected in association with the rotational position, and the target rotational position of the rotating body is variably adjusted so that the peripheral speed is constant. The amount of movement per unit time at the position, that is, the peripheral speed can be made constant.
[0014]
According to the first aspect of the present invention, the drive source is driven by a robust control system that takes into account the target position shift of the rotator due to parameter fluctuations and disturbances between the rotator and the drive source at the target rotation position. Therefore, even if the transmission characteristics of the control system fluctuate due to changes over time, temperature changes, and the like, that is, even if there are parameter fluctuations and disturbances between the rotating body and the drive source, position control can be performed stably with no follow-up delay.
[0015]
According to a second aspect of the present invention , in the rotating body drive control method according to the first aspect, the parameter variation of the rotating body is the moment of inertia, the parameter variation of the driving source is the torque constant of the motor, the armature resistance, and the inductance. A robust control system incorporated in the design as a multiplicative perturbation to the value is used. Therefore, even if the moment of inertia, motor torque constant, armature resistance, and inductance due to manufacturing variations, changes over time, temperature changes, etc. are multiplicative perturbations with respect to the specification values, a robust control system that incorporates them into the design. By using it, it is possible to follow the target value stably.
[0016]
According to a third aspect of the present invention, in the rotating body drive control method according to the first or second aspect , the target position deviation of the rotating body due to disturbance or the like is designed as the tracking accuracy of the target position with respect to the maximum eccentric disturbance amplitude and its frequency. The robust control system incorporated in is used. Therefore, the robust control system incorporated in the design as the tracking accuracy of the target position with respect to the maximum eccentric disturbance amplitude and its frequency is used. The amount of movement per unit time at the circumferential position, that is, the circumferential speed can be made constant.
[0017]
According to a fourth aspect of the present invention, in the rotating body drive control method according to any one of the first to third aspects, the robust control system is reduced in dimension. Accordingly, by reducing the number of dimensions, the amount of computation of the microcomputer can be reduced, and control can be performed with a general-purpose low-cost microcomputer without using an expensive digital signal processor or the like.
[0018]
According to a fifth aspect of the present invention, in the rotating body drive control method according to any one of the first to fourth aspects, the robust control system is discretized by the sampling time of the control calculation and is calculated by the software servo of the microcomputer. The result is given as input to the drive source. Therefore, since a controller for a robust control system is required in a continuous time system, if it is digitized as it is, it cannot be driven accurately due to the influence of the sampling time, but since it is discretized by the sampling time, it is calculated by the CPU as it is Compared with, the target value can be followed with high accuracy without being affected by the sampling time.
[0019]
According to a sixth aspect of the present invention, in the rotating body drive control method according to the first aspect, the frictional force is obtained from the current value in the steady rotation of the rotating body and the driving source, and the feedforward system is changed to the robust control system by the frictional force. Append. Therefore, since the frictional force is obtained from the current value in the steady rotation, a value suitable for an actual actual machine can be fed forward, and the target position tracking delay and the steady deviation due to the frictional force can be suppressed.
[0020]
DETAILED DESCRIPTION OF THE INVENTION
An embodiment of the present invention will be described with reference to the drawings. In the present embodiment, for example, a plurality of drum-shaped photoconductors in a tandem type color copying machine are used as rotating bodies to be controlled. FIG. 1 shows a drive system configuration for one photosensitive member 1 as a rotating member, and a rotating shaft 2 is fitted in the center of the photosensitive member 1. The rotating shaft 2 is connected to a motor 7 serving as a driving source through a transmission system such as pulleys 3 and 4, a timing belt 5, and a speed reduction mechanism 6. Reference numeral 8 denotes a flywheel that is mounted on the rotary shaft 2 to stabilize the rotation of the photosensitive member 1. In this embodiment, an organic photoreceptor (OPC) having a relatively soft surface is used as the photoreceptor 1. A rotary encoder 9 is attached on the shaft of the motor 7 and functions as rotational position speed detection means with an origin signal for controlling the motor. Further, an eccentricity detector 10 that functions as an eccentricity detecting means for detecting the eccentricity of the photosensitive member 1 is provided so as to face a part of the surface of the photosensitive member 1. As the eccentricity detector 10, a non-contact type such as a laser displacement meter or a capacitance displacement meter is used.
[0021]
Next, a hardware configuration centering on the control system will be described with reference to FIG. First, a microcomputer 16 that is responsible for overall control is provided. The microcomputer 16 includes a microprocessor (CPU) 17 that is a processor, a ROM 18, and a RAM 19. Here, the ROM 18 is a read-only memory, and stores programs executed by the CPU 17 and predetermined data. The encoder output a of the rotary encoder 9 provided on the shaft of the motor 7 is input to the microcomputer 16 via the state detection interface 20 and the bus 21. The detection output b of the eccentricity detector 10 is also input to the microcomputer 16 via the state detection interface 20 and the bus 21. The state detection interface 20 processes the encoder output a and converts it into a digital numerical value, and includes a counter for counting the number of encoder pulses. The state detection interface 20 also has a function of processing the detection output b and converting it into a digital numerical value to obtain eccentricity data. At this time, the state detection interface 20 has a function of associating (correlating) the amount of eccentricity on the photosensitive member 1 with the rotational position of the photosensitive member 1 by using the origin information of the rotary encoder 9. Yes. Therefore, in the present embodiment, the state detection interface 20 functions as an eccentricity / position association means.
[0022]
Further, the motor 7 is connected to the microcomputer 16 via the bus 21, driving interface 22 and driving device 23. The drive interface 22 has a function of converting a digital signal obtained as a result of calculation in the microcomputer 16 into a pulsed signal (control signal) for operating a power semiconductor, for example, a power transistor constituting the drive device 23. The driving device 23 operates based on this pulse signal and controls the voltage applied to the motor 7. As a result, as will be described later, the motor 7 is driven so as to follow a predetermined target rotational position. The rotational speed of the motor 7 at this time is detected by the rotary encoder 9 and the state detection interface 20 and is taken into the microcomputer 16.
[0023]
The rotation control means of the present embodiment is constituted by the CPU 17, the drive device 23, and the like. Further, the controller calculation function by the robust control system and the function of the means for obtaining the target value function (target speed) are executed by the calculation processing function in the CPU 17.
[0024]
In FIG. 2, the discrete type microcomputer 16 is used, but a microcomputer including one interface 20 and 22 may be used.
[0025]
Next, the configuration of a feedback control system that controls the rotational position of the photoconductor 1 through the motor 7 so that the peripheral speed of the photoconductor 1 is constant will be described with reference to the block diagram of FIG. This feedback control system is mainly executed as a software servo by the microcomputer 16. In the figure, “dist” represents disturbance such as eccentricity, and “Wp” represents a weighting function, which is used to relatively reflect desired performance in various frequency bands. “E” is a control amount, which also has implications as a tracking accuracy between the target rotational position input and the photoreceptor position. Now, expressed as a sensitivity function s,
s = e / dist = 1 / (1 + GK)
It becomes. Here, “K” is a robust controller.
[0026]
In the band of GK ≧ 1,
s ≒ 1 / GK
Thus, the reciprocal number (GK) of the sensitivity function s is called a one-round transfer function or an open-loop transfer function in the control system, and represents the tracking performance. For example, in order to obtain an eccentric outer diameter of 100 * 10 to ⁶ m, a frequency of 0.5 Hz, and a target tracking error of 10 * 10 to ⁶ m, the gain of 0.5 Hz is | GK (0.5 Hz) |> 20 log (100 ^{* 10 ~ 6/10 * 10} ~ 6) dB
And 20 dB or more is required. The weighting function Wp indicating this condition is as shown in FIG.
[0027]
Here, the details of the control object (G) are shown in FIG. That is, the total of the nominal value (nominal value = specification value) and the parameter fluctuation portion is the control target (G). The controlled object (G) includes a nominal model Gnom, Wdel representing the uncertainty in the model, and ΔG. This uncertainty is a multiplicative uncertainty, Wdel is a weight function representing uncertainty, and ΔG is a transfer function. The transfer function ΔG is stable,
‖ΔG‖ _∞ <1
The above conditions are satisfied.
[0028]
If the perturbation model is Gper,
Gper = (1 + Wdel * ΔG) Gnom
Than,
Wdel * ΔG = Gper / Gnom −1
It becomes.
[0029]
FIG. 6 is a graph showing the variation of Wdel · value when the inertia J is 80%, the torque constant Kt is 20%, and the armature resistance Ra is 500% with respect to the nominal value (nominal value). ΔG and Wdel are shown. The robust controller K can perform numerical calculation by selecting Wp and Wdel.
[0030]
Next, a method for obtaining the feedforward amount FF will be described. When the friction torque is Tf and the torque constant Kt, in the current amplifier system,
FF = Tf / Kt
Then, a feed forward amount FF that cancels the friction torque Tf is obtained.
[0031]
FIG. 7 is a block diagram showing the configuration of such a current amplifier system. In the figure, Ua: current amplifier input, Ga: gain determining the band of current amplifier, Gpi: primary filter, L: inductance of drive source (motor 7), Ra: armature resistance, Rs: current detection resistance, Kt Torque constant, Ke; induced voltage constant, J: inertia.
[0032]
Here, an example of a robust controller K which satisfies ‖Wp ⁽¹ + GK) ~ 1 ‖ _∞ <1. In terms of the state equation,
dx / dt = ak1 * x + bk1 * u
y = ck1 * x + dk1 * u
It becomes. u is a deviation of the observed output with respect to the target rotational position, and y is a control input given to the current amplifier. x is a state variable, ak1, bk1, ck1, and dk1 are each
ak1; 21 rows and 21 columns
bk1 ； 21 rows 1 column
ck1; 1 row 21 columns
dk1 ＝= 0
Is a state matrix of the size
[0033]
FIG. 8 shows the frequency response of the round transfer function (Gnom * K). According to the illustrated example, it can be seen that | Gnom * K (0.5 Hz) | has a gain of 20 dB or more, and that the obtained robust controller satisfies the control performance against disturbance.
[0034]
Next, in order to perform arithmetic processing by the microcomputer 16, the robust controller K is discretized by Tustin conversion at the sampling time Td. If the robust controller obtained by this discretization is DK,
x (n + 1) = dak1 * x (n) + dbk1 * u (n)
y (n) = dck1 * x (n) + ddk1 * u (n)
The following equation holds. u (n) is a deviation of the observed output with respect to the sampled target rotational position, and y (n) is a control input for giving the calculation result of the microcomputer 16 to the current amplifier every sampling time Td. X (n) is a state variable, dak1, dbk1, dck1, and ddk1 are each
dak1; 21 rows and 21 columns
dbk1; 21 rows and 1 column
dck1; 1 row 21 columns
ddk1; = 0
Is a state matrix of the size
[0035]
When computing with the microcomputer 16, such a determinant requires a long computation time. Therefore, in this embodiment, the order is reduced by reducing the dimension.
ak1; 10 rows and 10 columns
bk1 ； 10 rows 1 column
ck1; 1 row and 10 columns
dk1 ＝= 0
It will be lowered as follows. The robust controller obtained by the reduction processing is called DKre. FIG. 9 shows the frequency response characteristics (gain and phase) of the discretized robust controller DK and the reduced-order robust controller DKre, and it can be seen that the two match.
[0036]
Subsequently, as an example, a result of driving a rotating body (photosensitive body 1) having an eccentricity amount deltaR * cos (Θ) will be described. It is assumed that the target position function Θref of the drive source (motor 7), the motor speed in the steady state is Wref, and DKre subjected to the reduction processing is used as the robust controller. The target position function Θref without eccentricity is
Θref = Wref * t
It becomes. Where t is time.
[0037]
FIG. 10 shows time response characteristics between the target rotational position and the actual rotational body (photosensitive body 1) position when the target position function is not corrected (variably adjusted). According to FIG. 10, it can be seen that the rotating body position varies and the peripheral speed changes. FIG. 11 shows time response characteristics between the target rotational position and the actual rotational body (photosensitive body 1) position when the target position function is corrected (variably adjusted) according to the method of the present embodiment. The target position function Θref in the case where there is the above-described eccentricity deltaR * cos (Θ) with respect to the reference radius R0 is
Θref = Wref * t * R0 / (R0 + deltaR * cos (Θ))
It becomes. According to FIG. 11, since the target rotation position is changed, the position output of the drive source changes following the target rotation position, but it can be seen that the position of the rotating body changes linearly. In other words, it can be seen that the amount of movement (peripheral speed) per unit time at the circumferential position of the rotating body is constant. Incidentally, FIG. 10 and FIG. 11 show the result of the nominal value (Gnom) for the controlled object (G). FIG. 12 shows the time response characteristics between the target rotational position and the actual rotational body (photosensitive body 1) position when the torque constant Kt is increased by 20% from the nominal value, and FIG. 13 shows the inertia J by 80 from the nominal value. The time response characteristics of the target rotational position and the actual rotational body (photosensitive body 1) position when% is increased are shown. In either case, it can be seen that the target value is followed.
[0038]
The effect of the feedforward amount FF by the above-described current amplifier system will be described. FIG. 14 shows the time response characteristics of the deviation between the target rotational position and the actual rotational body (photosensitive body 1) position when feedforward is not performed. According to FIG. 14, it can be seen that the overshoot at the time of rising is large and the deviation of the position in the steady state is large (0.04 [rad]). On the other hand, FIG. 15 shows the time response characteristics of the deviation between the target rotational position and the actual position of the rotating body (photosensitive body 1) when feedforward is performed. According to FIG. 15, it can be seen that the overshoot at the time of rising is suppressed as compared with the case of FIG. 14, and the deviation of the position in the steady state is smaller than 0.005 [rad]. In other words, the steady-state position deviation is suppressed as an effect of the feedforward amount FF. In FIGS. 14 and 15, the friction torque is 1 Nm, and the results are obtained with a rotating body having no eccentricity.
[0039]
In the present embodiment, the example in which the photosensitive member 1 is used as the rotating member has been described. However, the present invention is not limited to the photosensitive member, and can be similarly applied to various rotating members that require constant peripheral speed. Of course. Further, the case where the rotating body has eccentricity has been described. However, it is obvious that even when the encoder 9 for detecting the rotating state of the rotating body has eccentricity, it can be corrected similarly using the eccentricity detecting means. is there.
[0040]
【The invention's effect】
According to the first aspect of the present invention, even if the rotating body is eccentric, the amount of eccentricity is detected in association with the rotational position, and the target rotational position of the rotating body is variably adjusted so that the peripheral speed is constant. By doing so, the amount of movement per unit time at the circumferential position of the rotating body, that is, the circumferential speed can be made constant.
[0041]
According to the invention of claim 1 Symbol placement, driving a drive source by the robust control system incorporating the design target position displacement of the rotor due to parameter variations and disturbance of the rotating body and the drive source to the target rotational position Therefore, even if the transmission characteristics of the control system fluctuate due to changes over time, temperature changes, etc., that is, even if there are parameter fluctuations and disturbances of the rotating body and drive source, there is no tracking delay and stable position control Can be performed.
[0042]
According to the second aspect of the present invention, the parameter variation of the rotating body is the moment of inertia, the parameter variation of the driving source is the motor torque constant, the armature resistance, and the inductance, and these are incorporated into the design as a multiplicative perturbation with respect to the specification value. Since a robust control system is used, even if there is a multiplicative perturbation with respect to the specification values of the moment of inertia, motor torque constant, armature resistance, and inductance due to manufacturing variations, changes over time, temperature changes, etc., the target value Can be made to follow stably.
[0043]
According to the third aspect of the invention, since the target position deviation of the rotating body due to disturbance or the like uses the robust control system incorporated in the design as the tracking accuracy of the target position with respect to the maximum amplitude of the eccentric disturbance and its frequency. Even if there is an eccentric disturbance or the like, the movement amount per unit time at the circumferential position of the rotating body, that is, the circumferential speed can be made constant by accurately following the target value.
[0044]
According to the invention described in claim 4, since the robust control system is reduced in dimension, it is possible to reduce the amount of calculation of the microcomputer, and without using an expensive digital signal processor, etc. It can be controlled by a microcomputer.
[0045]
According to the invention described in claim 5 , since a robust control system controller is sought in a continuous time system, if it is digitized as it is, it cannot be driven accurately due to the influence of the sampling time, but is discretized by the sampling time. Therefore, it is possible to follow the target value with high accuracy without being affected by the sampling time as compared with the case where the CPU directly calculates.
[0046]
According to the sixth aspect of the present invention, the frictional force is obtained from the current value in the steady rotation of the rotating body and the drive source, and the feedforward system is added to the robust control system by the frictional force. Since the frictional force is obtained from the current value, a value suitable for an actual actual machine can be fed forward, and a target position tracking delay and a steady deviation due to the frictional force can be suppressed.
[Brief description of the drawings]
FIG. 1 is a perspective view schematically showing a drive system configuration according to an embodiment of the present invention.
FIG. 2 is a block diagram showing a hardware configuration centering on a control system.
FIG. 3 is a block diagram showing a configuration of a feedback control system.
FIG. 4 is a frequency characteristic diagram of a weight function Wp.
FIG. 5 is a block diagram showing details of a control object (G) in the feedback control system.
FIG. 6 is a frequency characteristic diagram regarding parameter variation of the perturbation model Gper.
FIG. 7 is a block diagram showing the configuration of a feedforward current amplifier.
FIG. 8 is a frequency response characteristic diagram of a circuit transfer function.
FIG. 9 is a frequency response characteristic diagram of DK and DKre.
FIG. 10 is a characteristic diagram showing a time response between a target position and a rotating body position when the target position function is not corrected.
FIG. 11 is a characteristic diagram showing a time response between a target position and a rotating body position when a target position function is corrected.
FIG. 12 is a characteristic diagram showing a time response between a target position and a rotating body position when the torque constant Kt is increased by 20% from the nominal value.
FIG. 13 is a characteristic diagram showing a time response between a target position and a rotating body position when inertia J is increased by 80% from the nominal value.
FIG. 14 is a characteristic diagram showing a time response of a deviation between a target position and a rotating body position when feedforward is not performed.
FIG. 15 is a characteristic diagram showing a time response of a deviation between a target position and a rotating body position when feedforward is performed.
[Explanation of symbols]
1 Rotating body 7 Drive source 16 Microcomputer

Claims (6)

An eccentricity amount detecting step for detecting an eccentricity amount of a rotating body that is rotationally driven by a drive source in correspondence with the rotational position ;
And a variable adjustment step for variably adjusting the target rotational position of the rotating body so that the peripheral speed of the rotating body is constant based on the eccentric amount detected in the eccentricity detecting step and the corresponding rotational position. Shi
In the variable adjustment step, the drive source is driven by a robust control system that takes into account the target position deviation of the rotator due to parameter fluctuations and disturbances between the rotator and the drive source at the target rotation position.
Rotating body drive control method for image forming apparatus The parameter variation of the rotating body is the moment of inertia,
The parameter variation of the drive source is the motor torque constant, armature resistance and inductance,
Using a robust control system that incorporates these as multiplicative perturbations to the specification value,
Rotation driving control method for an image forming apparatus according to claim 1, wherein the this. The target position deviation of the rotating body due to disturbance etc. uses a robust control system incorporated in the design as the tracking accuracy of the target position with respect to the eccentric disturbance maximum amplitude and its frequency,
  3. The rotating body drive control method for an image forming apparatus according to claim 1 or 2, 4. The rotating body drive control method for an image forming apparatus according to claim 1, wherein the robust control system is reduced in dimension. The robust control system is discretized by a sampling time of control calculation, is calculated by a software servo of a microcomputer, and the calculation result is given as an input to the drive source.
  5. The rotating body drive control method for an image forming apparatus according to any one of claims 1 to 4. Friction force is obtained from the current value in steady rotation of the rotating body and the drive source, and a feedforward system is added to the robust control system by the friction force.
2. The rotating body drive control method for an image forming apparatus according to claim 1, wherein:

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